Corrosion_fatigue_and_fracture.pdf - UCL Discovery

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CORROSION FATIGUE AND FRACTURE MECHANICS OF HIGH

STRENGTH JACK UP STEELS

Peter Terence Myers

Submitted for the Degree of

Doctor of Philosophy

Department of Mechanical Engineering

University College London

February 1998

ProQuest Number: U641859

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ABSTRACT

Jack up platforms are self elevating mobile units used fo r drilling and production

of offshore oil and gas reserves. These platforms utilise high strength weldable

steels fo r the fabrication of the truss leg structures. The yield strength of these

steels is typically around lOOMPa compared with 350MPa in standard fixed

jacket structures. Concern regarding the performance of such steels was

heightened by the discovery of cracking in and around the spud can of several

jack up platforms operating in the North Sea. It is thought that the higher strength

steels are more susceptible to material degradation due to Hydrogen

Embrittlement.

An experimental investigation has been performed to investigate and quantify the

magnitude of such deleterious effects. Seven fatigue tests have been performed on

large scale welded tubular joints fabricated from SE702, a 690MPa steel

commonly used in jack up construction. Cathodic protection levels of -SOOmV and

-lOOOmV (versus Ag/AgCl) were used. Evidence from these tests suggests that this

particular steel performs at least as well as lower strength steels in air and under

cathodic protection.

The shape of the tubular joints in jack up structures can be significantly different

from those found in conventional fixed structures. This can have a significant

effect on the stress distribution at the intersection of the tubular members.

Accurate knowledge of the stresses at the intersection is needed fo r design and

assessment purposes. Although the stress distribution in unstiffened joints has

been heavily researched, little work has been done fo r joints representative of jack

up legs. For this reason an extensive thin shell finite element investigation has

been performed to determine the stress distribution across a wide range of jack up

leg geometries. The distribution of stresses at the surface and through the

thickness of the chord members has been quantified. The results show that the ‘hot

spot' SCF can be reduced by as much as 50% compared to the corresponding

unstiffened joint.

The results of this stress analysis study have been integrated into a fatigue

fracture mechanics analysis of jack up representative geometries. Additionally,

contemporary fracture mechanics models have been assessed against fracture

mechanics data extracted from the experimental fatigue rests.

- 1 -

ACKNOWLEDGEMENTS

I wish to acknowledge the advice and guidance of my supervisors. Professor W. D.

Dover and Dr. F. P. Brennan whose faultless supervision has helped bring the best

out of this work.

Additionally I would like to thank my colleagues at the NDE Centre, especially

Linus Etube, Efrain Rodriguez Sanchez and Farid Ud-Din who have all helped

relieve my workload whilst I was writing this thesis. The assistance of the staff in

the Mechanical Engineering workshop is also gratefully recognised.

Finally I would like to thank EPSRC whose financial support made this work

possible.

- 2

TABLE OF CONTENTS

ABSTRACT............................................................................................................... 1

ACKNOWLEDGEMENTS......................................................................................2

TABLE OF CONTENTS...........................................................................................3

LIST OF FIGURES................................................................................................... 8

LIST OF TABLES................................................................................................... 18

NOMENCLATURE.................................................................................................20

1. In t r o d u c t io n a n d B a c k g r o u n d ............................................................................ 23

1.1 Introduction..................................................................................................... 23

1.2 Background to Fatigue of Tubular Joints.......................................................24

1.3 The Jack Up Platform...................................................................................... 27

1.3.1 The Jack Up Concept................................................................................28

1.3.2 Jack Up Leg Design..................................................................................28

1.3.3 Weld Procedures....................................................................................... 30

1.4 Loads Experienced by Jack Up Platforms......................................................30

1.5 The Use of High Strength Steels Offshore......................................................32

1.6 The Tubular Joint Intersection........................................................................ 33

1.7 Stress Analysis of Tubular Joints.....................................................................34

1.7.1 Stress Concentration Factors (SCF) in Tubular Joints............................ 37

1.7.2 Parametric Equations for Prediction of SCF...........................................40

1.7.3 Stress Distribution in Tubular Y and T Joints.........................................44

1.7.4 Comparison of Parametric SCF Prediction.............................................. 44

1.7.5 Ratio of Bending to Membrane Stress in Tubular Joints.........................46

1.8 Fatigue Design Guidance for Tubular Joints...................................................47

1.8.1 Development of U.K. Fatigue Guidance.................................................. 48

1.8.2 Development of the T-Curve....................................................................48

- 3 -

1.8.3 Analysis of Experimental Data to Produce S-N Curve...........................50

1.8.4 Allowance Factors to be Used in Conjunction with the Basic S-N Curve.52

1.8.5 Design Code Treatment of High Strength Steels.................................... 55

1.9 Linear Elastic Fracture Mechanics................................................................. 56

1.10 Stress Intensity Factor Solutions for Welded Joints.................................... 61

1.11 Factors Affecting Fatigue Crack Growth in Tubular Joints.........................63

1.12 Environment Assisted Fatigue Mechanisms................................................. 64

1.12.1 Free Corrosion........................................................................................65

1.12.2 Cathodic Protection................................................................................ 66

1.13 Effect of Environment on Fatigue Crack Growth Rate............................... 73

1.14 Effect on Environment on the Fatigue Lives of Welded Joints................... 75

1.15 Aims and Objectives......................................................................................77

1.16 References...................................................................................................... 80

2. E x pe r im e n t a l Fa t ig u e T e stin g o f W e l d e d T u bu l a r J o in t s ............ 117

2.1 Introduction................................................................................................... 117

2.2 Tubular Joint Test Specimens....................................................................... 117

2.2.1 Dimensions..............................................................................................118

2.2.2 Specimen Fabrication..............................................................................119

2.2.3 Material Properties..................................................................................120

2.2.4 Mechanical Properties of SE702.............................................................121

2.3 Experimental Set Up...................................................................................... 122

2.3.1 Applied Loading...................................................................................... 122

2.3.2 Fatigue Crack Monitoring...................................................................... 123

2.3.3 Environment Chamber............................................................................ 128

2.3.4 Test Control and Data Acquisition........................................................ 129

2.4 Experimental Stress Analysis........................................................................ 130

2.4.1 Strain Gauge Siting...............................................................................132

- 4 -

2.4.2 Determination of SCF’s...........................................................................133

2.4.3 Experimental SCF Results...................................................................... 134

2.5 Fatigue Test Programme................................................................................136

2.5.1 Test Parameters...................................................................................... 137

2.5.2 ACPD Data Analysis...............................................................................138

2.5.3 Crack Shape.............................................................................................140

2.6 Fatigue Test Results...................................................................................... 140

2.6.1 S-N Data.................................................................................................. 141

2.6.2 Crack Growth Curves.............................................................................143

2.6.3 Fatigue Crack Growth Rates..................................................................144

2.6.4 Fatigue Crack Initiation.......................................................................... 145

2.6.5 Crack Shape Development..................................................................... 146

2.7 Examination of Fracture Surfaces.................................................................146

2.8 Discussion...................................................................................................... 147

2.9 Conclusions.................................................................................................... 149

2.10 References.................................................................................................... 151

3. St r e ss C o n c e n t r a t io n s in T u bu l a r J o in t s w it h R a c k / R ib P la t e

St if f e n e d C h o r d M em be r s U sin g Th e Fin it e E l e m e n t M e t h o d ........... 181

3.1 Introduction................................................................................................... 181

3.2 Scope..............................................................................................................181

3.3 Stress Analysis of Stiffened Tubulars............................................................182

3.4 Mesh Generation for Tubular Joints with Longitudinal Stiffeners.............. 186

3.5 Boundary Conditions..................................................................................... 190

3.6 Convergence and Model Verification............................................................190

3.7 Finite Element Investigation.......................................................................... 191

3.7.1 Effect of Rack Plate Thickness on SCF Distribution.......................... 191

- 5

3.7.1.1 Results........................................................... 191

3.7.2 Effect of Rack and Rib Plate Geometry on the SCF............................. 193

3.7.2.1 Results................................................................................................194

3.7.3 Investigation of Mechanisms Using Boundary Conditions....................197

3.7.3.1 Results................................................................................................197

3.7.4 Effect of a Continuous Thickness Rack Plate Across a Range of Joint

Parameters.........................................................................................................199

3.7.4.1 Results................................................................................................200

3.8 Conclusions and Recommendations............................................................. 201

3.9 References......................................................................................................203

4. T h e E f fe c t o f a Ra c k / Rib Pl a t e o n t h e D e g r e e o f T h r o u g h

T h ic k n e ss B e n d in g in Ja c k U p C h o r d s .................................................................. 233

4.1 Introduction...................................................................................................233

4.2 Scope............................................................................................................. 233

4.3 Through Thickness Stress Distributions in Tubular Joints...........................234

4.3.1 The Importance of Through Thickness Stress Distribution.................. 235

4.3.2 Determination of Through Thickness Stress Distribution.................... 239

4.4 Mesh Generation and Boundary Conditions................................................ 239

4.5 Convergence and Model Verification........................................................... 242

4.6 Finite Element Investigation.......................................................................... 243

4.6.1 Effect of Rack Plate Thickness on Through Thickness Stress

Distributions.....................................................................................................243

4.6.1.1 Results................................................................................................243

4.6.2 Effect of Rack and Rib Plate Geometry on Through Thickness Stress

Distributions.....................................................................................................245

4.6.2.1 Results................................................................................................245

4.6.3 Effect of Continuous Thickness Rack on Through Thickness Stress

Distributions Across a Range of Joint Parameters..........................................248

- 6 -

4.6.3.1 Results................................................................................................249

4.7 Discussion...................................................................................................... 250

4.8 Conclusions and Recommendations............................................................. 251

4.9 References...................................................................................................... 253

5. F r a c t u r e M ec h a n ic s M o d e l l in g o f Ja c k U p C h o r d D e f e c t s 276

5.1 Introduction...................................................................................................276

5.2 Stress Intensity Factors in Tubular Joints.....................................................277

5.3 Y Factor Predictions Using Empirical Models............................................. 278

5.3.1 Extraction of Y Factors from Crack Growth Data............................... 278

5.3.2 AVS Model............................................................................................. 279

5.3.3 TPM Model............................................................................................ 281

5.3.4 Modified AVS Model............................................................................. 282

5.3.5 Evaluation of Experimentally Derived Models......................................283

5.3.6 Fatigue Crack Growth Predictions.........................................................284

5.4 Finite Element Based Models........................................................................285

5.5 Flat Plate Derived Models............................................................................. 288

5.5.1 Newman-Raju Equations........................................................................288

5.5.2 Correction for Load Shedding............................................................... 291

5.5.3 Correction for Non Uniform Stress Distribution.................................. 292

5.5.3.1 Albrechts Method for Calculation of SIF’s ......................................292

5.5.4 Crack Shape Correction.........................................................................294

5.6 Effect of Rack Plate on Fatigue Crack Growth Predictions....................... 295

5.7 Conclusions....................................................................................................297

5.8 References......................................................................................................299

6. Su m m a r y , C o n c lu sio n s a n d Re c o m m e n d a t io n s ......................................... 315

7 -

L IS T O F F IG U R E S

C h a p te r O n e Page

Figure 1.1 Schematic of a typical jack up rig................................. 93

Figure 1.2 The four main chord designs.......................................... 94

Figure 1.3 Split tubulars with double racks. Range of chord sizes

and shapes..................................................................... 94

Figure 1.4 Tubular chords with central racks. Range of chord

shapes and sizes............................................................. 95

Figure 1.5 Tubular chords with offset racks. Range of chord

shapes and sizes............................................................. 95

Figure 1.6 Leg plan schematic showing main components 96

Figure 1.7 General view of jack up leg showing rack detail 96

Figure 1.8 Complex nature of leg bracing and span breakers in a

modern jack up.............................................................. 97

Figure 1.9 Overlapped bracing and weld detail in a modem jack

up leg............................................................................... 97

Figure 1.10 Common tubular joint configurations............................. 98

Figure 1.11 T joint parametric notation.............................................. 98

Figure 1.12 Jack up transportation modes.......................................... 99

Figure 1.13 The three tubular joint loading modes............................. 99

Figure 1.14 T joint response to axial loads.......................................... 100

Figure 1.15 Weld toe terminology...................................................... 100

Figure 1.16 UKOSRP and ECSC definition of Hot Spot Stress 101

Figure 1.17 Regions of strain linearity used to determine hot spot

stress................................................................................ 101

Figure 1.18 Modelling the weld intersection using thick shell

elements.......................................................................... 102

Figure 1.19 Thin shell FEA modelling of a tubular joint intersection 103

Figure 1.20 T joint stress distributions for axial, IPB and OPB

loading modes................................................................. 104

- 8

Figure 1.21 Parametric chord crown SCF prediction dependency

on Alpha......................................................................... 104


on Beta............................................................................ 105


on Gamma...................................................................... 105


on Tau.............................................................................. 106

Figure 1.25 Parametric chord saddle SCF prediction dependency

on Alpha......................................................................... 106


on Beta............................................................................ 107


on Gamma...................................................................... 107


on Tau.............................................................................. 108

Figure 1.29 16mm 50D fatigue life data together with mean and

design S-N curves.......................................................... 108

Figure 1.30 Thickness effect illustrated by 16 and 32mm fatigue life

data.................................................................................. 109

Figure 1.31 Nested T curves from thickness effect allowance 109

Figure 1.32 S-N curves for 16mm plates and tubulars in sea water

(free corrosion) and optimum cathodic protection 110

Figure 1.33 Cartesian co-ordinates for near crack analyses.............. 110

Figure 1.34 The three modes of crack growth................................... I l l

Figure 1.35 The three stages of fatigue crack growth...................... I l l

Figure 1.36 SIF development in tubular joints and welded plates.... 112

Figure 1.37 Crack depth development in tubulars and welded plates 112

Figure 1.38 The electrochemical corrosion process........................... 113

Figure 1.39 Impressed current cathodic protection........................... 113

- 9

Figure 1.40 Effect of CP potential on fatigue crack growth rate

(O.lHz, R<=0.1)............................................................. 114

Figure 1.41 Schematic da-dN plot showing plateau growth rate

region under CP conditions.......................................... 114

Figure 1.42 Independence of crack growth rate to AK in X65

under CP conditions...................................................... 115

Figure 1.43 High strength steel crack growth rates from Billingham

etal................................................................................. 116

Chapter TwoFigure 2.1 Nominal specimen dimensions for tubular welded T

joints................................................................................ 161

Figure 2.2 Position of seam welds in tubular T Joints...................... 161

Figure 2.3 Photograph of seam and intersection weld..................... 162

Figure 2.4 Definition of weld leg lengths......................................... 162

Figure 2.5 Isometric view of test rig................................................ 163

Figure 2.6 ACPD theory and notation.............................................. 163

Figure 2.7 Typical un-modified ACPD crack development data... 164

Figure 2.8 Typical modified ACPD crack development data 164

Figure 2.9 Experimental test setup.................................................. 165

Figure 2.10 Terminology for specimen / actuator alignment 165

procedure........................................................................

Figure 2.11 Strain gauge positions for experimental stress analysis. 166

Figure 2.12 Experimental stress analysis results................................. 166

Figure 2.13 S-N data from tubular joint tests on

SE702............................................................................. 167

Figure 2.14 Crack Growth Curve for Test ‘T T ................................. 167

Figure 2.15 Crack Growth Curve for Test ‘T2’ ................................. 168

Figure 2.16 Crack Growth Curve for Test T 3 ’ ................................. 168



- 10 -

Figure 2.19 Comparison of Fatigue Crack Growth Curves.............. 170

Figure 2.20 Crack Growth Rates recorded during Test T1............. 170



Figure 2.23 Crack Growth Rates recorded during..Test T4............. 172

Figure 2.24 Crack Growth Rates recorded during..Test T6............. 172

Figure 2.25 Comparison of Crack Growth Rates............................... 173

Figure 2.26 Early crack growth profiles showing initiation in a

typical test........................................................................ 173

Figure 2.27 Early crack growth data showing initiation in a typical

test................................................................................... 174

Figure 2.28 Ratio of initiation to total fatigue lives........................... 174

Figure 2.29 Initiation to propagation lives normalised to the T

curve................................................................................ 175

Figure 2.30 Graphical representation of the ratio of initiation to

propagation life............................................................... 175

Figure 2.31 Crack shape data.............................................................. 176

Figure 2.32 S-N curve showing all SE702 tubular joint data 177

Figure 2.33 Difference between axial and OPB loading modes for

50D steels........................................................................ 178

Figure 2.34 Life conversion factors for axial to OPB loading modes 178

Figure 2.35 S-N curve showing modified T joint results using

loading mode modification factor.................................. 179

Figure 2.36 Comparison of results with nominally identical

specimens made from lower strength steels................. 180

Figure 2.37 Comparison of results with database of cathodically

protected 50D specimens............................................... 180

Chapter Three

Figure 3.1 Tubular joint showing position of stiffener.................... 208

Figure 3.2 Tubular joint showing dual thickness stiffener.............. 208

- 11 -

Figure 3.3 Tubular joint showing non continuous stiffener.............. 209

Figure 3.4 Tubular joint with internal ring stiffeners...................... 209

Figure 3.5 Tubular joint with doubler plate..................................... 210

Figure 3.6 Sample T joint finite element mesh................................. 210

Figure 3.7 Effect of normalised stiffener thickness on SCF

distribution in an axially loaded T joint.......................... 211

Figure 3.8 Effect of normalised stiffener thickness on SCF

distribution for axially loaded Y joint............................. 211

Figure 3.9 Effect of plate thickness on Normalised SCF

distribution for axially loaded T joint............................. 212

Figure 3.10 Effect of plate thickness on normalised SCF

distribution for axially loaded Y joint............................. 212

Figure 3.11 Effect of plate thickness on SCF for IPB loaded T joint 213

Figure 3.12 Effect of plate thickness on SCF for IPB loaded Y

joint.................................................................................. 213

Figure 3.13 Effect of plate thickness on SCF distribution for OPB

loaded T joint.................................................................. 214


loaded Y joint.................................................................. 214


loaded T joint.................................................................. 215


loaded Y joint.................................................................. 215

Figure 3.17 Effect of plate thickness on saddle SCF for Axial and

OPB loaded T & Y joints............................................... 216

Figure 3.18 Terminology and notation used to describe models

with non-continuous stiffeners...................................... 216

Figure 3.19 Effect of rib plate on axially loaded T joint.................... 217



- 12 -

Figure 3.22 Effect of rib plate on OPB loaded T joint....................... 218



Figure 3.25 Effect of rack plate thickness for axially loaded joint... 220

Figure 3.26 Effect of rack plate thickness for OPB loaded joint 220

Figure 3.27 Effect of rack plate depth for axially loaded joint 221

Figure 3.28 Effect of rack plate depth for OPB loaded joint 221

Figure 3.29 Case 1 - Chord deformation restrained in all degrees of

freedom along line shown............................................... 222

Figure 3.30 Case 2 - Chord deformation restrained in Z direction

along line shown.............................................................. 222


and rotation about X axis along line shown.................. 223


and rotation about Y axis along line shown.................. 223


and rotations about X and Y axes along line shown.... 224

Figure 3.34 Case 6 - Chord deformation restrained in rotations

about X axis along line shown........................................ 224

Figure 3.35 Case 7 - Chord deformation restrained in Y and Z

direction and rotations about X axis along line shown.. 225

Figure 3.36 Simulation of the effect of a stiffener using boundary

conditions....................................................................... 225


conditions....................................................................... 226


conditions....................................................................... 226


conditions....................................................................... 227

Figure 3.40 Effect of Alpha on an axially loaded T joint.................. 227

- 13 -

Figure 3.41 Effect of Alpha on an OPB loaded T joint...................... 228

Figure 3.42 Effect of Beta on an axially loaded T joint...................... 228

Figure 3.43 Effect of Beta on an OPB loaded T joint....................... 229

Figure 3.44 Effect of Gamma on an axially loaded T joint................ 229

Figure 3.45 Effect of Gamma on an OPB loaded T joint................... 230

Figure 3.46 Effect of Tau on an axially loaded T joint...................... 230

Figure 3.47 Effect of Tau on an OPB loaded T joint......................... 231

Figure 3.48 Effect of Theta on an axially loaded T joint................... 231

Figure 3.49 Effect of Theta on an OPB loaded T joint...................... 232

Chapter Four

Figure 4.1 Tubular T joint showing position of constant thickness

stiffener........................................................................... 256

Figure 4.2 Tubular joint showing dual thickness stiffener.............. 256

Figure 4.3 Tubular joint showing non conditions stiffener 257

Figure 4.4 Effect of loading mode using experimental database

results............................................................................... 257

Figure 4.5 Through thickness stress distribution.............................. 258

Figure 4.6 Examples of various values of the DoB parameter 258

Figure 4.7 Change of bending and membrane stress component at

the cracked section from experimental measurements

on a large scale, axially loaded tubular joint.................. 259

Figure 4.8 Deformed mesh for axially loaded T joint....................... 259

Figure 4.9 Validation of FE model using acrylic model results 260

Figure 4.10 Comparison of thick and thin shell model DoB results.. 260

Figure 4.11 DoB values for a range of rack thicknesses under axial

loading............................................................................. 261

Figure 4.12 DoB values for a range of rack thicknesses under OPB

loading............................................................................. 261

Figure 4.13 DoB values for a range of rack thicknesses under IPB

loading............................................................................. 262

- 14

Figure 4.14 Normalised DoB values under Axial loading................. 262

Figure 4.15 Normalised DoB values under OPB loading.................. 263

Figure 4.16 Normalised DoB values under IPB loading.................... 263

Figure 4.17 Summary of normalised DoB data for tubular joints

with rack plates............................................................... 264

Figure 4.18 Terminology and notation used to describe models

with non-continuous stiffeners...................................... 264

Figure 4.19 Effect of rib plate on DoB in an axially loaded T joint.. 265



Figure 4.22 Effect of rib plate on DoB in an OPB loaded T joint.... 266



Figure 4.25 Effect of rib plate on DoB in an IPB loaded T joint 268



Figure 4.28 Dependency of DoB on ratio of chord length and

diameter (Alpha)............................................................. 270

Figure 4.29 Dependency of DoB on ratio of brace and chord

diameters (Beta).............................................................. 271

Figure 4.30 Dependency of DoB on ratio of chord diameter to

thickness (Gamma).......................................................... 272

Figure 4.31 Dependency of DoB on ratio of brace to chord

thickness (Tau)............................................................... 273

Figure 4.32 Dependency of DoB on brace angle (Theta).................. 274

Figure 4.33 Measure of accuracy of ‘Saddle’ parametric equation

of Connolly e ta l.............................................................. 275

Figure 4.34 Measure of accuracy of ‘Hot Spot’ parametric

equation of Connolly et at............................................... 275

- 1 5 -

Chapter 5

Figure 5.1 Centre cracked infinite plate........................................... 302

Figure 5.2 Yexp factors for Test T l ’ ............................................... 302

Figure 5.3 Yexp Factors for Test T2................................................ 303

Figure 5.4 Comparison of empirical SIF models with Y xp results

from Test T l .................................................................... 303

Figure 5.5 Comparison of empirical SIF models with Y xp results

from Test T2.................................................................... 304

Figure 5.6 Fracture mechanics crack growth results for Test T l. . . 304

Figure 5.7 Fracture mechanics crack growth results for Test T2 ... 305

Figure 5.8 Power Law fit for Yexp data from Test T l ................... 305

Figure 5.9 Power Law fit for Yexp data from Test T2................... 306

Figure 5.10 Chong Rhee Y Factors for Test T l ............................... 306

Figure 5.11 Chong Rhee Y Factors for Test T2............................... 307

Figure 5.12 Notation used by Newman Raju Equations.................. 307

Figure 5.13 Y Factors using flat plate based solutions for Test T l. 308

Figure 5.14 Y Factors using flat plate based solutions for Test T2. 308

Figure 5.15 SCF due to weld for tensile loading............................... 309

Figure 5.16 SCF due to weld for bending loading............................. 309

Figure 5.17 Albrechts Method for Calculating Yg............................ 310

Figure 5.18 Correction Factors (Yg) for non-uniform stress

distribution...................................................................... 311

Figure 5.19 Crack shape correction factors........................................ 311

Figure 5.20 AVS Model prediction of the effect of a rack plate on

crack propagation........................................................... 312

Figure 5.21 Modified AVS Model prediction of the effect of a rack

plate on crack propagation............................................. 312

Figure 5.22 AVS Model propagation lives normalised to that of the

unstiffened Joint.............................................................. 313

1 6 -

Figure 5.23 Crack shape development used with Newman Raju

model, derived from experimental data......................... 313

Figure 5.24 Effect of rack plate on crack propagation lives using

modified Newman Raju................................................... 314

17 -

L IS T O F T A B L E S

C h a p te r O n e Page

Table 1.1 Jack up design features.................................................... 90

Table 1.2 Jack up leg populations................................................... 90

Table 1.3 Truss leg design breakdown........................................... 91

Table 1.4 Recommended parametric equation for axially loaded

T joints...................................................................... 91

Table 1.5 Default geometric parameters used in model

Comparison............................................................... 91

Table 1.6 UK guidance S-N curves........................................... 92

Table 1.7 1984 Guidance on environmental effects....................... 92

Table 1.8 1990 Guidance on environmental effects....................... 92

C h a p te r T w o

Table 2.1 Ultrasonically measured wall thicknesses............... 154

Table 2.2 Seam welding details............................................... 154

Table 2.3 Intersection weld details........................................... 155

Table 2.4 Weld leg lengths....................................................... 155

Table 2.5 Chemical composition of SE702............................. 156

Table 2.6 Mechanical properties of SE702.............................. 156

Table 2.7 Measured mechanical properties............................. 156

Table 2.8 SE702 Charpy test data............................................ 157

Table 2.9 SE702 hardness data................................................ 157

Table 2.10 ACPD probe site locations...................................... 158

Table 2.11 Experimental SCF results from previous test

programme using same geometry........................... 158

Table 2.12 Experimental SCF results and parametric predictions... 159

Table 2.13 Original and revised test programme details........... 159

Table 2.14 S-N data for SE702.................................................. 160

- 18

Table 2.15 Summary of initiation data for all tests.............. 160

Table 2.16 Experimental results for parallel variable amplitude

study on SE702 Y joints.................................... 160

Chapter Three

Table 3.1 Non-dimensional joint parameters...................... 205

Table 3.2 Results of convergence study............................. 205

Table 3.3 Boundary conditions used to simulate the effect of a

rack/rib plate...................................................... 205

Table 3.4 Effect of Alpha on relative SCF....................................... 206

Table 3.5 Effect of Beta on relative SCF........................................ 206

Table 3.6 Effect of Gamma on relative SCF.................................. 206

Table 3.7 Effect of Tau on relative SCF.......................................... 206

Table 3.8 Effect of Theta on relative SCF....................................... 207

Chapter FourTable 4.1 Finite element model joint parameters................ 255

Table 4.2 Validation of FE model results........................... 255

Chapter Five

Table 5.1 Average stress parameters for different rack plate

thicknesses......................................................... 301

Table 5.2 Input parameters for adapted Newman Raju model

testing rack plate effect..................................... 301

- 1 9 -

NOMENCLATURE

û

4)

0

K.

4 x

(j)y

A

aa

A ,j

ACPD

Ag/AgCl

ASP

AVS

Pc

G, m

Cl, C2, C3, rrii, m2

CP

CPU

D

d

di

da/dN

Ac

DoB

A r

Brace angle

Relative permeability

Complete elliptical integral of second kind

Parameti'ic angle around intersection

Permeability of free space

Rotation about x

Rotation about y

Brace cross sectional area

Joint geometry factor, 2L/D

Crack Depth

AVS model parameters

Alternating Current Potential Drop

Silver / silver chloride reference electrode

Average stress parameter

Average stress model

Joint geometi-y factor, d/D

Surface crack half length

Paris Law constants

Empii'ical constants in crack growth law

Cathodic protection

Central processing unit

Chord diameter

Brace diameter

1-D crack depth

Crack Growth Rate

Cross crack probe spacing

Degree of Bending

Reference probe spacing

- 2 0 -

F Brace axial force

f AC frequency

Y Joint geometry factor, D/2T

Hv Vickers hardness

IPB In-Plane Bending

Ky SCF Correction Factor for stiffened tubulars

Ka / Kb Punching shear equation coefficients

Ka / Q’ Factors in Lloyds Register SCF Eqn.

Ki S-N Curve intercept

Ki Mode I SIF

Kn Mode II SIF

Kffl Mode II I SIF

L Chord length

1 Brace length

m Gradient of S-N curve

M, B, k, p TPM model parameters

Mx ACPD modifier

N Number of cycles

Ni Fatigue initiation life

Nt Total fatigue life

NT Life predicted by T Curve

OPB Out-of-Plane Bending

PWHT Post weld heat treatment

r Distance from crack tip

R Apphed stress ratio

a Stress / Conductivity

S Hot spot stress range

Ga Brace nominal axial stress

Cb Brace nominal bending stress / Bending stress

-21 -

S b Stress Range at Reference thickness, te

SCE Calomel reference electrode

SCF Stress concentration factor

SCFav Average intersection stress concentration factor

SCFh Hot spot stress concentration factor

SIF Stress Intensity Factor

Membrane stress

^nom Brace nominal stress

Gt Total stress, (Tm+Gg

G y y Crack opening stress

z Joint geometry factor, t/T

T Chord thickness

t Brace thickness

tl Rack plate thickness

a Rib plate thickness

te Reference thickness

Te Equivalent thickness

TPM Two phase model

Vc, Vci, Vc2 Cross crack potential drop

V r , V r i , V r2, V io Reference potential drop

Y SIF modification factor

z Rack plate depth

2 2 -

Chapter 1 - Introduction and Background to Fatigue of Tubular Joints

Chapter One

1. Introduction and Background

1.1 Introduction

High strength weldable steels, defined as having a yield point above 450MPa are

being used in ever increasing tonnages offshore. Unfortunately, information on the

properties of these steels is limited and this is reflected in the restrictions on the

applicability of S-N curves to relatively low yield strength steels and maximum

permissible yield ratio specified by offshore design codes. This has to some extent

limited the designers ability to maximise the potential benefits offered by high

strength steels.

One area where the use of high strength weldable steels is well established is in the

construction of jack up rig legs. These steels are utilised extensively in the

fabrication of the chord, rack and spud cans of these self elevating mobile units.

Concern about the performance of these steels in the severe environmental and

loading conditions in the North Sea was heightened by the discovery of cracking in

and around the spud cans of jack ups operating in the North Sea in the late 1980’s

[1.1].

Data from large scale welded tubular joint fatigue tests performed under

representative environmental conditions (i.e. sea water with cathodic protection

and overprotection) is needed if confidence is to be gained regarding the

performance of these steels offshore.

Experimental investigations performed as part of this PhD thesis aim to address

some of the shortfall in data for high strength weldable steels. The fatigue tests

presented in this thesis are amongst the highest strength large scale steel welded

tubular joints tested under conditions of cathodic protection performed world

wide. As such it is hoped that the current investigation will promote discussion and

2 3 -


further experimental investigations to enable the advantages and limitations of such

steels to be quantified.

1.2 Background to Fatigue of Tubular Joints

Fatigue and corrosion fatigue behaviour of tubular joints has been researched

extensively over the last two decades. This research has taken many forms

including full scale tubular welded joint fatigue tests, small scale tubular welded

joint fatigue tests, welded plate tests, simple specimen tests and finite element

analysis. All of the above wiU be discussed in detail in this Chapter. The individual

contribution of each of the techniques to the current knowledge of the (corrosion)

fatigue behaviour of tubular joints will be assessed.

The vast majority of this research has been focused on steels representative of

those used in the tubular connections of fixed jacket structures. One such steel,

BS4360 Gr5()D [1.2] (or BS7191 Gr355D [1.3]) has been the standard for the

construction of many fixed jacket platforms and thus has been by far the most

widely researched and the norm for laboratory tubular joint fatigue tests. As a

direct result, large amounts of data already exist for these medium strength

weldable steels. The pertinent conclusion drawn from this body of data by

researchers across Europe and to a lesser extent USA and Japan will be presented

in this Chapter. This will serve as a basis for assessing the performance of the steel

under investigation in this thesis.

The above mentioned body of data has allowed the formulation of fracture

mechanics models to predict the (corrosion) fatigue behaviour of welded tubular

joints. These models are of differing complexity and to a large extent accuracy. The

more widely recognised of the models will be presented and assessed in Chapter 5.

These models wül be compared against the results of the fatigue test programme

conducted for this PhD study.

- 2 4 -


The impetus for this research programme stems from the concerns regarding the

changing role envisaged for offshore jack up structures which utilise these higher

strength steels in the lattice leg structure. A typical jack up platform will be

described in detail later in the chapter with an emphasis on the leg structure and

chord design. Traditionally jack up rigs have been utilised for short term drilling

assignments. Such assignments last for a period of a few months at a single site

before the legs are raised out of the water and the vessel moved to a new site or to

dock. This short assignment cycle allows regular NDT (non destructive testing)

inspections to be undertaken with relative ease, with remedial action taken if

necessary. AH of this can be done with the legs fully raised out of the water

eliminating the need for expensive diving procedures and hyperbaric welding

operations.

Secondly the mobile nature of these rigs implies that they are likely to be operating

in differing water depths throughout their operational lives. The implications of

which are important if one considers the effect on the fatigue loading of individual

tubular connections in the leg lattice. It is thought to be likely that the most fatigue

critical location in the leg would be related to the position of the topside platform

along the leg lattice i.e. the water depth. Thus the most highly stressed region of

the leg structure at one water depth is unlikely to be the same when the rig is

operating in a greater or shallower water depth. This is in contrast to a jacket

structure where the most highly stressed regions are most likely to remain

stationary during the life of the structure, hence broadly speaking, most susceptible

to fatigue damage. A further area of concern for jack ups is near the spud can

where high bending stresses can be present under conditions of high fixity.

Thus mobile jack up rigs may be considered to be in a fortunate position as far as

fatigue is concerned and designers of such structures have in the past been more

occupied in ultimate strength design of the legs under the maximum operational

and environmental loads envisaged during the lifetime of the structure.

-25


This however is now changing as jack ups are being prepared for a new role as

production platforms rather than mobile drilling rigs. Compared to the more

traditional production platform designs, jack up structures are relatively cheap in

terms of construction and installation. Indeed a jack up can be considered as being

self installing, thus removing the need for expensive heavy lift equipment etc.

required during traditional jacket platform installations. As a direct result of this

B.P.’s ground breaking Harding platform, a jack up currently being used for

production purposes is expected to be one of the most economical platforms in

terms of cost per barrel in the whole of the North Sea [1.4]. The success of this

platform is likely to lead to wider use of this concept for the exploitation of more

marginal fields.

This however removes the beneficial effect of short term assignments and varying

water depths mentioned previously. A production jack up must be designed in

terms of fatigue life as well as ultimate strength considerations. A fatigue life equal

or greater than the anticipated viable field life, often around 35 years, must be

demonstrated. Areas likely to suffer fatigue damage are to be highlighted at this

stage. Inspection schedules must be planned accordingly and of course inspection,

repair and maintenance tasks are subject to the same underwater difficulties and

expense as fixed jacket structures.

A further complication arises from material choice for the leg structure. Weight

considerations demand the use of thinner section, higher strength steels. The use of

thinner section implies higher nominal stress levels, further amplifying the need for

accurate fatigue crack growth data on such steels in representative environments.

Unfortunately the fatigue and corrosion fatigue behaviour of these steels is much

less well understood compared to the heavily researched BS4360Gr50D. One must

consider the effects of variable amplitude loading, cathodic protection level, weld

profile, corrosive sea water environment including the presence of Sulphate

Reducing Bacteria (SRB) and material susceptibility to Hydrogen Embrittlement

2 6 -


caused by Hydrogen generated by the C.P. system and the aforementioned SRB’s

present in many seabed muds.

The current investigation aims to address a part of this shortfall of data for such

steels. It is not possible in the limited time available to quantify all the effects

identified above, e.g. SRB’s were not present in the sea water used in the corrosion

fatigue tests. This work does however, form a valuable insight into the effect of

cathodic protection on large scale tubular joint corrosion fatigue behaviour. It is

the first time that such a programme has been undertaken on this scale using this

particular steel.

The seriousness of the problem in hand is highlighted in [1.5]. It is noted that

fatigue, especially of the leg and other components fabricated from higher strength

steel, will become more dominant in the determination of the useful life of jack up

rigs, as they move towards operating in more extreme conditions for longer

periods.

Massie et al [1.5] quote a recent analysis of the jack up failure statistics from the

World Offshore Accident Databank and notes that jack ups appear to be between

30 and 60 times more accident prone than fixed structures. This alarming accident

rate is by no means solely attributable to fatigue. However leg fatigue failure is

quoted as a significant cause together with “punch through” during installation and

insufficient deck clearance during storm conditions.

1.3 The Jack Up Platform.

The jack up platform will be described here in some detail. Special emphasis will be

placed on the leg structure and chord design as these are central to the current

investigation.

2 7 -


It should be noted at this stage that jack up platforms can vary enormously from

design to design and no single variety can be considered fully representative. An

attempt will be made to present the main variations found in each of the categories

described above together, where possible with a distribution of the occurrences in

the world jack up population.

1.3.1 The Jack Up Concept

Offshore jack up platform evolution can be traced back to posted barges operating

in 5-6 metres of water in the Mississippi Delta. The 15 years preceding 1970 saw

the greatest advances in jack up design with impressive improvements in operating

capabilities such as load carrying capability and increased water depths. A close

look at the evolution of jack ups shows how each designer produced individual

solutions to the design problems they faced. This is illustrated by the great array in

features found on jack ups produced in this period. Some of the major differences

are summarised in Table 1.1 [1.6].

Designs have now consolidated somewhat and jack ups are usually 3 legged

structures often capable of operating in water depths of over 100m. A schematic

view of a typical jack up is shown in Figure 1.1. Despite this rationalisation there

still exists many differences in the leg design found in current structures.

1.3.2 Jack Up Leg Design

The majority of modern jack ups now have three legs which can be raised and

lowered independently. This design has evolved over the years from the very early

designs that often had many more legs, one design specified 2 2 legs.

Of most interest is the detailed leg design. Some jack ups, usually for use in calm

shallow waters have square or circular closed section legs. More severe

environments require the more familiar truss type design to be employed. A survey

of Noble Demons mobile rig data hbrary [1.7, 1.8] is summarised in Tables 1.2 and

1.3.

-28


Of these designs only the three tubular chord designs will be further considered

despite the triangular chord being the single most popular design. This is due to it

being the preferred design of one of the worlds largest jack up manufacturers,

Marathon Le Tourneau. However, the triangular chord design bears little

resemblance to the remaining three tubular designs which are all essentially

variations on a theme. Only tubular specimens are considered in this study.

Full details of the leg design survey can be found in [1.7]. The major structural

dimensions are detailed along with the material properties of the chord and rack in

individual designs. The four main chord designs are shown schematically in Figure

1.2. Typical dimensions are for jack up chord details are given by Stacey et al [1.9]

who notes that rack plate typically varies between 150 and 250mm, whilst the

chords often have a diameter of between 800 and 1200mm and a thickness of 35 to

80mm. Some of the chord designs have been drawn to scale [1.7] to illustrate the

wide variety of shapes and sizes currently used in chord designs. These are shown

in Figures 1.3, 1.4 and 1.5.

Common design details that further complicate the analysis of the fatigue behaviour

of jack up legs include webs, stiffeners and overlapped joints at brace to brace and

chord to brace connections. A plan view of a typical leg is illustrated in Figure 1.6.

Also shown in this figure are the Leg Guides. Leg guides are found at the upper

and lower hull / leg intersection points at each chord and restrict the deformation

of the leg as it passes through the hull. The potential importance of leg guides is

highlighted in Chapter 4.

A recent visit to a ‘Harsh Environment’ jack up in an operational condition in the

North Sea allowed the close inspection of the leg structure. Of particular interest

were the weld details, cathodic protection system and rack geometry. The jack up

in question was constructed in Singapore and is one of the most modern jack ups

currently operating in the North Sea. A general view of the leg structure illustrating

2 9 -


the rack detail is shown in Figure 1.7. Note the jack house at the bottom of the

picture in Figure 1.7. The jack house contains the leg jacking mechanism, in this

case large electric motors and a hydraulic jack and chock system which mates with

the rack teeth when the jack up is in location. This allows the load to be taken off

the jacking mechanism. Each of the three legs has its own jack house which can be

controlled independently from the bridge. The complex nature of the bracing and

span breaker configuration is illustrated in Figure 1.8 and overlapped chord / brace

intersection are shown in Figure 1.9.

1.3.3 Weld Procedures

The weld procedures followed during construction of jack up legs often stipulate

that all welding is to be carried out to AWS D l. l [1.10]. Weld preparation and

run layout schematics followed during construction show great similarity to the

procedures adopted for the fabrication of the specimens to be utilised in the

experimental element of this study. The weld procedures used for the fabrication of

the T joint test specimens can be found in Chapter 3.

1.4 Loads Experienced by Jack Up Platforms

The loads experienced by jack up platforms arise from a number of sources but can

be divided in to two main categories [1.11]. These categories are operationally

derived loads and loads due to towing and transportation. Operational loads

include wind, wave and current loads together with platform weight, leg weight

and additional topside loads. Towing , or more generally transportation of jack ups

occurs with the legs fully raised out of the water. Two types of jack up

transportation are possible. These are the Wet Tow where the jack up sails under its

own power or is towed by tugs and the Dry Tow where the jack up rides on a

Piggy Back Vessel with its hull raised completely out of the water. The two

transportation modes are illustrated in Figure 1.10. In the towing modes the loads

arise from inertia forces from the motion of the platform and the self weight of the

leg.

-3 0


The differences in jack up response to wave loading are highlighted by Kam and

Birkinshaw [1.11]. In particular attention is drawn to the non-linear dynamic

response of jack ups in different sea states. It is stated that a framework is required

for generating “typical” fatigue loading experienced by tubular components in jack

up rigs. Four features of this framework were identified for inclusion as follows:

a) the simulation of a random sequence of multiple sea states;

b) the simulation of random load histories within each sea state according to given

multiple peak power spectra and the spectra should reflect the non-linear

features of the dynamic response of jack ups;

c) the simulation of transport loading under different conditions, and

d) a machine independent simulation framework.

A random load history for the fatigue testing (and remaining life analysis) specific

to jack up structures has been developed at UCL [1.12]. Known as JOSH (Jack up

Offshore Standardised load History) this framework accurately models the dynamic

load response of jack up rigs. Each of the four points detailed above has been

included except for the transit loading. This has been omitted for a number of

reasons namely the lack of data on loads experienced during towing and the fact

that the impetus behind this study is the use of jack ups for long term production.

Obviously in this instance towing loads will only occur as the platform is

transported from its point of construction to its operational site and as such are

significantly less important. Additionally transportation induced loading will cause

damage at different parts of the structure and therefore is omitted from fatigue

analysis.

Ohta et al [1.13] present an innovative, accurate and time saving method for the

structural analysis of jack up leg lattices. A detailed description of this method is

beyond the scope of this Chapter but interested parties are referred to this paper.

31 -


1.5 The Use of High Strength Steels Offshore

Traditional jacket construction has utilised steels restricted to yield strengths of

approximately 350MPa. Recently, however some higher strength steels of around

450MPa have accounted for up to 25% of the total structural weight [1.14]

although this is thought to be mainly confined to topside apphcations and bracing

in non fatigue critical locations.

High strength steels have improved significantly in recent years in terms of their

weldabihty. Traditional high strength steels of the Ni-Cr-Mo type used rich

chemistries to achieve the desired strength levels and are well known as being

difficult and expensive to weld.

The improved properties of modern high strength steels have been achieved using

the following principles [1.15]:

a) Relatively low carbon content which is beneficial to parent plate toughness and

weldabihty. Plate hardness increases with increasing carbon content.

b) Improved strength and toughness through grain refinement

c) Addition of strengthening microaUoying elements (V, Nb, Al) during steel

processing, sohd solution strengthening or transformation strengthening using

Mn, Ni, Cr, and Mo.

d) Reduced sulphur and phosphorous leading to increased toughness and

improved homogeneity in through thickness properties. Resistance to lamellar

tearing during welding is also improved.

Healy et al [1.16] have examined a group of 5 steels of yield strength

approximately equal to 690MPa. The composition, process route and weldabihty

of these steels were examined. The steels investigated were Q2N, 0X812, SE702,

DSE 690V, and HSLAIOO. Q2N is a traditional Ni-Cr-Mo developed primarily for

UK Naval use. 0X812, SE702 and DSE690V are modern, boron treated.

- 3 2 -


microalloyed, quenched and tempered European high strength steels with

significantly leaner chemistries than Q2N. HSLAIOO also follows the quenched and

tempered route but uses a copper precipitation strengthening technique and

reduced carbon levels (0.06%) to achieve its strength levels. It was concluded that

the modern high strength steels (0X812, SE702 and HSLAIOO) possess the

necessary combination of material properties and weldabihty to be considered as

suitable materials for offshore construction. Lower hardenabihty and reduced cold

cracking susceptibihty was noted for these steels. It was also concluded that further

research effort needs to be directed towards matching strength consumables to

overcome welding process limitations.

1.6 The Tubular Joint Intersection

Tubular joints are a common component in structural engineering and especially so

in offshore structures. A number of reasons exist for their popularity ranging from

aesthetic properties in building design and architectural circles through to the

minimisation of wave and wind forces offshore. The intersection between tubular

members has proved an interesting problem for the fatigue speciahst, stress analyst

and mathematician alike.

Tubular joint configurations are often described by the letters of the alphabet to

which their shapes approximate. For example a single brace attached

perpendicularly to the chord may be described as a T-joint. The same joint with an

inclined brace can be denoted as a Y-joint. Some of the more common brace /

chord configurations are shown in Figure 1.11. Only the simple T-joint will be

analysed in this study.

The parametric notation describing the dimensions of a T-joint are presented in

Figure 1.12. The non-dimensional parameters are utilised in parametric equations

developed to describe the stress distribution in tubular joints. The stress

distribution in many joint configurations have been investigated using a variety of

- 3 3 -


experimental and analytical techniques. The most important research in terms of

stress distribution in T-joints will be presented here.

Welded tubular joints are known to suffer high stress concentrations around the

brace / chord intersection. These concentrations are such that modest nominal

stresses due to wind, wave or operational loading can contribute to fatigue

damage. This problem is compounded by the fact that these stress concentrations

are co-incident with the weld toe region of the intersection. The untreated weld toe

has been shown to provide a ready source of sharp defects likely to assist fatigue

crack initiation [1.17] and this important area will be dealt with in greater detail

later in this Chapter.

1.7 Stress Analysis of Tubular Joints

It is therefore of utmost importance to the designer to know, accurately the stress

concentration distribution around a welded intersection. Early attempts to produce

purely analytical solutions to this problem floundered as the complicated

intersection geometry meant unacceptable simplifications had to be made to the

established membrane theory being applied. Donnell (1934) [1.18] and Flugge

(1960) [1.19] both attempted to utilise classical thin shell theory. Roarkes’ [1.20]

empirical formulae for stresses and deflections in cylinders were utilised by Biljaard

(1954) [1.21] and Toprac (1966) [1.22] to develop expressions for the stress in T

and double T joints. Further efforts by Hoff (1953) [1.23] and Kempner (1957)

[1.24] advanced the earlier efforts of Donnell. The most complete analysis and the

first to explicitly include the brace in the model was completed by Dundrova in

1965 [1.25]. The design code of the American Welding Society [1.10] was forced

to specify simpler analysis to be utilised in the design of tubular joints. The

Punching Shear Stress concept whereby the nominal average shear stress through

the thickness of the chord around the intersection was used as the design criteria

was one such tool. The punching shear stress approach has been shown to give

conservative results [1.26] and can be determined from the following equation.

-3 4


This is given for completeness only and will not be discussed in detail as its

relevance is purely historical.

sintjp {1.1)

where T and t are the chord and brace thickness’ respectively; a A and aB

are the brace nominal axial and bending stresses; KA and KB are correction

factors; and tp is the angle between brace and chord.

The maximum stress level around the intersection is traditionally known as the Hot

Spot Stress. This location of this Hot Spot Stress is dependant on the joint shape

and loading mode. Any loading arrangement applied at the brace end of a tubular

can be resolved into three principal loading modes. These are Axial, In-Plane

Bending and Out-of- Plane Bending and are illustrated in Figure 1.13.

The stresses at the weld toe of a tubular joint ( brace and chord side ) can be

divided into three main components. The first arises from the basic structural

response of the joint to the applied load, this is known as the nominal stress. For

axially loaded joints this is given simply by:

Gnom = F / A (1.2)

Considering the differing deformation responses to an applied load allows the

second of the stress components to be visualised. For simplicity and immediate

relevance consider the case of an axial load applied to the brace of a tubular T-

joint. the brace will extend slightly under this applied load whereas the chord will

be forced to deform locally to maintain contact with the brace in the welded region.

Large bending stresses can result from this deformation along with a redistribution

of the associated membrane stress. The deformation of the chord and brace under

load is shown in Figure 1.14.

-35


Geometric discontinuity due to the weld toe is the source of the third and final

component of the stress distribution at the intersection. The change in section gives

rise to local stresses, which although not penetrated far through the thickness do

produce a region of stress tri-axiality at the weld toe. Kare [1.27] have shown the

local stress to be dependant on weld toe geometry and is increased by a larger weld

angle, a and decreasing the toe radius, r (i.e. a sharper notch). The weld toe

terminology is illustrated in Figure 1.15.

The localised nature of the notch effect makes it difficult to measure

experimentally. Large stress gradients at the weld toe mean a small error in the

positioning of a strain gauge can significantly affect the result. As stated

previously, the severity of the notch effect is dependant on the weld angle and toe

radius. However even the most carefully controlled welding will produce a

distribution of weld angles and toe radii with corresponding range of weld toe

stresses.

The presence of web plates, ring stiffeners and doubler plates which are all

common features of tubular joint design further complicate the stress distribution

and can have a significant effect on the stress distribution found at the intersection.

For this reason an extensive finite element stress analysis has been performed in an

attempt to quantify the effect of the rack plate on the stress concentration factors

at the intersection of the brace and chord. The rack plate has been shown to be a

common feature of jack up chord design in Section 1.3.2. The results of this

investigation are presented in Chapter 3. For this reason previous work on the

determination of stress distributions in simple tubular joints and the development of

parametric equations will be discussed in more detail than might otherwise be

necessary for the analysis of tubular joint fatigue test results.

3 6 -


1.7.1 Stress Concentration Factors (SCF) in Tubular Joints.

Before the stress distribution in tubular joints can be discussed in detail it is

important to define the stress concentration factor. Stress distributions and hot spot

stresses are usually defined in terms of stress concentration factors where:

(T = (T ,_x ^ C F (1.3)

cr Stress at point of interest around intersection

cTnom Nominal brace response to applied load

It is important to appreciate that the SCF at any angular position around the

intersection can be greatly influenced by the point at which the stress measurement

is taken due to the large stress gradient at the weld toe. Thus in the interests of

reproducibility it is important that a standard definition of SCF be adopted.

However a review of the literature reveals several such SCF definitions exist in

world-wide design codes and guidance documents which would result in differing

SCF for exactly the same Joint. This should be borne in mind when comparing

stress analysis results from different studies. A summary of the SCF definitions in

the design codes and standards is given by the Underwater Engineering Group

[1.28]. A summary of the relevant sections is given here.

(:) API RP-2A

The SCF is defined by API [1.29] as:

that 'which would be measured by a strain gauge element adjacent to and

perpendicular to the toe of the weld after stable strain cycling has been

achieved.

(ii) AWS D l.l (1984)

Similar to API the AWS [1.10] definition is:

3 7 -


the stress on the outside surface of intersecting members at the toe of the

weld joining them, measured after shakedown in a model or prototype

connection or calculated with the best available theory.

(iii) BS6235:1982

This British Standard document [1.30] is no longer used but is included here since

it was the first standard to require that the measured stress was not influenced by

the concentrating effect of the weld profile.

(iv) Norwegian Petroleum Directorate

The NPD [1.31] document simply states:

the hot spot stress can be obtained by multiplying the nominal stress by the

SCF.

(v) Det Norske Veritas

DnV [1.32] suggest that SCF’s may be obtained from relevant analysis. Individual

SCF’s for stress components are also permitted. DnV places a lower bound of 2.5

on SCF’s.

(vi) Lloyds Register of Shipping

This document [1.33] is the only one to recommend the use of parametric

equations for determining SCF’s. Wordsworth and Smedley [1.34] are specified for

T and X joints and Kuang [1.35] for K and KT joints. A lower bound SCF of 1.5 is

given compared to 2.5 for DnV. For other joint types blanket SCF’s are given.

Brace Side SCF =6.0 (1.4)

ChordSide (1.5)

- 3 8 -


1 Tr 1 / sin0where: Ka = ------------------------------- (1.6)

Q’P= 1 forp<=().6

= 0.3/p(l-0.833p) forp>0.6

The appropriate parametric equations will be presented in the next section.

(vii) UK DoE Guidance Notes

The definition of hot spot stress used in this document was drafted by the review

panel of the United Kingdom Offshore Steels Research Programme (UKOSRP).

This definition was adopted in the UK guidance notes [1.36] now published by the

U.K. Health and Safety Executive [1.37]. This definition is the closest to a world

wide standard currently available and wül be adopted for this study. The UK

definition of hot spot SCF ( hence all SCF since hot spot SCF is simply the greatest

SCF around the intersection) as presented below fulfils the following necessary

criteria:

a) Effects of chord and brace geometry.

b) Stiffening effects of welds.

c) Stress concentrating effects of the notch omitted,

d) Experimentally reproducible.

The hot spot stress is defined as :

the greatest value around the brace chord intersection of the extrapolation

to the weld toe of the geometric stress distribution near the weld toe. This

‘hot spot’ stress incorporates the overall effects of joint geometry ( i.e.

relative sizes of brace and chord) but omits the stress concentrating

influence of the weld itself which results in a local stress distribution.

- 3 9 -


The stress distribution is shown schematically in Figure 1.16 illustrating the ECSC /

UKOSRP definition of hot spot stress as used in the current U.K. design guidance.

The limits of the linear strain region differ around the intersection. These are

defined for the crown and saddle position in both brace and chord in the U.K.

D.o.E. guidance reproduced in Figure 1.17.

Some joint shapes have been shown to exhibit non linear strain distributions in

certain areas. Many researchers are said to use curvilinear extrapolation in these

circumstances

A further discrepancy between the codes can be found regarding the use of

parametric equations. UK DoE states that parametric formulae should be use with

caution in view of their inherent limitations.

This situation is currently being reviewed and the new fatigue guidance is likely to

permit the use of certain parametric equations for specific joint types and loading

configurations. The recommended equations have been validated against a database

of results from large scale steel models and some acrylic model data. The

recommendations applicable to axially loaded T joints is shown in Table 1.4 It is

noted that the use of parametric formulae not included in the above Table may lead

to underprediction of SCF’s.

1.7.2 Parametric Equations for Prediction of SCF

Only those parametric equations recommended in Table 1.4 will be presented here.

The results of the SCF predictions of each of the parametric equations will be

compared with the experimentally measured SCF’s in Chapter Two.

Wordsworth and Smedley produced the oldest of the recommended parametric

equations (1978) [1.34] and as such they are widely recognised and utilised.

- 4 0 -


Comparison with the SCF database has shown the equations to underpredict the

SCF at the chord crown and brace saddle positions. A tendency to return

conservative values at the brace crown position has also been identified.

The data used in the derivation of the parametric equations was obtained from

strain gauged acrylic joint tests with the general stress distributions being

determined by brittle lacquer techniques. Two steel joints were also tested as part

of UKOSRP.

A limitation of acrylic models is the lack of weld in the model. A correction is

therefore recommended to compensate for this omission in the data used in the

derivation of the original formula. The correction factor is only applicable to T and

90° X joints on the chord side.

The parametric equations of Efthymiou and Durkin are derived from the results of

a Finite Element stress analysis utilising a purpose built software package for the

analysis of tubular joints [1.38]. This package used 16 node thick shell elements to

model the tube walls and 8 node shell elements to model the weld. Modelling the

weld and intersection region using thick shell elements is illustrated in Figure 1.18.

By using 3 dimensional elements, extrapolation of the stresses to the weld toe can

be carried out according to the ECSC/UKOSRP recommendations previously

discussed. Other studies using thin shell elements give SCF’s at the chord / brace

midplane intersection which is quite different. It is stated that the SCF predictions

from the analysis fall within the scatter of experimental steel model SCF data.

Parametric equations were produced giving the hot spot SCF’s for the extreme

boundary conditions of fully built in and simply supported chord ands under axial,

IPB and OPB brace loads. Both crown and saddle positions are covered. The

equations are valid for long chord conditions (a > 12). For shorter chords

correction factors must be applied.

41 -


Interrupting the natural decay in chord ovalisation by using short chord lengths

reduces SCF’s at the chord and brace saddles. Crown SCF’s remain unaffected

apart from the expected change due to bending moment differences as a result of

the changed chord length.

The Underwater Engineering Group (1985) [1.28] approach involved a detailed

comparison of the most widely accepted parametric equations available at the time.

For T joints these included Kuang, Gibstein and the previously discussed

Wordsworth and Smedley. It should be noted that the Efythmiou and Durkin

equations were not available at the time of the UEG publication.

It is noted that the various equations have been produced from different analysis

methods and assumptions. Again the chord length utilised in the original analysis is

highlighted as being a direct influence on the SCF values obtained. It is stated that

the majority of the original analysis was carried out using chord lengths sufficient

to eliminate any interaction between the chord ends and the brace chord

intersection. UEG note that the crown position SCF is most susceptible to the

chord length effects. It should be clarified at this point that this is simply the

expected response to the increased bending moment experienced due to the longer

chord. It is not directly related to the chord ovalisation phenomena that effect the

saddle positions when one considers short chord effects. Each set of equations is

compared to experimental data from strain gauged steel models. An immediate

disadvantage with the Kuang and Gibstein models was discovered to be the limited

validity range of each set of equations. Only 3 for Kuang and 4 for Gibstein of the

2 2 steel model results met all the parametric limitations.

The Wordsworth and Smedley equations are identified as being the most reliable.

Evidence is presented for increasing the validity range of these equations from 8 <

a < 40 to 2.5 < a < 40. UEG recommends the Wordsworth and Smedley equations

- 4 2 -


be utilised in conjunction with specified geometric multipliers to compensate for

modelling deficiencies discovered during the analysis.

The Lloyds Register equations [1.39] hail from a UK Department of Energy

sponsored project, “Stress Concentration Factors for Simple Tubular Joints”

completed in 1990. The equations are based on existing steel and acrylic model

databases.

The equations were derived using a least squares multi-variable least squares curve

fitting procedure to the database SCF results. Included in these equations are

design safety factors, chord ovalisation effects due to short chord lengths,

stiffening factors due to the presence of an unloaded brace adjacent to the brace

under consideration and influence factors for adjacent loaded braces.

Hellier Connolly and Dover [1.40] completed an extensive FFA analysis in 1990 of

more than 900 thin shell models. These differ from those used by Efthymiou and

Durkin in that the weld was not explicitly modelled. The use of thin shell elements

means that in effect the mid-planes of the brace and chord are modelled. The

material thickness exists purely as a mathematical entity in the stiffness

calculations. This is shown graphically in Figure 1.19.

This error is thought to result in an overestimated SCF compared to steel model

results with the error on the brace side likely to be greater than that of the chord.

For the case in hand of an axially loaded T-joint, 5 parametric equations were

produced, namely:

a) SCF at both crown positions ((()=0 and 180)

b) SCF at Saddle Position

c) Hot Spot SCF

d) Angular Hot Spot Location

4 3 -


Hellier et al used the same finite element models to produce parametric models of

other important areas in stress analysis of tubular joints. Two important areas were

tackled and are described separately in Sections 1.7.3 and 1.7.5 .

1.7.3 Stress Distribution in Tubuiar Y and T Joints

The parametric equations developed by Hellier et al for the SCF’s at discrete

locations around the intersection are utilised in expressions developed to describe

the SCF variation around the intersection [1.41]. This allows the determination of

the SCF at any location around the intersection from a knowledge of the SCF at

the crown, saddle and hot spot locations. Expressions have been developed for

axial, IPB and OPB loading modes for both Y and T joints. Only those applicable

to T joints will be presented here. The stress distribution for an axially loaded T

joint is symmetrical about the saddle position with the hot spot located at the

saddle point. The predicted stress distributions for axial, IPB and OPB loading for

the tubular specimens used in this study are plotted in Figure 1.20.

1.7.4 Comparison of Parametric SCF Prediction

Each of the parametric models previously detailed have been plotted across the

specified validity limits of each geometrical parameter enabling a direct comparison

of the SCF predictions.

For the purposes of this comparison all geometrical parameters were held constant

bar the parameter to which the models response was being tested. The default

values for the constant geometrical terms were taken as those for the test specimen

in this programme as shown in Table 1.5.

- 44 -


It should be noted that the default alpha value hes slightly outside the specified

validity limits for Wordsworth and Smedley. This limit was subsequently extended

by UEG and thus the effect is not thought to be significant.

Efthymiou and Durkins’ pinned chord end model tends to produce the highest

chord crown SCF prediction in Figures 1.21, 1.22, 1.23 and 1.24. A much stronger

dependancy on alpha for this model is also noted in Figure 1.21. This would be

expected from simple beam bending considerations for simply supported and built

in beams. It is also noted from this Figure that the UCL equations show almost no

dependancy on alpha for the chord crown position. This reflects the fully restrained

boundary conditions used in the original FEA analysis. Figure 1.22 shows the

predicted responses to beta bounded by the two Efthymiou models. Wordsworth

shows a linear relationship with beta predicting lower SCFs at high beta values.

Note the Wordsworth and UEG models are co-incident for this combination of

parameters since gamma is less than twenty thus the correction factor is unity. The

effect of the correction factor can be seen in Figure 1.23 at higher values of gamma

( greater than 2 0 ).

The predicted SCFs at the chord saddle are shown in Figures 1.25, 1.26, 1.27 and

1.28. All models show a linear or near linear dependency on alpha above an alpha

of approximately ten. Figure 1.25 illustrates the strong dependency of the

Efthymiou models below this value. The UCL equations predict significantly higher

SCFs for a given alpha. Contrary to the situation at the chord crown, intermediate

values of beta are shown to result in the highest SCFs in Figure 1.26. Again the

UCL equations predict the highest SCF values.

The UEG equations extend the validity of their equations past the usual upper

gamma limit of 32 to a maximum of 40. A very strong relationship between chord

saddle SCF and gamma values above 32 for the UEG equation is shown in Figure

1.27. SCFs above 50 are predicted for the highest gamma. At lower gamma values

the UEG model lies within the scatter of the other models.

- 4 5 -


1.7.5 Ratio of Bending to Membrane Stress In Tubular Joints

As well as varying around the intersection the stresses in a tubular joint vary

through the wall thickness. Connolly et al (1990) [1.42] have investigated this

variation using the finite element technique.

Fracture mechanics analysis of crack growth in tubular joints requires a knowledge

of the stresses acting across the anticipated crack path. If one considers a surface

breaking crack propagating in a tubular joint, the crack will be expected to grow

around the intersection ( i.e to follow the weld toe) as well as through the

thickness. Thus knowledge of the stress distribution in both crack growth

directions is essential.

The need for geometric compatibility between brace and chord under load results

in a degree of wall bending being introduced in the brace and chord. This can be

observed by strain gauging the inner and outer surfaces of the chord or brace wall

in an acrylic or steel model. Without a bending component the stress at the inner

and outer surfaces would be identical. This is the situation in the brace of an axially

loaded T joint away from the influence of the intersection. Closer to the

intersection the discrepancy between inner and outer surface strain readings

increases, illustrating the growing bending component superimposed on the

nominal stress.

It is usual practice to use a simple linear interpolation to account for the bending

distribution.

Ob /O t = O b / (O b + O m ) f J ' /V

Ob Bending Stress

Cm Membrane Stress

C t Total Stress

4 6 -


The stiffening of a rack plate as found in jack up chords may affect the through

thickness stress distribution in the chord wall and thus the degree of bending

predicted by the parametric equations for simple joint shapes may not be

applicable. An comprehensive Finite Element investigation of jack up chord

geometries is presented in Chapter 4. The degree of bending found in such chord

shapes has been quantified and compared with comparable tubular joints without

the rack plate. The UCL Bending to Membrane parametric equations applicable to

T and Y joints will be discussed in detail in Chapter 4.

1.8 Fatigue Design Guidance for Tubular Joints

As with all major world-wide fatigue design codes for tubular welded joints, the

United Kingdom guidance specifies a curve, known as an S-N curve to enable the

designer to predict the safe operational life of a welded tubular intersection. Stress-

Life (S-N) curves for tubular joints plot the Hot Spot Stress on the ordinate axis

against the number of cycles to failure on the abscissa. Construction of an S-N

curve requires a large amount of experimental data from fatigue tests on

representative geometries and materials. Acquisition of this data is expensive and

time consuming as each test generates only a single data point. For this reason the

first published S-N curve for welded tubular joints was based on the results of

small scale fatigue tests on T and K joints. This was published by the American

Welding Society in the Structural Welding Code AWS D l. l [1.10] in 1972. The S-

N curve in this code ( and its subsequent modifications ) is known as the X-Curve.

The first U.K. fatigue guidance [1.43] contained the Q-Curve which was based on

the same database of results as A.W.S.’s X-Curve.

Two attempts were made to correlate the observed experimental fatigue lives with

loading conditions. Initially a nominal chord stress was used with fixed stress

concentration factors of 16 for T joints and 7.5 for the K joints. The second and

more successful approach used the now familiar hot spot stress concept which has

since become the standard approach. Care must be exercised that the hot spot

-47


stress is calculated in accordance with the définitions laid out in the code being

used as these vary from code to code.

1.8.1 Development of U.K. Fatigue Guidance.

Since the first United Kingdom fatigue design guidance was published by the

Department of Energy (DoE) in the form of the Q-Curve, two major revisions have

taken place. The first in 1984 [1.44] re-defined the recommended S-N Curve

following concerns that the Q-curve may be unconservative under certain

conditions. This was highlighted by results from the United Kingdom Offshore

Steels Research Programme (UKOSRP) and the European Coal and Steel

Community sponsored research programme [1.45,1.46]. The fatigue guidance was

revised using a screened database of experimental results from full scale tests on

tubular joints from world-wide test programmes. The S-N curve recommended in

this revision became known as the T-Curve. The screening and statistical analysis

procedure used during the development of this curve will be discussed in more

detail in the next section.

Experimental data arising in the period 1984 to 1990 has allowed further additions

and amendments to be made to the fatigue guidance. The major differences

between the 1984 and 1990 documents will be highlighted and the experimental

evidence behind these changes examined.

1.8.2 Development of the T-Curve

Experimental data from world-wide test programmes has shown the Q-Curve to be

inadequate under certain conditions. The Q-Curve was derived from small scale

tubular joint fatigue test results. The welds on these small specimens are now

considered to be disproportionately large compared to the joint geometry, both of

which are far removed from that found in offshore structures ( except perhaps for

the tubular connections found in crane booms ). Sufficient data from full scale

welded tubular joint tests had been gathered to enable an S-N curve to be

constructed without having to resort to small scale test data. However the test

- 4 8 -


programmes from which this data was gathered were undertaken throughout the

world and under a wide variety of conditions. It was important that a consistent

database was developed by implementing a suitable screening procedure to exclude

results from tests that may be non typical.

Any tests falling into one of the following categories were excluded from the final

statistical analysis.

a) Specimens tested in sea water with or without cathodic protection (C.P.).

b) Specimens subjected to variable amplitude loading.

c) Specimens which were stress relieved

d) Specimens unbroken at the end of the test.

e) Specimens which after being unbroken at the end of the first test were retested

at a higher stress.

In addition all joints with a wall thickness of less than 16mm were ignored. The

complete database used in the construction of the 1984 guidance S-N curve can be

found in [1.47].

This definition of failure for a cracked tubular joint has been the topic of much

discussion. Several stages can be identified in the life of a fatigue cracked tubular

joint from first crack initiation at the hot spot through to complete severance of the

brace member. Four définitions of failure are proposed:[1.48]

Ni First discernible surface cracking as noted by any available

method. This stage is considered to have passed if the initial

surface length is greater than 2 0 mm.

N] Intermediate surface cracking as detected by visual

examination without the use of crack enhancement fluids or

optical aids. If NDT techniques indicate a surface length of

- 4 9 -


greater than 30mm then this stage is considered to have

passed.

N 3 First through wall cracking as detected either visually or more

accurately noting loss of internal pressure or by monitoring of

strain gauges positioned adjacent to the deepest part of the

crack.

N4 End of test as occasioned by complete severance of the brace

member, extensive cracking leading to loss of load symmetry

or exhaustion of actuator stroke.

The definitions of failure in the earlier (1984) guidance are slightly different and

care should be taken that consistent definitions of failure are being used when

comparing results from different test programmes.

The number of cycles to first through wall cracking ( N? ) has been adopted as the

standard definition of failure as this is thought to be subject to smaller errors than

both Ni and N2. The final definition, N4 was discounted since a joint having

reached this condition is unlikely to be repairable and may well have shed load to

other joints causing further remote damage. Furthermore N3 can be accurately

measured using Alternating Current Potential Drop Techniques (A.C.P.D.), loss of

sea water in environmental tests or a pressure drop in internally pressurised chord

members.

1.8.3 Analysis of Experimental Data to Produce S-N Curve

The statistical analysis used in the derivation of the 1984 guidance required that the

experimental data be divided into subsets of approximately equal wall thickness.

Only the subsets for 16mm and 32mm wall thickness joints existed in sufficient

numbers to allow a meaningful statistical analysis to be undertaken. These data

subsets were analysed individually and as a whole, the final S-N curve was based

upon the mean of the 32mm data minus two standard deviations of the 16mm data,

representing a probability of failure of 2.3%. This combination was chosen to

- 5 0 -


reflect the reduced performance of the 32mm data and the greater scatter in the

16mm endurance data.

During the derivation of the 1990 guidance the experimental data was again sub

divided in to groups of approximately equal wall thickness. However for the 1990

guidance it was decided that only one wall thickness should be used in the

construction of the S-N curve. The 16mm data set was chosen since it was the

largest and it covered the most diverse range of joint geometry’s and loading

modes.

To remain consistent with the earlier guidance the best fit relationship was

calculated according to (1.8).

Logio(N) = Log,o(K,)-mLogi„(S) {1.8}

where:

N Number of cycles to failure

Ki Constant

m Gradient of S-N curve

S Hot Spot Stress (MPa)

In addition the slope was fixed at -1/3 as in previous guidance and other recognised

fatigue standards [1.49]. The design line was taken as two standard deviations of

the 16mm data below the calculated best fit line. Again this represents a 2.3%

probability of failure. A change of slope to -1/5 is implemented to represent an

endurance limit. An absolute endurance limit is not specified ( i.e S-N curve turns

horizontal ) since under variable amplitude loading even the small load cycles can

become damaging in the later stages of the joint life. The best fit and design curves

are summarised in Table 1.6.

The 16mm experimental data used in the analysis is plotted in Figure 1.29 together

with the mean and design S-N Curves.

51 -


1.8.4 Allowance Factors to be Used in Conjunction with the Basic S-

N Curve.

Only constant amplitude tests carried out in air are utilised in the construction of

the S-N curve. However effects such as environment have been shown to

significantly alter the observed fatigue life. These effects are accounted for by a

factor on life applied to the base line, constant amplitude air life as given by the

design S-N curve. Each of the allowances specified in the current guidance will be

examined below.

(i) The Thickness Effect on Fatigue Life

It has long been recognised that parent plate thickness has an effect on the fatigue

life of welded joints. The 1984 guidance [1.44], based on welded plate specified

the relationship given in (1.9).

s = s. (1.9)V /

where:

Sb Stress range at reference thickness, te

tB Reference thickness (32mm for tubulars)

t Plate / joint thickness

S Stress range resulting in same fatigue

endurance at thickness, t

The above relation was based on an initial suggestion for the form of the thickness

effect correction by Gurney [1.50].

Analysis of more recent tubular joint data has confirmed the existence of a

thickness effect in welded tubular joints. Plotting the endurance results in Figure

1.30 for the 16mm and 32mm joints illustrates this clearly.

- 5 2 -


Utilising the best fit S-N curves for the 16mm and 32mm data previously presented

leads to a thickness correction exponent of 0.29, somewhat higher than value of

0.25 used previously. The current guidance (1990)[1.48] thus recommends a

thickness correction exponent of 0.3 and a shift of the reference thickness for

tubulars from 32mm to 16mm since the thickness effect has been shown to persist

in joints thinner than 32mm.

Thus the recommended correction is given by (1.10).

S = Sb i lAQ)\ t y

where the nomenclature is the same as in (1.9) except that the base

thickness, te is now 16mm.

The thickness correction factor can be represented by a family of nested T-Curves

as shown in Figure 1.31. It is noted that the guidance could be overconservative

for certain geometry’s and loading modes. Allowance is made for less onerous

thickness correction exponents derived from analysis of appropriate experimental

data or from a validated fracture mechanics procedure.

Baerheim et al [1.51] note that the same thickness effect is to be included in the

new ISO code [1.52]. The ISO code is based on the API RP2A LFRD

specification but is likely to contain significant portions of the HSE guidance e.g.

S-N curve for tubular joints.

(ii) The Effect of Environment on Fatigue Life

The in service environment of a tubular joint is very likely to be different to that of

the dry air laboratory conditions in which the experimental data used to construct

the T-curve was generated. Three specific environments can be identified.

- 5 3 -


Air Environment

Intermittent Immersion

Constant Immersion

Tubular connections situated at or close to the

topside deck level most closely resemble the

laboratory air environment although the air is

likely to contain high levels of moisture and salt.

Connections located in the tidal zone or splash

zone will be subjected to repeated cycles of

immersion in sea water an air environments.

Joints situated below the lowest mean tide level

will be constantly immersed in sea water. These

joints are usually protected with a painted /

sprayed coating, some form of C.P. system or a

combination of the two.

A number of tubular joints have now been tested in air or sea water environments

both with cathodic protection [1.53, 1.54, 1.55] and without cathodic protection (

free corrosion) [1.56, 1.57, 1.58, 1.59]. The results of these tests have been used

to modify the previous guidance (1984). The 1984 guidance dealing with

environmental effects is summarised in Table 1.7

Experimental data from environmental fatigue tests on tubular joints and flat plates

can be expressed in terms of Environmental Reduction Factors (E.R.F.’s). E.R.F.’s

are defined as the ratio of the fatigue endurance in air to the endurance in the

specified environment. The endurance in air is calculated from the best fit S-N

curve for 16mm joints. Data from other joint thicknesses must be normalised using

a thickness correction exponent of 0.3 as discussed in the previous section.

The following conclusions were drawn from the data used during the 1990

guidance revision.

- 5 4 -


a) The detrimental effect of sea water environment with optimum cathodic

protection decreases with increasing endurance (i.e. with lower hot spot stress).

b) With optimum cathodic protection little effect is seen at lives greater than 10

cycles.

c) A freely corroding environment (i.e. sea water without cathodic protection) has

an increasingly detrimental effect with increasing endurance (i.e. decreasing hot

spot SCF).

The 1990 design guidance notes [1.48] have been modified to include the above

effects which were not accurately modelled in the previous 1984 design guidance

[1.47]. The revised guidance on the effect of environment on fatigue life of tubular

joints is summarised in Table 1.8.

The S-N curves for 16mm tubulars in free corrosion and sea water with optimum

cathodic protection are shown in Figure 1.32.

1.8.5 Design Code Treatment of High Strength Steeis

There is a distinct lack of published guidance in the form of design codes dealing

with the use of high strength steels offshore. Most codes place an upper limit on

material yield strength beyond which the S-N curves are no longer valid. The

reasons for this caution are simple and sound. Examination of the total number of

tubular joint fatigue tests performed using high strength steels (i.e. yield point

above 450 MPa) [1.9] shows that approximately 85% of these tests used steels

with a yield stress less than 500MPa. Of the total number of tests (approximately

180), less than 5 were performed in sea water under cathodic protection and no CP

tests have been performed for steels with yield stresses above 586 MPa. Although

it is likely that a number of tests have been completed since this review was

performed, it is likely that this limited database would be further restricted by

discarding tests performed under non representative conditions as was done for the

lower strength steels. It is extremely difficult therefore for the design codes and

- 55 -


standards to make safe recommendations on the use of such steels without a co

ordinated research effort.

The S-N curve of the UK design guidance [1.48] is restricted to steels with

minimum yield strength of up to 400 MPa for tubular joints. However allowance is

made for the use of higher strength steels if the S-N performance is validated from

experimental investigations such as the one presented in this thesis. The other

major design code to specifically cater for high strength steels is the DNV Rules

for Mobile Units [1.60] which contains a ‘extra high strength’ grade covering steels

with yield strengths up to 690MPa. The DNV Rules also permit CP levels of -

lOOOmV compared with the more conservative -850mV limit imposed by the HSE.

A further restriction on the use of high strength steels takes the form of a limitation

on the yield to ultimate ratio (YR) as discussed in [1.61]. The HSE guidance

recommends a limit of the YR to below 0.7 whilst API RP-2A specifies 2/3. The

reason for the YR limitations is to avoid the possibility of underestimating the

static strength of tubular joints fabricated from different steels.

1.9 Linear Elastic Fracture Mechanics

The fracture process can be considered to occur on several different scales ranging

from the initiation of microscopic defects of sizes comparable to the molecular

scale to the formation of visible macrocracks whose lengths can vary from a few

millimeters to several kilometers in the case of fractured gas pipelines. Fracture

mechanics applies the theory of continuum mechanics to the fracture process in an

attempt to explain and predict the behaviour of cracked bodies. Fracture

Mechanics has been described as “..the applied mechanics of crack growth from a

flaw” [1.62]

The presence of a crack in a body represents a stress singularity. This leads to

localised inelastic deformation upon loading of the body due to the high stresses at

- 56 -


the crack tip. In situations where the inelastic effects are small compared to the

crack size and characteristic length of the cracked body, linear theory can be

implemented to simplify the analysis. This is known as linear elastic fracture

mechanics (LEFM). The development and use of LEFM concepts is discussed

here. When conditions of small scale yielding are violated then the use of LEFM is

invalid and one must adopt different parameters which can be described under the

heading elastic plastic fracture mechanics (EPFM). Elastic plastic fracture

mechanics parameters include strain based parameters such as that proposed by

Tomkins [1.63], modified stress intensity factors which utilise cyclic strain range

information [1.64, 1.65], the cyclic J integral of Rice [1.66], or the CTOD criteria

suggested by Wells [1.67]. Only during early crack growth when the fatigue crack

is ‘short’ are the small scale yielding conditions likely to be violated. The behaviour

and characterisation of early fatigue crack growth in welded tubular joints has been

extensively investigated by Monahan [1.68]. Discussion at this stage will be limited

to the stress intensity factor.

Fundamental to fracture mechanics is an understanding of the stress / strain field

surrounding a crack tip. Considering the area surrounding the crack tip, where r is

the distance from the crack tip, it can be shown that the displacement is

proportional to the square root of the distance from the crack tip. Furthermore the

associated strain, where the strain is the rate of change of displacement with

respect to distance from the crack tip, must be proportional to the inverse of the

square root of the distance from the crack tip. The elastic stress field surrounding

the crack tip is directly proportional to the strain.( 1 . 1 1 )

‘"yy“7r

Thus as one approaches the crack tip the elastic stress attempting to pull the crack

faces apart approaches infinity. In practice this is not the case since the material

will deform plastically in a region local to the crack tip and the applied load

5 7 -


redistributed across the elastic ligament. The cartesian notation for the components

of stress acting upon an element near the crack tip are illustrated in Figure 1.33.

The full solutions for the stress and displacement tields near to a crack tip in an

elastic body can be found in any elementary text on fracture mechanics.

A constant of proportionality can been introduced into (1.11). This is known as the

Stress Intensity Factor, K. The stress intensity factor is essentially a measure of

how quickly the stress rises as the crack tip is approached. The crack tip stress field

is therefore given by ( 1 .1 2 ).

Note the subscript I attached to the stress intensity factor symbol in (1.12) denotes

the mode of crack surface displacement under consideration.

Three basic modes exist that can cause crack growth.

a) The opening mode. This is the most common loading mode and is the mode

that will be uniquely considered here unless specified here.

b) The edge sliding mode. The surfaces of the crack move normal to the crack

front and the crack remains planar.

c) The tearing mode. The crack surfaces slide relative to each other, parallel to

the crack front and remaining planar.

These modes are perhaps best understood via graphical representation as shown in

Figure 1.34.

The stress and displacement fields in the vicinity of any crack tip are identical. Thus

for equal values of stress intensity factor, K, the stress and displacement fields are

identical for a crack in a simple laboratory specimen and a crack in a complex

-58


machine component. Thus the stress intensity factor characterises the crack tip

environment regardless of geometry and loading conditions. This enables K to

characterise the residual strength of a cracked body. The value of K at which a

crack begins to propagate is known as the fracture toughness, Kc. Under

conditions of plane strain the fracture toughness can be considered as a material

property and is denoted by Kic.

The definition of K as shown in (1.12) is strictly only valid for a two dimensional

centre cracked infinite plate under a uniform tensile stress. Modifications are

required for other configurations, crack geometries and loading systems. These

modifications usually take the form of (1.13).

K = Y a ^ (1.13)

where a is the surface stress in the uncracked component, a is the crack depth and

Y is the modification factor. This factor has been determined by analytical or

experimental methods for a large number of geometric configurations. For example

the stress intensity factor for an edge crack in a semi infinite plate under tension or

pure bending is given by (1.14).

K = U2(jyf7m (1.14)

In this instance Y=1.12 and remains constant i.e. it is independent of the crack size.

In many cases, including tubular joints the Y Factor is a function of crack size.

Fatigue cracking of tubular joints is an especially complex problem since the

surface crack path is usually constrained to the weld toe and the through thickness

cracking can also be curved. This warped shape can often lead to a mixed mode

component of crack growth even for pure mode I loading. The crack growth

behaviour in this case might not be adequately described using mode I stress

intensity factors. In practice much of the difficulty involved in producing a fracture

59


mechanics solution lies in determining Y. Several models have been produced that

attempt to predict the shape of the Y curve for tubular joints.

Since the stress intensity is effectively a single all encompassing description of the

crack tip stress state it is a likely candidate for describing fatigue crack growth

behaviour. Indeed it was discovered that fatigue crack growth data could be

described by utilising the stress intensity factor range, AK where AK=Kmax-Kmm

where K ax and Kmm are the maximum and minimum values of stress intensity factor

during a full fatigue cycle. Many fatigue crack growth laws have been developed of

varying complexity. One of the simplest and most widely used of these models was

developed by Paris and Erdogan [1.69].(1.15)

— = C(AK)"' (1.15)(IN

where:

da/dN Fatigue Crack Growth Rate (m/cycle)

C,m Material Constants (Paris Constants)

AK Stress Intensity Factor Range.

In general fatigue crack growth can be divided into three regions. I, II, and I I I as

shown in Figure 1.35. Stage I crack growth is a region of very low growth rates

where the growth rates are not accurately predicted by (1.15). Reducing the value

of stress intensity factor range in this region leads to a point where crack growth

no longer occurs. This is known as the threshold value of stress intensity factor

range and is denoted by AKth. Fatigue crack growth in Region I is heavily

influenced by microstructural and mean stress effects. Stage I I consists of a linear

Log(AK) - Log(daZdN) relationship. This is the region described by most fatigue

crack growth models, including the Paris - Erdogan law described above. Crack

growth rates in this region are relatively insensitive to microstructural or mean

stress effects. Region II I consists of accelerating, rapid unstable crack growth and

is generally dependant on microstructure, mean stress and component thickness.

- 6 0 -


Other crack growth models attempt to cover all three regions of the sigmoidal

da/dN - AK curve. One such model is that of Saxena et al [1.70] which, for a given

constant load ratio defined the relationship between crack growth rate and stress

intensity factor range as (1.16)

da/dN (AA-)"- (NK)"^

where Ci, mi, C2, m2 are empirical constants, R is the load ratio and Kc is the

fracture toughness as described above. The constants m% and m2 represent the

slopes of the straight lines describing Regions I and 11 and Ci and C2 are the

intercepts of the straight lines when the stress intensity factor range is unity. The

crack growth model of Saxena et al has previously been used in fatigue fracture

mechanics models for welded tubular joints [1.71].

The number of cycles required to propagate a crack from a given initial to a final

crack length can be determined by rearranging (1.15) and integrating between the

specified crack sizes (1.17). In practice this integration is often done using a

numerical integration procedure as the expression for AK is rarely a closed form

solution.

.= 1 : '= (1-17)

1.10 Stress Intensity Factor Solutions for Welded Joints

The general shape of the Y factor curve defining the stress intensity factor

development during the fatigue life of a welded tubular joint is now known from

experimental crack growth measurements taken during full scale tubular joint tests.

This differs significantly from the Y factor function for a similar crack in a flat plate

-61 -


due to the differing structural restraint conditions between the determinate flat

plate and the indeterminate tubular joint. Several attempts have been made to

model fatigue crack growth in tubular joints using a variety of methods. Haswell &

Hopkins [1.72] have grouped these attempts into four categories, namely;

a) Semi Empirical Models

b) Plate Models

c) Cylindrical Models

d) Numerical Models

It is noted by Haswell [1.73] that no accepted bench mark solution exists for any

type of tubular joint making absolute comparisons of the accuracy of models

impossible. The closest to an accepted solution is the empirical data generated from

the crack growth measurements from full scale welded tubular joint tests. It was

found that all models, analytical, numerical or semi empirical were representative of

the observed behaviour of tubular joints but variations introduced by the

assumptions and boundary conditions used in the formulation of the models

resulted in unquantified variations in the predicted stress intensity factors. Adapted

plate models of Thorpe [1.74] and Burdekin et al [1.75] provide upper and lower

bounds respectively to the stress intensity factor solutions for cracked tubular

joints. Haswell concluded that although simple plate models and FE analysis of full

scale joints have proved reasonable methods for determining SIF’s, fracture

mechanics of tubular joints is not a well researched area and should be treated with

caution. The development of fracture mechanics models used to predict the crack

growth behaviour will be treated in detail in Chapter Six.

The stress intensity factor experienced at the deepest point of a fatigue crack in a

tubular joint is known to be significantly different from that of a similar defect in a

flat welded plate. The stress intensity factor experienced in a tubular joint rises

rapidly followed by plateau where the SIF remains almost constant for most of the

life. By contrast the SIF in the flat plate continues to rise rapidly once a fatigue

- 6 2 -


crack has initiated, as illustrated in Figure 1.36. This has important (albeit obvious)

implications for the crack growth behaviour in these two specimen types. Once a

fatigue crack has developed in a flat plate a significant proportion of its life has

already expired and relatively little time remains for remedial action to be taken.

Tubular joints are fortunate in that the ratio of the initiation to total life is relatively

small and the presence of a defect is not necessarily an immediate threat to the

integrity of the joint. The differing crack growth behaviour is shown in Figure 1.37.

1.11 Factors Affecting Fatigue Crack Growth in Tubular Joints

It is known that the behaviour of a propagating fatigue crack can be significantly

altered by the environment in which it is located. This is shown by the penalty

factors on life for joints in sea water imposed by the S-N design codes. A number

of other factors can also significantly affect the development of fatigue defects.

Several parameters, both mechanical and electrochemical have been identified as

having a significant effect on the fatigue behaviour of welded joints. It is felt that

the most relevant factors can be covered by the following topics;

a) Environmental Effects

b) Mean Stress

c) Precipitate Induced Crack Closure

d) Variable Amplitude Loading

e) Welding and Fabrication

It is recognised that in several areas the above categories overlap, e.g. mean stress

and crack closure. However, breakdown of the effects into the above categories is

considered appropriate providing that the areas of interdependency are recognised.

This thesis is concerned primarily with the corrosion fatigue characteristics of high

strength steel tubular joints. It is the difference in behaviour of tubular joints

63


fabricated from different strength steels that is under examination here rather than

tubular joint fatigue behaviour per se. As such the discussion here will be centred

around the environmental effects such as anodic dissolution, hydrogen

embrittlement and calcareous deposits within the crack as these are thought to be

the competing mechanisms responsible for differences in behaviour. It is however

recognised that a number of other factors and mechanisms exist and are needed to

fully describe the complex behaviour of fatigue crack growth in welded tubular

joints. A more general and detailed discussion of the factors controlling crack

growth behaviour in tubular joints is presented elsewhere [1.68, 1.76].

The competing environmental mechanisms wiU be presented together with

experimental evidence from medium (50D) and high strength steels where

available.

1.12 Environment Assisted Fatigue Mechanisms

Steel welded joints can be considered for the purposes of this review to operate in

one of four environments namely;

a) Laboratory Air

b) Free Corrosion (artificial or natural sea water)

c) Adequate Cathodic Protection (-850mV Ag/AgCl)

d) Cathodic Over-Protection (>-1.0V Ag/AgCl)

It is recognised that it could be argued that for the high strength steels considered

in this thesis that CP levels of less than l.OV or even less than 900mV could be

considered as overprotection. However the majority of data reviewed here was

generated using lower strength steels and for the purposes of discussion the above

categories are felt to be convenient and representative.

- 64


1.12.1 Free Corrosion

Steel surfaces immersed in a marine environment without or with inadequate

cathodic protection will suffer material loss due to corrosion. As well as general

material loss seen in terms of loss of section thickness, the corrosive attack can

also be localised leading to pitting.

Prior to considering how corrosion affects the fatigue behaviour, the

electrochemical process of anodic dissolution (corrosion) will first be considered.

A more comprehensive account of corrosion reactions and reaction kinetics can be

found in [1.77]. In aerated sea water, iron ions are released into the aqueous

environment according to the reaction.

2Fe + O2 + 2 H2O ^ 2Fe^ + 40H (1.18)

This is illustrated in Figure 1.38. The iron ions usually oxidise further and then

react with hydroxyl ions to produce ‘rust’ (Fe(OH)3). From the previous figure it

can be seen that the oxidation reaction responsible for the removal of iron ions

from the surface of the steel also releases electrons. This is the anodic reaction.

The water reduction reaction (the cathodic reaction) consumes these electrons at

the same rate. In practice the cathodic reaction is usually rate limiting, controlled

by the supply of oxygen and thus limited by flow rate and oxygen concentration in

the sea water.

The rate of metal loss due to corrosion of steel in a marine environment has been

put at 0.13 mm/yr [1.78]. This is said to be representative for fully immersed (i.e.

not splash zone) clean steel. Importantly however, it is noted that pits can develop

at three to ten times this rate. Splash zone corrosion rates can be many times higher

due to increased availability of oxygen.

The effect of free corrosion conditions on the fatigue life can be considered in two

parts. Firstly the localised corrosion (pitting) has been shown to reduce the

6 5 -


initiation life by forming effective stress concentrations at the weld toe.

Furthermore, free corrosion can change the characteristic crack shape by inducing

a more general distribution of initiated cracks along the weld toe. These defects

can coalesce to form long shallow defects or edge cracks in plate joints [1.79].

Secondly the crack growth rates can be increased simply via the removal of

material at the crack tip by anodic dissolution. This is thought to be the most

plausible explanation for the increased crack growth rates found under free

corrosion. Excessive dissolution at the crack tip has been said to retard crack

growth via crack tip blunting. This is not thought to be a significant consideration

for the current investigation.

Oxygen supply has already been identified as a rate limiting step in the corrosion

process. Scott and Silvester [1.80] studied fatigue crack growth rates in 50D

compact tension specimens using two natural sea water environments. One was air

saturated (7-8 mg/1) and the other had a much lower oxygen concentration of

lmg/1. The lower oxygen levels result in slightly slower crack growth rates.

Importantly, no significant effect of oxygen concentration was found for CP levels

lower (more negative) than -800mV. This suggests that the increase in crack

growth rates under free corrosion conditions is due to anodic dissolution

mechanisms at the crack tip.

1.12.2 Cathodic Protection

The principle behind cathodic protection is as simple as it is effective. Cathodic

protection moves the anodic oxidation reaction away from the steel surface and on

to an external anode. The steel surface is transformed into the cathode in the

electrochemical system and supports only cathodic reduction reactions. To achieve

this the surface of the steel is flooded with electrons to suppress the anodic

oxidation reaction. Two methods are available to achieve this and they are known

as the Sacrificial Anode method and the Impressed Current method.

- 66


In the sacrificial anode method, a metal less noble (more negative) than steel is

placed in electrical contact with the steel in the aqueous environment. Aluminium,

zinc or magnesium are suitable materials. These metals will corrode in preference

to the steel and supply electrons to support the cathodic reactions on the steel

surface. The impressed current method uses an external power source to lower the

potential of the steel surface. Noble metals are often used as the anode in

impressed current systems, sustaining anodic reactions other than the dissolution of

metal ions. This has the advantage that the anode is not consumed and does not

need to be replaced. The impressed current CP system is shown schematically in

Figure 1.39.

At the negative (electron rich) steel surface two reduction reactions are possible in

sea water, namely the reduction of dissolved oxygen (1.19)

O2 + 2 H 2O + 4e' 40H (1.19)

and the reduction of water ( 1 .2 0 )

H 2O + e —>Had.sorbcd + O H ( 1 . 2 0 )

It is the reduction of water reaction that is of most significance here as the

hydrogen atoms can diffuse through the steel lattice structure. Hydrogen is known

to promote brittle behaviour of normally ductile materials.

Discussion of the effect of cathodic protection an the fatigue crack growth process

can be divided into two distinct topics:

a) Effects due to hydrogen

b) Effects of precipitated mineral deposits (calcareous deposits)

(i) Hydrogen based effects

67


The production of hydrogen as a by product of cathodic protection has already

been discussed. Significant evidence exists to suggest that interstitially absorbed

hydrogen can adversely alter the ductility of some steels. High strength steels are

generally thought to be more susceptible than lower strength grades.

Loss of ductility due to the presence of hydrogen is commonly termed hydrogen

embrittlement. The term “hydrogen embrittlement” is used to cover a wide range

of observations where unusual material behaviour is observed where hydrogen gas

may be present. The effects of hydrogen are generally seen in parameters such as

elongation and reduction of area in tensile tests and fracture toughness values that

are highly dependant on strain rate.

The exact mechanism by which hydrogen causes the degradation of material

properties is not too clear. However it seems obvious from the literature that the

mechanism involves the transportation of hydrogen to a tri-axially stressed crack

tip or notch root. An increase in brittle fracture modes on the fracture surfaces of

cathodicaUy protected specimens helps to confirm hydrogen embrittlement as the

mechanism responsible for increased growth rates under CP conditions [1.81,

1.82]

A discussion on the theories behind hydrogen embrittlement is given by Cottis

[1.83] who notes that five main theories have been proposed to account for the

observed effect of hydrogen on high tensile steels.

(i) Pressure Theory. Hydrogen enters the metal lattice and migrates towards voids

and defects within the metal. Once at these sites the hydrogen forms pockets of

very high pressure gas. Blistering of pipelines carrying sour crude oil has been

known to occur lending some support to this theory. However experimental

evidence [1.84] on high strength steels has shown hydrogen embrittlement to occur

in low pressure (0.001 atm) hydrogen gas environments. In these instances it is hard

-68


to imagine the formation of high pressure pockets of gas suggesting that some

other mechanism may be (additionally) operative.

(ii) Decohesion Theory. This theory states that hydrogen weakens interatomic

bonds in steel facilitating grain boundary separation of cleavage crack growth.

(iii)Surface Energy Theory. Hydrogen lower the surface energy of newly formed

cracks thus reducing the SIF needed for brittle fracture.

(iv) Hydride Formation Theory. The presence of hydrogen causes the formation

of brittle hydride phases at the crack tip. However little evidence exists of hydride

formation in steels.

(v) Local Plasticity Theory. Hydrogen reduces the stress required for dislocation

movement.

Although experimental evidence exists to support each of the theories, it is thought

that the effect of hydrogen can be distilled down to the following:[1.83]

1) Hydrogen can decrease the strength of the metal - metal bond thus facilitating

brittle fracture.

2) Hydrogen can increase the stress required to emit dislocations from the crack

tip, making ductile failure more difficult.

Anodic dissolution has been shown to be responsible for the increased crack

growth rates under free corrosion conditions. This mechanism is not thought to be

significant in the case of cathodic protection since the oxidation reactions

responsible for the dissolution of iron ions should be suppressed at the potentials

under consideration here. Measurement of the potential at the crack tip of actual

and simulated cracks has shown that polarisation of the specimen is virtually as

- 6 9 -


effective at changing the potential within the crack as upon the external surface

[1.85].

The simultaneous application of mechanical strain and hydrogen charging appears

to be essential to the mechanism of hydrogen embrittlement. This is shown by slow

strain rate tensile tests in air using specimens which had previously been allowed to

soak under CP conditions in sea water [1.86]. After 100 hours exposure the

specimens were removed from the sea water and subjected to a tensile test in air.

The results show no loss of ductility occurs when the straining and hydrogen

charging are not simultaneous.

The dynamic strain rate is clearly an important variable in determining the potential

susceptibility to fatigue crack growth rate enhancement under cathodic protection

conditions. The effect of strain rate has been investigated by Proctor [1.87] who

performed tensile tests on X65 Linepipe steel in 3.5% NaCl solution at very

negative levels of CP. The results show increasingly ductile behaviour as the strain

rate increases. This has implications for the waveform used during testing with the

rise time being of particular importance. This has been demonstrated by examining

the crack growth rates of specimens subjected to square, sinusoidal and triangular

waveforms in 3.5% NaCl solution [1.88]. The triangular and sinusoidal growth

rates were similar to each other and consistently faster than the average of the air

data . However the square waveform resulted in a significantly lower growth rate,

only marginally faster than in air. This can also be translated into an effect of

frequency with the effect of environment likely to decrease with increasing

frequency. Atkinson and Lindley [1.89] came to much the same conclusion using

triangular and positive and negative saw tooth waveforms. It is postulated that

during dynamic straining new material is being exposed to the environment via the

disruption of passivating layers allowing the dissolution of iron ions to take place in

free corrosion and the adsorption of hydrogen under CP conditions. The

passivating layers are therefore assumed to reform rapidly once the peak load in

each cycle has been reached.

- 7 0 -


Naturally, any mechanism that encourages the absorbtion of adsorbed hydrogen

(rather than harmlessly bubbling away as a gas) is likely to magnify the measured

effects of hydrogen embrittlement. Sulphate Reducing Bacteria, common in natural

sea water environments are known to promote the absorbtion of hydrogen.

Cowling et al have studied the role of SRB extensively for 50D type steels [1.90].

The promotion of corrosion and corrosion fatigue by SRB’s is said to be due to the

following processes:

1) The ease with which SRB’s reduce sulphate ions to sulphide ions which rapidly

hydrolyse to form hydrogen sulphide.

2 ) T h e use b y th e b a c te r ia o f h y d ro g e n as an e n e rg y s o u rc e , th u s p ro d u c in g

c a th o d ic d e p o la r is a t io n (p ro m o t in g co iT O s ion ).

3) Enhanced hydrogen embrittlement due to increased permeation of atomic

hydrogen into bulk metal.

Tests were performed on 25mm thick, three point bend specimens at a CP level of

-850mV. Enhanced corrosion fatigue crack growth rates occur across a limited

range of AK and is noted as being increased by up to an order of magnitude. This is

the same region where enhanced crack growth rates due to cathodic protection are

found. Robinson and KilgaUon [1.91] have investigated the effect of SRB’s on

hydrogen damage in high strength steels. The general conclusion that SRB’s

considerably increased the level of absorbed hydrogen and thus the possibihty of

increased embrittlement was confirmed.

(ii) Calcareous Deposits

When a steel surface is cathodicaUy polarised in a natural or artificial sea water,

calcium and magnesium based mineral deposits can form on the surface of the steel

[1.92]. Oxygen reduction reactions at the steel surface increase the pH of the

solution adjacent to the steel. Other reactions also occur which have the same

71 -


effect. The increased alkalinity at the surface impedes the entry of into the metal

hydrogen by affecting the reduction reactions at the surface thus limiting the effect

of hydrogen embrittlement [1.93].

A further effect of this layer of more alkaline sea water adjacent to the steel is to

promote the following precipitation reactions:

O H - + H C O j- - 4 H 2O + C O j^ - ( 1 . 2 1 )

pptCO3" + ^ CaCOj (1.22)

CGj^' + Mg'^^MgCGjrp, (1.23)

2GH + Mg'+ Mg(GH )2 pp, ( 1.24)

Hodgkeiss et al [1.85] and Maahn [1.94] have both investigated the pH of the

solution within a fatigue crack. Both investigations noted that the pH within the

crack is commonly more alkaline than the pH of the bulk solution. The pH inside

the crack is typically between 10 and 13. This has been confirmed by the formation

of Mg(OH )2 within the confines of cathodicaUy polarised fatigue cracks.

Magnesium hydroxide does not form at pH more acidic than 10. Magnesium

hydroxide has been shown to form at a faster rate than calcium carbonate [1.95]

and results in a harder and stronger precipitate.

Formation of these precipitates, known as ‘calcareous deposits’ within a fatigue

crack has been shown to reduce the effective SIF range by wedging the crack open

at the lower loads in the fatigue cycle. This precipitate induced crack closure is

known to increase the minimum value of crack opening in a cycle whilst leaving the

maximum unchanged.

It is also thought that the calcareous deposits on the surface of the steel may inhibit

the entry of hydrogen into the steel by restricting the supply of water at the steel

surface therefore slowing the rate of water reduction and hydrogen evolution.

-72


1.13 Effect of Environment on Fatigue Crack Growth Rate

The electrochemical process of corrosion and cathodic protection have been

outlined. The mechanisms by which these environments are thought to affect

fatigue crack growth rates were also discussed. It is now appropriate to examine

the magnitude of these rate changes by reviewing experimental evidence.

Thorpe and Ranee [1.96] and Cowling and Appleton [1.97] have performed

extensive studies on the fatigue crack growth rates on 50D type steels. Fatigue

crack growth rates at a given value of AK are known to fluctuate with the level of

cathodic polarisation. In general it seems that the lowest growth rates occur at

approximately the same potential that just prevents anodic dissolution (0.8-0.85V

Ag/AgCl). More anodic potentials are thought to produce higher crack growth

rates due to increased anodic dissolution at the crack tip. Polarisation to more

cathodic potentials has been shown to increase growth rates by a factor of up to

six. Hydrogen embrittlement is thought to be the mechanism responsible for the

increased growth rates in this region as Neilsen and Maahn [1.98] showed the

hydrogen permeation current in 50D to exhibit a near logarithmic dependancy on

applied potential. It should be noted that none of the above environments restore

the growth rates found in air. This is summarised in Figure 1.40.

Under free corrosion conditions the growth rate depends on stress ratio with

increasing stress ratios resulting in increasing crack growth rates up to R ratios of

around 0.5 to 0.7 [1.96]. The increase was found to be the same for all AK.

Cowling et al [1.97] however failed to find the same dependency of crack growth

rates on R under free corrosion conditions. Austin [1.76] suggested the difference

could be caused by crack closure effects due to corrosion products within the crack

in the experiments by Scott and Thorpe. This appears to be a plausible theory and

would explain the diminishing effect as the crack opening increased with mean

stress.

- 7 3 -


Application of cathodic potential has repeatedly resulted in a plateau crack growth

region where the crack growth rate is independent of AK. This is illustrated

schematically in Figure 1.41. This behaviour has been found in 50D (e.g. Scott et

at. Cowling et al) and by Vosikovsky [1.99] for pipeline steels. Crack growth data

obtained by Vosikovsky for X65 type steels under cathodic protection at the zinc

potential shows the plateau behaviour clearly in Figure 1.42.

The effect of calcareous deposits is generally seen at lower values of AK. The

effect of calcareous deposits can be investigated by testing in ASTM sea water and

3.5% NaCl. The NaCl solution does not contain the magnesium and calcium

compounds needed to form calcareous deposits.

Such tests have been performed by Eggen and Bardai [ 1.100] on 30mm thick 50D

SEN specimens. A large difference in behaviour was found between the NaCl and

ASTM solution tests. At very low AK the behaviour is similar but at higher stress

intensity factor ranges (>8 MPaVm) the growth rates are significantly less in the

ASTM sea water. This behaviour was found at a stress ratio of 0.1. However

increasing the mean stress so that R=0.7 reduced the difference between the

environments to a much lower level for all AK. This presents clear evidence that

the formation of calcareous deposits within a crack can have significant benefits on

the fatigue crack growth rate.

Billingham and Laws [1.101] examined a number of steels with yield strengths

between 460 and 640 MPa in order to assess their suitability for offshore use in

terms of weldability and fatigue performance. The steels were produced via a

variety of processing routes including quenched and tempered and controlled

rolled. It was found that the high strength steels tested suffer from enhanced

fatigue crack growth rates with increasing negative polarisation. Growth rates at a

CP level of -llOOmV (SCE) were between 2 and 10 times faster than at -800mV.

This is illustrated in Figure 1.43. Increasing components of cleavage type facets on

-74


the fracture surface were noted at the more negative potential providing evidence

of hydrogen embrittlement mechanisms playing a significant role. It was concluded

that all the steels tested performed as well as or slightly better than conventional

350MPa steels.

1.14 Effect on Environment on the Fatigue Lives of Welded Joints

The first significant systematic investigation into the effect of environment on the

fatigue behaviour of welded joints was the United Kingdom Offshore Steels

Research Project - Phase I (UKOSRPI) [1.45]. The results suggested the following

environmental effects which were subsequently used for the basis of the design

guidance.

1. Free corrosion can reduce endurance by a factor of two

2 . Cathodic protection can restore the in air life

3. Under free corrosion conditions, fatigue damage continues to occur even below

the air fatigue limit.

It has know been recognised that the above conclusions can lead to non

conservative life estimates in some cases mainly due to the fact that recent tests

have shown that cathodic protection does not always restore the in air life.

Austin [1.76] has considered a significant amount of data generated under free

corrosion conditions outside UKOSRPI and he concludes that a factor of 2.5

would seem appropriate to account for the effect of environment. The data

considered included both plate and tubular joint tests. Additionally, higher

reduction factors were noted for post weld heat treated joints (PWHT) leading to

the conclusion that free corrosion conditions can negate the beneficial effect of

PWHT. A similar review [1.102] suggests the ratio between air and fatigue lives is

closer to 2.2. Additionally a distinct laboratory bias was noted in the results with

the UKOSRP falling towards the higher end of the scatter band.

75


The application of ‘adequate’ levels of cathodic protection make the trends less

clear as the reduction factor changes with apphed stress range. Several research

programmes testing welded plate joints suggest that fatigue hves are always at least

as long as those in air (reduction factor < 1 ) especially so at lower stress ranges e.g.

[1.103, 1.104]. However a significant amount of data has also been generated

suggesting that welded plates with adequate levels of CP result in hves between 2

and 3 times shorter than in air. In general it appears that the SN curve is rotated

counter clockwise resulting in lives longer than air only at low stress ranges.

Vosikovsky and Tyson [1.103] noted that the scatter in the CP data was increased

compared to the free corrosion data and that the noted laboratory bias was even

stronger than for free corrosion conditions. The best fit of all the adequate CP data

reviewed (from Canadian, Japanese, ECSC Dutch, ECSC German and UKOSRP)

showed a neghgible effect of CP on hves compared to those found in air. However

exclusion of the UKOSRP generated data from the analysis results in an average

reduction factor on life of 1.5.

The most plausible explanation of the bias is identified as the weld procedures used

to deposit the weld toe bead. Corrosion fatigue is thought to be more sensitive to

weld toe quahty than fatigue in air. Vosikovsky et al [1.105] monitored the number

of initiation sites and found that in general the number of sites increased under free

corrosion and decreased under CP than found in air tests. Examination of the

relationship between the resulting fatigue hves and the number of initiation sites

shows that the tests with few initiation sites produced significantly longer hves.

Thus the transition to an edge crack (in plates) is delayed and the defects grow as

semi-eUiptical fatigue cracks throughout most of the test. AdditionaUy, semi

elhptical defects are more susceptible to the beneficial effects of reduced stress

intensity factor due to crack wedging effects of calcareous deposits that may form

on the crack surfaces under CP conditions. The random variation of the number of

-76


initial defects severe enough to initiate a fatigue crack under CP conditions also

explains the increased scatter observed on the CP results.

Tubular joints performed as part of UKOSRPII [1.46] did not exhibit the same

beneficial effect of adequate CP levels found in UKOSRPI [1.45] plate tests.

Consideration of experimental data from various world wide sources [1.105]

suggests a factor of two on the corresponding air life accounts for the application

of adequate CP levels. The beneficial effect at lower stress ranges found for welded

plate tests was not found for welded tubular joints.

Cathodic over protection is limited mainly to welded plate tests and tends to show

a similar trend to the lower CP levels but with a greater reduction in life longer

lives are needed before the results approach the in air results. Smith [1.106]

performed ten fatigue tests on tubular joints fabricated from the high strength steel

API 5L X85. Five of the tests were performed with CP levels of -KXXlmV

Ag/AgCl. This steel has a yield strength of approximately 600MPa and is

commonly used in jack up construction. Smith concludes that the results of the

tests fell within the scatter of the tests used in the derivation of the UK fatigue

guidance and above the design curve. No comparison between the relative

endurance found from the air and CP tests is given. The welding procedure used

during the fabrication of some of the specimens was un-representative of those

used in previous tubular joint fatigue tests (weave rather than stringer beads) and

the through thickness crack paths highly unusual making interpretation of the

results difficult.

1.15 Aims and Objectives

The primary aim of this thesis is the study of fatigue crack growth behaviour of

large scale welded tubular joints fabricated using a high strength steel typical of the

modern micro-alloyed, quenched and tempered steels. Such steels potentially offer

significant advantages for offshore construction. Thinner sections may allow lower

fabrication costs to be realised due to reduced welding requirements and lighter

-77


structures can lead to reduced installation costs for jackets and topsides. Although

concerns about the weldability of such steels have largely been dispersed there still

exists a lack of published data on the fatigue behaviour of these steels, particularly

under cathodic protection conditions. A need for fatigue data from representative

geometries in realistic environments has been demonstrated in this Chapter. In an

attempt to satisfy a part of the shortfall of data, seven large scale welded tubular

joint fatigue tests have been performed. Two tests have been undertaken in a

laboratory air environment and the remaining five under conditions of cathodic

protection. Cathodic protection levels of -800 and -lOOOmV (Ag/AgCl) were used.

The results are presented in Chapter Two in S-N format and the fatigue crack

growth behaviour examined.

Currently the only offshore application for such steels is the fabrication of chord

and racks for mobile jack up platforms. The various designs of jack up platform

legs were presented in detail in this Chapter. It was noted that the stiffening effect

of the rack plate may well affect the stress distribution around the intersection of

brace and chord. The importance of the accurate knowledge of the intersection

stress distribution for the determination of fatigue life by S-N and fracture

mechanics methods has been demonstrated in this Chapter. For this reason an

extensive finite element stress analysis of uncracked tubular joints has been

performed on geometries representative of jack up platform construction. The

results of this investigation have been analysed in terms of the surface stress

concentration factor (SCF) for axial, in plane and out of plane bending loadcases.

The effect across a range of joint geometries has been quantified and an

investigation into the mechanism by which these changes are affected. This is

presented in Chapter Three.

The through thickness stress distribution is an important input parameter for

fracture mechanics models and is the subject of Chapter Four. The results of the

finite element study have been used to quantify the change in through thickness

degree of bending (DoB) caused by the rack plate. This is achieved by comparison

- 7 8 -


with the DoB found from tmite element models of the equivalent unstif'fened joint

and DoB predictions from parametric equations.

The topic of fracture mechanics modelling of fatigue crack growth in welded

tubular joints is dealt with in Chapter Five. By presenting a review of previous

attempts to predict the crack growth behaviour in tubular joints and taking into

account the information gained from the current experimental investigation,

contemporary models are investigated. The magnitude of the potential effect of the

rack plate on the subsequent crack growth in jack up chords is assessed by altering

the input parameters to the fracture mechanics models to reflect the geometry.

Finally the accuracy of the SIF solution for welded tubular T joints given in the

revised BS:PD6493 is assessed using the results obtained from the experimental

investigation.

A summary of the achievements and conclusions derived from the work presented

in this PhD Thesis are given in Chapter Six. Recommendations for future work are

also highlighted.

79


1.16 References

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[1.7] Dyer,A. MSc Thesis, Dept, of Mechanical and Process Engineering,

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[1.8] Recommended Practice for Site Specific Assessment of Mobile Jack Up

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1984

[1.11] Kam, J.C.P., Birkinshaw, M. “The simulation of Wave Induced Fatigue

Loading of Jack Up Tubular Components”, OMAE 1993, vlllb, pp 529-535

[1.12] Etube, L. ''Variable Amplitude Corrosion Fatigue and Fracture Mechanics

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[1.13] Ohta, T, Yamauchi, H and Toriumi, M. “Design Method o f Leg Structure of

Jack Up Rigs”, Proc. First Int. Offshore and Polar Engineering Conference,

- 8 0 -


Edinburgh, 11-16 August 1991, ppl38-142..

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- 8 1 -


1.26] Dover, W.D. “ Fatigue Fracture Mechanics Analysis of Offshore

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8 2 -


August 1991, pp475-483

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[1.48] UK Department of Energy, “ Background to New Fatigue Design Guidance

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[1.49] British Standards Institution, "Steel, Concrete and Composite bridges.”,

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[1.52] ISO, ISO 13819-2, "Petroleum and Natural Gas Industries - Offshore

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- 8 3 -


[1.53] Dover, W.D.. and Wilson, T.J., “ Corrosion Fatigue of Tubular Welded T-

Joints”, paper C l36/86, Proc. Int. Conf. on Fatigue and Crack Growth in

Offshore Structures, Institute of Mechanical Engineers, London 1986.

[1.54] Dover, W.D., Sham, W.P., and Peet, C., “Random Load Corrosion Fatigue

of Tubular Welded T-Joints”, Proc. Conf. on Fatigue of Offshore

Structures, London, 19-20 September 1988.

[1.55] Gerald, J. et al, “Corrosion Fatigue Tests on High Strength Steel Tubular

X-Nodes with Improved Welds”, Paper TS15, Proc. Third Int. ECSC

Offshore Conference on Steel in Marine Structures, Delft, June 15-18, 1987.

[1.56] de Back, J. and Vaessen, G. H. G ., “Effect o f Plate Thickness, Temperature

and Weld Toe Profile on the Fatigue and Corrosion Fatigue behaviour of

Welded Offshore Structures: Parts I and 11”, Final Report on ECSC

Convention 7210-KG/601 (F7.4/81), Stichting Materiaalonderzoek in de

Zee, May 1984.

[1.57] Wylde, J.G. and Yamamoto, N., “ Sea water Corrosion Fatigue Tests on

Steel Tubular Joints” , Paper 7921.01/87/589.2, The Welding Institute ,

March 1988.

[1.58] Hara, M., et al, “ Corrosion Fatigue Strength of 490 MPa Class High-

Strength Steels Produced by the Thermo Mechanical Control Process”,

Paper OTC 5311, Proc. 18th Offshore Technology Conference, Houston, 5-

8 May 1986.

[1.59] de Back, J., and Vaessen, G. H. G., “Fatigue and Corrosion Fatigue

Behaviour of Offshore Steel Structures. ”, Final Report on ECSC

Convention 7210-KB/6/602 (J.7.1 f/16), ), Stichting Materiaalonderzoek in

de Zee, April 1981.

[1.60] Rules for Classification, Mobile Offshore Units, Det Norske Veritas, Oslo,

July 1989

[1.61] Billingham, J., Healy, J., and Bolt, H., “The Question of High Yield /

Ultimate Ratio in High Strength Steels”, High Strength Steels in Offshore

Engineering, MTD Publication 95/100

- 8 4 -


[1.62] Pook, L.P. “Linear, Fracture Mechanics - What It Is, What It Does ”,

National Engineering Laboratory, East Kilbride, Glasgow, August 1970

[1.63] Tomkins, B., “Fatigue Crack Propagation - An Analysis”, Philosophical

Magazine, v l 8 , ppl041-1066 (1968)

[1.64] Gowda, C.V.B, Topper, T.H., “Crack Propagation in Notched M ild Steel

Plates Subjected to Inelastic Strains.”, Cychc Stress Strain Behaviour -

Analysis, Experimentation, and Faüure Prediction, ASTM STP 519, pp. 170-

184, 1973

[1.65] El Haddad, M.H., Smith, K.N., Topper, T.H., “A Strain Based Intensity

Factor Solution fo r Short Fatigue Cracks Initiating from Notches”, Fracture

Mechanics, ASTM STP 677, pp274-289, 1979

[1.66] Rice, J R., “A Path Independent Integral and the Approximate Analysis of

Strain Concentration by Notches and Cracks.”, Journal of Applied

Mechanics, v35, pp.379-386, 1968.

[1.67] Wells, A.A., “Unstable Crack Propagation in Metals: Damage and Fast

Fracture”, Proc. Crack Propagation Symposium, Cranfield, vl., pp 210-230,

1961

[1.68] Monahan, C.C., “Early Fatigue Crack Growth in Ojfshore Structures”, PhD

Thesis, UCL, 1994

[1.69] Paris, P. C. and Erdogan, F. “A Critical Analysis of Crack Propagation

Laws”, J. Bas. Engng, 1963, 85(4), 528-534.

[1.70] Saxena, A., Hudak, S.J., Jouris, G.M., “A Three Component Model for

Representing Wide Range Fatigue Crack Growth Rate Behaviour”,

Engineering Fracture Mechanics, vl2, pp. 113-118, 1979

[1.71] Gowda, S.S., Helenius, A., “Fatigue Crack Growth Analysis of Welded

Tubular Joints of Offshore Structures”, Proc. Int. Conf. Offshore Mechanics

and Arctic Engineering, v3, pp575-582, 1988

[1.72] HasweU, J and Hopkins, P. “A Review of Fracture Mechanics Models of

Tubular Joints” Fatigue Fract. Eng. Mater. Struct., vl4, n5 pp483-497,

1991

-85


[1.73] HasweU, J. “Simple Models fo r Predicting Stress Intensity factors for

Tubular Joints” Fatigue Fract. Eng. Mater. Struct., vl4, n5 pp499-513,

1991

[1.74] Thorpe, T. W. “A Simple Model of Fatigue Crack Growth in Welded

Joints”, Offshore Technology Report, OTH 86 225.

[1.75] Burdekin , F. M., Chu, W. H., Chan, W. T. W. and Manteghi, S. “ Fracture

Mechanics Analysis of Fatigue Crack Propagation in Tubular Joints”,

International Conference on Fatigue and Crack Growth in Offshore

Structures, April 1986, IMechE, C 141/86

[1.76] Austin, J, A., “The Role of Corrosion Fatigue Crack Growth Mechanisms

in Predicting the Fatigue Life o f Offshore Tubular Joints”, PhD Thesis,

UCL, October 1994

[1.77] MTD Ltd., “Design and Operational Guidance on Cathodic Protection of

Offshore Structures, Subsea Installations and Pipelines.”, Publication

90/102, 1990

[1.78] Rowlands, J.C., “Corrosion”, Ed. Newnes, L.L., Butterworth, London 1976

[1.79] Lambert, S B ., “Effect of Sea water on Fatigue Crack Shape Development.”,

Proc. 11 Offshore Mechanics and Arctic Engineering Conference, Calgary

1992.

[1.80] Scott, P.M., Silvester, P.R.V., “The Influence of Sea Water on Fatigue

Crack Propagation Rates in Structural Steel”, UKOSRP 3/03, December

1975.

[1.81] Saenz de Santa Maria, M., Proctor, R.. “Environmental Cracking

(Corrosion Fatigue and Hydrogen Embrittlement) of X-70 Linepipe steel”.

Fatigue and Crack Growth in Offshore Structures, Proc. IMechE, C l37/86,

1986

[1.82] Thorpe, T.W, Scott, P.M., Ranee, A., Silvester, D. “Corrosion Fatigue of

BS 4360:50D Structural Steel in Sea Water", Int.J.Fatigue, v5,n3,ppl23-

133,1983

[1.83] Cottis, R.A., “Stress Corrosion Cracking in High Strength Steels.”,

- 8 6 -


Corrosion, Ed. Shrier, Jarman, Burstein, 3"‘. Ed. 1994

[1.84] Oriana, R.A., Josephic, P.H., Acta Metall, v22. p i06.5, 1974

[1.85] Hodgkeiss, T.H., Cannon, M.J. ''Corrosion Fatigue of Steels in Sea Water;

Studies of Crack Tip Electrochemistry'", Dept. Mechanical Engineering,

Glasgow University, Project GL/MM6

[1.86] Scully, J.R., Morgan, P.J., "The Hydrogen Embrittlement Susceptibility of

Ferrous Alloys: The Influence of Strain on Hydrogen Entry and Transport"",

Hydrogen Embrittlement: Prevention and Control, ASTM STP 962, Ed.

Raymond, L. ASTM, pp387-402, 1988

[1.87] Proctor, R. P. M., "Detrimental Effects of Cathodic Protection:

Embrittlement and Cracking Phenomena"", Cathodic Protection: Theory and

Practice, Ed. Ashworth, V and Booker, C.J.L., 1986

[1.88] Barsom, J.M., "Effect of Cyclic Stress Form on Corrosion Fatigue Crack

Propagation Below KISCC in High Strength Steel"", Corrosion Fatigue:

Chemistry, Mechanics and Microstructure, NACE Handbook 2, 1973.

[1.89] Atkinson, J.D., Lindley, T.C., "The Influence of Environment on Fatigue"",

IMechE Proc., v4, 65-74, 1977

[1.90] Cowling, M.J., "Corrosion Fatigue In a Biologically Active Marine

Environment"", Fatigue Crack Growth In Offshore Structures, Ed. Dover,

Dharmavasan, Brennan, Marsh.p77-106, EMAS 1995

[1.91] Robinson, M.J., Kilgallon, P. "Cracking of Welded High Strength Low Alloy

Steels Controlling the Damaging Effects of Sulphate Reducing Bacteria"",

High Strength Steels in Offshore Engineering, MTD Publication 95/100,

1995

[1.92] Hopkins, R., Monahan, C. "Calcareous Deposits and the Fatigue Crack

Growth Behaviour of Offshore Steels Under Cathodic Protection in

Seawater"", Proc. Cathodic Protection: A + or - in Corrosion Fatigue?,

ppl07-133. Nova Scotia, 1986

[1.93] Scott, P., Thorpe, D., Silvester, D "Rate Determining Processes for

Corrosion Fatigue Crack Growth in Ferriric Steels in Sea Water"",

87


Corrosion Science, v23, n6, (1983)

[1.94] Maahn, E., ''Crack Tip Chemistry Under Cathodic Protection and its

Influence on Fatigue Crack GrowthC, Proc. Cathodic Protection: A + or -

In Corrosion Fatigue, Ed. Vosikovsky, O., Leewis, K, CANMET, Halifax,

Canada, 1986

[1.95] Habashi, M., Philiponneau, G., Widawski, S., Galland, J., "Interactions

between Fatigue Crack Growth Rate and Kinetics of Magnesium and

Calcium Deposit Formation at the Crack Tip of M ild Steel Cathodically

Polarised in Sea Water.”, Int. Conf of Fracture, New Delhi, 1984

[1.96] Thorpe, T., Rance, A., "Corrosion Fatigue Crack Growth in BS 4360:50D

Structural Steel in Sea Water Under Narrow Band Variable Amplitude

Loading”, Offshore Technology Report, OTH 86 232, 1986

[1.97] Cowling , M.J., Appleton, R.J., "Corrosion Fatigue of a C-Mn Steel in Sea

water Solutions”, Fatigue and Crack Growth in Offshore Structures, proc.\

IMechE, C145/86, 1986

[1.98] Neilsen, HP., Maahn, E., "Environmental Effects in Fatigue Crack

Initiation”, Proc. 3"** Int Conf. On Steel in Marine Structures, Delft, 1987

[1.99] Vosikovsky, O., J.Engng. Mater. Tech., Trans ASME, 102, 1975

[1.100] Eggen, T.G. , Bardai, E. "Corrosion Fatigue Crack Growth Rates in

Offshore Structural Steels”, Proc. Offshore Mechanics and Arctic

Engineering, v3, p207-213, 1993

[1.101] Billingham, J, Laws, P., "High Strength Micro-alloyed Steel fo r Use

Offshore - Materials and Welding Considerations”, High Strength Steels in

Offshore Engineering, MTD publication, 95/100

[1.102] Bignonnet, A., "Corrosion Fatigue of Steel in Marine Structures”, Proc.

Cathodic Protection: A 4- or - In Corrosion Fatigue, Ed. Vosikovsky, O.,

Leewis, K, CANMET, Halifax, Canada, 1986

[1.103] Vosikovsky, O, Tyson, W.R., "Effects of Cathodic Protection on Fatigue

Life of Steel Welded Joints in Seawater”, Cathodic Protection: a + or - in

Corrosion Fatigue, CANMET, 1986

-88


[1.104] Burnside , O. H., et a i, “Long Term Corrosion Fatigue of Welded Marine

Steels'’, Southwest Research Institute, March 1984

[1.105] Vosikovsky, O, Bell, R., Bums, D.J., Mohaupt, U.H., “Effects of Cathodic

Protection and Thickness on Corrosion Fatigue Life of Welded Plate T-

Joints”, Paper TS4, Proc. 3""* Int. Conf on Steel in Marine Structures, Delft,

1987

[1.106] Smith, A.T., “The Effect of Cathodic Over-protection on the Corrosion

Fatigue Behaviour of A P I 5L X85 Grade Welded Tubular Joints.”, PhD

Thesis, City University, London, 1995

- 8 9 -


Design Feature VariationsHull Shape Triangular

RectangularOctagonal

Legs Between 3 and 22 in number Truss type Tubular section Independent adjustment Mat supported Slanted legs

Jacking System Rack and Pinion ( Electric and Hydraulic versions )HydraulicPneumatic

Operating Modes Self containedTender assistedDrilling constructionIntegrated spud cansRemovable spud cansHelideck in top of legHelideck on accommodation moduleHelideck cantilevered outboard

Moving Mode Non-propelled Self-propelled Propulsion assisted Sail assistedOn-board leg removal capability

T a b l e 1 . 1 J a c k U p D e s i g n F e a t u r e s .

Jack Up Type No. o f RigsTruss Type Legs 303Single Chord Legs 113Leg Design Unknown 53Total 469

T a b l e 1 . 2 J a c k u p l e g p o p u l a t i o n s

- 9 0 -


Chord Design No. o f RigsTriangular chords (Le Tourneau type) 142Split tubular with double rack (F&G type) 43Tubular chord with central double rack 36Tubular chord with offset double rack 33Tubular chord with pinholes 20Other designs 22Chord design unknown 7Total no. of truss leg rigs 303

T a b l e 1 . 3 T r u s s l e g d e s i g n b r e a k d o w n

LoadingMode

Position Words. Efthy. Kuang U.E.G. LR. U.C.L

Chord Saddle / / X / y X

Axial Chord Crown X / N/A X y X

Brace Saddle X / X X y yBrace Crown c / c / N/A y c X y c

Key:y Recommended Words. Wordsworth Eqns. [1.34]y c Recommended but conservative Efthy Efthymiou Eqns. [1.38]N/A No equation for current

loadcaseUEG UEG Eqns [1.28]

X Not Recommended UCL UCL Eqns [1.40]

T a b l e 1 . 4 R e c o m m e n d e d p a r a m e t r i c e q u a t i o n s f o r a x i a l l y l o a d e d T j o i n t s

Parameter Defaulta 7.263 0.71Y 14.28X 10 90°

T a b l e 1 . 5 D e f a u l t G e o m e t r i c P a r a m e t e r s U s e d i n M o d e l C o m p a r i s o n

-91


S-N Curve Equation16mm Best Fit Curve (m=3) 32mm Best Fit Curve (m=3)

Log(N) = 12.942 - 3Log(S) Log(N)= 12.684- 3Log(S)

Basic design Curve (N<1E7) (N>1E7)

Log(N)= 12.476- 3Log(S) Log(N) = 16.127 - 5Log(S)

T a b l e 1 . 6 U K G u i d a n c e S - N C u r v e . s

Environment 1984 Design GuidanceFree Corrosion Penalty factor of 0.5 on the in air life.

No change in slope at 1E7 cycles.Adequate C.P. Use in air S-N curve

T a b l e 1 . 7 1 9 8 4 G u i d a n c e o n E n v i r o n m e n t a l E f f e c t s

Environment Joint Type Validity GuidanceFree Corrosion Plates All Lives Penalty factor of 1/3 for all geometry’s

No change in slope at lO' cycles.Tubulars All LivesSea water with Optimum C.P.

Plates < 10' Penalty factor of 1/3 on life Penalty factor of 1/2 on life Use in-air S-N curve Use in-air S-N curve

Tubulars < 10'Plates > 10'Tubulars > 10'

T a b l e 1 . 8 1 9 9 0 G u i d a n c e o n E n v i r o n m e n t a l E f f e c t s .

9 2 -


Jacking Unit

ZS

I

Leg Guides

F i g u r e 1 . 1

S c h e m a t i c o f a t y p i c a l J a c k U p R i g

- 9 3 -


Tubular Chotd Central Rack Sp lit Tubular Chord

Tubular Chord Offset Racks Triangu lar Chord Single Rack

F i g u r e 1 . 2

T h e f o u r m a i n c h o r d d e s i g n s

O w - 1:2) 44 0 * 1.00 ##Cf#

F i g u r e 1 . 3

S p l i t t u b u l a r s w i t h d o u b l e r a c k s . R a n g e o f c h o r d s h a p e s a m i s i z e s

- 9 4 -


^ 1

Scalt - 1:25 60 mm -

Ak J w

©W W

1 1, / f A1 1

w1 . 0 0 m e t re

1 1

w( . I I I

o.e # 2 1 #.so 0.7S 1.00

F i g u r e 1 . 4

T u b u l a r c h o r d s w i t h c e n t r a l r a c k s . R a n g e o f c h o r d s h a p e s a m i s i z e s

Scale - 1:25 40 mm - 1.00 metremetre*

1 T0.0 0.25 0.50 0.75 1.00

F i g u r e 1 . 5

T u b u l a r c h o r d s w i t h o f f s e t r a c k s . R a n g e o f c h o r d s h a p e s a n d s i z e s

- 9 5 -


Rib Plate

s p a n Breaker

Leg Guide

Rack Plate

F i g u r e 1 . 6

I . e g p l a n s c h e m a t i c s h o w i n g m a i n c o m p o n e n t s

F i g u r e 1 .7G e n e r a l v i e w o f j a c k u p l e g s h o w i n g r a c k d e t a i l

- 96 -


F i g u r e 1 . 8

C o m p l e x n a t u r e o f l e g b r a c i n g a n d s p a n b r e a k e r s i n a m o d e r n j a c k u p

F i g u r e 1 . 9

O v e r l a p p e d b r a c i n g a n d w e l d d e t a i l i n a m o d e r n j a c k u p l e g

- 9 7 -


R Piggy Back Vessel

Wet Tow Dry Tow

F i g u r e 1 . 1 0

J a c k u p t r a n s p o r t a t i o n m o d e s

Y JointT Joint

DT Joint Multiplane Joint

F i g u r e 1 . 1 1

C o m m o n t u b u l a r j o i n t c o n f i g u r a t i o n s

- 9 8 -


C row n

T

SaddleD

F i g u r e 1 . 1 2

T - J o i n t p a r a m e t r i c n o t a t i o n

Axial

O ut of P la ne Bend ing (O R B ) n P la n e Bending ( IP B )

F i g i a e 1 . 1 3

T h e t h r e e t u b u l a r j o i n t l o a d i n g m o d e s

- 9 9 -

. -


Brace wall — 7//

1 /iÎLà

-Regnn of ropidfy rrsinq stress (local stress)

Region of stress linearity I geometric stress ]

—Linear extrapotation of stress to weld toe

Stress distributionnot to scale

Chord wall.

F i g u r e 1 . 1 6

U K O S R P a n d E C S C d e f i n i t i o n o f H o t S p o t S t r e s s

Q ■ 0 2 Vrl; b jf riot smaller than 4mm

Line 2

B race

Line 3.

•Au

Line 4

Chord.

F i g u r e 1 . 1 7

R e g i o n s o f s t r a i n l i n e a r i t y u s e d t o d e t e r m i n e h o t s p o t s t r e s s

- 101 -


Weld(8 ■ node elemenJ

Brace(16 ■ node element)

Chord(16 - node element)

F i g u r e 1 . 1 8

M o d e l l i n g t h e w e l d i n t e r s e c t i o n u s i n g t h i c k s h e l l e l e m e n t s

- 102 -


Brace Mid Surface

Peak Chord Stress

Peak Brace Stress

Chord Mid Surface

Nodal Points

F i g u r e 1 . 1 9

T h i n s h e l l F E A m o d e l l i n g o f a t u b u l a r j o i n t i n t e r s e c t i o n

- 103


15 --

10 - -

-100 20 40 60 80 100 120 140 160 180

Angle Around Intersection (deg)

F i g u r e 1 . 2 0

T - . f o i n t . s t r e s . s d i s t r i b u t i o n s f o r a x i a l , I P B a m i O P B l o a d i n g m o d e s

20 - -

10 - -

5 --

0 5 3510 15 20 25 30 40

— Elthy (fix)

—>W— Efthy(pin)

UCL (KcO)

UCL (Kc180)

- 4 * — UEG (Kc)

Wofds. (Kc) —'— LR (Pinned)

—— LR (Fixed)

Alpha

Figure I .2 IParametric chord crown SCF prediction depemlencv on Alpha

- 104 -


6 - -

3 --

2

0.90.5 0.6 0.7 0.00 0.1 0.2 0.3 0.4

Efthy(fix)

Efthy(pin)

UCL(KcO)

UCL(Kc180)

UEG

-# — W ords.

_.i— |_n (Pinned)

— LR (Axed)

Beta

F i g u r e 1 . 2 2

P a r a m e t r i c c h o r d c r o w n S C F p r e d i c t i o n d e p e n d e n c y o n B e t a

6 - -

5 --

4 - -

3 --

2 --

35 400 5 10 15 20 25 30

Efthy(tix)

Efthy(pin)

UCL (KcO)

UCL (KciaO)

Words

UEG

LR (Pinned)

LR (Fixed)

G am m a

Figure 1.23Parametric chord crown S C F prediction dependency on Gamma

- 105 -


3 --

2 --

0.7 0 8 0.9 10 0.1 0.2 0.3 0.4 0.5 0.6

— Eflhy(fix) —4 — Efthy(pin)

UCL(KcO)

UCL(KclBO)

UEG

—# — Words

— !— LR (Pinned)

— LR (Fixed)

Tau

F i g u r e 1 . 2 4

P a r a m e t r i c c h o r d c r o w n S C F p r e d i c t i o n d e p e n d e n c y o n T a u

20

10-“

16 --

14 --

12 - -

§ 10 -

6 - -

4 --

2 -

35 400 S 10 IS 20 25 30

Alpha

Figure 1.25Parametric chord saddle SCF prediction deperuiency on Alpha

■ Efthy (fix) -Efthy (pin)

UCL (Ks)

UCL (Khs)

-U EG (Ks)

- Words. (Ks)

-LR (Pinned)

-LR (Fixed)

- 106 -


20 - ■

15 --

10 - -

5 --

0.90 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1Beta

F i g u r e 1 . 2 6

P a r a m e t r i c c h o r d . s a d d l e S C F p r e d i c t i o n d e p e n d e n c y o n B e t a

60

50 --

40 --

U 30 --

20 - -

10 - -

4025 350 5 10 15 20 30

G am m a

F i g u r e 1 . 2 7

P a r a m e t r i c c h o r d s a d d l e S C F p r e d i c t i o n d e p e n d e n c y o n G a m m a

- Efthy(fix)

- Efthy(pin)

UCL (Ks)

UCL (Khs)

-UEG

•W ords.

■ LR (Pinned)

-LR (Fixed)

Ellhy((ix)

Efthy(pln)

UCL (Ks) UCL (Khs)

UEG

Words

LR (Pinned)

LR (Fixed)

- 107 -


1 6 - -

1 4 - -

12 - -

10 - -

6 --

0 0.2 0.70.1 0.3 0.4 0.5 0.6 0.8 0.9 1

Efthy(fix)

Efthy(pin)

UC L(Ks)

UCL(Khs)

-4*— UEG

W ords

— LR (Pinned)

LR (Fixed)

Tau

F i g u r e 1 . 2 8

P a r a m e t r i c c h o r d s a d d l e S C F p r e d i c t i o n d e p e r u i e n c y o n T a u

% 100 cc

I

101.00E-MD4

N

I.OOE-mS I.OOE-rOe 1.00E-k07

Endurance (Cyctes)

I 16mm SOD Data

- - 16mm Mean

Design T Curve

i.ooE-me i.ooE-f09

F i g u r e 1 . 2 9

1 6 m m 5 0 D f a t i g u e l i f e d a t a t o g e t h e r w i t h m e a n a n d d e s i g n S - N c u r \ ' e s

- 108 -


1000

I 16mm 500 Data

32mm 500 Data

- 16mm Mean

-D es ign T Curve

I 100

:cn

1.00E+05 1.00E+06 1.00E+07 1.00E+08Endurance (Cycles)

F i g u r e 1 . 3 0

T h i c k n e s s e f f e c t i l l u s t r a t e d b y I 6 m m a n d 3 2 m m f a t i g u e l i f e d a t a

1000

IS, 16mmI ;

— 32mm100

I 48mm

II

72mm

1 OOE+03 1 006*08 1 006+09

Lfe (cycles)

F i g u r e 1 . 3 1

N e s t e d T c u r v e s f r o m t h i c k n e s s e f f e c t a l l o w a n c e

- 109 -


! I 1 I 1 1 1 1tl 1 1 M M- - - -50D 16mm mean

r' Air Curve

'■

-- -

— - - -

c 1005

10

1 00 E+04 1.00E+05 1.00E+06

Endurance (Cycles)

F i g u r e 1 . 3 2

S - N c u r v e s f o r 1 6 m m p l a t e s a n d t u h u l a r s i n s e a w a t e r ( f r e e c o r r o s i o n ) a n d o p t i m u m c a t h o d i c

p r o t e c t i o n

Crack Tip

F i g u r e 1 . 3 3

C a r t e s i a n c o - o r d i n a t e s f o r n e a r c r a c k a n a h ' s e s

- 1 1 0 -


Mode 1

Mode

Mode

F i g u r e 1 . 3 4

T h e t h r e e m o d e s o f c r a c k g r o w t h

Paris Law

Region 3Region 2Region 1

da I dN

AK

F i g u r e 1 . 3 5

T h e t h r e e s t a g e s o f f a t i g u e c r a c k g r o w t h

- I l l -


W elded P la teo

Tubular JointC

CO

1.00.0 0.5

Non Dimensional C rack Depth, a/t

F i g u r e 1 . 3 6

S i r d e v e l o p m e n t i n t u b u l a r j o i n t s a n d w e l d e d p l a t e s

caCLa>o

Tubular JointO05O

W elded Pla

1.00.0 0.5

Fraction of fatigue life

F i g u r e 1 . 3 7

C r a c k d e p t h d e v e l o p m e n t i n t u b u l a r J o i n t s a n d w e l d e d p l a t e s

- 112


C o r r o s i v eenvironm ent

2 0 H ' 2 0 H "

S u r f a c e

F i g u r e 1 . 3 8

E l e c t r o c h e m i c a l c o r r o s i o n p r o c e s s [ 1 . 7 7 ]

P ro te c te d S tru c tu re

\

P o w e r S u p p ly

4e-

Og+2HgO

O H '

4cr

2 C I.

Im p re s s e d C u rre n t A n o d e

F i g u r e 1 . 3 9

I m p r e s s e d C u r r e n t C a t h o d i c P r o t e c t i o n [ 1 . 7 7 ]

- 1 1 3 -


6 -■

5 -- Free Corrosion

4 --

3 --

2 - -

Normal CP

"Crack propagation rale in air

Scatter band in air

- 0.6 -0.7 -0.8 -0.9CP Potential (Ag/Agcl) V

- 1.1 - 1.2

F i g u r e 1 . 4 0

E f f e c t o f C P p o t e n t i a l o n f a t i g u e c r a c k g r o w t h r a t e ( 0 . 1 H z , R < = 0 . 1 )

1E-6

^ I E - 7

E-8

o

1E -1 0

1 10010

Stress Intensity Factor R ange (M P a m ^ O .5 )

F i g u r e 1 . 4 1

S c h e m u t i c d a / c I N - A K p l o t . s h o w i n g p l a t e a u g r o w t h r a t e r e g i o n u n d e r C P c o n d i t i o n s

- 1 1 4 -


10

voaiKOvsxr

pi^euNe sreet x»a CÂTHOOIC P K O r e c T i o H ziMC p orenT iÂ L

- 810uNEE

Ht

-a10 0 1 H i

iSJiuy10

(0 0 Mi

-71020 30 50 70 1002 4 6 B 10

AK STRESS INTENSITY (MPaVmJ

F i g u r e 1 . 4 2

I n d e p e n d e n c e o f c r a c k g r o w t h r a t e t o A K i n X 6 5 u n d e r C P C o n d i t i o n s

- 115 -

--

CL

E

en ru CL OCL

-k :


6 5 5 F MZSE 5 0 0

O H S L A 8 0X HS 4 2 0• 4 5 0 EM 2o X A O O 5 0 0

12 U 16 18AK

20 22 24

(a) -950mV

55 F M2 SE 5 0 0 H S L A 80 HS 4 2 0 4 5 0 EMZ X AO Q 5 0 0 TiO

8

2

012 1614 2220

AK

(b) -1100mV

F i g u r e 1 . 4 3

H i g h s t r e n g t h s t e e l c r a c k g r o w t h r a t e s f r o m B i l l i n g h a r n e t a l

- 1 1 6 -

Chapter 2 - Experimental Fatigue Testing of W elded Tubular Joints

Chapter Two

2. Experimental Fatigue Testing of Welded Tubular Joints

2.1 Introduction

Large scale tubular joint fatigue tests have been performed for a number of

decades. The expense and difficulty involved in testing such specimens is Justified

on the grounds that the crack growth behaviour of tubular joints is unique and

complex and to date all attempts at reproducing the fatigue crack growth

behaviour in tuhulars using simple welded specimens have failed.

The amount of information that it is now possible to extract from each test has

increased enormously in recent years. It is hoped that the fracture mechanics

models proposed to predict the crack growth behaviour can be refmed and made

more accurate and reliable using information gained from tests such as these.

The current test programme will be described in detail. This will include all

hardware, software and procedures used during the preparation and execution of

each test. The extraction and analysis of the raw data will be described and all

relevant results will be presented. The information presented here will be used in

Chapter 5 to critically assess the capability of the current state of the art in terms of

fatigue fracture mechanics models used for predicting the fatigue crack growth

behaviour of these joints.

2.2 Tubular Joint Test Specimens

The test specimens will be described in this section. This will include the nominal

and actual joint dimensions, mechanical and chemical properties of the parent plate

and weld metal as well as the weld procedures and consumables used during

fabrication.

117 -


2.2.1 Dimensions

The six specimens tested during this investigation were all T-shaped large scale

tubular welded joints. The nominal specimen dimensions are illustrated in Figure

2.1. Also included are the non-dimensional parameters commonly used to describe

tubular joints. Non dimensional parameters are particularly useful for presentation

of SCF’s in parametric form.

The specimen dimensions have been chosen to allow direct comparison with earlier

tubular joint test programmes performed at UCL using lower strength steels. In

addition, modifications to the fatigue test rig are minimised.

The actual specimen dimensions agree closely with the nominal values in all cases.

A small degree of out of roundness of the members was detected due to the

method of manufacture of the tubes (see Section 2.2.2).

The greatest manufacturing inaccuracy in terms of percentage differences was

found to be the wall thickness of the brace and chord. The wall thickness was

measured ultrasonically using a SONATEST STEELGAGE M at six sites around

the intersection of the brace and chord of each specimen. In each case the wall

thickness was found to be greater than the nominal 16mm. The CLi specified

tolerance for rolling SE702 to 16mm is 0.8mm, in the ranges 4-/-0.4mm and 0 to

+0.8mm [2.1]. The ultrasonically measured wall thicknesses are given in Table 2.1.

The thicker brace values at the saddle are due to the presence of a seam weld

running the length of the brace. Ultrasonic measurements of wall thickness were

also taken at intervals around the chord ends. This was performed in order to

confirm the accuracy of the technique on this particular steel geometry

configuration as Vernier measurements of the thickness can also be taken at this

point. Comparison of the two methods shows the maximum difference to be

0.1mm.

- 118 -


The potential significance of variations in wall thickness was highlighted by Austin

[2.2]. The parametric formulation of Kuang was used to calculate the SCF and a

single segment SN curve with a negative inverse slope of 3 to determine the

corresponding endurance. Using this data Austin found that the scatter in tubular

joint endurance data could be entirely accounted for by variations in wall thickness

alone. Although this may be the case from theoretical considerations it is not

suggested here that this is the sole or even dominant source of scatter from

experimental data.

2.2.2 Specimen Fabrication

Unlike earlier tubular joint test programmes at UCL the tubular members were not

fabricated from seamless tubing. In this instance both the brace and chord were

rolled in two halves and subsequently seam welded together. The position of the

seam welds are illustrated in Figure 2.2. This is not thought to be significant in

terms of the subsequent fatigue performance of the specimens. The weld details are

given in Table 2.2 for the seam welding.

The post weld heat treatment specified is only applicable to the seam welds used to

form the tubes. It is important to note that no PWHT was specified for the

completed joints.

Of more significance is the welding of the intersection between the brace and

chord. It has been shown in Chapter 1 that the weld detail exerts a significant effect

on the fatigue life. It was imperative therefore that the welding was representative

of that used in the construction of offshore structures. The welding contractor,

PAUMECA S. A. of Le Breuil, France was involved in the construction of the BP

Harding Jack Up. Weld procedures from previous tubular joint specimens

fabricated by Highland Fabricators for UCL and colour photographs of the weld

detail were also supplied to PAUMECA. Additionally the contractor was visited

during the welding of the first joint. It was noted that the contractor intended to

- 119 -


undertake inter-run grinding to improve the weld profile. This was thought to be

unrepresentative and as such the contractor was requested to modify his procedure.

No inter-run or weld toe grinding was subsequently performed. The run sequences,

welding speed and joint preparation were recorded by PAUMECA. The

intersection welding details are given in Table 2.3. The preheat values of 125°C

and welding heat input of 1.5KJ/mm have been shown to avoid cold cracking

problems in SE702 [2.3].

A photograph of the intersection and seam weld of a representative joint is shown

in Figure 2.3. All welds successfully passed a full ultrasonic inspection in

accordance with the French standard NFP22-471 [2.4].

Chord and brace weld leg lengths have been measured using a weld profile gauge.

The definition of weld leg lengths is illustrated in Figure 2.4. The weld profile was

measured at five sites around both saddles on the chord and brace side. The

measured leg lengths are given in Table 2.4.

The Dime Test [2.5] was performed on all welds and no weld completely failed the

test. However all joints failed at certain points around the intersection, some near

to the saddle region. No correlation between these regions and the subsequent

fatigue crack initiation site were found.

2.2.3 Material Properties

The use of state of the art steel making processes allows the manufacturer to

guarantee high performance material properties to within close limits. This is due

to the very low levels of sulphur, hydrogen, high cleanliness due to low oxygen

content and very precise chemical composition. Guaranteed and actual chemical

compositions for SE702 are detailed in Table 2.5. A sample of steel cut from one

of the tuhulars has been analysed independently [2.6].

- 120


It can be seen that the CLi’s chemical analysis of the current batch of steel meets

the specified standard for each of the alloying elements except for manganese

which is higher than the guaranteed maximum. Manganese acts as a de-oxidiser,

lowers the transition temperature and acts as a hardenability agent. The

discrepancy is not thought to be significant in terms of this study.

The independent analysis agrees well with the CLi analysis of the same batch of

steel. Again manganese is the only element which falls outside the specified

composition. A ll other elements meet the specification.

2.2.4 Mechanical Properties of SET02

The specified mechanical properties for SE702 are shown in Table 2.6.[2.7].

Independent tensile tests on steel from the same batch as that used to fabricate the

tuhulars has been performed at Cranfield University. The tests were performed

using 5.5mm diameter specimens. Details of the orientation of the specimens in

terms of the rolling direction of the parent plate etc. are not known. All specimens

are assumed to be nominally identical. The results are summarised in Table 2.7.

Data from Charpy impact tests performed at Cranfield is tabulated in Table 2.8.

Vickers Hardness Data has been obtained by CLi and Cranfield for parent plate,

weld metal and the heat affected zone of a T-Butt weld qualification specimen. A

summary of this data is given in Table 2.9. The CLi data given in the first table

used a load of 5kg and the Cranfield data in the second table used 10kg. The

Vickers Hardness Test is designed in such a way that the results are independent of

the load used and standard loads of between 1 and 120kg are used. Thus the CLi

and Cranfield data can be directly compared.

The parent plate values of approximately 250HV are reasonable for a steel of this

strength. Values quoted in [2.8] suggest that a carbon or alloy steel with a HV

value of 250 should have a UTS of around 800MPa. This is almost identical to the

strength of this material.

- 121 -

Chapter 2 - Experimental Fatigue Testing of Welded Tubular Joints

Healy et al [2.3] examined the weldability of a number of modern high strength

steels, including SE702. It was noted that parent plate hardness values for such

steels were typically in the range 260-280Hv. A maximum HAZ hardness limit of

400Hv is a commonly applied industry standard to avoid problems such as

hydrogen induced cold cracking susceptibility and stress corrosion cracking in

service. SE702 has been shown to satisfy this requirement even under the most

severe welding conditions of low heat input (IKJ/mm) and no pre-heat.

2.3 Experimental Set Up

Tubular joint fatigue tests are difficult to perform. The tests are expensive, time

consuming and complex. In view of the very limited number of specimens available

it is essential that great care and attention is taken during the setting up and

execution of each test.

The hardware and software used during the fatigue tests is discussed in detail. In

particular the monitoring and recording of the crack growth process requires

meticulous preparation and will be discussed in depth.

2.3.1 Applied Loading

Fatigue loading is supplied by a IM N servo-hydraulic INSTRON actuator. The

actuator is controlled via an INSTRON mini-controller. The actuator can be

controlled under position or load feedback loops. All tests conducted here were

performed under load control. In this mode the specimen is subjected to load cycles

of a pre-defmed amplitude regardless of any change in stiffness of the specimen or

until the stroke of the actuator is exhausted. A purpose buUt test rig has been

constructed around the actuator. Axial loads are applied to the brace end and are

reacted at the chord ends where axial and radial displacements are restrained. The

connection between the brace end and the actuator is made via a swivel head

connector. An isometric view of the test rig is shown in Figure 2.5.

- 1 2 2 -


2.3.2 Fatigue Crack Monitoring

The fatigue crack development in the tubular joints was monitored by taking

Alternating Current Potential Drop (ACPD) crack depth measurements at fixed

points around each expected crack location. By choosing suitable inspection

intervals it should be possible to follow crack growth from initiation (N i) to

through wall penetration ( N 3 , see Section 1.8.2).

The ACPD technique utilises the thin skin effect whereby a high frequency

alternating current will be confined to a thin layer when flowing through ferrous

materials. A function of the permeability and conductivity of the material and the

frequency of the alternating current, the skin depth is given by (2.1) [2.9].

s = I (2.1)VHUoOitf

where:

|io Permeability of Free Space

\i Relative Permeability of Metal

a Conductivity of Metal

f A C. Frequency (5KHz)

If an alternating current is forced to flow across a surface breaking defect as

illustrated in Figure 2.6, the current will flow down one crack face and up the other

side. Since a linear potential gradient is assumed to exist on the metal surface and

on the crack faces, measurement of the potential drop across the crack and

adjacent to the crack allows the calculation of the 1-D crack depth as follows:

Vr - A(2 2)

V c - ( A + 2di) ^

Therefore,

123 -


‘i . = f[ H

(Z3)

Where:

Vc Cross Crack Potential Drop

V r Potential Drop Adjacent to Crack (Reference)

A Probe Spacing

di 1-D Crack Depth.

Strictly (2.3) is only valid for an infinitely long crack in an infinite plate. However

for the case of semi-elliptical or circular arc cracks as found in tubular joints,

modifying factors have been derived to modify the 1-D depth estimation [2.10].

These modifiers are functions of the crack surface length, 2c, the probe gap. A, and

the distance to the crack midpoint. The modifiers vary from a maximum at the

crack mid point to zero at the crack ends. With the above information, the

modification factor, Mx can be calculated from a series of theoretical curves to

give the true crack depth using (2.4).

d = M ,d , (2.4)

Fatigue cracks in tubular joints have been shown to maintain a low aspect ratio,

often with di/2c = 0.1 [2.11]. The modification factors have been shown to be less

than 1.05 for cracks of this shape [2.12] and thus the 1-D crack depth estimate can

be used without modification.

Two methods for calculating the crack lengths from ACPD crack depth data have

been attempted previously. Connolly [2.13] developed a numerical differentiation

procedure to locate the points of inflection in the surface voltage measurement

data. Difficulties can arise when trying to utilise this method using data taken from

fixed probes since the probe locations are usually weighted around the hot spot

where the deepest part of the crack is expected. As a consequence the probes may

124


be 15 - 20 mm apart in the region where the crack ends would be expected to be in

the later stages of life.

A simpler alternative involves truncating the crack depth readings near the crack

ends. Crack lengths produced using this technique have been shown to lie within a

15% error band on optically measured crack lengths.[2.12]. This technique was

adopted here.

Siting of the fixed ACPD Probes requires careful consideration in order to

maximise the usefulness of the data. Crack growth is expected to initiate at the hot

spot site and the deepest point of the crack is expected to remain in this region. In

addition for a balanced axially loaded T joint, two potential crack sites exist, one at

each saddle.

ACPD measurements were performed using a UlO Crack Microguage with an

integral 128 channel multiplexer unit [2.14]. A single ACPD site requires two

channels, one each for the crack and reference readings resulting in a total capacity

of 64 fixed ACPD sites. The 64 ACPD sites were divided equally between each

saddle since both are potential crack locations. The probe sites were weighted

towards the hot spot region where the fatigue cracks were expected to initiate. The

locations of the fixed probes relative to the saddle position are detailed in Table

2.10. The UlO supports the use of 4 sets of field injection points. Two fields were

used for each saddle. Each field therefore covers 16 ACPD sites to one side of the

saddle.

The durability of the ACPD probes is an important consideration. The probes can

be submerged in a corrosive sea water environment for anything up to six months.

It is essential that the probes do not degrade due to this environment as valuable

data would be lost. It is difficult if not impossible to replace or repair probes once

the test is underway.

125 -


Preliminary investigations were performed to identify the most durable probe set

up. The outcome of this investigation resulted in a set up that proved highly

reliable with very few failures occurring during testing. The surface of the tubular

was cleaned down to shiny bare metal as this gives the best surface for the

attachment of the probes by spot welding. Several grades of steel wire were

examined and the one resulting in the strongest weld to SE702 was selected. This

was a steel wire of approximately 0.6mm diameter. Once welded to the specimen

surface the probes were cut to a height of 3 to 4mm. Bootlace ferrules (0.5mm^)

were placed over these pins and filled with solder to ensure a low resistance

connection. Electrical connection to the UlO was made by twisted pair multiplexer

ribbon which was terminated in the solder filled ferrule. For the sea water test each

of the 272 individual probes and earth connections were encapsulated in bitumen to

prevent environmental attack. This is an extremely time consuming and repetitive

task but the result is a highly reliable electrical connection that will allow

automated crack depth measurements to be taken underwater, day and night for

many months.

The raw data collected from a typical Test ( ‘T l ’) is shown in Figure 2.7. This data

is completely unmodified and illustrates the repeatability and accuracy of the

ACPD technique for capturing ‘snapshots’ of the crack growth process.

Techniques have been developed to remove some of the ‘peaks’ found in the raw

data. These techniques and the underlying causes are discussed later in this Section.

These anomalies are obviously not representative of the actual crack shape which

are known to have smooth semi-elliptical profiles from post failure sectioning of

cracked members.

The 1-D crack depth equation (2.3) was derived using the assumption that the

cross crack probe gap and the reference probe gap were the same. This is the case

with a standard hand held probe. However inaccuracies in siting the spot welded

fixed probes means that it can no longer be assumed that the probe gaps are equal.

- 126


Determination of the cross crack probe gap is especially difficult since it is sited

across the weld toe. However examination of the 1-D crack depth equation for the

case where Ac Ar shows that the increment of crack growth between successive

ACPD scans is independent of the cross crack probe spacing, Ac.

Thus:

V R - A ,

Vc «^(Ac + ld j )

Vc Ac+2di

(2.5)

(2.6)

and:

d.= — Vcv V r ^ r y

(2.7)

The crack growth increment between successive ACPD scans, d / and di is given

by:

d f - d l = ^ Vc2R y

Vci ^c

R y(2.8)

A d = d ? - d ; = - ^ Vc2 Vc,V,Vr2 V,Ri y

Thus only the reference probe gap is necessary to determine Ad.

(2.9)

By developing a procedure briefly outlined by Austin [2.2], the actual reference

probe spacings have been calculated from the deviations in the raw reference

probe data. The first five sets of reference probe readings taken on the uncracked

joint were averaged for each site. A second order polynomial was subsequently

fitted to the averaged data. A separate curve was fitted to each of the four fields.

The actual reference probe spacings can then be back-calculated from the deviation

of the actual reference as shown below.

- 127 -


VocA

Therefore assuming the actual reference is Ar, and the nominal spacing is 10.

V r= kAR

Vio = klO

Thus;

Ar = 10(Vr / V io) (2.10)

Non zero crack depth readings are expected at some sites even before fatigue

testing has commenced. This is due to errors in the placement of the fixed probes

and some non uniformity of the field. In an attempt to maintain field uniformity two

AC field injection points are employed on each side of the joint each serving 16

ACPD sites. Subtraction of the initial ACPD crack depth readings on the

uncracked joint from all subsequent ACPD scans should give an accurate measure

of crack development. The modified ACPD crack development plot for a typical

test is shown in Figure 2.8. Two inspection intervals were used during the test. The

shorter inspection interval can clearly be seen from the spacing of the crack profile

lines earlier in the test.

2.3.3 Environment Chamber

For the corrosion fatigue tests, the welded intersection where the fatigue crack is

expected to grow must be immersed in sea water. This is achieved via an

environment chamber that bolts around the chord / brace intersection. A water

tight seal was achieved using ribbed rubber strips and silicon sealant. The weight of

the water filled chamber was supported using steel bands around the brace and

chord. Artificial sea water made to ASTM D1141 [2.15] is pumped from a

reservoir through a closed loop passing through the environment chamber. The

fully aerated sea water is maintained between temperature limits of 8-10°C via an

external chiller and between pH 7.8-8.2.

The cathodic protection (CP) system consists of two W ENKING MP81

potentiostats, two platinum coated anodes and two Ag/AgCl reference electrodes.

- 128 -


The top and bottom saddle CP systems were independent. A submersible reference

electrode was used for the lower saddle.

Prior to application of fatigue loading, each joint was subjected to a ‘soak time’

where the joint was submerged in sea water with the CP switched on at the

appropriate level. A soak time of two weeks was implemented to achieve

polarisation of the specimen and allow hydrogen to diffuse through the steel.

The time required to achieve a uniform through thickness hydrogen concentration

is dependant on the diffusion coefficient for the material. Unfortunately such data

in the literature is scarce and the values that are quoted can vary by orders of

magnitude or more [2.16]. The soak time for tubular joints is considered less

important than that for simple specimen tests that may only last a day or two. For

the simple specimen case, if the hydrogen has not permeated through the steel

before the crack growth commences it is possible that the crack may grow faster

than the hydrogen diffuses through the metal. This may mask the effect of the

environment on the crack growth rate. For tubular joints however the tests may

last for several months making the through thickness hydrogen concentration

gradient at the commencement of loading less critical.

2.3.4 Test Control and Data Acquisition

Previous tubular joint fatigue tests at UCL have been controlled using the

proprietary FLAPS software [2.17]. FLAPS controls the waveform generation and

ACPD data capture and storage tasks automatically. The particular strength of this

software is its ability to ‘replay’ complex variable amplitude, variable frequency

load sequences such as WASH [2.18]. It does however have certain drawbacks.

The communication protocol used by the software does not allow it to

communicate directly with the UlO crack microguage. Thus during ACPD data

capture the internal UlO switching unit must be replaced by an external switching

unit. It also has more subtle practical implications regarding the test set up and data

storage. Additionally an INSTRON Harrier interface is required to complete the

129


waveform generation task. Practical constraints and reliability considerations

dictated that an alternative computer control routine be sought.

As a result a PASCAL test control routine originally written at UCL [2.19] for

controlling simple specimen tests has been modified for this investigation.

Interfacing with a data acquisition board, this program eliminates the need for the

Harrier interface and auxiliary switching unit for the UlO. This flexible routine

allows the user to control the waveform generation by supplying the amphtude and

the frequency for the sinusoidal waveform. ACPD crack depth scans can be

performed automatically at user defined intervals or on demand. ACPD crack

depth and voltage data is stored electronically in a spreadsheet readable format. A

hard copy of the results can also be obtained.

A schematic of the complete experimental test set up showing all aspects of test

control, data acquisition and environmental control is shown in Figure 2.9.

2.4 Experimental Stress Analysis

The hot spot stress concentration factor was measured experimentally using strain

gauges. The steep stress gradient close to the intersection combined with the fact

that a strain gauge averages out the distribution of strains over which they are

located and the anticipated hi-axial stress state resulted in a requirement for small

rosette gauges to achieve maximum accuracy. Three element, 45° rosettes with

over-layed gauge lengths of 2mm were selected and used for all the tubular joints

tested in this study.

A balanced axially loaded T-joint should yield similar hot spot stress concentration

factors for both saddle regions. This of course assumes identical weld profiles at

both hot spot sites and a high level of precision in fabrication in order that the mid

planes of both brace and chord are co-incident to minimise bending effects.

However in reality manufacturing tolerances can result in some variation in hot

- 130 -


spot SCF’s at opposing saddles in an axially loaded T- joint. Examination of

previous test results show differences of 10% to 15% to be typical. Experimental

SCF results from a previous test program using a similar geometry [2.2] are shown

in Table 2.11.

The percentage difference is calculated as shown in (2.11 )

MaxSCF - MinSCF Ï S S S ? — >“ «>

The fatigue test rig is designed in such a way as to allow limited adjustment to be

made to the chord position in the vertical plane. This is to allow the alignment of

the T joint mid-plane and the mid-plane of the loading actuator. Mis-alignment

would result in an out of plane bending component being introduced since the

chord ends are fixed. This would affect the experimental stress concentration

factors accordingly.

As a result it was necessary to repeat the experimental stress analysis a number of

times at different chord heights prior to the first fatigue test. The chord height was

subsequently fixed at the position that resulted in the least discrepancy in the

experimental stress concentration factors between the two saddle regions. This was

assumed to indicate joint alignment with the actuator loading axis.

The first fatigue test resulted in a fatigue crack at only one saddle point (the one

with the highest SCF). Although this is reasonably common for such tests, it was

decided that a more scientific approach should be taken to the alignment of the

joint and actuator mid planes.

In consultation with the Department of Photogrammetry and Surveying [2.20] a

procedure was developed to adjust the height of the chord ends to ensure that the

centre lines of the actuator and brace were co-incident. This also ensured that the

131 -


chord lay level. A tripod mounted Sokkia Automatic Level was used to determine

the height of collimation of two points known to lie along the centre plane of the

actuator. By measuring the distance between these two points the slope of the

actuator could be determined. It was found that the actuator lay on a slope of 3mm

/ m. Extrapolating this to the chord centre line gave the required height of the

chord. The Sokkia Level was then used to set three points along the chord at the

appropriate height. Hand operated hydraulic jacks were used to move the chord

ends. This process is illustrated in Figure 2.10.

A further factor produces a discrepancy between the SCF results between the two

saddles. This is the bending load due to the self weight of the brace and the swivel

head adapter that forms part of the load train. Therefore it is necessary to zero the

strain gauges under a small tensile load. This has the effect of straightening the

brace and thus reducing the effect of the bending load. This effect was also

identified by Austin [2.2].

The loads applied to the T-Joint during the stress analysis were always significantly

less than the load to be used during the subsequent fatigue test. Strain readings

were taken from each gauge at four increments during both loading and unloading.

The slope of the best fit line to this data was then used to recalculate the strains for

each gauge.

2.4.1 Strain Gauge Siting

For each joint the SCF was determined at up to five sites around each saddle as

shown in Figure 2.11. Only the chord side were investigated as the SCF’s are

known to be higher around the chord than the brace for this particular joint /

loading mode configuration. The strain gauges were located symmetrically about

the saddle and identical locations used for both saddles. Two rosettes were placed

in diametrically opposite positions on the brace remote from the intersection to

measure the nominal strains. It is essential that the hot spot SCF is determined for

each individual joint as this is used to calibrate the loads applied to the joint during

132 -

Chapter 2 - Experimental Fatigue Testinq of W elded Tubular Joints

the fatigue test. The remaining sites on each side were placed at different angular

locations for each test. As the tubular specimens are nominally identical the SCF

results for each joint can then be compiled to allow a more complete assessment of

the SCF distribution without excessive strain gauging of a single joint.

The principal strains, stresses, and the principal angle (j) can be determined from the

strains indicated by each of the three gauges in the rosette, Ea £b & £c as shown in

[2.21].

The UKORSP definition of stress concentration factor was used to determine the

hot spot SCF utilising the maximum principal stress from each rosette. All rosettes

were aligned so that Ea is the component of strain perpendicular to the weld toe.

The angle ({) thus represents the angle with which the direction of the maximum

principal stress deviated from the perpendicular to the weld toe. This angle will

vary around the intersection.

2.4.2 Determination of SCF*s

All SCF’s were determined in accordance with the UKOSRP guidelines as outlined

in Chapter One. For the current joint geometry the guidance on the regions of

strain linearity stipulates that at each position at which the SCF is to be determined,

one gauge is to be placed 10mm from the weld toe and a second 20mm from the

toe in line with the first. Extrapolating the maximum principal stresses calculated

from the strain readings of each gauge, to the weld toe gives the stress level to be

used in the calculation of the SCF.

Since the strains should be fully elastic under the loads being applied during the

stress analysis it is expected that the strains will be a linear function of the applied

load. In practice however slight differences exist between the loading and

unloading traces due to zeroing errors and hysteresis effects. The average gradient

of the strain-load line was determined for each gauge using a least squares linear

regression on the loading and unloading data. This gradient was used to modify the

133 -


strains to account for any non linearity that may occur. Failure to modify the strains

in this manner can result in varying SCF values for each load increment during

loading and unloading. Theoretically the SCF at each site should be constant for

any load level. In practice however the steep stress gradient near the weld toe and

the small spacing of the gauges at each site results in large changes in weld toe

stress levels for small variations in measured stresses due to the magnification

effect of the extrapolation procedure. Using modified strains ensures that the SCFs

at a particular load level are the same for loading and unloading since the stresses

used in the extrapolation procedure are equal.

2.4.3 Experimental SCF Resuits

The choice of SCF to use in the calculation of load in the subsequent fatigue tests

is not as straightforward as may first be thought. Although the SCF should be

independent of applied load the actual experimental results exhibit some scatter.

Each analysis is repeated twice and there are of course two saddle positions to

consider.

The question arises as to exactly which component of the results are chosen as the

definitive SCF for each joint. Several different SCF’s are plausible choices, some of

the factors are detailed below:

1. Which load level to choose? Average across loads or highest SCF

2. Which saddle to consider? Absolute highest SCF or average of each saddle.

3. Which repetition of the stress analysis to choose? Average or highest

4. Use theoretical or measured brace nominal stresses?

The SCF used here for the calibration of the applied load is the average of the

SCF’s recorded at both saddles during each repetition. The exception to this rule is

for the final test, T6. The experimental SCF was determined four times. After the

first two experimental SCF investigations the joint was removed and replaced and

the SCF investigation performed a further two times. The agreement between these

- 134 -


four results was excellent and showed that the SCF at the upper saddle was

significantly and repeatedly lower than that at the bottom saddle. No errors in the

positioning of the strain gauges was found. For these reasons the SCF used during

the calibration of the applied loads for T6 was the average of the measured SCF at

the bottom saddle only. The SCF is determined using the measured brace nominal

stress. The measured brace nominal stresses showed good agreement with the

theoretical nominal in all cases. The SCF’s are shown in Table 2.12. Included in

this Table are the maximum and minimum SCF recorded during the investigation of

each joint.

It is noted that the scatter in the experimentally measured SCF’s is quite

considerable. Across the nominally identical joints SCF the minimum SCF can

represent as little as 75% of the maximum recorded SCF. The scatter in the

average SCF’s used to calculate the applied load is somewhat less, with the

difference between the maximum and the minimum SCF representing 16% of the

peak average SCF. This uncertainty in the actual SCF is the reason why the SCF’s

are measured experimentally for each joint rather than solely relying on parametric

SCF predictions or experimentally measured SCF’s on similar joint shapes. The

degree of scatter is typical for specimens of this type.

Experimental stress analysis results for each test are shown in Figure 2.12 together

with the HCD SCF distribution prediction. Austin [2.2] performed similar

experimental SCF investigation on specimens of nominally identical shape. A

Sin(20) function was proposed as a best fit to his experimental data normalised to

the peak SCF. This normalised distribution has been converted into SCF using the

average saddle SCF from the current investigation. This curve has also been

included in Figure 2.12.

- 135 -


2.5 Fatigue Test Programme

The two major variables in the current test program are the hot spot stress used

and the apphed levels of cathodic protection. The necessary background required

to make an informed decision on the appropriate levels of each variable is

presented.

It has been stated that basic design curves for welded tubulars and plates should

not be applied to tubulars of yield stress greater than 400MPa.[2.22], until

experimental verification from programmes such as this can be obtained. It is

important therefore that the hot spot stress levels for the six tests in this

programme be chosen with care. In terms of fracture mechanics data some of the

most useful results can be obtained from long life tests operating close to

threshold. However in this region the risk of the test becoming a run out is real.

Guidance on the use of cathodic protection offshore states that the question of the

effect of cathodic protection on the hydrogen embrittlement is mainly relevant to

high strength materials. Thus a greater effect on the corrosion fatigue behaviour of

cathodic protection can perhaps be anticipated in the current programme than

previous programmes utilising lower strength steels such as BS4360;50D.

A review of UK and other design guidance suggests that potentials more negative

than minus 900mV (Ag/AgCl) may be detrimental to steels with strength levels

above 700MPa and even -800mV may be harmful to steels with strength levels

above 800MPa.[2.23]

A total of five corrosion fatigue tests were performed in this programme to

investigate the effect of the impressed current cathodic protection level. Tests have

been undertaken at a C.P. levels of -800mV and -lOOOmV (overprotection) both vs

Ag/AgCl. From the above it could even be argued that for SE702 with a measured

yield strength of approaching 750 MPa that -800mV could be classed as

- 136


overprotection. However the utilisation of lower levels is not thought to be

representative.

The air tests were run at close to the machine limitation of IHz. The corrosion

fatigue tests however had to be run at a representative frequency since the crack

growth mechanism is time dependant. Thus a frequency of 0.2Hz was adopted for

the 5 sea water tests. The frequency of 0.2 Hz is slightly higher than the 0.167 Hz

previously used in tubular joint corrosion fatigue tests. This is the frequency at

which most of the energy of the loading spectrum is concentrated in the variable

amplitude load sequence JOSH [2.24]. JOSH (Jack Up Offshore Standardised

Load History) is a pseudo random variable amplitude load sequence based on the

WASH framework. JOSH was based on the results of an extensive analysis of the

differing dynamic behaviour of jack up structures compared to fixed jacket

structures. JOSH has been validated using actual service data from jack ups in the

North Sea. JOSH has been used in the parallel fatigue test programme using

tubular welded Y joints fabricated from the same steel [2.25]. The results of this

parallel programme will be presented here in S-N format only.

2.5.1 Test Parameters

The parameters for the six tests must be chosen with care due to the limited

number of specimens. The original test programme was designed to cover a wide

range of hot spot stress levels from 400 down to 180MPa. This represents

approximately 60% to 25% of the material yield stress. The air tests were to be

performed at the higher stress levels of 400MPa and 300MPa with two corrosion

fatigue tests at 225MPa and two at ISOMPa. For each stress level in the corrosion

fatigue tests, one test was performed using cathodic protection levels of -lOOOmV

and the other at -800mV (both vs. Ag/AgCl).

The unexpected occurrence of a ‘run-out’ during Test T5 (see Section 2.6.1)

required the test program to be modified for the final two tests. The fifth test

specimen was re-tested at a higher hot spot stress level of 300MPa with the same

- 137


CP level of -lOOOmV. The sixth and final test was also performed at 300MPa but

with a CP level of -800mV.

The original and modified test program is outlined in Table 2.13. The results of the

re-tested T5 will not be presented here in any great detail as the effect of the

previous testing at the lower stress levels cannot be quantified.

2.5.2 ACPD Data Analysis

The raw data from the fatigue tests is in the form of discrete crack depth

measurements at 64 sites around the brace chord intersection. The computer

control routine monitors the development of the crack by taking a crack depth

measurement at each of the ACPD sites in turn at the required inspection interval.

The inspection interval can be pre-set to any required level prior to commencement

of the test. In addition, supplementary inspections can be performed on demand

during the test. As a result the amount of data collected can be sizeable and a

procedure for analysis of this data to extract the relevant sections must be

implemented.

The raw data file is stored in a spreadsheet readable from by the control routine.

The ACPD reference and cross crack probe potentials are logged in addition to the

measured crack depth at each site. A Microsoft Excel spreadsheet template has

been created to analyse the raw ACPD crack depth data. The spreadsheet

automatically completes the following tasks.

a) Modification of the calculated crack depths using the back calculated reference

probe spacing rather than the nominal 10mm with which the control routine

calculates crack depths.

b) Extraction of crack depth data, leaving the cross crack and reference voltages

behind.

c) Subtraction of initial crack depths measured on the uncracked joint at each site

from all subsequent measurements at that site. This resets all ACPD sites to a

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S ta rtin g c ra c k d e p th o f 0.0mm a nd re m o ve s e r ro rs d u e to p ro b e p o s it io n in g and

f ie ld n o n u n ifo rm ity . T h e d a ta is f i l te re d to re m o v e c ra c k in d ic a t io n s o f less

th a n 0.05mm (n o is e ).

d) Extract the deepest recorded crack depth from each inspection.

e) Smooth the deepest point data using the Seven Point Incremental Polynomial

Technique (see below).

f) Calculation of crack growth rates, stress intensity factors and Y factors (the

SIF and Y Factors will be presented in Chapter 5).

The fatigue crack growth rate, experimental SIF and hence the experimental Y

solution are determined from the deepest point of the dominant crack in the tubular

joint over successive inspections. The position of the deepest point may change

between inspection intervals but is not expected to move far from the hot spot. The

filtered crack depth data is scanned and the magnitude and position of the deepest

crack indication is logged. The position of the deepest point is checked to ensure it

is within close proximity to the hot spot. If the deepest point of the crack occurs

away from the saddle then this suggests an erroneous ACPD crack measurement

and is investigated further.

If the raw filtered data is used the scatter in the calculated fatigue crack growth

rate increases with increasing crack depth. This scatter makes subsequent analysis

of the data more difficult. A data reduction technique has thus been implemented to

smooth the data relating to the deepest crack depth. The Seven Point Incremental

Polynomial Technique [2.26] was used. A second order polynomial (a parabola) is

fitted to the three data points from the inspections either side of every data point

except for the first and last three inspections intervals. The crack depth at each site

was then recalculated using the polynomial fitted to the adjacent points and the

fatigue crack growth rate determined from the first derivative of this polynomial.

This parabola was fitted using a least squares method and solving the resulting

linear system using a pivoted gaussian elimination.

139


Since this process is computationally intensive and must be repeated for all but six

of the inspections completed during the test, the spreadsheet template has been

designed to perform this task automatically.

2.5.3 Crack Shape

The ratio of the surface length of the fatigue crack to its depth at the deepest point

changes as the crack propagates through the chord wall The crack shape changes

can reveal information, such as the coalescence of adjacent defects, that can help

explain features of the crack growth process.

The Excel spreadsheet used to perform the basic analysis of the ACPD data

(Section 2.5.2) also provides the input data for a FORTRAN routine that calculates

the crack shape. The spreadsheet filters through the crack depth data for each

inspection at each probe site and returns a T ’ if a crack deeper than 0.1mm is

present and a ‘0’ otherwise. The FORTRAN routine scans through this data and

picks up the end positions and maximum depth of up to 5 defects for each

inspection and each saddle. The positions of each probe are known and therefore

the routine can automatically calculate the surface length of each defect. The

length, depth, and shape of each defect is output in spreadsheet readable form. The

defect with the longest surface length is extracted in each case. It is this defect that

is presented in the next Section.

2.6 Fatigue Test Results

The raw ACPD data has been analysed as outlined earlier in this Chapter. The

results of this analysis are presented here. This will include the fatigue life of each

specimen presented in S-N format, crack growth curves and crack growth rates for

each defect, a study of the initiation behaviour of each specimen and the crack

shape results.

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2.6.1 S-N Data

The end of each test is defined as the attainment of a through wall fatigue crack.

This is marked by a sudden increase in the indicated ACPD crack depth and a loss

of sea water in the corrosion fatigue tests. The experimental fatigue life ( N 3 ) of

each specimen is detailed in Table 2.14. Also included is the predicted fatigue life

utilising the mean of the 16mm tubular joint data used during the development of

the guidance for lower strength 50D steels (Nap) and the ratio between the two

(Na/Nsp) known as the ‘Reduction Factor’. The fatigue lives predicted by the T

Design Curve for Air and Sea Water environments together with the mean of the

16mm 50D joint data used during the formulation of the fatigue design guidance is

included in an adjacent Table for comparison.

The results are shown graphically in Figure 2.13 together with the design S-N

curves for Air and Sea Water & CP. The mean of the 16mm 50D joint data is also

included for comparison. Error bands have been included on the stress axis for

each test result. These correspond to the stresses that would have resulted had the

maximum or minimum SCF recorded during the stress analysis of each joint had

been used in the calibration of applied loads.

The two air tests (T l & T2) and the -lOOOmV test at 225MPa (T3) all lie on

approximately the same straight line. This is shown by the fact that each of these

tests displays a similar ‘reduction factor’ in Table 2.14. All lives exceed the T ’ Air

Design Curve but fall short of the mean line.

Reducing the applied CP level to -800mV for the fourth test (T4) but leaving the

hot spot stress level unchanged at 225 MPa resulted in an increase in life of almost

40% over the third test.

The fifth test was declared a run-out after completing over 2.25 million cycles

without any crack initiation taking place. This number of cycles equates to almost 6

months of continuous, 24 hour testing. This represents an excellent result for the

- 141 -


Steel as the mean of the 50D data suggests a life of 1.5 million cycles. All the

previous tests had fallen short of the mean 50D line. A closer look at the fatigue

life data contained in the Background to New Fatigue Design Guidance [2.22] for

50D tubular joints tested in sea water under cathodic protection shows that only

eight specimens had fatigue lives approaching or exceeding 2 million cycles. Only

constant amplitude loading has been considered here as the ‘peaks’ in variable

amplitude loading can initiate fatigue cracks in tests where the equivalent stress

range may lie below the fatigue limit for constant amplitude tests. By far the

longest of these tests was 2.7 million cycles at a hot spot stress level of only

82MPa [2.27]. However this was performed using a sea water temperature of 20°C

under free corrosion conditions. Such conditions are likely to favour early fatigue

crack initiation. The remaining tests were performed at hot spot stress levels of

between 81 MPa (19% of yield) and 150 MPa (38% of yield) with resulting lives of

between 1.74 and 2.3 million cycles.

Considering air tests only, 15 had initiation lives exceeding 2 million cycles. Of

these 5 were axially loaded T joints. The hot spot stress levels for these tests

ranged between 105 and 135 MPa. The lack of any other tubular joint data

showing similar initiation lives at such stress levels makes the declaration of this

test a run-out a reasonable one.

The specimen was re-tested at 300MPa and failed after 130,(KK) cycles. The results

of this re-test on specimen T5 will not be considered in any subsequent fracture

mechanics analysis as the effect of the earlier testing is unknown. The two sea

water tests (T5 Re-test and T6) both resulted in similar fatigue lives of 130,000

and 138,000 cycles respectively. The test with the lower CP level of -800mV (T6)

gave the longest life in agreement with Test T3 and T4. However in view of the

small difference in life and the fact that T5 Retest had previously been subjected to

2.25 million cycles at 180 MPa, caution should be exercised when drawing

conclusions from these results.

- 142


2.6.2 Crack Growth Curves

Figures 2.14 to 2.18 show the crack growth curves for Tests T l to T4 and Test

T6. Test T5 (re test) is included in Figure 2.19. Included in each of these Figures is

the raw ACPD depth data and the ‘smoothed’ data using the Seven Point

Incremental Polynomial Technique. In each case it can be seen that very little

smoothing was necessary due to the accuracy and repeatability of the crack depth

data. For the Test where a fatigue crack developed at each saddle, both crack

growth curves have been presented on the same axis. The fatigue crack that first

penetrates the chord wall is labelled as the Primary Crack. In each case it can be

seen that large amounts of high quality data has been collected.

The classic tubular joint crack growth curve in air is shown in Figure 2.14 for Test

T l. This shows the defect initiating and propagating through the chord wall

(16mm). It can clearly be seen that after the crack attains a depth of about 4 mm

the slope of the crack growth curve is constant. At lower crack depths the slope of

the curve gradually increases and much important data has been collected in this

region. Although this region accounts for only one quarter of the wall thickness it

occupies approximately half of the total life. This explains the importance of the

data collected in this region when it comes to developing fracture mechanics

models for the prediction of crack growth.

The second and final Air Test ‘T2’ is shown in Figure 2.15. In this case two defects

initiated at approximately the same time, however the low slope of the Secondary

defect crack growth curve meant that it was ‘overtaken’ by the defect that went on

to penetrate the chord wall first. The characteristics of the classic crack growth

curve described above are again found in the Primary crack. The Secondary defect

attained a depth of approximately 12mm at the end of the Test.

The situations becomes somewhat more complex with the introduction of the sea

water environment with cathodic protection. This is demonstrated by Test T3

(Figure 2.16) where it can be seen the crack growth curve found in the two air

- 143


tests is no longer applicable. Instead, there are several distinct regions where the

crack growth curves take on different linear slopes. This behaviour is found in the

other corrosion fatigue tests in this study.

Plotting all the crack growth curves on the same axis in Figure 2.19 shows some

interesting points. Tests T3 and T4 were performed at the same hot spot stress

level of 225MPa but with the lower CP level (-800mV) being used in the latter.

Looking at the crack growth for the first 2mm the two tests appear to be behaving

identically. They initiate at approximately the same time and follow the same curve.

However after attaining a depth of approximately 2mm the slope of the curve for

the Primary defect in T4 suddenly falls. In the time it takes the fatigue crack in Test

3 to penetrate the chord wall, the crack in T4 has only grown a further 2mm. One

possible explanation for this sudden change in behaviour of the primary defect in

T4 is the initiation of a second defect at the opposite saddle at approximately the

same time. The initiation behaviour of each of these specimens is dealt with in

Section 2.6.4.

A ll cracks grew on a plane approximately perpendicular to the chord surface

2.6.3 Fatigue Crack Growth Rates

The gradient of the crack growth curves presented in the previous Section gives

the crack growth rate. This data is presented in Figures 2.20 to 2.24.

The feature of crack growth particular to welded tubular joints whereby the crack

growth rate is almost constant for most of the crack propagation process is very

clearly shown in Figure 2.20 for T l and to a lesser extent in Figure 2.21 for T2.

The changes in slope of the crack growth curves for Tests T3 and T4 reported

previously are clearly seen on Figures 2.22 and 2.23 as large fluctuations in the

crack growth rate.

144 -


As would be expected the crack growth rate is generally highest for the tests

employing the highest stress levels. This is clearly shown in Figure 2.25 where the

crack growth rates for each of the dominant defects is shown.

2.6.4 Fatigue Crack Initiation

Inspection of the ACPD data collected during the early portion of each test has

shown the ACPD technique to be capable of detecting crack growth increments of

less than 0.1mm. Figure 2.26 shows early crack profiles for a test that appears to

have initiated from two separate defects which subsequently coalesce. This

detection capability is important when it comes to determining the point of

initiation of each defect. Early crack growth data from a typical test is shown in

Figure 2.27. Note that the defect has been detected at depths of less then 0.1mm

and is reliably monitored as it begins to propagate. The definition of initiation. Ni

was therefore taken as the attainment of a 0.1mm deep defect indication. The

initiation lives were determined graphically using the smoothed crack growth data.

The results are summarised in Table 2.15.

The Ni/Nt ratio (initiation to total life) gives a measure of the importance of the

initiation period to the overall fatigue life. Welded tubular joints are generally

known for their short initiation and long propagation lives. These have been

calculated and are shown in Table 2.15 and plotted in Figure 2.28. Determination

of an exact initiation life for Test T6 proved difficult due to a hardware problem.

However the indications suggest a short initiation life of 10,000 cycles of less. The

trend noted by Austin [2.2] was for lower Ni/Nt ratios for higher stress levels. This

effect is certainly not so clear in this instance although the limited number of data

points make it difficult to draw firm conclusions.

The relative importance of initiation to total life can be seen in Figure 2.29. In this

figure the initiation (Ni) and propagation (Nt-Ni) are shown normalised to the T air

curve prediction. The two air tests both show broadly similar proportions of the

total fatigue life taken up by the initiation and propagation phases. The lower stress

- 145


(300MPa) air tests shows a slightly shorter proportion of the total life spent

initiating a defect and a slightly longer propagation period.

Both sea water tests show delayed initiation over air tests with Ni/NT (where NT

is the life predicted by the T curve) ratios of approximately 0.4. It is clear from this

figure that the longer life found in Test 4 was due to slower crack growth in the

propagation phase as the relative initiation lives are very similar.

The initiation and total fatigue lives for each of the tests are plotted on an S-N

diagram with the design and mean S-N curves superimposed in Figure 2.30. The

initiation lives all fall below the CP Design Curve.

2.6.5 Crack Shape Development

The development of the shape of the fatigue cracks can be found by plotting the

crack aspect ratio (a/c) against the normalised crack depth (a/t). This data is shown

in Figure 2.31 for all the fatigue cracks produced during this investigation. Each

defect is shown to initiate with a very low aspect ratio (a/c<0.05) meaning that the

depth of the defect is very small compared to the length. Whilst there is little doubt

that the defects are in fact very shallow when first detected, the length of these

defects is subject to a little more uncertainty. The finite spacing of the probes at the

initiation site (4 to 6mm) means the determination of accurate length is difficult for

the smaller defects.

2.7 Examination of Fracture Surfaces

Examination of the fracture surfaces can yield important information on the

dominant crack growth mechanisms in operation. In particular the presence of

‘brittle’ fracture facets on the crack surface can give an indication of the

importance of the role played by hydrogen embrittlement mechanisms.

Additionally, comparison of the optically measured crack shape with the ACPD

- 146 -


measurement allows the accuracy of the technique to be demonstrated. This has

been demonstrated many times previously however e.g.[2.2].

Unfortunately at the time of writing this thesis, all the cracked tubular joints were

being used for an experimental investigation into the remaining strength of cracked

tubulars. As a result the fracture surfaces are not currently available for destructive

sectioning. However following completion of the remaining strength investigation

the fracture surfaces will be examined at Cranfield University.

2.8 Discussion

The S-N data presented in this Chapter has been derived from tests performed on T

joints fabricated from SE702 and tested under constant amplitude loading. A

parallel experimental investigation has researched the effect of a realistic variable

amplitude loading sequence on the fatigue crack growth behaviour of the same

steel using Y joint specimens tested under OPB loading [2.25]. The test parameters

for this investigation are given in Table 2.16. Included in this table are the

normalised initiation lives and the experimental fatigue life of each specimen. The

S-N data from this parallel investigation is given in Figure 2.32.

It has long been recognised that the loading mode has an effect on the fatigue life

of tubular welded joints. Although a single S-N curve is used for all loading modes,

examination of the data used to derive the curve illustrates the difference between

tubular joints tested at the same hot spot stress level under different loading modes.

S-N data for the 50D type steels [2.22] has been grouped and analysed according

to loading mode. This is illustrated in Figure 2.33 where the results of the axial and

OPB loaded joints used in the derivation of the guidance have been plotted

together with the individual mean life lines. A clear distinction can be seen between

the loading modes with the longest lives resulting from OPB loading. The

difference is greatest for higher hot spot stresses and diminishes at the lower stress

ranges. The mean axial and OPB lines have been used to derive a curve giving the

- 147 -


factor on life between the two loading modes in terms of the applied stress range.

This is illustrated in Figure 2.34. These factors have been applied to the axially

loaded test results presented in this Chapter and these are shown together with the

OPB Y joint results in Figure 2.35. The test results now all lie along what appears

to be a single curve.

A useful benchmark for the comparison of the current test results are those of

Austin [2.2] and Vinas-Pich [2.28]. These tests were performed at UCL prior to

the current work. The dimensions of the test specimens employed by Austin were

nominally identical to the T joint test specimens reported here and those of Vinas

Pich were the same as the Y joints reported from the JÎP. Both Austin and Vinas-

Pich used WASH based multi-seastate variable amplitude loading and the

specimens were tested in sea water with cathodic protection. Both sets of test

specimens were fabricated using the lower strength 50D type steels.

The S-N data from Austin and Vinas-Pich is included with the data from the

current test programmes in Figure 2.36 . An immediate observation is that the

lower strength steel data points all lie below the T ’ Air Design Curve whilst the

SE702 data points all lie above this line. The data points from the high strength

steel appear to lie on a line of shallower slope, diverging at lower stresses. There

exists a clear trend for longer lives at lower stress levels for the high strength steel.

Also included in this figure are three test results also from Vinas-Pich but this time

the tubulars were fabricated from 45OF grade steel (yield strength 450 MPa).

It was noted by Austin that no indication of a fatigue limit was found for multi-

seastate (variable amplitude) loading at stress levels as low as 90MPa for the lower

strength 50D steel. However, data from the IIP tests which were also subjected to

multi-seastate loading appear to confirm the divergence of the test results at the

lower stress levels. Together with the constant amplitude ‘run-out’ at ISOMPa

these results offer some evidence of a higher fatigue limit being operational for this

higher strength steel.

148 -


A database of tubular joint fatigue tests performed in sea water with CP is included

in the current design guidance [2.22]. This database is not restricted to any

particular joint shape or loading mode. Normalising this database to a wall

thickness of 16mm using the thickness correction factor included in the guidance

enables the comparison of this database with the current test results. This is shown

in Figure 2.37. There exits a tendency for the results from SE702 to lie towards the

upper end of the scatter band of the 50D tubular data. This is especially so for

lower stress ranges.

2.9 Conclusions

Seven constant amplitude fatigue tests on large scale welded tubular joints have

been performed. A further four variable amplitude tests have been conducted in a

parallel study. The joints were fabricated from SE702, a 7(X)MPa yield steel

commonly specified during jack up construction. Tests have been performed in air

and in sea water with cathodic protection levels of -800mV and -lOOOmV (vs.

Ag/AgCl). A wide range of hot spot stresses from 400MPa to ISOMPa have been

used.

Examination of the 50D tubular joint database shows an effect of loading mode on

the subsequent fatigue life. This data has been used to derive life correction factors

as a function of applied stress range. Application of these factors show aU axial and

OPB SE702 fatigue lives to lie on approximately the same straight line which is

coincident with the mean of the 50D data.

The fatigue life results from the current investigation and the parallel variable

amplitude study suggest that tubular joints fabricated from SE702 lie within the

scatter of the 50D tubular data. There is certainly no evidence to suggest that

SE702 tubular joints suffer from inferior fatigue performance in comparison to 50D

type steels. Indeed comparison with results on nominally identical tubular joints

149 -


fabricated from 50D and tested at UCL, show SE702 to offer enhanced fatigue

performance across the range of stresses tested. All tests exceeded the design S-N

life.

The occurrence of a run out at a hot spot stress range of 180 MPa at -lOOOmV

Ag/AgCl is very encouraging. Although this is the lowest stress range used in this

test series it represents a moderate stress range for 50D (approx. 50% yield). No

evidence of similarly long lives was found from the 50D database at similar stress

levels. This suggests that the change in slope of the S-N curve may occur at higher

stress levels for high strength steels such as SE702. Further tests on tubular joints

fabricated from SE702 are recommended. These tests should employ hot spot

stress ranges of less than 200MPa.

No evidence has been found to support the abolition of a change in slope for multi-

seastate loading as was found for lower strength steels. However further variable

amplitude tests at lower stress levels will have to be performed to confirm this.

Increasing the cathodic protection level from -SOOmV to -lOOOmV results in a

shorter fatigue life in each case examined here. For hot spot stress levels of around

200-225MPa a factor on life of around 30% appears appropriate. Fears regarding

the susceptibility of high strength steels to enhanced fatigue crack growth rates due

to Hydrogen Embrittlement at high levels of cathodic protection (-lOOOmV) appear

unfounded from the results of this study. However such effects are likely to be very

material dependant and this statement should be considered in the context of the

scope of this investigation.

150 -


2.10 References

[2.1] Coudert, E., Private Communication, Creusot Loire Industrie, October

1997

[2.2] Austin, J. A. ''The role of Corrosion Fatigue Crack Growth Mechanisms

in Predicting the Fatigue Life of Offshore Tubular Joints’\ PhD Thesis,

UCL, October 1994

[2.3] Healy, J., Billingham, J., Chubb, J., Jones, R., Galsworthy, J. "Weldable

High Strength Steels fo r Naval Construction \ Proc. Int. Conf. Offshore

Mechanics and Arctic Engineering, v3A, pp 189-198, ASME, 1993

[2.4] Norme Français, NE P 22 471, "Assemblages Soudés. Étendues des

contrôles non destructifs. ”1986

[2.5] Smith, A., "The Effect of Cathodic Overprotection on the Corrosion

Fatigue Behaviour of AP I 5LX85 Grade Welded Tubular Joints'\

AppendixII, PhD Thesis, City University, London, 1995

[2.6] Stanger Science & Environment, Acrewood Way, St. Albans, Herts. AL4

OJY. "Chemical Composition of Steel Sample ED3639453”, 5 November

1997.

[2.7] Baron, G. "Super Elso SE702’\ Creusot Loire Industrie, February 1989

[2.8] Dowling, N.E., "Mechanical Behaviour of Materials: Engineering

Methods fo r Deformation, Fracture and F a t i g u e Prentice HaU

International, 1993

[2.9] Dover, W .D, Collins, R, "Recent Advances in Detection and Sizing of

Cracks using Alternating Current Field Measurement (A C FM )'\ British

Journal of NDT, Nov. 1988, pp 291-295

[2.10] Collins, R, Michael, D.H., "Crack Monitoring using AC Field

Measurements - Multipliers for Semi Elliptical Cracks" Contract Report

No. NCS 362/3007, London Centre for Marine Technology, UCL, (1982)

[2.11] Ma, C.N., Kam, J.C.P., "Crack Shape Evolution in Tubular Welded

Joints"., NDT&E International v24, n6, pp291-302, 1991

[2.12] Kam, J.C.P., "Structural Integrity of Offshore Tubular Joints Subject to

151


F a t ig u e PhD Thesis, UCL, 1985

[2.13] Connolly, M.P.M., “A Fracture Mechanics Approach to Fatigue Analysis

of Offshore Tubular Y and K Joints.”, PhD Thesis, UCL, 1985.

[2.14] TSC Ltd., 'A C FM Crack Microguage - Model UIO User Manual.”, April

1991, Milton Keynes

[2.15] American Society for Testing and Materials, "'Specification for Substitute

Ocean Water.”, ASTM D1141, 1980

[2.16] Laws, P.A., "Corrosion Fatigue Performance of Welded High Strength

Low Alloy Steels for Use Offshore”, PhD Thesis, Cranfield University,

1993

[2.17] Technical Software Consultants Ltd., FLAPS Fatigue Test Control

Software, Milton Keynes

[2.18] Pook, L.P., Dover, W.D., "Progress in the Development of Wave Action

Standard History (WASH) for Fatigue Testing Relevant to Tubular

Structures in the North Sea.”, Development of Fatigue Loading Spectra,

Eds. Watanabe, R.T., Potter, J.M., ASTM STP 1006, American Society

for Testing and Materials, pp99-120 (1989)

[2.19] Faulke, D.A., PASCAL Test Control Routine, University College London,

1993

[2.20] Gilman, J., Private Communication, Department of Photogrammetry and

Surveying, UCL.

[2.21] . Dally, J.W., Riley, W.F., "Experimental Stress Analysis”, McGraw-Hill

Inc, 1978, pp321-327

[2.22] UK Department of Energy, "Background to New Fatigue Design Guidance

for Steel Welded Joints in Offshore Structures”, November 1990

[2.23] Marine Technology Directorate Limited, "Design and Operational

Guidance on Cathodic Protection of Offshore Structures, Subsea

Installations and Pipelines.”, MTD Publication 90/102

[2.24] Etube, L., Brennan, F., P., Dover, W. D., "Service Load Simulation for

Fatigue Testing of Jack Up Steels”, Recent Advances in Corrosion

- 152 -


Fatigue, Institute of Materials, Sheffield, April 1997

[2.25] Etube, L., "''Variable Amplitude Corrosion Fatigue and Fracture

Mechanics of High Strength Jack Up Steels'\ PhD Thesis, To be submitted

to University of London, 1998

[2.26] American Society for Testing and Materials, “Standcjrd Test Method for

Measurement of Fatigue Crack Growth Rates'\ Appendix: Recommended

Data Reduction Techniques, ASTM E647-88, 1988

[2.27] De Back, J., Vaessen, G.H.G. “Fatigue and Corrosion Fatigue Behaviour

of Offshore Structures’'. Final Report on ECSC Convention 7210-

KB/6/602 (J.7.1F/76) Stichting Materiaalonderzoek in de Zee, April 1981

[2.28] Vinas-Pich, J., “Influence of Environment, Loading and Steel Composition

on Fatigue of Tubular Joints.", PhD Thesis, University College London,

1994

153


Wall Thickne.ss (mm)Distance from Test 1 Te.st 2 Test 3Saddle (mm) Upper Lower Upper Lower Upper Lower

-150 16.8 16.9 16.7 16.8 16.8 17.2-75 16.9 17.0 16.8 17.0 17.2 16.8

Chord 0 16.8 17.2 17.0 16.9 17.4 17.175 16.9 16.8 16.7 16.8 16.9 16.8150 16.9 16.8 16.7 16.8 17.1 17.0

Average 16.9 16.8 17.0-150 16.8 16.9 16.7 16.7 16.9 16.9-75 16.7 17.1 16.7 16.9 17.0 16.8

Brace 0 18.0 19.0 19.2 18.8 18.6 19.375 16.6 16.7 16.5 16.8 17.1 16.8150 16.7 16.7 16.5 16.8 17.0 16.7

Average 16.8 16.7 16.9

Wall Thickness (mm)Distance from Test 4 Te.st 5 Te.st 6Saddle (mm) Upper Lower Upper Lower Upper Lower

-150 17.0 16.9 16.8 16.7 16.9 17.0-75 16.9 16.7 16.8 16.7 17.0 16.9

Chord 0 16.8 16.6 16.9 16.9 16.9 16.975 17.0 16.9 16.9 16.8 16.9 16.7150 17.1 17.0 16.7 16.8 16.9 16.8

Average 16.9 16 8 16 9-150 16.9 16.8 16.8 16.8 16.9 16.9-75 16.9 16.8 16.7 16.9 16.9 16.7

Brace 0 18.0 19.0 18.8 18.6 19.1 18.975 16.8 16.9 16.5 16.8 16.8 16.8150 16.8 16.7 16.6 16.7 16.8 16.7

Average 16 8 16 7 16 8

T a b l e 2 . 1

U l t r a s o n i c a l l y m e a s u r e d w a l l t h i c k n e s s e s

W e l d P r o c e s s Semi Automatic M A GW e l d C o n s u m a b l e Oerlikon Fluxocord 42 / O P IT T

P r e / P o s t h e a t 125°C for lh30mH e a t I n p u t <2.5KJ/mm

P W H T 620°C for Ih

T a b l e 2 . 2

S e a m w e l d i n g d e t a i l s

- 154 -


W e l d C o n s u m a b l e Oerlikon Tenacito 75P r e / P o s t h e a t 125°C

H e a t I n p u t <1.5KJ/minP W H T None

T a b l e 2 . 3

I n t e r s e c t i o n w e l d d e t a i l s

Weld Leg Lengths (mm iDistance from Test I Te.st 2 Te.st 3Saddle (mm) Upper\Lower Upper Lower Upper Lower

-150 20 24 30 28 21 24-75 26 30 30 28 30 30

Brace 0 20 30 32 29 28 3075 23 24 27 27 25 25150 27 24 26 28 20 20

Average 24.8 28 .5 25 .3-150 12 14 12 11 12 10-75 10 15 11 12 10 8

Chord 0 10 8 13 12 15 675 10 13 16 15 15 11150 15 15 16 14 8 10

Averai^e 12.2 13.2 10.5

Weld Leg Lengths (mm)Distance from Test 4 Te.st 5 Te.st 6Saddle (mm) Upper Lower Upper Lower Upper Lower

-150 24 25 26 25 27 26-75 27 28 26 30 24 27

Brace 0 28 30 28 29 26 2975 24 24 28 25 28 26150 24 23 27 26 27 26

Average 25.7 27 26 .6-150 9 9 10 9 11 12-75 9 10 9 8 10 11

Chord 0 8 4 7 10 9 1175 5 8 11 8 8 9150 10 10 10 10 10 10

Average 8.2 9.2 10.1

T a b l e 2 . 4

W e l d l e g l e n g t h s

- 155 -


S E 7 0 2 C h e m i c a l C o m p o s i t i o n %

E l e m e n t S p e c i f i e d C U A n a l y s i s U C L A n a l y s i s

C <0 .14 0.125 0.12Mn < 0 .9 1.1 1.05Si < 0 .3 0.256 0.25S <0.004 <0.0005 <0.001P <0.01 0.007 0.009

Ni < 1 .5 1.404 1.34Cr < 0 .7 0 . 4 6 1 0.51Mo <0 .55 0.474 0.48B <0.003 0.0012V <0.05 0.008 0.02

Cu - 0.185 0.19Sn - 0.003A1 - 0.069 0.08T i - 0.003 <0.01Co - 0.011 0.01Nb - 0.004 <0.01As - 0.007Pb - 0.003

T a b l e 2 . 5 .

C h e m i c a l c o m p o s i t i o n o f S E 7 0 2

M a t e r i a l a y ( M P a ) U T S ( M P a ) E l o n j ^ a t i o n ( % )

SE702 700 min 790 / 940 16

T a b l e 2 . 6

M e c h a n i c a l p r o p e r t i e s o f S E 7 0 2

S p e c i m e n N o . ( j y ( M P a ) U T S ( M P a ) R e d u c t i o n i n

A r e a ( % )

E l o n } > a t i o n Y i e l d R a t i o

( a y / U T S )

1 755 823 66 21 0.922 744 813 61 20 0.913 744 807 65 20 0.924 750 816 64 20 0.925 750 815 64 20 0.92

A v e r a g e 748 815 63 20 0.92

T a b l e 2 . 7

M e a s u r e d m e c h a n i c a l p r o p e r t i e s

- 156


T e m p e r a t u r e ( ° C ) S p e c i m e n C h a r p y E n e r g y , J

Room Temp S I 149S2 152

-40 S3 127S4 112

-60 S5 92S6 79

T a b l e 2 . 8

S E 7 0 2 C h a r p y t e s t d a t a

L o c a t i o n H a r d n e s s ( H v )

Parent Plate =250H A Z 272 -> 374

Weld Metal 252 ^ 297

(i) Creusot Loire Data(5 Kg Load)

W e l d M e t a l C G H A Z P A R E N T

S p e c i m e n C A P R O O T C A P R O O T

A v e r a g e 1 305 249 392 311 2532 305 253 389 300 260

R a n g e 1 276 - 336 2 4 5 -2 5 1 373 - 409 262 - 363 242 - 2682 260 - 336 247 - 258 363 - 401 272 - 345 243 - 274

S a m p l e S i z e 1 10 4 8 10 112 10 4 9 10 11

(ii) Cranfield Data

(10 kg Load)

T a b l e 2 . 9

S E 7 0 2 H a r d n e s s d a t a

- 157-


P r o b e P o s i t i o n ( m m ) P r o b e P o s i t i o n ( m m )

1 -150 17 22 -135 18 63 -120 19 104 -105 20 155 -91 21 216 -78 22 287 -66 23 368 -55 24 459 -45 25 5510 -36 26 6611 -28 27 7812 -21 28 9113 -15 29 10514 -10 30 12015 -6 31 13516 -2 32 150

T a b l e 2 . 1 0

A C P D p r o b e s i t e l o c a t i o n s

E x p e r i m e n t a l S C F

S p e c i m e n N o . T o p S a d d l e B o t t o m S a d d l e A v e r a g e % D i f f e r e n c e

C l 12.1 13.9 13.0 12.94C2 11.9 12.5 12.2 4.80C3 11.2 13.2 12.2 15.15C4 11.5 11.9 11.7 3.36D1 9.8 10.0 9.9 2.00D2 10.1 9.8 10.0 2.97

T a b l e 2 . 1 1

E x p e r i m e n t a l S C F R e s u l t s f r o m p r e v i o u s t e s t p r o g r a m m e u s i n g . s a m e g e o m e t r y

- 158 -


T l T2E x p e r i m e n t a l S C F V a l u e

T3 T4 T5 T6M i n .

M a x .

A v e .

10.92 9.29 11.48 10.96 11.24 10.32

11.49 11.63 10.34 12.13 11.76 12.54 11.16 12.75 11.7 12.3 10.69 12.41

P a r a m e t r i c S C F P r e d i c t i o n s

Efthymiou & Durkin (Fixed) 11.65Efthymiou & Durkin (Pinned) 13.23

Wordsworth & Smedley 13.96UEG 14.16

Hellier, Connolly & Dover 17.85

T a b l e 2 . 1 2

E x p e r i m e n t a l S C F R e s u l t s a n d P a r a m e t r i c P r e d i c t i o n s

O r i g i n a l P r o g r a m m e R e v i s e d P r o g r a m m e

T e s t E n v i r o n m e n t C . P . f ( H z ) ( ^ H S E n v i r o n m e n t C . P . /( M P a ) ( m V ) ( M P a ) ( m V ) ( H z )

T l 400 A ir - 1T2 300 A ir - 1T3 225 Sea Water -1000 0.214 225 Sea Water -800 0.2T5 180 Sea Water -1000 0.2 300 Sea Water -1000 0.2T6 180 Sea Water -800 0.2 300 Sea Water -800 0.2

T a b l e 2 . 1 3

O r i g i n a l a n d R e v i s e d T e s t P r o g r a m m e D e t a i l s

- 159-


E x p e r i m e n t a l 5 0 D M e a n R e d u c t i o n F a c t o r

T e s t S t r e s s ( M P a ) N s N _ i p N M

T l 400 73,000 137,000 1.87T2 300 180,000 324,000 1.80T3 225 395,000 768,000 1.94T4 225 548,000 768,000 1.40T5 180 2,246,000 1,500,000 -

( Run Out)T5 (Re-test) 300 130,000 324,000 -

T6 300 138,000 324,000 2..348

T C u r v e P r e d i c t i o n s

S t r e s s ( M P a ) A i r C u r v e S e a W a t e r & C P 1 6 m m 5 0 D M e a n

400 45,800 23,400 137,000300 111,000 55,400 324,000225 263,000 131,000 768,000180 513,000 257,000 1,500,000

T a b l e 2 . 1 4

S - N D a t a f o r S E 7 0 2

T e s t N o . C o n d i t i o n s N i N t N i / N t

T l 400MPa (A ir) 13,000 74,000 0.176T2 300MPa (A ir) 24,000 180,000 0.133T3 225MPa (-lOOOmV) 115,000 194,000 0.292T4 225MPa (-800m V) 105,000 548,000 0.192T5 180MPa (-lOOOmV) Run Out - -

T6 300MPa (-800m V) <10,000 138,000 <0.072

T a b l e 2 . 1 5

S u m m a r y o f I n i t i a t i o n d a t a f o r a l l t e s t s

T e s t

E q u i v a l e n t H o t

S p o t S t r e s s

R a n g e ( M P a )

E n v i r o n m e n t N i / N t N t

( C y c l e s )

Y1 180 A ir 0.291 2,130,000Y2 260 -800mv Ag/AgCl 0.026 380,000Y3 200 -800mv Ag/AgCl 0.032 1,545,000Y4 200 -lOOOmv Ag/AgCl 0.158 1,140,000

T a b l e 2 . 1 6

E x p e r i m e n t a l R e s u l t s f o r P a r a l l e l V a r i a b l e A m p l i t u d e S t u d y o n S E 7 0 2 Y j o i n t s

- 160-


16mm324mm

a = 7 .26 p = 0.71

Y = 14.28

1660mm

0457mm

F i g u r e 2 . 1

N o m i n a l . s p e c i m e n d i m e n s i o n s f o r t u b u l a r w e l d e d T j o i n t

S e a m w elds from Tube fabrication

F i g u r e 2 . 2

P o s i t i o n o f . s e a m w e l d s i n t u b u l a r T j o i n t s

- 161 -


F i g u r e 2 . 3

P h o t o g r a p h s o f t y p i c a l s e a m w e l d a n d i n t e r s e c t i o n w e l d

Brace

Chord

Chord Leg length

Brace Leg length

F i g u r e 2 . 4

D e f i n i t i o n o f w e l d l e g l e n g t h s

- 162-


R e a c t ion F ra m eActuator

S p e c i m e n

Sw ive l H e a d C o n n e c te r

F i g u r e 2 . 5

I s o m e t r i c v i e w o f t e s t r i g

Field In Field Out

F i g u r e 2 . 6

A C P D t h e o r y a r u l n o t a t i o n

- 163 -


18 +

16 +

8 +

6 +

4 +

2 +

■150 -100 ■50 50 100 1500Distance From Saddle (mm)

F i g u r e 2 . 7

T y p i c a l u n - t n o d i f i e d A C P D c r a c k d e v e l o p m e n t d a t a

■50 0 50

Distance From Saddle (mm)

F i g u r e 2 . 8

T y p i c a l m o d i f i e d A C P D c r a c k d e v e l o p m e n t d a t a

- 164-


INSTRON Mini Controller

PC Test Control

U10 Crack Microguage

Ctiiller

Poter

Sea Water Resevior

Environment Ctiamber

Sea Water Loop

CP Working ElectrodeCP Counter Electrode CP Reference Electrode Cooling Circuit

ACPD Wiring

Test Control Circuit

F i g u r e 2 . 9

E x p e r i m e n t a l t e s t s e t u p

Actuator Swivel Head Connector Specimen

■i r l - — “ '

F i g u r e 2 . 1 0

T e r m i n o l o g y f o r s p e c i m e n / a c t u a t o r a l i g n m e n t p r o c e d u r e

- 165-


W e l d

1 0 m m

R e m o t e Brace Site

1 0 m m

R o s e t t e G a u g e

F i g u r e 2 . 1 1

S t r a i n G a u g e p o s i t i o n s f o r e x p e r i m e n t a l s t r e s s a n a l y s i s

14 --

12 - -

A10 - -

6 - -

4

150 1800 30 GO 90 120Angé Around Intersection (deg)

F i g u r e 2 . 1 2

E x p e r i m e n t a l s t r e s s a n a l y s i s r e s u l t s

------------- HCD Distribution

- - - - JA Distribution

- 1 6 6 -


Ï

-m -------- 50 0 16mm mean

---------- T A ir Curve

r C P Curve

■ Test1

* Test 2

A Test 3

• Test 4

□ Test 5 (Run-out)

X Test 5 (Re-Test)

Test 6

1 00E«O6 L ie (Cycles)

F i g u r e 2 . 1 3

S - N d a t a f r o m t u b u l a r j o i n t t e s t s o n S E 7 0 2 .

18

cxP0.10

03

L

O Raw Data

Smoottied Data

10000 20000 30000 40000 Cycles. N

50000 60000 70000 80000

Figure 2.14Crack growth cur\>e for Test ‘Tl ’

- 167-


20

10 --

Primary Crack16 --

14 --

t:5 Secondary CrackÜ

I6 - •

4 --

2 --

0 20000 40000 60000 160000 18000080000 100000 120000 140000

O Raw Data

Smoothed Data

Cycles, N

F i g u r e 2 . 1 5

C r a c k g r o w t h c u r v e f o r T e s t ‘ T 2 ’

20

18 ■■

16 --

14 -•

r :6 - •

4 --

2 -•

0 100000 150000 250000 350000 400000200000 300000

O Raw Data

Smoothed Data

Cycles. N

Figure 2.16Crack growth curve fo r Test ‘T3 '

- 168 -


16 --

14 --

12 - -

Defect 1Defect 2

B --

4 --

2 --

4iunuii[niHinnfl300000

Cycles, N

F i g u r e 2 . 1 7

C r a c k g r o w t h c u r v e s f o r T e s t ‘ T 4 ’

Smoothed DataO Raw Data

20

18 --

16 --

14 --

I 12 --Î

2Or -

6 --

4 --

2 --

0 20000 120000 14000040000 60000 80000 100000

O Raw Data

Smoothed Data

Cycles, N

Figure 2 .18Crack growth curve fo r Test ‘T 6 ‘

169-


20

18 --

14 --

:1 0 --

Q 8 --

6 ■ -

4 --

2

D T I

# T2 - Primary

X T2 - Secondary

AT3O T4 - Defect 1

X T 4 -D e te c t 2

0 T 5 (Re-Test)

+ T6

300000 Cycles, N

F i g u r e 2 . 1 9

C o m p a r i s o n o f C r a c k G r o w t h C u r v e s

1.00E-06

I 1.00E-07-J

I i □ T1

1g 1.00E-08Ü

I1.00E-09

0 0.2 0.8 1 1.20.4 0.6

Normalised Crack Def^h, a/t

Figure 2 .20Crack Growth Rates recorded during Test T l

170-


1 .OOE-06

□□□□□□□□□□ ° ° ° °

1.00E-07AA

f-R 1.00E-08

.OOE-090 0.2 0.4 0.6 0.8 1 1.2

Normalised Crack Depth, a/t

F i g u r e 2 . 2 1

C r a c k G r o w t h R a t e s r e c o r d e d d u r i n g T e . s t T 2

□ T2 - Primary

A T 2 - Secondary

1.00E-06

1.00E-07 -■

cc

S 1 .00E -08 -

1.00E-09

f

0.2 0.4 0.6 0 .8

Normaised Crack Depth, a/t

□ T3

Figure 2.22Crack Growth Rates recorded during Test T3

- 171 -


1.00E-06

ÎI

1.00E-07 --

1.00E-08

1.00E-09

□ T4 - Pnmary

^ T 4 - Secondary

H—^ —'—'—I—'—'—'—'—I—'—'—'—'—I—'—'— '—'—h 0.2 0.4 0.6 0.8 1


F i g u r e 2 . 2 3

C r a c k G r o w t h R a t e s r e c o r d e d d u r i n g T e s t T 4

1.00E-05

K 1.00E-06

S 1.00E-07

I 1 .0 0 E -0 8 -:

1 .OOE-09

0 0.2 0.4 0.8 1.2 1.40.6 1


Figure 2.24Crack Growth Rates recorded during Test T6

□ T6

172


1 .OOE-05

^ 1.00E-06

T l

12 - Primary

13

14 - Primary

T5 (Re-test)

16

& 1.00E-07

so 1.00E-08

1 .OOE-090.4 0.6 0.8 1

NotmaSsed Crack Depth, a/t

F i g u r e 2 . 2 5

C o m p a r i s o n o f C r a c k G r o w t h R a t e

1.4 -■

1.2 -■

II O .S ..

,1

0.4 --

0.2 -■

-50 -40 -30 -20 30 50-10 10 20 400

Distance from Saddle (mm)

F i g u r e 2 . 2 6

E a r l y c r a c k g r o w t h p r o f i l e s s h o w i n g i n i t i a t i o n i n a t y p i c a l T e s t

173


0.6

0.5 --

0.4

□ Raw Data

Smoothed Data0.3 - -

Test T1

< 0.2 - -

0 .1mm

0 2000 4000 18000 200006000 8000 10000 12000 14000 16000

Cycles, N

F i g u r e 2 . 2 7

E a r l y c r a c k g r o w t h d a t a s h o w i n g i n i t i a t i o n i n a t y p i c a l T e s t

0 30

0 25 -

0 20

0.15

0 10

005

000150 200 250 300 350 400 450

Hot Spot Stress Range (MPa)

F i g u r e 2 . 2 8

R a t i o o f i n i t i a t i o n t o t o t a l f a t i g u e l i v e s

- 174 -


300 (Air)225(-1000mV)

Hot Spot Stress (MPa) 225 (-SOOmV)

Propagation

F i g u r e 2 . 2 9

I n i t i a t i o n t o p r o p a g a t i o n l i v e s n o r m a l i s e d t o t h e T c u r v e

1000

1 OOE+04 1 OOE+05 1 OOE+06 Endurance (Cycles)

1 OOE+07

50D 16mm mean

V Air Curve

V C P Curve

o Initiation Life

o Total Life

1 OOE+08

F i g u r e 2 . 3 0

G r a p h i c a l r e p r e s e n t a t i o n o f t h e r a t i o o f i n i t i a t i o n t o p r o p a g a t i o n l i f e

- 175 -


5III

f^>fm/ttiMdCrnck Deiih»

F i g u r e 2 . 3 1

C r a c k s h a p e d a t a

^ T? • Pnmarv

- # • T2 ■ Secrndary

- O -T 4 D * ia c i2

- 1 7 6 -


1000

S100

500 16mm mean

T' Air Curve

T 'C .P . Curve

T5 (Run Out) T5 (Re-lest) T6

Y3Y4

1.00E+04 1.00E+05 1.00E+06 Endurance (Cycles)

1.00E+07 1.00E+08

F i g u r e 2 . 3 2

S - N C i i r x ’e . s h o w i n g a l l S E 7 0 2 t u b u l a r j o i n t d a t a

- 177 -


1000

O Axial

Axial (Moan)

A OPB

- - - -OPB (Moan)

1.00E+05 1.00e*06 1 OOE+07 1.00E+08Fatigue Life, (cycles)

F i g u r e 2 . 3 3

D i f f e r e n c e b e t w e e n a x i a l a n d O P B l o a d i n g m o d e s f o r 5 0 D s t e e l s

2.5 --

I ...

Io 1.5 ■-U5

0.5 --

500 6000 100 200 300 400

-OPB/Axial

Hot Spot Stress(MPa)

F i g u r e 2 . 3 4

L i f e C o n v e r s i o n F a c t o r s f o r a x i a l t o O P B l o a d i n g m o d e s

- 178 -


1000

§ 100 ct

-

X XX

s -XX s

-X

X\X

X

I'm

«

X ,

X

\ 0X

ss

' N

X»

" N

>

XXX

—

— - - - 50D 16mm mean

T' Air Curve

— — T 'C .P . Curve

A T Modified

# Y Joint

— - -O P B Mean

1 1 I 1 1 M i 1101.00E+04 1.00E+05 1 OOE+06

Endurance (Cycles)

1 OOE+07 1.00E+08

F i g u r e 2 . 3 5

S - N c u r v e . s h o w i n g m o d i f i e d T j o i n t r e s u l t s u . s i n g l o a d i n g m o d e m o d i f i c a t i o n f a c t o r

- 179-


« 100 cc

- - - 5CID 115mrn n

N,X

N ■— T' C.P. Curve

1 T1X

- -

•«A

T2T3T4T5 (Run Out)T5 Re-test T6

1 Y1 Y2 Y3 Y4

1 Austin 1 Vinas-Pich SOD

VInas-Pich 4S0F

" XX

XX

c

N,A

X+X0

V * N

à > ►- o

X

X

N

-

oA«

9

X

s

1.00E+06

Endurance (Cycles)

F i g u r e 2 . 3 6

C a m p a r i . w n o f r e s u l t s w i t h n o m i n a l l y i d e n t i c a l . ' s p e c i m e n s m a d e f r o m l o w e r s t r e n g t h . s t e e l s

- 1X0-


- - - SOD 16mm mean----------- T'Air Curve----- — T'C.P. Curve

■ T1• T2♦ 13 A 14X IS (Run Out)+ T5 Re-test X T6 □ Y1 O Y2 O Y3 A Y4+ CP Database

X

XX

s- V

' " xX

X Nci

X ,A

s.s.

4

sV 4

jf.

Ns X

s

1 OOE+06 Endurance (Cycles)

1 OOE+07

F l i r e 2 . 3 7

C o m p a r i s o n o f r e s u l t s w i t h r i o t a b a s e o f c a t h o d i c a i i y p r o t e c t e d 5 0 D s p e c i m e n s

- 180a-

Chapter 3 - Stress Concentrations in Tubular Joints with Rack / Rib Plate

Chapter 3

3. Stress Concentrations in Tubular Joints with Rack / Rib

Plate Stiffened Chord Members Using The Finite Element

Method

3.1 Introduction

It is known that stiffener plates can have a large effect on the stress concentration

factors found at the intersection of welded tubular joints. The strong relationship

between the fatigue life of these tubular joints and the stresses experienced at the

intersection make the accurate knowledge of the SCF’s in this region of crucial

importance. The current investigation aims to quantify the effect of the central

stiffener plate often found in jack up leg chords. The results of almost 400 finite

element models are presented in this Chapter. The common chord configurations

used in jack up leg design were detailed in Chapter One. Due to the variety of

chord configurations it will not be possible to study every case. Instead some of the

most popular chord designs will be studied extensively. Stress analysis work on a

geometry with this kind of stiffener has not previously been published. However

several other stiffener configurations have been investigated and these are

discussed in Section 3.3.

3.2 Scope

Three primary chord designs are to be investigated. The first consists of a tubular

brace to chord connection with a plate stiffener of constant thickness running the

length of the chord as shown in Figure 3.1. This is a first approximation to some

of the most common brace to chord joints found in jack up truss legs. Secondly a

more complex and more realistic chord design containing two distinct stiffener

sections, known as the rack and rib plates will be studied. This design is shown in

181 -


Figure 3.2. The third case represents the extreme of the second design where the

thinner central section of the stiffener is completely removed. This design is shown

in Figure 3.3. Each design will be discussed in more detail in Section 3.7.

Initially a single set of joint parameters will be studied for T and Y shaped joints in

order to reduce the number of variables. Axial, In Plane and Out of Plane Bending

loadcases will be investigated. The chord and brace thickness are both 20mm and

all other dimensions are based on a chord diameter of 0.6m. The joint parameters

are as shown in Table 3.1.

Once the effect of the stiffener is reasonably well understood, an attempt will be

made to quantify it across the range of joint parameters for which the Hellier,

Connolly, Dover parametric equations are valid [3.1].

Finally the mechanism by which the stiffener affects the changes will be

investigated using evidence gained from applying various translational and

rotational restraints to the chord surface of an unstiffened joint along the line where

the central plane of the rack plate would intersect if it were present.

AH the results presented here are from the chord side of the intersection as these

are the highest values, unless stated otherwise.

3.3 Stress Analysis of Stiffened Tubulars

Much effort has been concentrated on determining the SCF formulae for simple

tubular joint configurations subject to different loading conditions. The significant

contributions to this field by Kuang [3.2], Wordsworth and Smedley [3.3],

Efthymiou and Durkin [3.4] and Hellier, Connolly and Dover [3.1] were discussed

in detail in Chapter 1.

182 -


In addition to this work on simple joint configurations, significant research effort

has been focused on the behaviour of tubular joints with ring stiffened chord

members. Such joints are quite common as internal ring stilTeners provide a cheap

and effective solution to punching shear problems in design. A tubular joint

reinforced with ring stiffeners is shown in Figure 3.4.

Amongst the most significant works in this area is that of Dharmavasan and

Aaghaakouchak [3.5] who showed that in the case of axial and OPB loading,

careful positioning of the stiffeners greatly reduces the stress concentrations and

gives a more uniform distribution of the stresses around the intersection. Various

stiffener configurations and stiffener sizes were analysed and recommendations

made on the optimum designs. It was shown that stiffener height has a more

significant effect on SCF than the stiffener thickness leading to the conclusion that

the moment of inertia of the stiffener is the main factor in controlling the SCF’s.

The use of very tall thin stiffeners was warned against as this results in significant

SCF’s in the stiffener. This situation should be avoided since access to the stiffener

for inspection and repair purposes is likely to be difficult if not impossible. A

minimum stiffener thickness equal to the brace thickness was postulated.

The most effective position for ring stiffeners was found to be dependent on the

loading mode. For axial and out of plane bending the middle half' of the plug is the

optimum position. For in plane bending the optimum positions are the outer

quarters of the plug although it is noted that the stiffeners are less effective at

reducing the SCF’s for this load case. The use of a single stiffener at the saddle

position is not recommended since it produces a region of high local stiffness

through which a high proportion of the load is transferred causing high SCF’s on

the chord and brace side.

An attempt is made to predict the SCF’s in the stiffened tubulars using the Ky

correction factor to account for the increased chord inertia when using parametric

- 183 -


equations detailed in [3.6] based on a recommendation by Lloyds Register of

Shipping [3.7]. The modified value of y is given by (3.1).

r =D

2 K J

K^ =(T e \

Axial Loading

OPB Loading

IPB Loading

(3.1)

Using the parametric equations by Wordsworth et al to calculate the SCF for the

chord side and Kuang et al for the brace side, it was found that this method

produced a reasonable estimate of the SCF’s in the ring stiffened tubulars provided

that the stiffeners were located in the optimum positions. It was noted that the

value for Ky for OPB loading should be modified to the same value as for axial

loading for a more accurate representation. In addition, the effect of the stiffeners

for IPB was even less than predicted using the exponent of 0.3.

Further finite element analysis of ring stiffened tubular joints has been undertaken

by Ramachandra et a /.[3.8]. In addition to the numerical analysis, experimental

static and fatigue tests were performed on large scale welded tubular joints. The

conclusions from Dharmavasan et al regarding the optimum size and configuration

for the stiffeners were essentially confirmed. Ramachandra et al have also

produced a set of parametric equations claiming to provide SCF’s for ring stiffened

T and Y joints for both the brace and chord side under each of the three modes of

loading. Concern must be noted about the fact that these parametric equations are

based on the results of only 135 FE models. Closer inspection of these equations

shows that the parameters used do not follow the standard joint parameter

definitions. Indeed it appears that parameters such as the chord length are not even

184


considered. It is suggested that these equations should be treated with some

caution until further validation has been performed.

Seetharaman et al [3.9] have also produced similar Imite element results to

Dharmavasan et al confirming the importance of stiffener position for maximum

benefit.

An alternative and common solution to punching shear problems is the use of

doubler plates. Doubler plates are generally used when the chord diameter is such

that the fabricator is not able to gain access to the interior of the chord to weld the

stiffener plate in position. A tubular joint reinforced with a doubler plate is shown

in Figure 3.5.

Soh and Soh [3.10] have performed important initial work in this area. Doubler

plates have shown their usefulness when dealing with axial compression but little

was known about their response under other loading conditions. Extensive FE

analysis on representative tubular joints with a range of doubler plate sizes led to

the conclusion that joints reinforced with a doubler plate are not subject to more

severe fatigue problems compared to the corresponding unreinforced joints

provided that certain conditions regarding the doubler plate sizes are met. These

criteria essentially govern the doubler plate thickness and state that the doubler

plate thickness should approach that of the chord and should be no more than

approximately 1.4 times the brace thickness.

The only work on stiffener configurations similar to those under investigation here

was concerned with the ultimate strength of these joints rather than the stress

concentration factors experienced at the intersection of the brace and chord. The

study was conducted by Matsuishi et al [3.11]. Despite the differing aims of the

investigations it is worthwhile summarising the salient points of this work as the

geometric similarity mean that some of the conclusions are of direct interest here.

185 -


The leg guides, detailed in Chapter One have been shown to increase the ultimate

strength of unstiffened T joints by 30 to 40 %. Leg guides have not been

incorporated in the current study but this result shows that this is an area of study

that is likely to show a significant effect on the SCF distribution at the intersection.

Furthermore, the addition of a centre plate increased the ultimate strength of a T

joint over an unstiffened joint supported by a leg guide by a further 20%.

Longitudinal chord stiffeners have also been investigated by Choo for X joints

[3.12]. The stiffeners in this case however have more in common with the ring

stiffeners or doubler plate techniques as they are proposed as a solution to

punching shear problems. The stiffeners, although longitudinal are turned through

90° in order to provide a direct load path from brace to brace. In addition the

stiffeners are not continuous along the chord length but instead local to the brace.

3.4 Mesh Generation for Tubular Joints with Longitudinal Stiffeners

The large number of possible variables (e.g. joint and stiffener dimensions,

boundary conditions etc.) necessitate the creation and solution of a large number of

finite element models. Two finite element packages, IDEAS and ABAQUS were

evaluated for this work. IDEAS (Integrated Design Engineering Analysis

Software) [3.13] is an integrated package of mechanical engineering software

tools, including finite element modelling application. ABAQUS [3.14] is a well

established dedicated finite element analysis package. ABAQUS operates in a

‘batch’ mode and does not therefore have the interactive interface offered by

IDEAS. All model information, including nodal and element definitions are

included in an input data file which is generated ‘off-line’. The criteria used for the

selection of the package to be used during this study were based around the degree

of automation that it is possible to introduce to the mesh generation, model

- 186


solution and results extraction and evaluation phases. This was necessary to ensure

the maximum amount of information was obtained from the limited time available.

It was discovered that the ABAQUS batch mode of operation lent itself more

readily to automation of the process. ABAQUS and a similar package PAFEC have

been used extensively in the past within the Department of Mechanical Engineering

at UCL. As a result FORTRAN programs existed to produce ABAQUS model

input files for a tubular joint. In addition it is possible to request a text file

containing the results at the nodes of interest. This avoids the need of manually

extracting the results using a post processor. It was concluded that ABAQUS was

the most the appropriate package for the current study.

The mesh generator was originally written by Dharmavasan [3.15] for the study of

simple T and Y joints. Modifications were subsequently made to the program by

Chang [3.16]. The program allows the user to input the joint dimensions and the

number of elements to be formed around the chord - brace intersection. The degree

of mesh refinement is controlled by the number of elements at the intersection.

Although the framework of the mesh generator was available, several major

modifications were needed. Firstly, subroutines were added to generate the nodes

and elements on the chord stiffener. Secondly it was discovered that the program

did not work for certain joint shapes, namely all joints with an angle between the

brace and chord of less than 89°. Modifications to the way the program used

triangular elements around the intersection solved this and the program now

reliably handles all T and Y tubular joint shapes. The tinal major modification

involved the addition of subroutines to transform the model from S4R5 f ABAQUS

4 noded thin shell elements) to S8R5 fABAQUS 8 noded thin shell elements).

Geometry considerations required the use of a small number of 6 noded triangular

elements, known as STRI65, primarily in and around the plug region. The ability to

replace some or all of the S8R5 thin shell elements with S8R thick shell elements

was also included in the program. Further smaller additions were made enabling the

- 187 -


program to output a complete ABAQUS input file with no further user editing.

This included the assignment of material properties and thickness to the elements,

application of all loading and boundary restraint conditions and specification of all

output variables.

The loads are automatically scaled by the program to give a unit nominal stress for

all load cases. This enables the stress concentration factors to be read directly from

the output file. This saves significant time in the processing of the results.

A simple FORTRAN program was written to extract the principal stresses for the

inner and outer surfaces at the points of interest from the ABAQUS results file.

Specifically this means all nodes along the intersection for the chord and brace side.

The data for these nodes are then automatically written into a much smaller and

more manageable text file in a spreadsheet readable format to facilitate the later

analysis of the results.

Chang [3.16] noted an effect of brace length during his study of SCFs’ in X and

DT joints. He noted that there exists a critical ratio of brace length to brace

diameter, beyond which the brace length has little effect. He recommends the use

of brace lengths which are at least 0.4 times the chord length. All brace lengths

used in the current study comfortably meet this criteria.

The eight noded thin shell elements, S8R5 are reduced integration, doubly curved

shells with 5 degrees of freedom, three translational motions, x, y, and z, and two

in surface rotations. The 8 noded thick shell elements are also reduced integration,

doubly curved shells but with 6 degrees of freedom, three translational motions and

three rotational degrees of freedom, (j) , ({)y, and (|)z.

Shell elements are recommended for use when the shell thickness is less than 10%

of the main global dimension, typically the diameter or radius of curvature. Based

on shell theory they approximate the three dimensional continuum to two

188 -


dimensional theory and have been widely used for analysis of tubular joints. There

are two types of shell elements, known as thick and thin. The choice of which

element type to utilise depends on the importance of shear deformation in the

structure under investigation. The importance of shear deformation generally

increases with increasing ratio of wall thickness to chord diameter Prior to

commencing this investigation many of the models were solved using both thick

and thin shell elements. In each case the difference was less than 1%. For this

reason thin shell elements have been used in this investigation.

An often noted drawback of using thin shell elements to model tubular joints is the

lack of any weld detail. In addition, as shell elements are essentially two

dimensional, possessing thickness in a mathematical sense only, we are effectively

modelling the mid-planes of each tubular. This fact becomes significant at the

intersection of brace and chord resulting in the stresses being calculated at a point

which is not coincident with the weld toe. This error has been found to be quite

small for the chord side but can be significant on the brace side of the intersection.

This point was discussed in some detail in Chapter 1.

A sample mesh is shown in Figure 3.6. Note the refinement of elements around the

stiffener where the stress gradients are greatest and the gradual coarsening of the

mesh remote from this region where the stresses become more uniform. Careful

positioning of the nodes allows the stretch and distortion of the elements to be

reduced to a minimum. Since triangular shell elements are less accurate than

quadrilateral shell elements, their use has been kept to a complete minimum.

Triangular elements are only used where necessary due to reasons of geometric

compatibility around but some distance from the intersection and within the plug

region. Generation of a typical mesh takes just a few seconds and a complete

solution for an average model containing 858 elements can be obtained in 45

seconds of CPU time. AH analysis was performed on a DEC Alphastation

255/233MHZ.

189 -


3.5 Boundary Conditions

Symmetry of the model in the X Y plane allows a half model analysis to be

performed providing the correct boundary conditions are applied to the nodes on

the plane of symmetry. Reducing the size of the model in this manner saves

significant CPU time and disk storage space. ABAQUS provides a ZSYMM

function to allow the automatic application of the appropriate translational and

rotational restraints to simulate symmetry in the Z direction. The constraints

imposed on aU nodes on the plane of symmetry are zero displacement in the z

direction and aU rotations associated with the thin shell elements are fixed at zero.

For chord designs containing a stiffener that passes through the whole of the chord

diameter, the same symmetry boundary conditions are applied to the stiffener.

Stiffener designs where the plate is not continuous through the chord (see Figure

3.3)have no symmetry boundary conditions applied at the free edge.

The symmetry conditions are violated for the Out of Plane Bending loading

condition, but Hellier et al [3.1] discovered that it is still possible to use half joint

meshes with acceptable accuracy by restraining in plane displacements.

The chord ends are modelled as ‘built-in’ with all degrees of freedom being

restrained. No boundary conditions are applied to the brace end other than the

distributed external loads applied at each node.

3.6 Convergence and Model Verification

Prior to any comprehensive investigation of any particular geometry, care must be

taken that the model is behaving as would be anticipated. Primarily this involves a

convergence study to ensure that the mesh density is sufficient to accurately predict

the stresses at the points of interest. In the case of a tubular joint, this region is

usually the intersection of the brace and chord. A steep stress gradient exists within

this region and the stresses can be erroneously predicted if the mesh is too coarse.

- 190 -


On the other hand, too tine a mesh will waste computational effort and therefore,

time and money. A preliminary study was implemented to ensure that mesh density

at the intersection was sufficiently fine. Models with 12, 16, 20 and 24 elements

around the intersection were solved. The results are shown in Table 3.2.

3.7 Finite Element Investigation

3.7.1 Effect of Rack Plate Thickness on SCF Distribution

Several stiffener plate thicknesses of up to 1/3 of the chord diameter have been

investigated and the SCF results around the intersection on the chord side are

presented here. Each of the stiffeners had a constant thickness and was continuous

through the chord diameter. The investigation covered both T and Y joints under

Axial, IPB and OPB loading modes. This stiffener type is illustrated in Figure 3.1

3.7.1.1 ResultsThe SCF distribution around the intersection for axially loaded T and Y joints are

shown in Figures 3.7 and 3.8 respectively. It is noted that the shape of the SCF

distribution around the intersection remains essentially unchanged by the presence

of a stiffener except for the case of a Y joint under axial loading. In this instance

the distribution becomes slightly skewed as the hot spot stress site moves away

from the saddle with the introduction of thicker stiffeners. Even the thinnest

stiffeners produce very significant reductions in peak SCF for both joint shapes.

For comparison purposes. Figures 3.9 and 3.10 present the SCF distribution as the

SCF found in the stiffened joint, normalised against the SCF at the corresponding

angular position around the intersection in the unstiffened joint. It can be seen that

hot spot SCF, i.e. highest SCF around the intersection, for each stiffener thickness

is significantly lower than that of the unstiffened joint. The SCF at the crown is

however greater than that found in the unstiffened joint for both joint shapes. This

increase is not significant in terms of fatigue design as it is considerably lower than

the hot spot SCF. The SCF at the crown appears to be almost independent of

- 191


Stiffener thickness except for the very thickest stiffener. In this instance there is

some evidence of a flattening of the SCF distribution with the SCF at the crown

decreasing and interestingly a slight increase in the SCF at the saddle. This

phenomenon is seen in both joint shapes.

When the same T and Y Joints are subjected to IPB loading the stiffener appears to

have little or no effect. Figures 3.11 and 3.12 illustrate the insensitivity of the

intersection SCF’s to the thickness of the rack plate. In the light of this discovery,

IPB loadcases will not be considered any further in this section.

Out of plane bending is more interesting. Figures 3.13 and 3.14 show the

distribution of SCF around the intersection for the T and Y joints respectively.

Again the SCF distribution for the unstiffened joint is included for comparison. As

would be expected, the SCF at the crown position approaches zero and is

independent of the thickness of the stiffener. For this reason, discussion will be

centred around the saddle region where the effect of the stiffener is greatest and the

SCF highest. The SCF values normalised to the unstiffened joint SCF’s are shown

in Figures 3.15 and 3.16. Out of plane bending does not show the same tendency

towards a flatter SCF distribution for the thicker stiffeners. The SCF at the saddle

decreases with increasing stiffener thickness for all stiffener thicknesses. The

apparent large variations in the normalised SCF values at the crown positions (0°

and 180°) in Figures 3.15 and 3.16 at first appear to contradict the earlier

observation that SCF at the crown is independent of stiffener thickness for OPB

loading. However as the SCF value at the crown of the unstilïened joint is very

close to zero any small change in SCF for the stiffened joint will appear relatively

large when normalised to the unstiffened result.

The SCF data from the saddle position for T and Y joints under Axial and OPB

loading is shown in Figure 3.17. The SCF data is normalised to the peak SCF

found in the corresponding unstiffened geometry. This clearly shows the extra

effectiveness of the stiffener at reducing SCF’s under axial loading than OPB

- 192 -


loading conditions. Additionally it can be seen that the percentage reductions are

very insensitive to joint shape. Reductions of the order of 20% for OPB loading

and 40 to 50% of the unstiffened SCF for axial loading modes have been achieved.

The effect of increasing stiffener thickness rapidly converges for axial loading but

OPB loading shows a rapid initial reduction in SCF followed by a slower but linear

reduction for the three thickest stiffeners.

3.7.2 Effect of Rack and Rib Plate Geometry on the SCF

Some jack up chord designs employ stiffener plates that do not have a constant

cross section through the chord diameter. Examples of this were given in Chapter

One. The behaviour of such chords designs will be investigated here. A typical

chord design of this type is shown in Figure 3.18 detailing the notation and

terminology that will be employed to describe the variations in geometry between

individual finite element models.

The relative thickness ( tl/t2 ) and the depth, z of the rack plate (see Figure 3.18)

will be varied. The variation in the relative thickness of the two plates will be

continued up to the extreme where the thinner rib plate tends to a thickness of

zero. Although this situation is not commonly found in practice it forms a useful

extreme case as it eliminates the possibility of direct load transfer resulting from the

deformation of diametrically opposing chord surfaces. Any resistance to chord

wall deformation must then be provided by some form of bending mechanism

similar to the ring stiffeners presented in Section 3.3. This should allow an insight

into the predominant mechanisms by which the stiffener affects the changes in SCF

at the brace chord intersection.

The forces exerted on the rack plate are considerable and arise from the static

weight of the jack up barge and clamping forces within the jackhouse. This

necessitates a thick solid rack plate. By comparing the SCF’s with those of the

designs utilising a constant thickness rack plate it should be possible to evaluate the

potential for weight saving in the leg section by utilising thinner sections across

193 -


part of the chord diameter. The lack of any compressive clamping forces acting on

the rack plate in this investigation may be significant. Phenomena such as the

buckling of the thinner rib plate under the compressive clamping load are not

considered here but must of course be considered in design.

3.7.2.1 ResultsThe three major variables in this section of the investigation are the thickness of the

rack plate, t l, the thickness of the rib plate, t2 and the depth of the rack plate, z.

Each of the variables will be presented normalised to the diameter of the chord, D.

The SCF presented is the highest around the intersection. In each case the peak

SCF occurred on the chord side. The SCF is presented normalised to the SCF

found in the equivalent unstiffened tubular. This facilitates the quantification of the

relative effect of the presence of a stiffener.

Figures 3.19, 3.20 and 3.21 display the primary results illustrating the effect of a

dual thickness stiffener under axial loading. Each of the three plots represents a

different relative rack plate thickness namely tl/D ratios of 0.08, 0.17 and 0.33

respectively. Each has been plotted on the same scale for ease of comparison. Also

included on each plot is a line indicating the reduction of the peak SCF by the

presence of a stiffener of constant thickness equivalent to that of the rack plate, t l.

This enables an easy visual measure to be formed of how closely the effect of the

presence of the thinner rib plate converges towards that of the heavier continuous

rack plate.

Several trends can be identified from the normalised data. Firstly the rack plate

thickness, t l is seen to be of secondary importance. The maximum difference in

SCF between the thickest and the thinnest rack plate for any given geometry is less

than 1 % of the corresponding unstiffened SCF.

Three normalised rib plate depths of 0.2, 0.4 and 0.6 times the chord radius were

examined. The results show a reduction in SCF with increasing depth, z. The SCF

- 194


was reduced across the range of the rack and rib plate thicknesses tested here.

Again the effect is small, although noticeable and consistent. The maximum

difference in SCF between the most shallow and deep rib plates was less than 4%

of the unstiffened SCF.

The effect of the thickness of the rib plate was shown by examining four different

plate thicknesses for each combination of rack plate thickness and depth. The

normalised rib plate thicknesses of 0.002, 0.008, 0.017 and 0.033 were significantly

thinner than the rack plates. The effect of the rib plate thickness is seen to converge

rapidly in each case.

Figures 3.22, 3.23, 3.24 illustrate the same data for the OPB loadcase. Again all

plots utilise the same scale for ease of comparison. The first observation is that the

effectiveness of the stiffener in reducing the peak SCF around the intersection is

significantly reduced in comparison with the axial loadcase. The maximum

reduction is less than 20% with some stiffener configurations producing reductions

of less than 2%. The effect of the rack plate thickness is again seen to be of

secondary importance. Increasing the rack plate thickness four-fold reduces the

SCF by just a few percent.

The same range of rack plate depths and rib plate thicknesses were examined for

the OPB loadcase as the Axial loadcase. Once again, increasing the depth of the

rack plate reduces the SCF across the range of rib plate thicknesses tested. The

average reduction obtained by increasing the normalised rack plate depth from 0.1

to 0.3 is between 4% and 5% of the unstiffened SCF.

Increasing the rib plate thickness results in an almost linear decay in peak

intersection SCF. The same pattern is found across the range of rack plate depths

and thicknesses tested. This is in contrast with the axial loadcase where the effect

of the plate thickness converged rapidly. This suggests that the mechanism by

which the plate affects the changes is different for axial and OPB loadcases.

- 195 -


For both axial and OPB loadcases the results tend towards those of the continuous

thickness stiffener but do not reach it, the difference however is usually only a few

percent.

Reducing the rib plate thickness to zero represents the extreme case for this chord

design. By removing the possibility of direct load transfer between the deformed

chord walls any change in SCF must be due to the added chord wall stiffness

provided by the rack plate. The two variables in this instance are the rack plate

depth, z and thickness, tl.

The effect of the non continuous rack plate is evaluated by varying the thickness tl

and the depth z. Normalised stiffener depths , z/D of 0.1, 0.2, 0.3, 0.4, and 0.5 and

normalised thicknesses, tl/D of 0.017, 0.033, 0.083, 0.167 and 0.333 have been

investigated.

The results for the hot spot SCF are shown in Figures 3.25, 3.26. Significant

reductions in the peak SCF are achievable using this chord design. However the

reductions are not as significant as those achieved using a continuous rack / rib

plate design. The reduction in SCF with increasing rack plate thickness does not

show the very rapid convergence found in the chord designs with continuous

stiffener plates. In fact the results for the OPB loadcase do not show any sign of

convergence even with the thickest rack plates. The peak reductions of around

30% for the axial loadcase are approximately double that of the OPB loadcase.

The effect of stiffener depth z is illustrated in Figures 3.27, 3.28. For both

loadcases the SCF decreases almost linearly with increasing z. The rate of SCF

reduction with depth appears to be almost independent of the rack plate thickness,

tl.

- 196 -


3.7.3 Investigation of Mechanisms Using Boundary Conditions

In an attempt to understand the mechanism by which the presence of a rack or rib

plate affects the stress distribution in tubular joints, a number of additional models

have been analysed. These models are based on an unstiffened tubular joint but

with additional boundary conditions applied to the chord surface where the

stiffener would intersect the chord. Seven different combinations of boundary

conditions were selected and T and Y joints were modelled under axial and out of

plane bending loading conditions. The seven boundary condition cases are detailed

in Table 3.3 together with references to the figures illustrating the constraints

schematically. It is hoped that this will allow an insight in to the behaviour of the

stiffeners by mimicking their effect using applied boundary conditions.

3.7.3.1 ResuitsIt has been possible to simulate the effect of the stiffener plate by applying specific

rotational and translational restraints on the chord surface. Figures 3.36 to 3.39

illustrates the results for a T joint under axial loading. The same behaviour was

found for a Y joint under axial loading and the discussion below applies equally to

both joint shapes.

It might be expected that the effect of the thicker rack plates would converge

towards the situation where the chord surface is restrained in all degrees of

freedom ( ‘built in’) along the line of intersection with the stiffener. It can be seen

from Figure 3.36 that this is quite clearly not the case. The built in model (Case I)

results in SCF’s which are significantly greater at the saddle position and lower at

the crown compared to the results for one of the thicker stiffeners (100mm).

Restraining only rotation about the x axis (Case 6) is shown to have no effect on

the SCF results with the results closely mimicking the ‘no stiffener’ case.

It is immediately obvious and intuitive that the most important factor is the

restraint of deformation in the z direction. This is the mode of deformation that

would produce compressive stresses in the stiffener plate. Cases 3 and 5 very

- 197 -


closely mimic the behaviour of the 100mm stiffener as shown in Figure 3.37. The

difference between these two cases is the addition of a restraint on (f>y in Case 5

suggesting that this mode of deformation has little effect at reducing the SCF. The

same conclusion can be drawn by comparing the results from Cases 2 and 4 in

Figure 3.38. These two Cases result in the same crown SCF as the models

containing stiffeners and a saddle SCF that lies between the thickest and thinnest

stiffeners. The rotational displacement 0y seems therefore to have very little

relevance to the behaviour of these stiffeners.

Returning to the ‘built-in’ Case 1 it appears that the reasons for the poor modelling

of the stiffener effect is due to the additional restraint of the translational

deformation in the y direction. This is shown by adding restraint in Y to Case 3

forming Case 7. Case 7 closely mimics the built in Case 1 as illustrated in Figure

3.39. Deformation in the x direction (along the chord length) is minimal and the

effect of restraining (py has been shown to have little effect

For axial loading some evidence has already been obtained that there exists an

optimum stiffener thickness beyond which the SCF at the saddle increases and that

at crown decreases. This is the same situation as found with the ‘built in’ Case 1.

This suggests that there are essentially two effects of a rack plate. Firstly even

relatively thin rack plates are effective at restraining chord deformation in the z

direction. This has the immediate effect of reducing the SCF at the intersection. As

the stiffener becomes thicker the restraint to deformation in Y (i.e. direction of

brace loading) becomes more significant. Restraining deformation on Y results in a

tendency towards higher saddle SCF and lower crown SCFs as seen in the built in

case.

This is not thought to be too significant a problem as it only affects axial loading

and the size of the stiffener required to produce significant Y restraint would not be

encountered in practice. In any case even the built in situation produces SCF values

significantly lower than the unstiffened joint.

- 198


For OPB loading a similar pattern emerges for both T and Y joints. Cases 3 and 5

produce SCF which approach those of the thicker stiffeners. The major difference

however is the fact that the built-in case (Case 1) provides a lower bound to all the

results. This suggests that increasing restraint in the Y direction does not have the

detrimental effect on peak SCF for OPB loading as found for axial loading. The

crown position SCF’s are all very similar for all cases and close to zero.

3.7.4 Effect of a Continuous Thickness Rack Plate Across a Range

of Joint Parameters

The investigation thus far has centred around a single set of joint parameters with

two different brace angles. In order to be able to form an idea of the effect of a

stiffener in different joints a single constant thickness stiffener has been inserted

into joints covering the range of parameters for which the Hellier, Connolly, Dover

parametric equations [3.1] are vahd. The parameter ranges covered are given

below:

6.21 < a < 13.1

0.2 < p <0.8

7 .6 < y < 3 2

0.2 < T < 1

35° < 0 < 90°

The geometric parameters were varied one at a time across the validity ranges

given above. All other parameters were constant at the values given in Table 3.1.

The joint dimensions were calculated using a chord diameter of 0.6m and a chord

thickness of 0.02m. The stiffener thickness was the same as the chord thickness.

This was chosen as an intermediate thickness stiffener which is well suited to being

modelled using thin shell elements and which showed a significant effect on the

SCF for both loadcases.

199 -


For each set of joint parameters investigated two models were produced, one with

and one without a stiffener. This is to ensure that the differences in SCF obtained

are due to the presence of the stiffener rather than any errors introduced from

calculating the unstiffened SCF using parametric equations.

The variation of the absolute value of the hot spot SCF will be presented for

stiffened and unstiffened models across the range of each parameter for axial and

OPB loadcases.

3.7.4.1 ResultsIn each of the figures in this Section, the annotation adjacent to each stiffened data

point represents the normalised SCF (SCF in stiffened joint / SCF in unstiffened

joint).

The variation of hot spot SCF with increasing alpha (i.e. increasing chord length) is

illustrated in Figures 3.40 and 3.41 for axial and OPB loadcases respectively.

Immediately noticeable is the insensitivity of the stiffened model to the increase in

chord length. This is in contrast to the unstiffened model which displays a strong

relationship with alpha, showing an increasing in peak SCF of approximately 30%

across the range of alpha. This results in the situation where the greatest benefit

from the rib plate can be obtained for greater alpha ratios. By contrast, the peak

SCF in the stiffened joint under OPB loading shows the same dependency on alpha

as the unstiffened joint resulting in nested curves in Figure 3.41. Table 3.4 gives the

ratio of the stiffened SCF / unstiffened SCF for each value of alpha tested for both

loadcases.

Both the stiffened and unstiffened geometries show similar responses to an

increasing Beta ratio (i.e. increasing brace radius). For the axial loadcase there

appears to be an intermediate value of Beta (around 0.4) which produces the

highest SCF values with and without a stiffener as illustrated in Figure 3.42. The

stiffener results in a continuously decreasing relative SCF with increasing Beta

- 2 00 -


ratio. This is illustrated in Table 3.5. For OPB loading the stiiïener has almost no

effect at the lowest Beta values as shown in Figure 3.43. However the difference

between the stiffened and unstiffened SCF increases continuously with increasing

Beta.

Both stiffened and unstiffened joints under axial and OPB loading display a very

strong relationship with Gamma (Le. decreasing chord thickness). This is as would

be expected since decreasing the relative chord thickness will increase the

deformation of the chord due to its reduced stiffness. Under axial loading the

greatest relative benefits in terms of SCF are obtained at the lower values of

gamma. For OPB loading the effect of the stiffener remains essentially constant

across the range of gamma values investigated. This is illustrated in Figures 3.44

and 3.45 and Table 3.6.

The ratio of the brace to chord thickness, t, does not alter the beneficial effect of

adding a stiffener. This is true for both loadcases. Table 3.7 gives the ratio of the

stiffened to unstiffened SCF for each Tau ratio which are shown to be consistent.

The results are illustrated in Figures 3.46 and 3.47.

Finally the brace angle is shown to have little effect for brace angles greater than

approximately 60° for axial loading and no effect for OPB loading. This is

illustrated in Table 3.8 and Figures 3.48 and 3.49.

3.8 Conclusions and Recommendations

A comprehensive finite element stress analysis study has been completed, covering

a variety of chord rack configurations commonly found in leg structures of jack up

platforms. The effect of the various rack plates on the SCF distribution and in

particular the hot spot SCF at the chord brace intersection has been quantified.

Axial, IPB and OPB loading modes have been considered.

-201 -


For every rack plate configuration considered the hot spot SCF was found to be

reduced compared to the corresponding unstiffened joint. In general stilfeners that

are continuous through the chord diameter are the most effective at reducing the

SCF. For axial loading reduction of 50% of the unstiffened joint hot spot SCF were

approached. The reduction under OPB loading was shown to he less but still

significant at around 20%. In each case, even the thinnest stiffeners had a

significant effect which converges rapidly, especially for axial loading.

The SCF was unaffected under IPB loading as would be expected from the

different positions of chord wall deformation.

The mechanism by which the changes in SCF are achieved have been investigated

by restraining displacements and rotations on the chord surface. This has showed

that there are essentially two separate effects of a rack plate. The first and most

significant is the restraint of chord wall radial deformation. This is the mechanism

that caused the large reductions in intersection SCF. Additionally, thicker rack

plates also provide restraint to the chord deformation in the direction of the brace

axis. This mode of restraint decreases the SCF at the crown positions but increases

the hot spot SCF at the saddle. These two competing mechanisms suggest that

there exists an optimum ratio of rack plate thickness to chord diameter ratio.

The effect of a continuous thickness stiffener has been evaluated across a wide

range of joint parameters for axial and OPB loading. In general the effects

geometry are strongest for axial loading.

Additional restraint provided by leg guides at the hull - leg intersection have been

noted as potentially significant in terms of the SCF at the intersection of the chord

and brace. Leg guides have not been modelled in the current investigation but it is

recommended that their potential effect be evaluated.

-202


3.9 References

[3.1] Hellier, A.K., Connolly, M.P., and Dover, W.D. ''Stress Concentration Factors

for Tubular Y and T Joints'' Int. J. Fatigue, v l2 (l) , 13-23 (1990)

[3.2] Kuang, J.G., Potvin, A.B. and Leick, R.D. "Stress Concentration in Tubular

Joints" Proceedings of the Seventh Annual Offshore Technology Conference,

OTC 2205, Houston. (1975) pp.594 - 612

[3.3] Wordsworth, A C., Smedley, G.P. "Stress Concentrations at Unstiffened Tubular

Joints" European Offshore Steels Research Seminar, Cambridge, (1978) Paper 31

[3.4] Efthymiou, M, Durkin, S. "Stress Concentrations in T/Y and Gap / Overlap K

Joints. ” Behaviour of Offshore Structures, Amsterdam (1985), pp.429-440

[3.5] Dharmavasan, S., Aaghaakouchak, A.A. "Stress Concentrations in Tubular

Joints Stiffened by Internal Ring Stiffeners", Seventh International Conference

on Offshore Mechanics and Arctic Engineering, Houston (1988), pp. 141-148

[3.6] UEG / CIRIA, "Design of Tubular Joints fo r Offshore Structures", Part F5, Vol.

3,1985

[3.7] Lloyds Register of Shipping, "Complex Tubular Joints: Assessment of Stress

Concentration Factors for Fatigue Analysis" HMSO, 1985

[3.8] Ramachandra Murthy,D.S., Madhava Rao, A.G., Ghandi, P. Pant, P.K.

"Structural Efficiency of Internally Ring-Stiffened Steel Tubular Joints", Journal

of Structural Engineering, v l l8 ,n i l , Nov., 1992.

[3.9] Seetharaman, S, Sreedhar, D.S., Madhava Rao, A.G. "Effect of Internal Ring

Stiffeners on the Stress Distribution in Tubular T-Joints", International Offshore

and Polar Engineering Conference”, 14-19 June 1992, pp394-399

[3.10] Soh, A.K., Soh, C.K. "Stress Analysis of Axially Loaded T Tubular joints

Reinforced with Doubler Plates", Computers & Structures (1995), v55, nl,

pp.141-149.

[3.11] Matsuishi, M., Ishihama, T., Iwata, S, Ueda, Y., Nakacho, K. "Ultimate Strength

of Legs fo r Jack-Up Rigs (First Report) - Local Strength of Tubular Joints” ,

203 -


Hitachi Zosen Technical Review, 1984, v45, pp31-37.

[3.12] Choo, Y.S. “Strength Evaluation of X Joints Internally Stiffened with

Longitudinal Diaphragms”, Fourth International Offshore and Polar Engineering

Conference, Osaka, Japan. pp21-29, 1994

[3.13] Structural Dynamics Research Corporation, IDEAS Master Series, vl.3

[3.14] Hibbitt, Karlsson & Sorenson (HKS) Inc., ABAQUS v5-5.1.

[3.15] Dharmavasan, S. “Fatigue Fracture Mechanics Analysis of Tubular Welded Y

Joints”, Ph.D. Thesis, University College London, 1983

[3.16] Chang, E., Dover, W.D. “Stress Concentration Factor Parametric Equations for

Tubular X andD T Joints”, Int. J. Fatigue, vl8, n6, pp363-387,1996

2 0 4 -


J o i n t . S h a p e

P a r a m e t e r T Y

a 10 10

P 0.66 0.66

Y 15 15T 1 10 90° 60°

T a b l e 3 . 1

N o n d i m e n s i o n a l j o i n t p a r a m e t e r s

C h o r d

N o . o f E l e m e n t s C r o w n S a d d l e

A x i a l

12 5.324 10.2516 5.314 10.3520 5.301 10.3424 5.333 10.37

I P B

12 5.03 0.50216 5.019 0.49820 4.994 0.49924 5.012 0.509

O P B

12 0.432 13.4716 0.437 13.4620 0.430 13.4124 0.426 13.44

T a b l e 3 . 2

R e s u l t s o f c o n v e r g e n c e . s t u d y

F i x e d T r a n s l a t i o n s F i x e d R o t a t i o n s

C a s e N o . X Y Z 4 ^ I l l u s t r a t i o n

1 y / / y y Figure 3.292 y Figure 3.303 y y Figure 3 314 y y Figure 3.325 y y y Figure 3.336 y Figure 3.347 y y y Figure 3.35

T a b l e 3 . 3

B o u n d a r y c o n d i t i o n s u s e d t o s i m u l a t e t h e e f f e c t o f a r a c k / r i b p l a t e

- 2 0 5 -


S C F R a t i o

A l p h a A x i a l O P B

6.21 0.69 0.908 0.59 0.9010 0.54 0.9012 0.52 0.89

13.1 0.52 0.89

T a b l e 3 . 4

E f f e c t o f A l p h a o n r e l a t i v e S C F

S C F R a t i o

B e t a A x i a l O P B

0.2 0.88 0.990.4 0.76 0.970.6 0.6 0.920.7 0.51 0.89

T a b l e 3 . 5

E f f e c t o f B e t a o n r e l a t i v e S C F

S C F R a t i o

G a m m a A x i a l O P B

7.6 0.58 0.9116 0.55 0.9024 0.61 0.9032 0.69 0.89

T a b l e 3 . 6

E f f e c t o f G a m m a o n r e l a t i v e S C F

S C F R a t i o

T a u A x i a l O P B

0.2 0.55 0.870.4 0.54 0.880.6 0.54 0.880.8 0.54 0.891.0 0.54 0.89

T a b l e 3 . 7

E f f e c t o f T a u o n r e l a t i v e S C F

-206


S C F R a t i o

T h e t a A x i a l O P B

35 0.74 0.8960 0.55 0.8970 0.54 0.8990 0.54 0.89

T a b l e 3 . 8

E f f e c t o f T h e t a o n r e l a t i v e S C F

- 2 07 -


Br ace

Ch or d

Ra c k P lat e

F i g u r e 3 . 1

T u b u l a r j o i n t s h o w i n g p o s i t i o n o f s t i f f e n e r

Brace

Chord

Rack Plati

Rib Plate

F i g u r e 3 . 2

T u b u l a r J o i n t s h o w i n g d u a l t h i c k n e s s . s t i f f e n e r

- 208 -


Br a c e

C h o r d

Ra ck Pl ate

F i g u r e 3 . 3

T u b u l a r j o i n t s h o w i n g n o n c o n t i n u o u s . s t i f f e n e r

Ring St i f f ene

F i g u r e 3 . 4

T u b u l a r j o i n t w i t h i n t e r n a l r i n g . s t i f f e n e r s

- 209 -


I

F i g u r e 3 . 5

T u b u l a r j o i n t w i t h d o u b l e r p l a t e

F i g u r e 3 . 6

S a m p l e T . J o i n t f i n i t e e l e m e n t m e s h

- 2 1 0 -


O 10 --

t l / D

No Stiffener

O 0.0033

A 0.0167

X 0.0333

X 0.0833

O 0.1667

60 90 120

Angle Around inlerseclion

150 180

F i g u r e 3 . 7

E f f e c t o f n o r m i i l i s e d s t i f f e n e r t h i c k n e s s o n S C F d i . s t r i h u t i o n i n a n a x i a l l y l o a d e d T J o i n t

No Sm ener

0.0033

0.0167

0.0333

0.0833

0.1667

60 90 120

Angle Around Inlerseclion

150

Figure 3.8E ffect o f normalised stiffener thickness on SCF di.strihution fo r a.xially loaded Y jo in t

- 2 1 1 -


1.40

1.20

11/D1.000.0033ÜL0.0167

0.80 --0.0333

0.08333 0.16670.60 - -ll

0.3333

0.40 --

0.20 --

0.000 30 60 90 120 150 180

Angle Around Intersection

F i g u r e 3 . 9

E f f e c t o f p l a t e t h i c k n e . s s o n N o r m a l i s e d S C F d i s t r i b u t i o n f o r a . x i a l l y l o a d e d T j o i n t

1.2 --

t l /D

0.0033■o 0 . 8 - -

0.0167

0.0333

0.6 -- 0.0833

0.1667

0.33330.4 --

0.2 --

0 15030 60 90 120 180


Figure 3.10E ffect o f plate thickness on normalised SCF distribution fo r a.xially loaded Y jo in t

- 2 1 2 -


R a c k P l a t '

2 --

O 0

-2 -■

-4 --

0 20 40 60 to o 120 140 160 18080

t l / D

- No Stiffener

o 0.0033

A 0.0167

X 0.0333

X 0.0833

o 0.1667


F i g u r e 3 . 1 1

E f f e c t o f p l a t e t h i c k n e s s o n S C F f o r I P B l o a d e d T j o i n t

60 90 120

Angle A round Intersection

150

t l / D

- No Stiflener

O 0.0033

A 0.0167

X 0.0333

X 0.0833

o 0.1677

Figure 3.12Effect o f plate thickness on SC F fo r IP B loaded Y joint

- 2 1 3 -

Chapter 3 - Stress Concentrations in Tubu'ar Joints with Rack / Rib Plate

14 --

10 --

6 --

Y2 --

0 20 40 60 80 100 140 160 180120

t l / D

■ No Stiffener

0.0033

0.0167

0.0333

0.0833 0.1677


F i g u r e 3 . 1 3

E f f e c t o f p l a t e t h i c k n e s s o n S C F d i s t r i b u t i o n f o r O P B l o a d e d T j o i n t

t l / D

• Unstiffened

0.0033

0.0167

0.0333

0.0833

0.1677

60 80 100 120


180

Figure 3.14E ffect o f plate thickness on S C F di.strihution fo r OPB loaded Y jo in t

- 2 1 4 -


1.05

0.95 --

11/D0.9 --

0.003

0.017§ 0.85 --

0.033

0.0830.8 --0.167

0.75 -- 0.333

0.7 -■ j-----

0.65 --

0.60 150 18030 60 90 120


F i g u r e 3 . 1 5

E f f e c t o f p l a t e t h i c k n e s s o n S C F d i s t r i b u t i o n f o r O P B l o a d e d T j o i n t

1.2

1.15 --

1.05

0.85 --

0 .8 - -

0.75 --

0.7150 1800 30 60 90 120

tl/D• 0.003

■0.017

0.033

0.083

0 .167

0 .333


Figure 3.16E ffect o f plate thickness on SC F di.strihution fo r OPB loaded Y jo in t

- 2 1 5 -


0.9 --

0.8 -■

T Axial

Y Axial

TO PB

Y OPB

% 0 .7 -

0.6

0.5 --

0.40 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Normalised Stiffener Thickness T/D

F i g u r e 3 . 1 7

E f f e c t o f p l a t e t h i c k n e s s o n s a d d l e S C F f o r A x i a l a m i O P B l o a d e d T & Y j o i n t s

Rib Pla teR a c k P la te

Figure 3.18Terminology and notation used to describe models with non-contmuous stiffeners.

- 2 1 6 -


t1/D = 0.080.620

0.610 --

0 .600 --

0.590 --

0 .580 - -

•o 0.570 --

I 0.560 --

\ 0 .550 --

& 0.540 --

0 .530 --

0.520 --

0.510 --

0.500

0.00 0.01 0.01 0.02 0 .02 0.03

Rib Plate Thickness / Chord D iam eter (t2 /D )

0.03

Continuous

0.04

0.500

0.00

F i g u r e 3 . 1 9 .

E f f e c t o f r i b p l a t e o n a x i a l l y l o a d e d T j o i n t

t1/D = 0.170.620

0 .610 --

0.600 --

0 .590 - -

LL 0 .580 +

■O 0 .570 +

g 0 .560 -- Continuous

0.550 --

0 .540 --

0 .530 --

0 .520 - -

0 .510 --

0.01 0.01 0.02 0 .02 0.03

R t Plate Thickness / Chord Diameter (t2/D)

0.03 0.04

F i g u r e 3 . 2 0

E f f e c t o f r i b p l a t e o n a x i a l l y l o a d e d T j o i n t

- 2 1 7 -


t l /D = 0.33

fe 0 .560 -- tn

0 .550 --

O0 .540 4-

0 .530 - -

0 .520 --

0 .510 --

0 .500

0.00 0.01 0.01 0 .02 0 .02 0.03

Rib Plate Thickness / Chord Diameter (tZID)

0.620

0 .610 --

0 .600 --

0 .590 --

0 .580 - -

t j 0 .570 --

Continuous

0.03 0.04

F i g u r e 3 . 2 1

E f f e c t o f r i b p l a t e o n a j c i a l l y l o a d e d T j o i n t

t1/D = 0.081.000

0.980 --

0.960 --

0.940 - -

U 0.920 --

c 0.900 --

■Ç 0.880 --

Ü 0 .8 6 0 - -

0.840 --

0.820 - -

0.800 - -

0.780

0.000 0.005 0.010 0.015 0.020 0.025

Rib Plate Thickness / Chord D iam eter ( t2 0 )

F i g u r e 3 . 2 2

E f f e c t o f r i b p l a t e o n O P B l o a d e d T j o i n t

0.030

Continuous

0.035

- 2 1 8 -


0.000

tl/D = 0.171,000

0.960 - -

0.960 - ■

0.940 - -

Ù 0.920 -.

0.900 --

:§ 0.880 - -

bS 0.860 - -

0.840 - -

0.820 --

0.800 --

0.7800.005 0.010 0.015 0.020 0.025

Rib Plate Thickness / Chord Diameter (t2/D)

0.030

z/D

Continuous

0.035

0.000

F i g u r e 3 . 2 3


0.005

t l/D = 0.331.0000.980

0.960 --

0.940

O 0.920 --

0.900 -■

0.880 - -

0 .860--

0.840 - ■

0.820 - ■

0.800 - -

0,7800.010 0.015 0.020 0.025

Rib Plate Thickness / Chord Diameter (t2,V)

0.030

z/D

Continuous

0.035

F i g u r e 3 . 2 4


- 2 1 9 -


0.000 0.050

0.95 -■

0.9 -■

0.85 --

CO 0.8 -■

LL 0.7 - -

0.65 --

0.6 -■

0.55 -■

0.5

0.100 0.150 0.200 0.250Norm alised Rack Plate Thickness, t l / D

0.300 0.350

f i g u r e 3 . 2 5

E f f e c t o f r a c k p l a t e t h i c k n e s s f o r a x i a l l y l o a d e d j o i n t

Norm alised Rack Plate Thickness, t1/D

F i g u r e 3 . 2 6

E f f e c t o f r a c k p l a t e t h i c k n e s s f o r O P B l o a d e d j o i n t

0.98

0.96

Ll% 0.94T3

Z/D

?^ 0.92

I0.20.3

0.4

0.5

0.88

0.86

0.84

0.000 0.050 0.100 0.250 0.300 0.3500.150 0.200

- 2 2 0 -


Normalised Stiffener Deptti (z/D)

F i g u r e 3 . 2 7

E ffe c t o f r o c k p l a t e d e p t h f o r a x i a l l y l o a d e d j o i n t

Normalised Stiffener Depth (z/D)

F i g u r e 3 . 2 8

E f f e c t o f r a c k p l a t e d e p t h f o r O P B l o a d e d j o i n t

0.95

0.9

O 0.85

^ 0.75

0.7

0.65

0.60.1 0.15 0.450.2 0.25 0.3 0.35 0.4 0.5

t l /D■0.017

■0.033

■0 083

■ 0 .167

■0.333

0.98

0.96

0.94

OCO-o 0.92

I%[Z 0.88OCO

0.86

0.84

0.82

0.80.1 0.15 0.2 0.4 0.45 0.50.25 0.3 0.35

tl/D

■0.017

■ 0.033

■ 0.083

■0.167

■ 0.333

- 2 2 1 -


R o t a t i o n a l R e s t r a i n t

T r a n s l a t i o n a l R e s t r a i n t

F i g u r e 3 . 2 9

C a . s e 1 - C h o r d d e f o r m a t i o n r e s t r a i n e d i n a l l d e g r e e s o f f r e e d o m a l o n g l i n e . s h o w n


Figure 3.30Case 2 - Chord deformation restrained in Z direction along line shown.

- 222 -


Rota t ion a l R e s tra in t

Translational R e s tra in t

F i g u r e 3 . 3 1

C a s e 3 - C h o r d d e f o r m a t i o n r e s t r a i n e d i n Z d i r e c t i o n a n d r o t a t i o n a b o u t X a x i s a l o n g l i n e

s h o w n

R o ta t iona l R e s tra in t

T ranslational R e s tra in t

Figure 3.32Case 4 - Chord deformation restrained in Z direction arui rotation about V axis along line

shown.

- 223 -




F i g u r e 3 . 3 3

C a s e 5 - C h o r d d e f o r m a t i o n r e s t r a i n e d i n Z d i r e c t i o n a n d r o t a t i o n s a b o u t X a n d Y a x e s a l o n g

l i n e s h o w n .


Figure 3.34Ca.se 6 - Chord deformation restrained in rotations about X axis along line .shown.

- 2 2 4 -




F i g u r e 3 . 3 5

C a s e 7 - C h o r d d e f o r m a t i o n r e s t r a i n e d i n Y a n d Z d i r e c t i o n a n d r o t a t i o n s a b o u t X a x i s a l o n g

l i n e s h o w n .

16 - -

14 --

No Stiffener

12 --

100mmu 10 --Case 1 (Built In)

8 --

Case 6

6 --

2 -

0 20 40 140 160 18060 80 100 120Angle Around Intersection

F i g u r e 3 . 3 6

S i m u l a t i o n o f t h e e ffe c t o f a s t i f f e n e r u s i n g b o t t m i a r y c o n d i t i o n s

- 225 -


20

16 - ■

14 - -

No Stiffener

12 --1mm

100mmo lO --

Case 38 -■

6 --h—

4 - -

160 1801400 20 40 60 80 100 120Angle Around Intersection

F i g u r e . 3 . 2 7

S i m u l a t i o n o f t h e e ffe c t o f a s t i f f e n e r u s i n g b o u n d a r y c o n d i t i o n s

20

16 - -

14 - -

-O-O 10 --

6 - -

4 - -

160 1801400 60 100 12020 40 80

Angle A round Intersection

F i g u r e 3 . 3 8

S i m u l a t i o n o f t h e e f f e c t o f a s t i f f e n e r u s i n g b o u n d a r y c o n d i t i o n s

No Stiffener

- 1mm

- - - 100mm

Case 2

o Case 4

- 226 -


16 --

No Stiffener

12 -■

- 100mm

Case 1 (Built In)B --

Case 7

4 --

2 -■

0 140 160 18020 40 60 80 100 120^ngie Around intersection

F i g u r e 3 . 3 9

S i m u l a t i o n o f t h e e ffe c t o f a s t i f f e n e r u s i n g b o u n d a r y c o r u i i t i o n s

20

19 --

18 --

17 --

16 --

15 --

Unstiffened

StiffenedO 14 --

13 --

12 --

0.69 0.59 0.54 0.52 0.52

10 --

9 --

6 7 8 12 13 149 10 11Alpha

Figure 3.40E ffect o f Alpha on an axially loaded T jo in t

- 2 2 1 -


15 --

14 --

0.89

Unstiffened

Stiffened

0.9U 13 --

0.9

1 2 - -

105 76 14a 9 10 11 12 13

A p h a

F i g u r e 3 . 4 1

E f f e c t o f A l p h a o n a n O P B l o a d e d T j o i n t

21 - -

20 - -

19 - -

17 - -

16 - -

O 15 - - 0 .760.88

14 - -

13 - -

12 - -0.6

10 - -

0.519 - -

0 0.1 0.2 0 .3 0 .4 0.5 0.6 0 .7 0.8

Beta

Figure 3.42Effect o f Beta on an axia lly loaded T jo in t

■ Unstiffened■ Stiffened

- 228 -


15 --

14 --

0.9213 --

12 - -

1.97

O 1 0 - -

9 --

8 - -

7 --

6 - -

0.99

5 --

0 0.1 0.2 0.5 0.6 0.7 0.80.3 0.4

Unstiffened

- Stiffened

Beta

F i g u r e 3 . 4 3

E f f e c t o f B e t a o n a n O P B l o a d e d T j o i n t

30 - -

25 --

1.69

20 - -

0.6115 --

[5510 - -

5 --

5 350 2510 15 20 30

■ Unstiffened • Stiffened

Gamma

Figure 3.44Effect o f Gamma on an axia lly loaded T jo in t

- 2 2 9 -


30 --

25 -- t).88

20 - -

0.9

15 --

10 - -

0.915 --

350 305 2510 15 20

• Unstiffened• Stiffened

Gamma

F i g u r e 3 . 4 5

E ffe c t o f G a m m a o n a n O P B l o a d e d T j o i n t

20

18 --

16 - '

14 --

12 - -

O 1 0 - -

0.548 - -

0.546 - -

0.544 --

0.54

0.55

0.2 0.90.3 0.4 0.8 10.5 0.6 0.7

-Unstiffened

■ Stiffened

Tau

F i g u r e 3 . 4 6

E ffe c t o f T a u o n a n a x i a l l y l o a d e d T J o i n t

230


14 --

12 - - 1.89

10 - - 0.89

0.886 - -

4 -- 0.88

2 - -

0.87

0 0.2 0.4 0.6 0.8 1Tau

F i g u r e 3 . 4 7

E f f e c t o f T a u o n a n O P B l o a d e d T j o i n t

■ Unstiffened■ Stiffened

20

18 --

16 --

14 --

12 - -

O 1 0 - -0.54

8 - -

1.55

6 - -

0.744 --

2 - -

30 40 50 70 80 9060

■Unstiffened

■ Stiffened

Theta

F i g u r e 3 . 4 8

E f f e c t o f T h e t a o n a n a x i a l l y l o a d e d T j o i n t

-231 -


1 4 . .

13 --0 .54

12 - -

0.54

11 - -

10 - - 0.55

9 --

8 - -

7 -■

6 - -

5 --

0.744 --

3 --

30 40 50 60 70 9060Theta

-Unstiffened

-stiffened

F i g u r e 3 . 4 9

E f f e c t o f T h e t a o n a n O P B l o a d e d T j o i n t

- 2 32 -

Chapter 4- The Effect of a Rack / Rib Plate on the Degree of Through Thickness Bending

Chapter 4

4. The Effect of a Rack / Rib Plate on the Degree of Through

Thickness Bending in Jack Up Chords

4.1 Introduction

It was shown in Chapter 3 that the presence of a Rack or Rib plate as commonly

found in jack up chords can have a significant effect on the SCF’s found at the

intersection between the brace and the chord. Accurate knowledge of the SCF

distribution, and in particular the peak SCF is important for the prediction of

fatigue lives at the design stage using the S-N approach.

For the assessment of defects discovered in service however the S-N approach is

no longer appropriate. For such an analysis the science of fracture mechanics must

be implemented. Any detailed fracture mechanics analysis requires the prior

knowledge of the stress distribution along the anticipated crack path. For tubular

joints this means an accurate knowledge of the proportion of through thickness

bending, commonly called the Degree of Bending (DoB) together with a model of

the load redistribution or ‘load shedding’ that is known to occur.

The results of approximately 500 finite element models will be presented in this

Chapter in an attempt to quantify the effect of a central longitudinal chord stiffener

on the through thickness stress distribution.

4.2 Scope

Three distinct chord designs used in jack up construction were identified and

described in detail in Chapter 3. These three designs are shown schematically in

Figures 4.1 to 4.3. The same three chord designs wiU be investigated here across

- 233 -


the same range of parameters. In the interest of brevity the chord designs will not

be presented again here, instead reference is made to Section 3.3.

Each of the three chord designs will be investigated under axial, in-plane bending

and out of plane bending. As in Chapter 3, initially a single set of joint parameters

will be investigated. The joint parameters are detailed in Table 4.1 and were chosen

as being representative values which results in a high quality finite element mesh

with little element distortion.

The sensitivity of the through thickness stress distribution to the joint parameters

will then be investigated across the range of joint parameters for which the

parametric equations by Connolly et al are valid. [4.1]. This set of parametric

equations will form the basis for comparison during this study and will be discussed

in detail in the next section.

All results presented here are from the chord side as this was shown in Chapter 3

as having the highest stress concentration factors.

4.3 Through Thickness Stress Distributions in Tubular Joints

Conventional fatigue design uses the peak surface SCF to determine the fatigue life

of a tubular joint utilising experimentally derived S-N curves. However

examination of the experimental database used during the derivation of the S-N

Curves [4.2] shows that the ‘hot spot stress’ alone is insufficient to completely

describe the crack growth behaviour in tubular joints. This conclusion was reached

when it became clear that tubular joints with similar hot spot stress levels but

different loading modes often resulted in different fatigue lives. The effect of

loading mode is shown in Figure 4.4 where the axial and OPB loading mode

database has been plotted. Also included in this figure are the mean fatigue life

lines for each loading mode. It can be seen that these mean lines converge at lower

stress levels as change in slope of the design S-N curve is approached. However at

- 234-


the higher stress levels, out of plane bending produces fatigue lives approximately

2.5 times longer than an axially loaded joint at the same stress level.

Holdbrook [4.3] suggests that these differences are due to differences in crack

growth which in turn must depend on the through thickness stress distribution as

well as the hot spot stress level.

The through thickness stress distribution is most commonly described by a simple

linear interpolation between the maximum and minimum principal stresses found on

the inner and outer tubular surfaces respectively as illustrated in Figure 4.5. The

stress concentrating effect of the notch (weld toe) is omitted as it is in the

determination of surface stress concentration factor (SCF). The degree of bending

(DoB) is defined as shown in Eqn (4.1)

DoB = (Ji, /(<T, +cr^) (4.1)

where the subscript represents the bending (b) or the membrane (m) component. A

graphical representation of the make up of different DoB values is given in Figure

4.6

4.3.1 The Importance of Through Thickness Stress Distribution

Several researchers have attempted to account for the through thickness stress

distribution in fracture mechanics models. Most of the models implement some

form of ‘load shedding’ mechanism whereby the bending component of the through

thickness stress distribution is redistributed through alternative load-paths within

the statically indeterminate structure of the tubular joint. The first and most widely

recognised of these models is that of Aaghaakouchak et a! [4.4] who investigated

the discrepancy between the flat plate SIF solution of Newman and Raju [4.5] and

the weight function of Oore and Bums [4.6] with the experimentally derived stress

intensity factors from tubular joint fatigue tests. Noting that both methods

significantly over predicted the stress intensity factors in tubular joints it was

- 235 -


postulated that this was due to incomplete modelling of the phenomenon called

‘load shedding’ caused by the complex boundary conditions found in tubulars. A

finite element study [4.7] of flat plates and rings with edge cracks was analysed

under different boundary conditions. It was found that the statically indeterminate

models (models containing degrees of redundancy) resulted in significantly lower Y

Factors than the statically determinate models. Examination of the reactions at the

supports as the crack depth increased showed that as the crack length increased,

the behaviour of the cracked section approached that of a hinge . A Linear Moment

Release model was proposed whereby the membrane stress remains constant but

the bending stress at the cracked section is continuously and linearly released with

increasing crack depth according to Eqn. (4.2)

— '^boI tj(4.2)

where Sb is the bending stress at the crack tip and Sbo is the surface bending stress

at the surface. It was reported that in conjunction with the Newman - Raju

equations that this model produced Y Factors within the scatter band of

experimentally derived Y Factors for crack depths of between 0.1 < a/T <0.8 for a

range of loading modes and joint shapes.

Forbes et al [4.8] carried out a series of tests on large scale tubular joints and wide

plates to experimentally measure the magnitude of load shedding that occurs in

tubular joints. The data from these tests was used to essentially confirm the initial

postulation of Aaghaakouchak et al with regard to the presence of a load shedding

mechanism. The experimentally derived membrane and bending stresses at the

cracked section were used in conjunction with the SIF solutions of Newman and

Raju [4.5] and the weight function of Oore and Bums [4.6]. It was noted that

improved agreement was found regardless of which analytical technique was used.

It is important to note that Forbes et al did not assume a constant membrane stress

at the cracked section as suggested by Aaghaakouchak et al and the membrane

- 236-


stress used in the calculation of SIF was adjusted with crack depth in line with

experimental measurements. Forbes et al present the variation in experimental

stress measurements with normalised crack depth for the inner and outer surfaces

of a tubular joint under axial brace loading. The information is presented

graphically in terms of the stress normal to the crack surface. The stresses are

normalised to that found on the outer surface of the uncracked joint. The fact that

the stress presented is the stress normal to the crack surface rather than the

maximum principal stress is not thought to be significant as the maximum principal

stress has been shown from the FE analysis to be approximately perpendicular to

the weld toe at the saddle of an uncracked joint. The normalised stresses found on

the inner and outer surfaces of the tubular specimen have been extracted from the

figure and decomposed into normalised bending and membrane components for

normalised crack depths of 0 < a/T < 0.8. The stress measurements were taken a

distance of approximately twice the chord wall thickness from the crack plane. It

was assumed that this would be sufficient to detect changes in the chord wall stress

but sufficiently far away from the crack so as not to be affected by the local stress

relief caused by the crack itself. This information is presented in Figure 4.7. The

stresses are presented normalised to the peak normal surface stress in the

uncracked joint. It is clear from this figure that the hypothesis of Aaghaakouchak et

al that the membrane stress component remains unchanged by the presence of a

fatigue crack is not supported by this experimental evidence. However the bending

component appears to quite closely follow the Linear Moment Release theory,

tending to zero as the crack approaches through wall thickness. The importance of

the positioning of the experimental measurements is unclear but the assumption

made by Forbes et al seems reasonable.

Berge et al [4.9] present the variation of experimentally measured bending and

membrane stresses with increasing crack depth. The stresses were measured a

distance of 24mm from the weld toe. The Linear Moment Release model (4.2) is

shown to under-predict the degree of moment release. The results also show that

the membrane component tends to zero at a/T values of approximately 0.5.

- 237-


Unfortunately the experimental results are only shown for the normalised crack

depth range 0<a/T<0.6 so it is not possible to confirm whether the membrane

stresses become compressive at deeper depths as noted earlier using the data

presented by Forbes et al.

Berge et al have conducted a fracture mechanics study of tubular joints in an

attempt to explain the reasons why the results of a series of tubular joint fatigue

tests fell below the S-N Design curve for 32mm tubular welded joints. The

specimens in question consisted of a single chord with two perpendicular braces

lying in the same plane, acting as a self reacting frame. It was postulated that this

loading arrangement results in a lower degree of bending (DoB) due to an

increased membrane component. The investigation aimed to asses whether this

increased membrane component could be used to explain the short lives found in

the tubular joint fatigue tests.

The fracture mechanics model used by Berge et al is outlined in detail by Haswell

[4.10]. The Y Factors were calculated using thin sheU FE techniques containing

line spring elements to model the crack. Using the Reference State Solution a

weight function was derived using the Y Factors from the FE modelling. A

constant aspect ratio of a/2c=0.1 for cracks deeper than 4mm was assumed. This

fracture mechanics model will be assessed in detail in Chapter 5. FE models of the

uncracked joints show the DoB to decrease from 0.73 to 0.62 with the addition of

the extra brace to form the self reacting frame. This difference in DoB, which was

implicitly included in the line spring FE models resulted in fatigue lives that were

shorter by a factor of two for the double braced model and agreed closely with the

experimental results. The investigation concluded that DoB can significantly affect

the fatigue life of a tubular joint, and in some cases where the DoB is low, the Hot

Spot stress approach can be unconservative.

A simpler fracture mechanics model based on the Linear Moment Release model of

Aaghaakouchak et al and the Shen - Glinka weight function [4.11] was also used.

- 238-


Increasing the DoB from an unrealisticaUy low 0.45 to 0.9 increased the predicted

life by a factor of 2.25. It was stated that the simple model gave results in good

agreement with the 3-D analysis.

4.3.2 Determination of Through Thickness Stress Distribution

By far the most comprehensive investigation into the through thickness stress

distributions have been performed by Connolly et al [4.1] for Y and T Joints and

more recently by Chang for X and DT joint shapes [4.12]. Both investigations

produced parametric equations describing the variation of degree of bending in

terms of the joint parameters.

Connolly et al produced the DoB parametric equations using results from the same

finite element study that Hellier at al [4.13] used to derive SCF parametric

equations for the same joint shapes. Based on a thin shell finite element model, a

database of almost 900 joint shapes under each of axial, IPB and OPB loading was

developed. The weld was not modelled and advantage was taken of symmetry

during the generation of the finite element meshes. The chord ends were

constrained in all degrees of freedom and all loads were applied as uniformly

distributed loads along the brace ends. Verification of the model was achieved by

comparison with experimental results from strain gauged acrylic models.

Several other investigators quote DoB results for single geometries, either from

finite element investigations of individual joint shapes [4.14] or from experimental

results from large scale welded tubular joints e.g.[4.15]. Some such results will be

used for validation of the current finite element model.

4.4 Mesh Generation and Boundary Conditions

The results presented in this Chapter are derived from models sharing a common

heritage with those presented in Chapter 3. In the interests of brevity only a

239-


summary of the mesh generation and boundary condition detail will be presented

here. For full details reference is made to Section 3.4.

The general purpose finite element package ABAQUS [4.16] was used throughout

this investigation. Finite element models were generated using a modification of a

FORTRAN program previously used to analyse simple planar tubular joints (see

Section 3.4 for full details). The mesh generator reliably handles a wide range of

joint shapes and sizes. Mesh refinement is controlled by specifying the number of

elements around the intersection of brace and chord. AU loads are automaticaUy

scaled to give unit nominal stress at the intersection. This enables SCF’s to be read

directly from the output files without further processing. FORTRAN routines have

been developed to automaticaUy open the ABAQUS results files and extract the

relevant information from the nodes of interest. This information is then written

into a file in a spreadsheet readable format.

SheU elements were used throughout this investigation. For models utilising thin

sheU elements these were S8R5 (8 noded quadrilateral) elements with a smaU

number of STRI65 (6 noded triangular) elements for geometric compatibUity in

and around the plug region. A number of models using thick sheU elements have

also been solved. These models used S8R (8 noded quadrilateral) elements. Models

employing thick shell elements will be clearly indicated.

The eight noded thin sheU elements, S8R5 are reduced integration, doubly curved

shells with 5 degrees of freedom, three translational motions, x, y, and z, and two

in surface rotations. The 8 noded thick sheU elements are also reduced integration,

doubly curved shells but with 6 degrees of freedom, three translational motions and

three rotational degrees of freedom, <j)x, (j)y, and (|)z.

A sample mesh is shown in Figure 4.8. Note the refinement of elements around the

intersection where the stress gradients are greatest and the gradual coarsening of

the mesh remote from this region where the stresses become more uniform. Careful

- 240-


positioning of the nodes allows the stretch and distortion of the elements to a

minimum. Since triangular shell elements are less accurate than quadrilateral shell

elements, their use has been kept to a minimum. Triangular elements are only used

where necessary due to reasons of geometric compatibility around but some

distance from the intersection and within the plug region. Generation of a typical

mesh takes just a few seconds and a complete solution for an average model

containing 858 elements can be obtained in 45 seconds of CPU time. AU analysis

was performed on a DEC Alphastation 255/233MHz.

Symmetry of the model in the X Y plane aUows a half model analysis to be

performed providing the correct boundary conditions are applied to the nodes on

the plane of symmetry. Reducing the size of the model in this manner saves

significant CPU time and disk storage space. ABAQUS provides a ZSYMM

function to aUow the automatic application of the appropriate translational and

rotational restraints to simulate symmetry in the Z direction. The constraints

imposed on aU nodes on the plane of symmetry are zero displacement in the z

direction and aU rotations associated with the thin shell elements are fixed at zero.

For chord designs containing a stiffener that passes through the whole of the chord

diameter, the same symmetry boundary conditions are applied to the stiffener.

Stiffener designs where the plate is not continuous through the chord (see Figure

4.3) have no symmetry boundary conditions applied at the free edge.

The symmetry conditions are violated for the Out of Plane Bending loading

condition, but ConnoUy et al [4.1] discovered that it is stiU possible to use half joint

meshes with acceptable accuracy by restraining in plane displacements.

The chord ends are modeUed as ‘built-in’ with aU degrees of freedom being

restrained. No boundary conditions are applied to the brace end other than the

uniformly distributed external loads applied at each node.

- 241-


4.5 Convergence and Model Verification

Convergence of the models was demonstrated in Section 3.6 by comparing the

SCF at the crown and saddle for models with 12, 16, 20 and 24 elements around

the intersection. It was noted that 16 elements around the intersection forms a

reasonable compromise between accuracy and computational cost.

Connolly et al [4.1] presented a comparison of the bending to total stress ratio

from an acrylic model under axial and IPB loading with the results from the finite

element study. A model with the same geometric parameters has been produced

here for comparison with the result from Connolly et al and the acrylic model. The

results are presented in Table 4.2.

Bending to Total stress ratio results from around the intersection of the acrylic

model are shown in Figure 4.9. Axial and IPB loading modes are shown. Also

presented are the results from the current finite element study for a model with the

same geometric parameters as the acrylic model. The IPB results are only shown

between 0° and 60° as past this point it becomes difficult (and irrelevant) to

determine the appropriate principal stresses as the neutral axis is approached.

In general the results agree well and closely follow the same trends. A tendency for

the FE model to over predict the degree of bending at the hot spot for each loading

mode has been identified. Furthermore the degree of bending is under predicted

compared to the acrylic model 90° away from the hot spot. Connolly et al reported

the same trends and the results of the two finite element based investigations agree

closely.

Several models were created and solved using thick shell elements. Thick shell

elements are different to thin shell elements in that they are capable of transmitting

shear forces. The results have shown that there is little difference between the thick

242 -


and thin shell elements. This was found across a range of joint shapes, stiffener

thicknesses and loading mode. The case of an axially loaded T joint is typical and is

illustrated in Figure 4.10. In this figure it is demonstrated that the difference

between the DoB predicted by the thick and thin shell models is of the order of 1%

across the complete range of stiffener thicknesses examined here. For this reason

all further results presented in this Chapter were generated using thin shell

elements.

4.6 Finite Element Investigation

The results and discussion presented here are limited to the DoB found at the hot

spot stress site as this is where the deepest point of the fatigue crack is known to

occur. It is the crack growth at this point that fracture mechanics models strive to

simulate. The DoB at other points around the intersection is largely irrelevant as

the surface crack growth is controlled by the surface stress distribution and fatigue

cracks in tubular joints are known to be approximately semi-elliptical in nature.

4.6.1 Effect of Rack Plate Thickness on Through Thickness Stress

Distributions

Several stiffener plate thicknesses of up to 1/3 of the chord diameter have been

investigated and the SCF results around the intersection on the chord side are

presented here. Each of the stiffeners had a constant thickness and was continuous

through the chord diameter. The investigation covered both T and Y joints under

Axial, IPB and OPB loading modes.

4.6.1.1 ResuitsThe results will first be examined in terms of the absolute DoB found across the

range of stiffener thicknesses for T and Y joints under each loading mode. The

same results will then be presented normalised to the DoB predicted by the

parametric equations of Connolly et al at the hot spot. Presenting the results in this

way will give a measure of the potential for the parametric equations to predict the

DoB in joints of this type.

- 243 -


The absolute DoB values for each of Axial, OPB and IPB are illustrated in Figures

4.11 to 4.13. For the axial and OPB loading modes the introduction of a stiffener

reduces the DoB , i.e. increases the membrane component. For the axial loadcase

this change is approximately 6% and for OPB 2%. For IPB the bending component

is increased by approximately 2%. It is observed that in each case the behaviour is

independent of brace angle and the effect of the brace angle on the actual DoB

measured is minimal, especially for IPB loading. As with the SCF, the effect of the

stiffener converges very quickly with the greatest changes occurring with the

thinnest stiffeners.

The results normalised to the DoB at the hot spot predicted by the parametric

equation of Connolly et al are shown in Figures 4.14 to 4.16. As would be

expected the greatest errors in the predicted to actual DoB ratio are found for the

axial loadcase as this produced the greatest effect on DoB. The errors in this case

are approximately 9% for the thickest rack plate. Such a discrepancy is likely to

adversely affect the accuracy of any fracture mechanics crack growth prediction of

a tubular joint with a thick rack plate using DoB based on the parametric equations

for unstiffened joints.

For OPB loading the basic effect of the stiffener is less for this loading mode, thus

the parametric prediction is within 4% of the actual DoB. For OPB loaded T joints

the parametric equation actually under predicts the DoB and over predicts for Y

joints. For IPB loading the parametric equations over predict the DoB for each

joint shape with the biggest over prediction being for Y joints. Increasing the

stiffener thickness actually improves the accuracy of the parametric prediction for

this loadcase highlighting a possible deficiency in the parametric equations. A

summary of the normalised DoB data for each of the cases presented above is

given in Figure 4.17.

244-


4.6.2 Effect of Rack and Rib Plate Geometry on Througfi Thickness

Stress Distributions

Some jack up chord designs employ stiffener plates that do not have a constant

cross section through the chord diameter. Examples of this were given in Chapter

One. The behaviour of such chord designs will be investigated in this section. A

typical chord design of this type is shown in Figure 4.18 detailing the notation and

terminology that will be employed to describe the variations in geometry between

individual finite element models.

The relative thickness ( tl/t2 ) and the depth, z of the rack plate will be varied. The

variation in the relative thickness of the two plates will be continued up to the

extreme where the thinner rib plate tends to a thickness of zero. Although this

situation is not commonly found in practice it forms a useful extreme case as it

eliminates the possibility of direct load transfer resulting from the deformation of

diametrically opposing chord surfaces. Any resistance to chord wall deformation

must then be provided by some form of bending mechanism similar to the ring

stiffeners presented in Section 3.3. This should allow an insight into the

predominant mechanisms by which the stiffener affects the changes in DoB at the

hot spot.

4.6.2.1 ResultsThe three major variables in this section of the investigation are the thickness of the

rack plate, t l, the thickness of the rib plate, t2 and the depth of the rack plate, z.

Each of the variables will be presented normalised to the diameter of the chord, D.

The DoB presented is that found at the hot spot. In each case the DoB is presented

for the chord side.

Figures 4.19 to 4.21 display the primary results illustrating the effect of a dual

thickness stiffener under axial loading. Each of the three plots represents a different

relative rack plate thickness namely tl/D ratios of 0.08, 0.17 and 0.33 respectively.

Each has been plotted on the same scale for ease of comparison. Also included on

- 245 -


each plot is a line indicating the DoB found in the FE model with a stiffener of

constant thickness equivalent to that of the rack plate, tl. This enables an easy

visual measure to be formed of how closely the effect of the presence of the thinner

rib plate converges towards that of the heavier continuous rack plate.

Several trends can be identified from the DoB data. Firstly the rack plate thickness,

t l is seen to be of secondary importance. The maximum difference in DoB between

the thickest and the thinnest rack plate for any given geometry is very much less

than 1%.

Three normalised rib plate depths of 0.2, 0.4 and 0.6 times the chord radius were

examined. The results show a reduction in DoB with increasing depth, z. The DoB

was reduced across the range of the rack and rib plate thicknesses tested here.

Again the effect is small, although noticeable and consistent. The maximum

difference in DoB between the most shallow and deep rib plates was less than 2%.

The effect of the thickness of the rib plate was shown by examining four différent

plate thicknesses for each combination of rack plate thickness and depth. The

normalised rib plate thicknesses of 0.002, 0.008, 0.017 and 0.033 were significantly

thinner than the rib plates. The effect of the rib plate thickness is seen to converge

rapidly in each case.

Figures 4.22 to 4.24 illustrate the same data for the OPB loadcase. Again all plots

utilise the same scale for ease of comparison. The first observation is that the

effectiveness of the stiffener in reducing the peak DoB around the intersection is

significantly reduced in comparison with the axial loadcase. The effect of the rack

plate thickness, tl, is again seen to be of secondary importance.

The same range of rack plate depths and rib plate thicknesses were examined for

the OPB loadcase as the Axial loadcase. Once again, increasing the depth of the

rack plate reduces the DoB across the range of rib plate thicknesses tested. The

- 246-


average reduction obtained by increasing the normalised rack plate depth from 0.1

to 0.3 is less than 1%.

Increasing the rib plate thickness results in an almost linear decay in DoB. The

same pattern is found across the range of rack plate depths and thicknesses tested.

This is in contrast with the axial loadcase where the effect of the plate thickness

converged rapidly. This suggests that the mechanism by which the plate affects the

changes is different for axial and OPB loadcases. The same observation was

observed for SCF’s in Chapter 3.

For both axial and OPB loadcases the results tend towards those of the continuous

thickness stiffener but do not reach it. The degree of convergence decreases

slightly with increasing rack plate thickness, tl. However in each case it is a small

fraction of 1% DoB.

For IPB the pattern of behaviour is different in that the degree of bending increases

with both rib plate thickness and rack plate depth. This behaviour is illustrated in

Figures 4.25 to 4.27. The maximum change in DoB across the range of geometries

tested under IPB loading is less than 1% DoB.

The preceding commentary describes detailed changes that occur in the measured

DoB for a variety of models with dual thickness stiffeners. It should be borne in

mind however that the maximum change in DoB is less than 2% regardless of

loading mode and stiffener geometry. The small size of these changes largely

makes the detailed changes in the DoB described in this section of little

importance. The errors involved in the calculation of DoB using thin shell elements

are likely to be of similar order of magnitude. In any case the fracture mechanics

models in which this DoB information will ultimately be used have not been

developed to such an extent that warrants DoB details to such accuracy. The errors

involved in each of the available fracture mechanics models, or even in the choice

- 247-


of crack growth law is likely to be many times greater than the changes in

predicted fatigue life produced by more accurate DoB data.

4.6.3 Effect of Continuous Thickness Rack on Through Thickness

Stress Distributions Across a Range of Joint Parameters

Previous discussions have been limited to a single joint geometry with different

stiffener plate configurations. However this gives little information as to whether

the existing DoB parametric equations can be used to predict DoB across a range

of joint geometries.

The applicability of the DoB parametric equations of ConnoUy et al to tubular

joints with a longitudinal chord stiffener will be assessed in this section. For the

purposes of this assessment a single thickness, continuous stiffener has been used.

The thickness of the stiffener is equal to the chord wall thickness in every case. The

dimensions of the tubular joint have been altered in a systematic manner to examine

the effect of the stiffener across the complete range of parameters for which the

parametric equations are valid as shown below.

6.21 < a < 13.1

0.2 < p < 0.8

7 . 6 < y < 3 2

0.2 < X < 1

35° < 0 < 90°

The geometric parameters were varied one at a time across the validity ranges

given above. All other parameters were constant at the values given in Table 4.1.

The joint dimensions were calculated using a chord diameter of 0.6m and a chord

thickness of 0.02m. The stiffener thickness was the same as the chord thickness.

This was chosen as an intermediate thickness stiffener which is weU suited to being

modelled using thin shell elements and which showed a significant effect on the

SCF for axial and out of plane bending loadcases in Chapter 3.

- 248-


For each set of joint parameters investigated two models were produced, one with

and one without a stiffener. This is to ensure that the differences in DoB obtained

are due to the presence of the stiffener rather than any errors introduced from

calculating the DoB using parametric equations. This also allows judgement on the

applicability of the parametric equations for joints of this type to be made in the

light of the errors involved in the prediction of DoB for unstiffened joints of the

type for which the equations were developed.

The variation of the absolute value of the hot spot DoB will be presented for

stiffened and unstiffened models across the range of each parameter for axial, OPB

and IPB loadcases. This will be compared directly with the parametric DoB

predictions for the hot spot and the saddle / crown as appropriate depending on

loading mode.

4.6.3.1 ResultsThe variation of DoB with alpha (D/2T) is shown in Figure 4.28. It can be seen

that the DoB is relatively independent of alpha for both the stil'fened and

unstiffened joints. For axial and OPB loading the stiffened model gives a DoB

which is less than the unstiffened. For axial loading this difference is about 4%

DoB and approximately 1% DoB for OPB loading. In each case the difference is

independent of alpha. IPB loading also displays a difference between the stiffened

and unstiffened variants which is independent of alpha. However in this case the

DoB is higher in the stiffened model (reduced membrane component).

Under axial loading the DoB reaches a peak at intermediate values of Beta (d/D) as

shown in Figure 4.29. For both OPB and IPB the membrane component increases

with increasing Beta i.e. lower DoB. The DoB for the stiffened model is reduced

in comparison with the unstiffened model for Axial and OPB loading whereas the

opposite is true for IPB loading.

- 249-


Increasing Gamma (D/2T) shows a strong effect for the stiffened model under axial

loading. The DoB is reduced by approximately 10% at low gamma values as

shown in Figure 4.30. The effect of the stiffener diminishes with increasing

Gamma. For OPB and IPB loading the effect of the stiffener is less pronounced but

is again the effect diminishes with increasing Gamma. Again only under IPB

loading is the beneficial effect of higher DoB found.

The dependency of DoB on Tau (t/T) and brace angle, Theta is illustrated in

Figures 4.31 and 4.32 respectively. The strongest effect on DoB is found for

axially loaded joints with small brace angle. In this case the DoB was reduced by

approximately 15%. Reductions of this magnitude have significant effect on the

fatigue life of tubular joints. Berge et al [4.9] demonstrated that a reduction of

DoB of 11% accounted for a factor of two on life. The factor on life will of course

be material dependant as it will depend on the Paris constants used in the crack

growth integration.

4.7 Discussion

It has been shown that the presence of a stiffener can in some instances

significantly affect the DoB by as much as 15%. However in many cases the

difference in DoB between the stiffened and unstiffened models is minimal. A

general trend has emerged from the analysis showing the presence of a stiffener

resulting in lower DoB values for axial and OPB loading and higher DoB values

for IPB loading although the increases for IPB loading are generally modest. The

implications of this are that the presence of a stiffener (rack plate) will result in

shorter fatigue lives for Axial and OPB loading but longer fatigue lives for IPB

loading.

In order to accurately predict the crack growth behaviour in tubular joints with

rack plates using fracture mechanics, an accurate measure of DoB is needed for the

geometry under consideration. At present no parametric equations exist that will

predict the DoB specifically for tubular joints with rack plates. However DoB

- 250 -


parametric equations do exist for simple T and Y joints and the suitability of these

equations has been assessed here. Two parametric equations exist for each loading

mode, one for the ‘hot spot’ position and one for the saddle or crown position

depending on the loading mode. These have been included in Figures 4.28 to 4.32.

The applicability of these equations to the current geometry has been assessed by

comparing the DoB from the finite element model to the DoB predicted by the

parametric equations. This has been done for the stiffened and unstiffened models

presented in Section 4.6.3. The saddle / crown DoB parametric equation is

considered in Figure 4.33 and the hot spot equation in Figure 4.34. Also included

in these Figures are error bands showing +/- 5% DoB. Any point above the line on

the diagram indicates an under prediction of the finite element DoB by the

parametric equation and vice versa. Under prediction of the DoB would result in

desirable conservatism in the results of the fracture mechanics models that would

use this data.

It is clear from Figure 4.33 that the parametric equations are able to accurately and

conservatively predict the DoB in unstiffened joints. Almost all the points lie above

the line and most below the 5% over prediction line. However a number of the

stiffened joint results are shown to be unconservatively predicted by the parametric

equations although never by more than 5% DoB.

The ‘hot spot’ parametric equation (Figure 4.34) is clearly shown to be less

accurate by the increased degree of scatter in the results. This applies equally to the

stiffened and unstiffened models.

4.8 Conclusions and Recommendations

An extensive thin shell finite element study has been performed. This has given an

insight into the effect of a central longitudinal stiffener (similar to a rack plate in a

jack up chord) on the through thickness stress distribution in chord wall of tubular

-251


joints. The through thickness stress distribution has been represented by the Degree

of Bending (DoB) parameter.

In general the presence of a rack plate decreases the DoB in all tubular joint

geometries under Axial and OPB loading and increases under IPB loading. Higher

DoB can be translated as slower crack growth and longer fatigue hves. However in

most cases the changes were modest. The behaviour of several types of rack plates

have been investigated and quantified.

The apphcabihty of existing parametric equations has been assessed and it has been

shown that the DoB parameter can in most cases be predicted within +/-5% DoB

for stiffened joints via the use of the appropriate parametric equation. However a

tendency for the parametric equations to return unconservative DoB values has

been identified.

Experimental crack growth data from unstiffened welded tubular joints was

presented in Chapter Two. The similarity of the DoB results from unstiffened and

stiffened models allows greater confidence to be placed in the direct apphcabihty of

these results to the stiffened geometries found in jack ups.

- 252 -


4.9 References

[4.1] Connolly, M.P., Hellier, A.K., Dover, W.D. and Sumo to, J. “A Parametric

Study of the Ratio of Bending / Membrane Stress in Tubular Y and T JointsT

Int. J. Fatigue. v l2 , n l, pp 3-11., 1990

[4.2] UK Department of Energy, 'Background to New Fatigue Design Guidance for

Steel Welded Joints in Offshore Structures”, November 1990

[4.3] Holdbrook, S.J. "The Application of Linear Elastic Fracture Mechanics to

Fatigue Crack Growth in Tubular Welded Y and K Joints”, PhD Thesis,

University College London, 1980

[4.4] Aaghaakouchak, A., Glinka, G., Dharmavasan, S., "A Load Shedding Model

fo r Fracture Mechanics Analysis of Fatigue Cracks in Tubular Joints”, Proc.

8® Int. OMAE, 1989, ppl59-165

[4.5] Newman, J. C. and Raju, I. S., "An Empirical Stress Intensity Factor Equation

for the Surface Crack.”, Engineering Fracture Mechanics, v l5, n2, 1981,

ppl85-192

[4.6] Gore, M. and Burns, D. J. "Estimation of Stress Intensity Factors fo r Irregular

Cracks Subjected to Arbitrary Normal Stress Fields”, Proc. 4^ Int. Conf. On

Pressure Vessel Technology, London, IMechE, 1980, vl,ppl39-147

[4.7] Aaghaakouchak, A., Dharmavasan, S., Glinka, G., "Stress Intensity Factors for

Cracks Under Different Boundary Conditions.”, Eng. Frac. Mech., v37, n5,

p p l125-1137, 1990

[4.8] Forbes, J., Glinka, G., Burns, D.J., "Fracture Mechanics Analysis of Fatigue

Cracks and Load Shedding in Tubular Welded Joints”, Proc. Int. Conf.

Offshore Mechanics and Arctic Engineering, v3, pp307-313, 1992

[4.9] Berge, S., HasweU, J., Engesvik, K., "Fracture Mechanics Analysis of Tubular

Joints Tests Degree of Bending Effects”, Proc. Int. Conf. Offshore Mechanics

and Arctic Engineering, v3, ppl89-194, 1994

[4.10] HasweU, J. "A methodology fo r assessing cracks in complex tubular Joints

- 253-


subject to complex loading''. Integrity of Offshore Structures Symposium,

Glasgow, 1990.

[4.11] Shen, G., Glinka, G., “Weight functions for a surface semi-elliptical crack in a

finite thickness plate". Theoretical and Applied Mechanics, v l5 , ppl47-155,

1991.

[4.12] Chang, E., “Parametric Study of Non Destructive Fatigue Strength Evaluation

of Offshore Tubular Welded Joints", PhD Thesis, October 1997

[4.13] Hellier, A.K., ConnoUy, M.P., Dover, W.D. “Stress Concentration Factors for

Tubular Y and T Joints", Int. J. Fatigue, v l2 (l), 13-23 (1990)

[4.14] Bowness, D, Lee, M.M.K. “Stress Fields and Stress Intensity Factors in

Tubular Joints", Proc. Int. Conf. Offshore Mechanics and Arctic Engineering,

v3, pp839-846, 1993

[4.15] Tubby, P.J., Eide, 0.1., SkaUerud, B., Berge, S. “Variable Amplitude Fatigue

of Steel Tubular Join ts in Sea Water with Cathodic Protection", Proc. Int. Conf

Offshore Mechanics and Arctic Engineering, v3, ppl81-187, 1994

[4.16] Hibbitt, Karlsson & Sorenson (HKS) Inc., ABAQUS v5-5.1.

[4.17] Chang, E., Dover, W.D., “Stress Concentration Factor Parametric Equations

for Tubular X and ST Joints", Int. J. Fatigue, vl8, n6, pp363-387,1996

- 254-


Joint ShapeParameter T Y

a 10 10P 0.66 0.66Y 15 15T 1 1e 90° 60°

T a b l e 4 . 1

F i n i t e E l e m e n t M o d e l J o i n t P a r a m e t e r s

Bending / Total Stres s

Location Loading Mode Acrylic Connolly et at CurrentChord Saddle Axial 0.82 0.83 0.85Chord Crown IPB 0.75 0.77 0.78

T a b l e 4 . 2

V a l i d a t i o n o f F E M o d e l R e s u l t s

- 255-


Brace

Chord

Rack Plate

F i g u r e 4 . 1

T u b u l a r T j o i n t s h o w i n g p o s i t i o n o f c o n s t a n t t h i c k n e s s s t i f f e n e r

Brace

C h or d

Ra c k Plati

Rib Plate

Figure 4.2Tubular jo in t showing dual thickness stiffener

- 256 -


Brace

Chord

Rack Plate

F i g u r e 4 . 3

T u b u l a r j o i n t s h o w i n g n o n c o n t i n u o u s s t i f f e n e r

1000

> Axial

Axial (Mean)

k OPB

- . OPB (Mean)100

101.00E+05 1.00E+06 1.00E+07

Fatigue Life, (cycés)

1.00E+08

F i g u r e 4 . 4

E ffe c t o f l o a d i n g m o d e u s i n g e x p e r i m e n t a l d a t a b a s e r e s u l t s

- 257 -


Th r o u g h T h i c k ne s s St res s Dist r ibut ion

Notch Re g i on O m m i t ed

F i g u r e 4 . 5

T h r o u g h t h i c k n e s s s t r e s s d i s t r i b u t i o n

+

+

+

4-

DoB < 1

DoB = 1

DoB > 1

F i g u r e 4 . 6

E x a m p l e s o f v a r i o u s v a l u e s o f t h e D o B P a r a m e t e r

- 258-


0.7 --

0.6 --

I 0 5a01 0.3 -- CÔI 0.2

-0.1 --

-0.20 0.1 0.2 0.3 0.5 0.7 0.80.4 0.6

■Bending

-Membrane

Normalsed Crack Depth, a/t

F i g u r e 4 .7C h a n g e o f b e n d i n g a n d m e m b r a n e s t r e s s c o m p o n e n t a t t h e c r a c k e d s e c t i o n f r o m e x p e r i m e n t a l

m e a s u r e m e n t s o n a l a r g e s c a l e , a x i a l l y l o a d e d t u b u l a r j o i n t

Figure 4.8Deformed mesh fo r axially loaded T jo in t

-2 5 9 -


0.95 -- IPB

Axial

0.85 --

0.8 -■

0.75

0.65 - ■

0.6 - -

0.55

0.50 10 7020 80 9030 40 50 60

Ang\e Around Intersection

Current FEAO Acrylic - Axial

A Acrylic - IPB

F i g u r e 4 . 9

V a l i d a t i o n o f F E m o d e l u s i n g a c r y l i c m o d e l r e s u l t s

0.1 0.15 0.2 0.25

NormaSsed Stiffener Tfiickness, tl/D

- Axial T

0.35

Figure 4.10Comparison o f thick and thin shell model D oB results

- 260 -


0.95 --

0.9

0.85

Axial T

Axial Y

0.8a

0.75 - ■

Rack Plate

0.7

0.65

0.60.2500 0.3000 0.35000.0000 0.0500 0.1500 0.20000.1000

Normalsed Rack Thickness. 11/D

F i g u r e 4 . 1 1

D o B v a l u e s f o r a r a n g e o f r a c k t h i c k n e s s e s u n d e r a x i a l l o a d i n g

0,0000 0.0500

0.95 --

0.85 --

1 0.8

0.75 -- Rack Plate

0.7 -■

0.65 --

0.60.1000 0.1500 0.2000 0.2500 0 3000 0.3500

Normaised Stiffener Thickness, t1/D

■T Joint

- Y Joint

Figure 4.12DoB values fo r a range o f rack thicknesses under OPB loading

- 261 -


0.95 -

0.85 - •

m 0.8a

0.75 - -

Rack Plate0.7 -

0.65 - -

0.6----0.0000 0.0200 0.1400 0.1600 0.18000.0400 0.0600 0.0800 0.1000 0.1200

-T Joint

- Y Joint

Normaléed Rack Thickness, t l/D

Figure 4.13DoB values fo r a range o f rack thicknesses under IP B loading

0.99 -■

0.98 --

Rack Plate

0.97

0.96

^ 0.95 -

0.94 -

0.93

0.92 -

0.91

0.90 0.05 0.350.1 0.15 0.2 0.3

N orm aisod Rack Plata Thickness, t l /D

Figure 4.14Normalised DoB values under A xia l loading

-T Joint

- Y Joint

- 262-


1.08 ■ -

1.06

1.04 - -

® 1.02 - -

^ 0.98 - -

0 .96 - -

0 .94 ■ -

0 .92 - -

0 .9

0 0.05 0 .2 5 0.3 0.350.1 0.15 0.2

-T Joint

- Y Joint

Normalised Rack Thickness, t l/D

F i g u r e 4 . 1 5

N o r m a l i s e d D o B v a l u e s u n d e r O P B l o a d i n g

0.99

0.98

0.97 ■ -

m 0.96

0.95

0.94

Rack Plate0.93

0.92

0.91 --

0 .9

0 0.16 0.180.02 0.04 0.12 0.140.06 0.08 0.1

- T Joint

-V Joint

Normalised Rack Thickness, tl/D

Figure 4.16Normalised DoB values under IPB loading

- 263-


1.04

1.02 - -

0.98 - -

5 0.96

0.94

0.92 --

0 0.05 0.1 0.25 0.3 0.350.15 0.2Normalised Rack Plate Thickness, t1/D

•T Axial

- Y Axial

-T O P S

-Y O P B

■T IPB

Y IPB

F i g u r e 4 . 1 7

S u m m a r y o f n o r m a l i s e d D o B d a t a f o r t u b u l a r j o i n t s w i t h r a c k p l a t e s

Rib Pla teR a c k P la te

F i g u r e 4 . 1 8

T e r m i n o l o g y a n d n o t a t i o n u s e d t o d e s c r i b e m o d e l s w i t h n o n - c o n t i n u o u s s t i f f e n e r s

- 264 -


ti/D=o.oa

fl/b Plato Thicknoss / Chord Diarr^ter (t2/D)

F i g u r e 4 . 1 9

E jfe c t o f r i b p l a t e o n D o B i n a n a x i a l l y l o a d e d T j o i n t

t1/D=0.17

0.83

0.825 --

0.82 -- z/D

0.1000.815 --

0.2

0.30.81 -■

Continuous

0.805 ■ -

0.80 0.025 0.03 0.0350.005 0.01 0.015 0.02

0.83

0.825 - -

0.82 - -

o 0.815 --

0.81 --

0.805 ■ -

0.80.005 0.01 0.015 0.02 0.025


Continuous

0.03 0.035

Figure 4 .20Ejfect o f rib p late on D oB in an ax ially loaded T joint

- 265 -


t1/D=0,33

0.83

0.825 --

0.82 --Z/D

0.1o 0.815 "

0.20.3

0.81 --Continuous

0.805 --

0.80.0350 0.005 0.025 0.030.01 0.015 0.02


F i g u r e 4 . 2 1

E f f e c t o f r i b p l a t e o n D o B i n a n a x i a l l y l o a d e d T j o i n t

t1/D=0.08


Figure 4.22Effect o f rib p late on DoB in an O PB loaded T Joint

0.89

0.885 ■-

0.8a--Z/D

0.1o 0.875 - -

0.20.3

0.87 - - — ■ " Continuous

0.865 ■ -

0.860.0350 0.005 0.0250.01 0.030.015 0.02

- 266-


t1/D=0.17


F i g u r e 4 . 2 3

E f f e c t o f r i b p l a t e o n D o B i n a n O P B l o a d e d T j o i n t

t1/D=0.33

Rib Plate Thickness / Chord Dmmeter (t2/D)

Figure 4.24Effect o f rib plate on DoB in an O PB loaded T Joint

0.89

0.885 --

0.88 - -

Z/D

g 0 .875-- 0.20.3

0.87 - - ' Continuous

0.865 - ■

0.860.03 0.0350 0.0250.005 0.01 0.015 0.02

0.89

0.885 --

0.88 --2/00.1

o 0.875 --0.20.3

' Continuous

0.865 --

0.860.0350.025 0.030 0.005 0.020.01 0.015

- 267-


t1/D=0.08

0.810.808 -■

0.806 - -

0.804 --

0.802 -- -O

1 0.8 --

0.798 - ■

0.796 - ■

0.794 - ■

0.792 --

0.790 0.005 0.0250.01 0.015 0.02 0.03 0.035

Z/D

0.10.20.3

— Continuous


F i g u r e 4 . 2 5

E jfe c t o f r i b p l a t e o n D o B i n a n I P B l o a d e d T J o i n t

t1/D=0.17

0.81

0.808 -■

0.806 --

0.804 - ■Z/D

0.802 -- 0.1S 0.8- 0.2

0.30.798 --

Continuous0.796 --

0.794 - -

0.792 -■

0.790 0.005 0.025 0.030.01 0.015 0.02 0.035

Rb Plate Thickness /Chord Diameter (t2/D)

Figure 4.26Ejfect o f rib p late on DoB in an IP B loaded T jo in t

- 268 -


t1/D=0.33

0.81

0.808 - -

0.806 - -

0.804 --Z/D

0.802 -- 0.1020.30.798 - -

0.796 - ■

0.794 - -

0.792 - -

0.790 0.005 0.01 0.015 0.02 0.025 0.03 0.035

R t Plate Thickness / Chord Diameter (t2/D)

F i g u r e 4 . 2 7

E f f e c t o f r i b p l a t e o n D o B i n a n I P B l o a d e d T j o i n t

- 269-


0 87 -

0 8 5Q

0 83 --

0.82

0 81

0 65 6 7 8 9 10 11 12 13 14

Alph*

i ) A x i a l l o a d i n g

0 8 2

0 8 1

5 6 7 14a 9 10 11 12

Alphm

i i ) O P B l o a d i n g

- - - HCO Saddle------------HCO Hot Spot

A UnstifteoedO StiHened

- - - HCO Saddte

-----------HCO Hot Spot

6 Unsltfenad

O Stillaned

s-H(.0 HU

UnshMwiM

H i ) I P B l o a d i n g

F i g u r e 4 . 2 8

D e p e n d e n c y o f D o B o n r a t i o o f c h o r d l e n g t h a n d d i a m e t e r ( A l p h a )

- 270 -


. - -

---------- H(DHrtA IJrml0wiwl O StiMMNNi


S«la


09 2

0 89

- - - HCO S«ddl»

-------------- HCO Ho( Spot0 88

?

08 5

0 83080 8 0,70 0 1 0 2 0 3 0 4 0 5

0 9

0 8 2

Q

0 7 2

0 80 70 0.1 0 2 0 3 0 4 0 5 0 6

- - - HCOSadde-----------HCO Hot Spot

A UnstxMened O Sifferwd


F i g u r e 4 . 2 9

D e p e n d e n c y o f D o B o n r a t i o o f b r a c e a r u l c h o r d d i a m e t e r s ( B e t a )

- 271 -


0.75 30 362S

- -

A I


§


0 92

0 5 10 IS 20 25 30 35

- - - HCO SmddI#

--------------HCO Hot Spot

A Un»tiM#n*d

O SlffiOAd

i i i ) I P B l o a d i n g

F i g u r e 4 . 3 0

D e p e n d e n c y o f D o B o n r a t i o o f c h o r d d i a m e t e r t o t h i c k n e s s ( G a m n u i )

- 272 -


0 7 2

0 0,2 0,3 0 4 0.5 0 6 0 7 0 8

Tau


Tau


- - - HCO SaddI#

------------- H C O H o*S oo(

AO Siffanad

Q

0 0 1 0 2 0 3 0 4 0 5 0 7 0 8 0 9 10 6

- - - H C O S a d d a

----------- HCO Hotspot

A Unsortened

O S#Maned

. - - HCOSwhk,------------HCX) Hi SjMl

A llimttlMMii

O SI4t«fHNl

0 1 0.2 0.3 0 4 0.5 0 6 0,7 0,6 0 « 1

Tau


F i g u r e 4 . 3 1

D e p e n d e n c y o f D o B o n r a t i o o f b r a c e t o c h o r d t h i c k n e . s . K ( T a u )

- 273-


<s

Bm ctA ng tt Thsts


B itc e Angle. Thetm

i t ) O P B l o a d i n g

0,91

0.87

0,8520 30 50 60

. . -

-------------- H (T > H nl SfMi

4 U iiMrfffV im i

0 78

0.74

0,72

0.720 50

- - HCO

----------HCO Hi4 Spi4

A UriMWIWMMl

o

B rx 0 Angt0. Th»m


F i g u r e 4 . 3 2

D e p e n d e n c y o f D o B o n b r a c e a n g l e ( T h e t a )

- 274 -


0.95 --

^ 0.85 --I.2 0.8 - -

i !CD

•0

g 0.75 --

0.7 --

0.65 - -

0.60.6 0.65 0.7 0.75 0.85 0.9 0.950.8 1

DoB Predicted

# Unstiffened

O Stiffened

- - - - +/- 5% DoB

F i g u r e 4 . 3 3

M e a s u r e o f a c c u r a c y o f ‘S a d d l e ’ p a r a m e t r i c e q u a t i o n o f C o n n o l l y e t a l

0.95 - -

0.9 --

c 0 .8 5 --

0.65 ■ -

0.65 0.7 0.75 0.8 0.85

DoB Predicted

0.9

* Unstiffened

O Stiffened

- - - - +/- 5% DoB

0.95 1

F i g u r e 4 . 3 4

M e a s u r e o f a c c u r a c y o f ‘ H o t S p o t ’ p a r a m e t r i c e q u a t i o n o f C o n n o l l y e t a l

- 275 -

Chapter 5 - Fracture Mechanics Modelling of Jack Up Chord Defects

Chapter 5

5. Fracture Mechanics Modelling o f Jack Up Chord Defects

5.1 Introduction

Accurate predictions of fatigue crack growth in tubular joints are required for

defects discovered in service. Fatigue cracks found during periodic inspections

must be assessed in order to ensure the structural integrity of the installation is not

compromised. Depending on the outcome of the investigation, remedial action

such as repair grinding, clamping of the joint or simply monitoring of the defect via

more frequent inspections can be implemented.

A number of fracture mechanics models for predicting fatigue crack growth in

tubular welded joints have been published in the literature. A selection of these

models will be presented and assessed here. These will include adapted flat plate,

empirical and analytical (PEA) derived models. The basis and background to each

model will be presented before assessing the accuracy of the models by comparing

the SIP predictions with those derived from the experimental fatigue tests

presented in Chapter Two. Additionally the PEA derived solution of Chong Rhee

et al [5.1] will be evaluated. This model is singled out for separate inspection since

it is to be incorporated as the recommended fracture mechanics solution for welded

tubular T joints in the forthcoming revision of PD6493 [5.2] and the new ISO code

on the Design of Offshore Structures [5.2].

The influence of a rack plate on the stress distribution in jack up chords has been

quantified in Chapters Three and Pour. This information will be integrated into the

models shown to most accurately model the crack growth behaviour from the

experimental study. This should allow an insight in to the manner in which a rack

plate will change the fatigue crack growth behaviour in jack up chords.

276 -


5.2 Stress Intensity Factors in Tubular Joints

The concept of Stress Intensity Factors being used to characterise the crack tip

stress field and thus fatigue crack growth behaviour was discussed in Section 1.9.

Analytical solutions exist for certain idealised situations. The SIP for an infinite

centre cracked plate under uniform tension as shown in Figure 5.1, is given by

(5.1).

K = a 4 m (5.1)

This is obviously far removed from a semi-elliptical surface crack, in a complex

stress field as found in welded tubular joints. The SIF Modification Factor Y, was

also introduced in Section 1.9 as a means of accounting for effects of geometry

and loading conditions. Additionally Y often varies with crack size.

The Y Factor can be thought of as being the product of several individual factors

each accounting for specific effects. For the case of a tubular joint, the following

corrections are thought to be necessary (5.2).

Y = (5.2)

where

Ys Free surface correction

Yg Non-uniform through thickness stress distribution

Yw Finite plate width correction

Yk Correction for geometrical discontinuity at weld

Yc Crack shape correction factor

Ym Correction for changes in structural restraint

The above breakdown is especially helpful when attempting to adapt Hat plate

based models for cracks in simple stress fields. For empirically derived models.

- 277 -


each of the above effects is of course, implicitly included via the experimental data

used in the derivation of the model

5.3 Y Factor Predictions Using Empirical Models

A number of models have been developed using Y Factor information derived from

crack growth data generated from fatigue tests on large scale welded tubular joints.

The ability to capture accurate crack depth and shape data using the Alternating

Current Potential Drop Method (ACPD) was demonstrated in Chapter Two. This

information can be manipulated to yield Y Factor information provided that the

da/dN - AK relationship (i.e. C and m Paris Law data) is known for the material to

be tested. Prior to presentation of the development of the empirical models derived

to date, the extraction of Y Factors from crack growth data will be outlined. This

procedure has been applied to the data derived from the expeiimental test

programme presented in Chapter Two and will serve as the basis for the

comparison of the accuracy of each of the models presented in this Chapter.

5.3.1 Extraction of V Factors from Crack Growth Data

By monitoring the crack depth at discrete points along the crack front, the

development of the defect from initiation to through wall penetration can be

captured. The deepest point along the crack front can be determined for each

inspection and this data used to determine the crack growth curve (a versus N).

Using the procedure described in Chapter Two, the experimental crack growth

rates can be determined from the first differential of second order polynomials

fitted around each data point.

With knowledge of the hot spot stress range, Ac, the Paris constants C and m, the

instantaneous crack depth, a, and the experimental crack growth rate (da/dN^xp) at

that point, the experimental Y factor, Ycxp can be determined using (5.3)

- 278 -


da

V y j

l/m

n .p = — ^ r - (5 3)

The results obtained from this method obviously depend on having accurate Paris

Law data for the material and environment in which the test was performed.

Unfortunately reliable Paris Law data is not available for the CP levels used during

the corrosion fatigue tests. For this reason the fracture mechanics modelling

presented in this Chapter will be limited to the data derived from the air tests, T1

and T2. A simple single segment Paris Law crack growth model was used during

the analysis of the data from tests T1 and T2 as shown in (5.4).

- ^ = 2.72x 10-‘^AA:” ” (5.4)dN

The Paris Law constants presented in (5.4) are from compact tension (CT)

specimen tests performed in air by Creusot Loire Industrie [5.4]. Data was supplied

for the parent plate and HAZ. It is the parent plate values that were used here as

this is the most appropriate for the chord side cracks observed in this study. The

Ycxp Factors determined using the above procedures for tests T1 and T2 are

illustrated in Figures 5.2 and 5.3 respectively.

5.3.2 AVS Model

Fatigue crack growth data from large scale tubular tests using a number of joint

types and loading modes has allowed the development of empirical models to

predict fatigue crack growth in tubular joints. It was noted that the hot spot stress

was insufficient to describe the fatigue crack growth alone as joints tested at the

same hot spot stress level but under different loading modes yielded different lives.

This was discussed in Chapter Two. The stress distribution around the intersection

together with the loading mode, joint geometry and joint size are other parameters

- 2 79 -


that also have an effect on joint endurance. The first of these, the stress distribution

around the intersection was considered the most important during the development

of the Average Stress Model (AVS) [5.5]. Central to this model is the average

stress parameter,ASP (5.5).

where

ASP=SCFh /SCFav

SCFh Hot Spot Stress

SCFav Average Stress

(5.5)

and SCFav is given by (5.6) for in plane bending and (5.7) for out of plane bending

and axial loading.

k / 2

SCF^ = - \SCF{<}>)cl(l>^ - f f / 2

(5.6)

where

1 *(5.7)

(j) Angle around intersection

(tc/2 is the saddle position)

Specimen geometry / loading mode combinations resulting in average stress

parameters between 1.18 and 2.22 were used during the development of the model.

The Y factor is given by (5.8).

Y = A

where

A = 0.73-0.18ASP

(5.8)

(5.9)

- 2 8 0 -


j=0.24+0.06ASP (5.10)

The five data sets used during the development of the model were derived from

tests on tubular joints with wall thicknesses of 16mm. No thickness correction will

therefore be necessary during the application of this model.

5.3.3 TPM Model

The AVS Model was further developed to better model the early crack growth

phase. It was noticed from fatigue tests on tubular joints of different wall thickness

that increasing the joint size affects the early crack growth phase. The model is

based on data collected from chord side fatigue cracks in joints covering the

parameter range:

0.21 <P <0.76

2.66 < SCFh < 9.4

1.51 < SCFav <6.35

16mm < t < 45mm

The Two Phase Model [5.6] defines the Y Factor function as shown in (5.11).

Y = MBrji Me

(5.11)

where;

M = 1 for a/T > 0.25

M = (0.25T/a)-^ for aTT < 0.25.

The parameters B and k are functions of size and average stress as given in (5.12)

and (5.13).

B = (0.669 - 0.1625ASPKT/0,016)""" (5.12)

k = (0.353 + 0.057ASP)(T / 0.016)’"''” (5.13)

281


The function p controls the early crack growth phase (5.14).

p = 0.231(1/0.016)-'’ ‘’ 'P“ ‘SCFb‘” * (5.14)

It should be noted that both the TPM and AVS model take no account of crack

aspect ratio. The crack shape is assumed to take the form of the crack shapes

encountered in the experimental tests on which the models were based.

5 .3.4 Modified A VS Model

It was noted by Austin [5.7] that the Average Stress Model tended to over predict

the experimental Y factors derived from variable amplitude corrosion fatigue tests

on axially loaded T joints. This over prediction was by a factor of approximately

15%. The majority of the data used in the formulation of the AVS model was

derived from variable amplitude fatigue tests employing a single double peaked

power spectrum [5.8]. However a simple stress range cycle counting algorithm was

used to determine the weighted average stress range used to characterise the load

sequence. Austin notes that if the more complex ‘rainflow’ cycle counting

technique had been used (as was used by Austin to characterise the multi-sea state

WASH load sequence) then the parameter A in the AVS model (5.8) would be

different.

Austin attempted to infer the difference in the equivalent stress range predicted by

range and rainflow counting, noting that the difference is likely to be dependant on

the sequence bandwidth. The difference between the rainflow and range derived

equivalent stresses at bandwidth representative of the double peaked power

spectrum was found to be a factor of 1.15. Austin thus proposed a modification to

the AVS model which was simply to reduce the Y Factor predicted by the AVS

model by 15% resulting in an improved fit to experimentally derived Y factors.

Each of the three empirically derived models outlined above will be compared with

the experimental results from the current investigation in the next Section.

2 8 2 -


5.3.5 Evaluation of Experimentally Derived Models

The AVS, TPM and modified AVS models are plotted in Figures 5.4 and 5.5

where they are compared with the experimentally derived Y Factors from Tests T1

and T2. Although the TPM is the most sophisticated of the empirical models it is

clearly seen to poorly model the early crack growth region (a/t <0.25), under

predicting the Y Factors significantly. This is perhaps surprising as this was the

region where the TPM model was supposed to offer improved modelling of the

thickness effect. Both of the AVS models offer improved correlation with the

experimental results, predicting the shape of the curve very well. In particular the

Modified AVS model is seen to perform particularly well providing an excellent fit

to Ycxp for both tests at all crack depths.

This suggests that the difference between the AVS model and the experimental

results of Austin [5.7] was a geometry effect rather than an artefact of cycle

counting method. The geometry tested by Austin was identical to that used during

this investigation however constant amplitude loading was used in this case. This

discounts the possibility of using variable amplitude based arguments to explain the

difference. It is therefore suggested that the argument used by Austin to justify the

factor applied to the AVS model, whilst valid, is not the sole or even dominant

source of the error. However regardless of the source of the error the quality of the

fit appears to provide a good basis for accurate fracture mechanics crack growth

predictions for the test geometry. However this observation is specific to the

geometry under consideration here.

The second comment that arises from the close agreement of the model and the

experimental based results concerns the Paris Law data used in the derivation of

the Yexp factors from the crack depth information. Greater confidence can now be

placed in these values which were derived from simple specimen tests. This crack

growth model was used for all fatigue crack growth modelling presented in this

Chapter.

- 283 -


5.3.6 Fatigue Crack Growth Predictions

The AVS models have been shown to provide an excellent fit to the experimental

data. Thus the AVS and Modified AVS models have been chosen as the basis for

the fatigue crack growth predictions presented in this Section.

The procedure used for the crack growth predictions was as follows:

1) The crack depth range under consideration was divided into 250 linear

intervals. Logarithmic intervals were also used initially for comparison

purposes, however the differences in resulting lifetimes was negligible.

2) The value of AK at the beginning and end of each interval was calculated and

the average was used as the representative SIF for the interval. The SIF values

were calculated using the appropriate Y Factor Model.

3) The average crack growth rate for the interval was calculated from the

representative SIF range according to (5.4)

4) The number of cycles required to propagate the crack across the interval, from

ai-i to ai was calculated according to (5.15)

5) The total number of cycles required to propagate a crack to a given depth a,

from an initial depth ao is given by (5.16).

TV, = %ATV, (5.16)

- 2 8 4 -

Chapter 5 - Fracture Mechanics Modelling of Jack U p Chord Defects

The initial crack size used in these calculations was 0.1mm. A survey of the

hterature reveals much attention has been placed on the initial crack size to be used

in fracture mechanics models. Such judgements are usually based on the sizes of

the weld toe defects inherent to untreated welded joints. However in this instance

the procedure is simple as the intention is to model the crack propagation period

found in the tubular joint tests. The ACPD results presented in Chapter two

showed the technique to be able to reliably detect and size defects smaller than

0.1mm. A depth of 0.1mm was set as the criteria for determining the initiation life

for each test. For this reason the summation of the number of cycles used during

each crack growth interval was commenced at the measured initiation life (Ni)

rather than zero. The initial crack depth was set as 0.1mm.

The results of the crack growth modelling using the AVS and modified AVS

models are shown in Figures 5.6 and 5.7. Despite the excellent fit of the models to

the experimentally derived Y Factors, both models under predict fatigue crack

growth hves. The improved fit of the modified AVS over the AVS model results in

more accurate predictions, however they are still a significant underestimation of

the experimental lives. The above applies equally well to both tests T1 and T2.

A simple power law was fitted to the Yexp results from both tests. The equation

was of the form used by the AVS model (5.8) as shown in Figures 5.8 and 5.9.

Although the co-efficients A and j are only slightly different to those predicted by

the AVS model the resulting crack growth predictions are much improved as

shown in Figures 5.6 and 5.7.

5.4 Finite Element Based Models

The finite element based SIF solution of Chong Rhee et al [5.1] provides a fracture

mechanics model for tubular T joints under axial, IPB and OPB loads. The solution

was based on 40 finite element models of cracked tubular T joints. The intersection

between the brace and chord was modelled using 20 node isoparametric elements

285 -


and 8 noded thick shell elements formed the remainder of the joint. The crack was

modelled using collapsed quarter point elements. The model has been

recommended for inclusion in the revised BS PD6493 [5.9] and for the new ISO

code for fixed steel offshore structures [5.10]. The model is said to be valid over

the following range of joint size and crack shape parameters.

a=12

0.40< P < 0.80

1 0 . 0 < y < 2 0 . 0

0 .3 < t< 1.0

0.05 < a/t < 0.80

0.5 <3c/d< 1.20

where a is the crack depth, c is the crack half length and d is the brace

diameter

The chord length parameter (a) was set at 12 which was assumed sufficient to

neglect the boundary effect of the chord. Apart from the chord length / diameter

ratio (a), all other criteria are met by the tubular T joint fatigue tests described in

Chapter Two. This makes the Yexp factors derived from these tests ideal for

assessing the accuracy of this model.

The stress intensity factors for the deepest point along the crack front for a tubular

T joint under axial loading is given by (5.17)

(5.17)

where

Yg is the joint geometry factor

Yi is a crack size factor

Ys is a joint and crack coupling factor

- 2 8 6 -


On is the brace nominal stress

The stress intensity factors are given as equivalent SIF’s, where K<; is defmed as

(5.18)

and Y — Q 2 *7 ^ Ç ^ “®-^225-1.26851n/î^ 1.3191-0.1661 In T ^ l .6621+0.37041n ^

_ j^0.3562M-0.0956C^0.0983A+0.2298C+0.0817C^ ^-0.0762i4

y, = (a / tYi'ic I d)'

p = -0.8669 - 0.2198A - 0.0162A^ - 0.4750C^ - 0.1667C’ - 0.01930"

r = 0.0777+1.0531A + 0i820A^ + 0.0810A’ - 0.7001C-0.0604C^ +0.0060C’

A = ln

C = In

{ - K t)

Using the crack shape data measured in Tests T1 and T2, Y Factors have been

calculated using this solution and are compared to the Yexp factors in Figures 5.10

and 5.11. The Stress Intensity Factors predicted by this model are clearly over

conservative in both cases. The sensitivity of the fatigue life predictions to SIF

input data has been demonstrated by performing fatigue crack life integrations

based on the AVS model in the previous section. Even the excellent fit of the AVS

model produced crack propagation lives shorter than the experimental life by a

factor of two or more. It seems unlikely therefore that this model will help produce

accurate predictions of fatigue crack growth in cracked tubular T joints.

-287 -


Furthermore it can be seen that the vahdity range of the model in terms of crack

depth is severely restricted in Test T2. This is due to the fact that the crack shape

development was different in the second test, with the crack surface length tending

to be slightly longer. This results in the situation where the restriction on the

surface crack length parameter (3c/d) is violated for crack depths deeper than

approximately 10mm.

From this limited investigation into the capability of these equations to accurately

model the crack growth behaviour in tubular T joints, it seems difficult to

understand the reasons for their future inclusion in influential standards. From the

evidence presented here they are unlikely to provide more than a very conservative

estimate of the crack growth behaviour across a limited range of crack depths. It is

suggested that such a function could be equally well performed by a fiat plate based

model such as Newman Raju as presented in the next Section.

5.5 Flat Plate Derived Models

Models have been developed to calculate the SIF for semi-elliptical surface cracks

in flat plates under tension and bending loads. The most widely used of these

models include the equations derived by Holdbrook and Dover [5.11] and Newman

and Raju [5.17]. The Newman-Raju equations were utilised by Monahan [5.12] to

develop a fracture mechanics model to predict the early fatigue crack growth

behaviour in tubular X and more complex multi-brace tubular joints. The Newman

Raju equations and the modifications implemented by Monahan will be presented,

assessed, and modified here.

5.5.1 Newman-Raju Equations

The Newman-Raju equations were developed using the results of a 3-D finite

element analysis of semi-elliptical cracks in an elastic fiat plate. For cracks with

very low aspect ratios, edge cracked plate FEA data were also included during the

development of the equations. The resulting equation takes the form of Eqn (5.19)

and accounts for both tensile and bending loads.

288


(5.19)

The equations are valid in the range

0<a/c< 1.0

c/b < 0.5

0<(j)<7:

where (|) is the parametric angle around the crack front as illustrated in Figure 5.12.

In this instance, only the SIF at the deepest point of the defect is of interest (i.e. (j)

= 7c/2). The SIF at this point is given by (5.20)

CD(5.20)

where F™ is the boundary correction factor for membrane (tension) loading, as

given by (5.21)

where

= / .

M , =1.13-0.093

0.89M ,- - 0 .5 4 + o 2 + ( « / c)

M , = 0 .5 -1.0

0.65 + [a! c)

and/w is a finite width correction factor

+ 14V c j

(5.21)

(5.22)

(5.23)

(5.24)

289


/w = secnc a2b \7

1/2

(5.25)

In this case the plate half width was assumed to be one half of the brace diameter.

In all cases yw was less than 1.25. The boundary correction factor for bending is

given by (5.26)

where

H = l + G , - + G J -t j

G, = -1 .22 -0 .21

G2 = 0 .5 5 -1 .0 5 |-

VC

+ 0.47<c

(5.26)

(5.27)

(5.28)

(5.29)

The shape factor >, is a complete elliptical integral of the second kind, an

approximation to which is given by (5.30).

0 = J l+ 1.464\ c j

(5.30)

The Y Factor given by the Newman Raju equation is therefore given by (5.31)

F^{\ — DoB) + FfjDoB 0 (5.31)

where DoB is the degree of through thickness bending (Le. bending to total stress

ratio).

The Y Factors (Y n & r ) predicted using this model are shown in Figures 5.13 and

5.14 for tests T1 and T2. The experimentally measured crack shape (a/c) was used

-290


as the input for this model and the degree of bending (DoB) was determined from a

thin shell finite element model. As would be expected the flat plate model over

predicts the SIF for all crack depths where a/t>0.1 (i.e. away from the influence of

the weld discontinuity).

5.5.2 Correction for Load Shedding

One reason for the poor correlation lies in the difference in the boundary conditions

found in a flat plate and a tubular joint. As was discussed in Chapter 4 the statically

indeterminate tubular joint differs from the statically determinate flat plate. The

moment through the cracked ligament is known to be dependant on the crack

depth in tubular joints whereas it is constant in cracked flat plates. This is

commonly referred to as load shedding and will result in decreased SIF’s for

deeper cracks. A common assumption which has been shown to yield reasonable

results is to leave the membrane component of the through thickness stress

independent of crack depth but decrease the bending component according to

(5.32) as proposed by Aaghaakouchak et a/ [5.14].

Cr. =<T;bo 1-----tJ

(5.32)

where Ch is the bending stress at the crack tip and Cho is the bending stress at the

surface. This can be incorporated into the flat plate solution as shown in (5.33)

F ^ ( l-D o B )+ F i^ D o B il-a / t)^ N & R +IM R ~ 0

The Y Factors predicted by Y N&R+LMR (Figures 5.13 & 5.14) show improved

agreement with the experimental data for crack depths satisfying a/t > 0.1.

However it is clear that the effect of the weld on the SIF’s for small cracks must be

accounted for if the flat plate based solutions are to be effective.

291


5.5.3 Correction for Non Uniform Stress Distribution

Accounting for the stress concentrating effect of the weld on the resulting Y Factor

requires prior knowledge of the through thickness stress distribution derived from

a model accounting for the presence of a weld. Such an analysis has been

performed by Monahan [5.13] who noted that Karé [5.15] had shown that the

effect of the weld on the stress distribution in a tubular joints could be predicted by

T-plate models providing the weld geometries were the same. Based on the results

of a T plate FE study, Monahan presents parametric equations predicting the

through thickness stress distributions for tension and bending. The equations are

dependant on the weld toe radius and the weld angle. The predicted distributions

for tension and bending are illustrated in Figures 5.15 and 5.16 for a weld angle

of 45° and ratio of weld toe radius to plate thickness, p/t of 1/25. Monahan used

these equations in combination with the procedure outlined by Albrecht at a I [5.16]

to calculate the Yg factors used to account for the weld toe discontinuity.

5.5.3.1 Aibrectits Method for Calculation of SIF'sThis method allows the computation of a non-uniform stress concentration

correction factor (Yg) from a known through thickness stress distribution in the

presence of a weld. In this instance this information will be obtained from the

parametric equations presented by Monahan [5.13]. The method is summarised in

Figure 5.17. A detailed description of the theory behind the method is not

necessary but the steps involved in the application of the model are as follows:

1) Determine the stress distribution along the anticipated crack path in the

uncracked component. The stress distribution is to include the effect of the

weld toe discontinuity.

2) Insert a crack of a given length. The crack is then divided into n separate

elements. Each element is subjected to a discrete stress range, Gxi which is

determined from the stress distribution from step one.

292 -


3) Using a solution based on the mode I SIF for an infinite centre cracked panel

subjected to a two pairs of opening line forces, symmetrical about the centre of

the crack and a distance x from it, the following solution can be derived for Yg.

• -1 SinX

'■+1 -1- smX :

(5.34)

where cr is the ‘nominal stress’ without the stress concentration for the

element under consideration, and a is the crack length. Repeating this procedure

for different crack lengths allows the determination of Yg for the range 0 < a/t < 1.

For the case of a tubular joint where the through thickness stress distribution has a

membrane and bending component, separate Yg factors can be calculated for each.

However, Albrecht [5.16] notes that the solution requires special treatment for the

case of pure bending. Attempts to apply the method to a pure bending situation

have shown the model to break down when a/t = 0.5 is approached (i.e neutral axis

for flat plates in pure bending).

The Yg Factors for pure tension have been calculated using (5.34) and the

parametric equation presented by Monahan [5.13]. This is shown in Figure 5.18.

As expected from the stress distribution, the Yg factor quickly diminishes to unity

(i.e. no effect on SIF) with little effect being seen for crack depths greater than a/t

= 0.2. The same situation would be expected for the bending case as the stress

distribution presented in Figure 5.14 again shows little effect for crack depths

deeper than approximately one tenth of the wall thickness. For this reason the Yg

factor calculated for membrane loading will also be applied to the bending

component. The flat plate based Y Factor now accounts for the effects of load

shedding and the non uniform stress concentration and can be calculated as follows

- 293 -


„ F j J \ - D o B ) + F J ^ „ D o B ( \ - a l t )^ N & R + L M R + N S C ~ ^ ( j . O j )

where Ygm is the Yg factor for membrane loading as shown in Figure 5.15.

The above assumption appears reasonable as the agreement with experimental Y

Factors is now much improved in the early crack growth region (a/t < 0.2) and

models the shape of the Y Factor curve for Tests T1 and T2 well.

5.5.4 Crack Shape Correction

Monahan [5.13] suggests the use of one final correction factor to account for

differences in crack shape. The suggested form of the correction factor is

Y = — ------- (5.36)^ N A R + N S C + I M R

Plotting Y against the crack shape (a/c) for Tests T1 and T2 in Figure 5.19 shows

some correlation. The approximation to this behaviour derived by Monahan has

been modified to better suit the current data set and is included in Figure 5.19. The

Shape Correction Factor is given by

y/ = 0.9 for a/2c < 0.05 (5.37)

¥ = l + 0.7(fl/2c-0.04) 0.4 - 0.1 for a/2c>0.05 (5.38)

The flat plate based Y Factor accounting for the non linear stress distribution,

linear moment release and crack shape is given by

(1 - DoB) + FJ^„DoB(\

0y — ____________ _^ N & .R + L M R + N S C + C S C ~ ^

294


This model is shown to accurately predict the Y factors determined experimentally.

It offers advantages over the empirically derived models in that it allows more

control over the input parameters than the AVS based models. This includes the

degree of through thickness bending, crack shape, effect of the weld and moment

redistribution. This flexibihty is important when attempting to model jack up chord

cracks where the stress distribution is known to be different and thus factors such

as crack shape may well be altered compared to unstiffened tubular joints.

5.6 Effect of Rack Plate on Fatigue Crack Growth Predictions

The rack plate has been shown in Chapter 3 and 4 to alter the stress distribution in

two ways for axially loaded T joints. Firstly, a significantly flatter stress distribution

around the outside surface of the intersection results in lower hot spot SCF’s. The

magnitude of the reduction depends on the joint geometry but can be of the order

of 50%. Secondly, a smaller effect on the degree of through thickness bending

(DoB) has been identified. The tendency is for a shght decrease in DoB (i.e.

increased membrane component) although the change is limited to a few percent.

The effect of the changed surface stress distribution on the resulting crack

propagation life can be investigated using the AVS model and its derivative. This

model cannot however take any account of the altered through thickness stress

distribution or any resulting change in crack shape. The AVS model has been

applied to an axially loaded T joint with a number of different stiffener thicknesses.

The tubular joint geometry investigated is that presented in Figure 3.17 of Chapter

3. Rack plate thicknesses of 1, 2, 10 , 20 , and 50mm were examined. Using the

intersection stress distribution determined from the finite element model results the

Average Stress Parameter (5.5) for each stiffener thickness was calculated. The

calculated ASP values for each stiffener are given in Table 5.1. Using these, the

fatigue propagation lives for each of the joints has been calculated using the AVS

and modified AVS models. A hot spot stress range of 400MPa was applied to the

unstiffened joint. The hot spot stress concentration factor was used to calculate the

nominal stress. This nominal stress was then apphed to each of the stiffened models

- 295 -


and the hot spot stress calculated accordingly. The crack growth results are

illustrated in Figure 5.20 for the AVS model and Figure 5.21 for the modified AVS

model. The results show the logarithmic dependency on hot spot stress as would be

expected. The factor by which the crack propagation lives are changed due to the

rack plate is shown in Figure 5.22. The propagation lives are shown normalised to

the life for the unstiffened joint. This curve is obviously independent of whether the

AVS or modified AVS models are used in its formulation. This analysis of course

takes no account of changes in initiation life due to the lower intersection stresses

and assumes the crack shape found in the experimental data on which it is based.

The Newman Raju based model of Monahan was described in Section 5.5. This

Model was adapted to better model the experimental data from the current test

series. The flexibility of this model in terms of control over the input data makes it

ideal for modelling defects in jack up chords. Factors such as crack shape

development and load shedding characteristics of cracks in jack up chords are

likely to be different to unstiffened tubulars. Unfortunately experimental data

covering the above areas is not currently available for input into the model. In the

absence of this the effects of the known variations in stress distribution were tested

using crack shape and load shedding data derived from unstiffened tubulars. The

Linear Moment Release method described in Section 5.5.2 was used to account for

load shedding. Crack shape development was assumed to be the same as the

experimental investigation presented in Chapter 2. Figure 5.23 shows the fatigue

crack half length c, plotted against the crack depth at the deepest point, a, from

tests T1 and T2. A third order polynomial has been fitted to this data as shown on

the chart. Crack shape development will follow this trend in all Newman Raju

based modelling presented here. The uncertainties discussed above combined with

the demonstrated sensitivity of fatigue life predictions to SIF accuracy combine to

dictate that the results of any analysis presented here are subject to significant

error. However the model can still be utilised to demonstrate the relative

importance of the beneficial surface SCF changes and the onerous reduction in

DoB for tubulars with rack plates.

-296


Firstly, the analysis presented above using the AVS models has been repeated using

the Newman Raju based model ( Y n & r + l m r + n s c 4C s c ) . The degree of bending

remained unchanged for each stiffener thickness and was equal to that of the

unstiffened model This was done since the DoB cannot be controlled in the AVS

models and since the model was based on the experimental results of unstilïened

joints the unstiffened DoB is most appropriate. The absolute values of the

normalised propagation lives will not be identical due to inherent differences in the

models. However the trends should be similar and we would expect both models to

predict propagation increased by an order of magnitude over their unstiffened

counterparts. This can be seen in Figure 5.24 where the Newman Raju model

predicts an even greater increase in life for the stiffened tubulars over the

unstiffened variety.

One would expect this increase in life to be tempered somewhat by the decrease in

DoB which would be expected to adversely affect propagation lives. The analysis

was therefore repeated but this time the decrease in DoB was implemented in the

model. The values of hot spot SCF and DoB used in this analysis are detailed in

Table 5.2. Accounting for the change in DoB is seen to reduce the propagation

lives (Figure 5.24) for the stiffened tubulars although the reduction in peak SCF

(and therefore hot spot stress range) is clearly the dominant factor.

5.7 Conclusions

Several tubular joint fracture mechanics models from the literature have been

presented. Models based on experimental tubular joint data, finite element data and

solutions for semi elliptical cracks in fiat plates have been included. Each has been

compared against the experimental results derived from the test series presented in

Chapter Two. It appears that all models lack ‘portability’ to a greater or lesser

extent. That is to say that the most accurate models are likely to be specific to

certain joint shapes and sizes and the more general models tend to be subject to

- 297 -


significant errors. The sensitivity of fatigue crack propagation lifetime predictions

compared to accurate SIF data was demonstrated. This sensitivity was magnified

by the high stress level (300 to 400MPa) used during the modelling.

A model based on the flat plate solution of Newman Raju (developed by Monahan)

was presented as a general fracture mechanics model shown to be able to predict

the shape of the Y Factor curve in tubular joints well. The advantage of this model

is the control the user has over the input parameters such as crack shape, weld

profile, load shedding characteristics etc. which is not available with the other

models. This model has been used to perform some preliminary analysis of crack

growth in jack up chord members using stress distribution information obtained

from the finite element analysis presented in Chapters 3 and 4.

Finally the SIF solution of Chong Rhee [5.1] was assessed against the fracture

mechanics information obtained from the experimental fatigue test on tubular T

joints. The model appears to be extremely over conservative and in some cases of

limited apphcability due to restrictions on allowable crack shapes. However the

solution is conservative over the entire range of crack depths whereas others may

model crack growth better but display unconservative behaviour at different stages

of crack development.

- 298 -


5.8 References

[5.1] Chong Rhee, H., Han, S., Gibson, G., "'Reliability of Solution Method

and Empirical Formulas of Stress Intensity Factors for Weld Toe Cracks

of Tubular Joints’\ Proc. Tenth Offshore Mechanics and Arctic

Engineering Conference, ASME, v3-B, pp441-452, 1991

[5.2] BS PD 6493:1991 "Guidance on Methods fo r Assessing the

Acceptability of Flaws in Welded Structures’', British Standards

Institution, London, 1991

[5.3] ISO 13819-2, "Petroleum and Natural Gas Industries - Offshore

Structures, Part 2: Fixed Steel Structures", To be published

[5.4] Balladon, P., Coudert, E., ‘TPG 500 Structural Assessment”, Rapport

Technique 95072 C, September 1995

[5.5] Dover, W.D., Dharmavasan, S., "Fatigue Fracture Mechanics Analysis

of Tubular T and Y Joints", Proc. Int. Offshore Technology Conference,

Houston, 1982, Paper OTC 4404

[5.6] Kam, J.C.P., Topp, D.A., Dover, W.D., "Fracture Mechanics Modelling

and Structural Integrity of Welded Tubular Joints in Fatigue", Proc. 6 '

Int. Offshore Mechanics and Arctic Engineering Symposium, ASME, v3,

pp395-402, 1987

[5.7] Austin, J.A., "The Role of Corrosion Fatigue Crack Growth Mechanisms

in Predicting the Fatigue Life of Offshore Tubular Joints.", PhD Thesis,

UCL, October 1994

[5.8] Dover, W.D., "Variable Amplitude Fatigue of Welded Structures.",

Fracture Mechanics: Current Status, Future Prospects, Cambridge, UK,

1979

[5.9] Stacey, A., Burdekin, P.M., and Maddox, S.J., "The Revised BS PD6493

Assessment Procedure - Application to Offshore Structures.", Int. Conf.

Offshore Mechanics and Arctic Engineering, v3, p i3-33, 1996

[5.10] Baerheim, M ., Stacey, A., Nichols, N., "Proposed Fatigue Provisions in

- 2 9 9 -


the New ISO Code for Offshore Structures'', Int. Conf. Offshore

Mechanics and Arctic Engineering, v3, p513-519, 1996

[5.11] Holdbrook , S.J., Dover, W.D., ''The Stress Intensity Factor for a Deep

Surface Crack in a Finite Plate.", Engineering Fracture Mechanics, vl2,

pp347-364, 1979

[5.12] Newman, J.C., Raju, I.S., “An Empirical Stress Intensity Factor Equation

for the Surface Crack.”, Engineering Fracture Mechanics, vl5, nl-2,

ppl85-192, 1981

[5.13] Monahan, C.C., "Early fatigue Crack Growth in Offshore Structures.",

PhD Thesis, UCL, 1994

[5.14] Aaghaakouchak, A., Glinka, G., Dharmavasan, S., "A Load Shedding

Model fo r Fracture Mechanics Analysis of Fatigue Cracks in Tubular

Joints", Proc. 8 Int. Conf. Offshore Mechanics and Arctic Engineering,

ppl59-165, 1989.

[5.15] Kare, R.F., "Influence of Weld Profde on Fatigue Crack Growth in

Tubular Welded Joints.", PhD Thesis, City University, London, 1989

[5.16] Albrecht, P., Yamada, K., "Rapid Calculation of Stress Intensity

Factors.", Journal of the Structural Division, ASCE, pp377-389, 1977.

300 -

Chapter 5 - Fracture Mechanics Modeling of Jack U p Chord Defects

Rack Plate Thickness, TS (mm) Average Stress Parameter, ASP0 1.7981 1.4092 1.37110 1.33820 1.32650 1.286

Table 5.1Average Stress Parameters for different rack plate thicknesses

Normalised Rack Thickness, TS/D

SCF DoB

0.000000 19.04 0.8650.001667 11.85 0.8330.003333 11.19 0.8270.016667 10.54 0.8190.033333 10.35 0.8160.083333 9.74 0.809

Table 5.2Input parameters for adapted Newman Raju model testing rack plate effect

301 -

Chapter 5 - Fracture Mechanics Modeling of Jack U p Chord Defects

a

Figure 5.1 Centre cracked infinite plate

3.5

I1.5 - - 0

0 .5 --0 ^0 0 ^ 0 0 ^0 0 ^ 0 0 ^ 0 0 0 ^ 0 0 0 0 O o

0.2 0.30 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1

O T 1

Normalised Crack Depth, aA

Figure 5.2Y exp factors fo r test T I

302 -

Chapter 5 - Fracture Mechanics Modeling of Jack Up Chord Defects

2,5

t ^

0.5 -- OOOOOOO o o o oo OOOOOOO <

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0 T 2

Normaised Crack Depth, aA

Figure 5.3 Yexp factors for test T2

3 5

2 5 >

o

g

0,5 -- ooooooooooooo ooooo o oooooo O O

0 7 0.90 5 0 6 0.8 10 0 1 02 0 3 0 4

O Yexp

McxJ AVS

Normalised C rack Depth. aA

Figure 5.4Comparison of empirical SIF models with Yexp results from Test Tl

- 303 -


2.5

2 - ;

&15 --

'Ooo o o0 5 00&0000 0000000 o o Ô

H-------- h0 0 1 0 2 0 3 0 4 0.5 0 6 0 7

Normalised Crack Depth. aA0.8 0 9 1

O Yexp AVSMod AVS

TPM

Figure 5.5Comparison of empirical SIF models with Yexp results from Test T2

1

0.9

0.8

% 0.7

tg 0.6

^ 0.5

•S2 0.4

0.2

0.1

070000 8000030000 40000 50000 6000010000 20000

Cycles, N

Figure 5.6Fracture mechanics crack growth results for Test Tl

-T1

AVS

Mod. AVS

Best Fit Y

- 304 -


0.9

0.7

0.6

2 0.3

0.2

80000 100000 120000 140000 160000 180000600000 20000 40000

T2AVSMod. AVS

Best Fit Y

Cycles. N

Figure 5.7Fracture mechanics crack growth results for Test T2

y = 0 .3 3 8 1 x ° ^ ^ ® ® r2 = 0.9944

2.5

I

0.5

- t-—

0.2 0.7 0.8 0.9 10.4 0.5 0.60.1 0.3

O T lBest Fit Y

NormaSsed Crack Depth, aA

Figure 5.8Power Law F it fo r Yexp data from Test T l

- 305 -


2.5

I

0.5 --

0 0.5 0.70.1 0.2 0.3 0.4 0.6 0.8 0.9 1

O T2 Best Fit Y

Normalised Crack Depth, aA

Figure 5.9Power Law Fit for Yexp data from Test T2

2.5

0.5 -■

0.5 0.70 0.1 0.2 0.3 0.4 0.6 0.8 0.9 1

Yexp (T1 )O Chong Rhee

NormaHsed Crack Depth, aA

Figure 5.10Chong Rhee T Factors fo r Test TI

3 0 6 -

1 ( 1-------1—0.4 0.5 0 ,6 0 .7 0.8

Normatsed Crack Depth, a /t

Figure 5.11 Chong Rhee T Factors fo r Test

02

2t) Y

.................................... ..


2.5

2 -■

1.5 -

OO>-

BBS0.5 -■

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

O YN&R

□ Y N&R+LMR

A Y N&R+LMR+NSC

AVS

Mod. AVS

# Y N&R+LMR+NSC+CSC

Normalised Crack depth, a/t

Figure 5.13Y factors using flat plate based solutions for Test Tl

2.5

2 --J

IO O

g g g

HB BH H0.5 -

0 0.2 0.3 0.50.1 0.4 0.6 0.7 0.8 0.9 1

o YN&R

□ Y N & R 4 IM R

A Y N&R+LMR+NSC

AVS

---------Mod AVS

+ Y N&R+LMR+NSC+CSC

Normalised Crack Depth, art

Figure 5.14y factors using flat plate based solutions for Test T2

- 308 -


2.5 -

2 -

I

0 --

-0.5 --

0.4 0.6 0.80 0.2 1xA

Figure 5.15 SCF due to weld toe for tensile loading

3.5

3 -

2.5 -

£

0.5 --

0 --

-0.5 --

0.5 0.70.2 0.3 0.4 0.6 0.8 0.9 10 0.1

x A

Figure 5.16 SCF due to weld toe for bending loads

■Tension

• Bending

-309

Chapter 5 • Fracture Mechanics Modeling of Jack Up Chord Defects

i L

2 x

2a

— X

A

\ /

2 a

X

X

Figure 5.17Albrechts Method for calculating Yf, (taken from [5.10])

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2.5

1.5 --

0.5 --

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

■ Membrane

aA

Figure 5.18Correction Factors (Yg) for non-uniform stress distribution

0.7 --

0.6 - -Test T l

Test T2

- CSC0.5 -

0.4 --

0.3 --

0.2 - -

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

a/2c

Figure 5.19Crack shape correction factors

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0 9 -■

0 6 - -

0 4 -■

2 0.3

0 2 -■

0 100,000 200,000 300,000 400,000 500,000 600,000

TS=20TS=50

Cycles N

F i^ re 5.20A l S Model prediction of the e ffect of a rack plate on crack propagation

0 9

IQI 0 5O

I

02

0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,00

TS=0

TS=20TS=50

Cycles. N

Figure 5.21Modified AVS Model prediction of the effect of a rack plate on crack propagation

- j 12 -


12

Ü: 10--

8 -■

6 -■

2 -

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

■AVS Ufe

Normalised Stiffener Thickness, TS/D

Figure 5.22AVS Model propagation lives normalised to that of the unstiffened Joint

160

140

O O o o o o oo o o o120 - -

1 ,00- S 80 -

I■g 60

40 -

<D OOOCD

lO O O O O O O OO

O T 1 & T 2

Best FitO O

= 0.0499x - 1 S689x^ + 26.046X - 0.9238 = 0.9686OO

20

0 2 4 6 8 10 12 14 16

C rack Depth, a(m m )

Figure 5.23Crack shape development used with Newman Raju model, derived from

experimental data

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25

® 20 - -

10 -

5 -

0.05 0.06 0.07 0.090 0.01 0.02 0.03 0.04 0.08

- - O - SCF & DoB

— □ SCF only

Normalised Stiffener Thickness, TS/D

Figure 5.24Effect of rack plate on crack propagation lives using modified Newman Raju

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Chapter 6 - Summary. Conclusions and Recommendations

Chapter 6

6. Summary, Conclusions and Recommendations

The use of high strength steels in jack up platforms was introduced in Chapter One.

Concern regarding the use of these steels (which commonly have a yield stress of

around 700MPa) was heightened by the discovery of cracking in and around the

spud can of several jack ups operating in the North Sea. The treatment of high

strength steels by design codes was examined. It was concluded that the lack of

reliable information on the behaviour of these steels under environmental

conditions offshore has effectively excluded them from design codes. Limits on the

applicability of the S-N curves in terms of yield strength limits on the maximum

allowable yield / ultimate ratio restrict the use of these steels. Modern micro

alloyed, quenched and tempered steels enjoy good weldability and this should not

be seen as an obstacle to their use. It was concluded that a need existed for fatigue

tests data on tubular joints fabricated from high strength steels. A fatigue test

programme was implemented involving seven fatigue and corrosion fatigue tests on

large scale tubular joints fabricated from Super Elso SE702. In addition four

further tests were performed under variable amplitude loading using tubular Y

joints fabricated from the same material in a parallel investigation. The results of

these tests allowed the following conclusions to be drawn.

• No evidence was obtained from the experimental study to suggest that the high

strength tubular welded joints suffer from inferior fatigue performance in

comparison with medium strength weldable steels such as BS4360:50D. The

fatigue lives of all the joints tested exceeded the design S-N life. Comparison

with the results of geometrically identical joints fabricated from 50D type steels

suggests that the fatigue performance for the higher strength steels is superior.

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Some evidence was obtained suggesting that the change of slope of the S-N

curve for tubular joints fabricated from this steel occurs at higher stress ranges

than for the 50D type steels. It is recommended that further fatigue tests be

performed on similar high strength tubular joints to confirm this. Hot spot

stress ranges of 200MPa or less should be used.

Increased crack growth rates were noted for tests under cathodic protection at

CP levels of -800 and -lOOOmV (Ag/AgCl) however these increases were

modest. The feared susceptibility of these steels to large increases in crack

growth rates due to hydrogen embrittlement mechanisms was not found.

However this is likely to be material specific and should be taken in context. The

role played by hydrogen embrittlement in these tests can be assessed from the

proportion of brittle fracture modes on the fracture surface. It has not been

possible to destructively section the crack sites although this will be performed

and reported at a later date.

A review of the typical chord shapes and dimensions for the leg structures was also

presented. The use of a thick longitudinal stiffener, the rack plate was noted. It was

concluded from this review that the stress distribution at the brace-chord

intersection was likely to be significantly different to that in unstiffened tubulars.

An extensive finite element investigation has shown that the presence of a rack

plate can significantly affect the surface SCF distribution at the intersection of the

brace and chord. Several different chord-rack configurations were examined

including designs employing a thinner central section known as a rib plate and

designs where the rack is not continuous through the chord diameter. The effect

has been quantified for a wide range of joint shapes covering the validity range of

common parametric equations. Peak chord SCF’s can be reduced by up to 50% in

comparison with unstiffened joints for axial loading. For OPB loading the

reduction was around 20%. No affect was found for IPB loading. The mechanism

by which the rack brings about these changes was investigated using boundary

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condition sets applied to the chord surface, Thetestriction of chord wall radial

deformation has been shown be the dominant mechanism.

Further work is recommended to quantify the effect of the leg guides commonly

found at the leg-huU intersection. These have been shown elsewhere to have a

significant effect on the ultimate strength of jack up geometries. The significance of

the rack plate has now been demonstrated. It is suggested that more detailed work

on representative joint shapes be performed. This could include modelling the

thicker rack plates using brick rather than thin shell elements. Examining

overlapped bracing and other complicating factors often found in jack up leg

design is also recommended.

The through thickness stress distribution is also altered by the rack plate. This has

again been quantified for a wide range of rack designs and joint geometries. In

general the presence of a rack plate decreases the DoB in all tubular joint shapes

under axial and OPB loading and increases under IPB loading. Higher DoB can be

translated as slower crack growth and longer fatigue crack propagation lives. It

was shown that existing parametric equations for unstiffened joints could predict

the DoB to within +1-5% DoB for the geometries under consideration here.

However a tendency to return unconservative DoB values has been identiifed.

Several contemporary fracture mechanics models have been evaluated against

fracture mechanics data derived from the tubular joint tests mentioned earlier. Of

these the empirically based AVS models performed the best providing an excellent

fit to the experimental Y Factor curve. However attempts to use these models to

predict the observed crack growth in the tubular joint test showed the results to be

subject to large errors. However it should be noted that the stress levels used in the

analysis were extremely high (400MPa and 300MPa) which would of course

amplify any small error in the predicted stress intensity factor.

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A fracture mechanics model based on the flat plate solution of Newman-Raju was

presented as being suitable for the analysis of chord side defects in jack up legs.

The flat plate model was corrected for the effect of the weld toe, load shedding and

crack shape. This model was shown to accurately predict the experimentally

derived Y Factors. The usefulness of this model is its flexibility in terms of input

parameters. The model allows user defined DoB, weld shape and crack shape, all

of which may be important when modelling jack up chord defects. This model was

used to predict fatigue crack propagation lifetimes using the stress distributions

found from the finite element analysis. The model correctly predicted a large

increase in fatigue crack propagation lifetime due to the reduction in peak SCF and

a smaller but significant deleterious effect of the decreased DoB for an axially

loaded T joint.

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