Journal Pre-proof

Assessment of corroded API 5L X52 pipe elbow using a modified failure assessmentdiagram

Bassam Gamal Nasser Muthanna, Omar Bouledroua, Madjid Meriem-Benziane,Mahdi Razavi Setvati, Milos B. Djukic

PII: S0308-0161(20)30266-0

DOI: https://doi.org/10.1016/j.ijpvp.2020.104291

Reference: IPVP 104291

To appear in: International Journal of Pressure Vessels and Piping

Received Date: 1 October 2020

Revised Date: 19 December 2020

Accepted Date: 22 December 2020

Please cite this article as: Nasser Muthanna BG, Bouledroua O, Meriem-Benziane M, Setvati MR,Djukic MB, Assessment of corroded API 5L X52 pipe elbow using a modified failure assessmentdiagram, International Journal of Pressure Vessels and Piping (2021), doi: https://doi.org/10.1016/j.ijpvp.2020.104291.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the additionof a cover page and metadata, and formatting for readability, but it is not yet the definitive version ofrecord. This version will undergo additional copyediting, typesetting and review before it is publishedin its final form, but we are providing this version to give early visibility of the article. Please note that,during the production process, errors may be discovered which could affect the content, and all legaldisclaimers that apply to the journal pertain.

© 2020 Published by Elsevier Ltd.

Author Statement

Corresponding author: Bassam Gamal Nasser Muthanna As corresponding author, I am responsible for ensuring that the descriptions are

accurate and agreed by all authors. I inform you that all authors have contributed in

this project.

Title of Paper

Assessment of corroded API 5L X52 pipe elbow using a modified failure assessment

diagram

Authors name:

Bassam Gamal Nasser Muthanna,

Omar Bouledroua,

Madjid Meriem-Benziane,

Mahdi Razavi Setvati,

Milos B. Djukic

Journ

al Pre-pro

of

1

Assessment of corroded API 5L X52 pipe elbow using a modified failure

assessment diagram

Bassam Gamal Nasser Muthanna1*, Omar Bouledroua2, Madjid Meriem-Benziane1,

Mahdi Razavi Setvati3, Milos B. Djukic4

1 LRM, Faculty of Technology, Hassiba Benbouali University of Chlef, Esalem City, 02000, Chlef, Algeria. 2 LPTPM, Hassiba BenBouali University of Chlef, P.O.Box. 151 Hay Salem, 02000 Chlef, Algeria.

3 Faculty of Technology, Design and Environment, Oxford Brookes University, Oxford, United Kingdom. 4 University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade 11120, Serbia.

*E-mail: b.muthanna@univ-chlef.dz; bassam.gamal36@gmail.com Abstract:

Pipe elbows (bends) are considered critical pressurized components in the piping systems and

pipelines due to their stress intensification and the effect of bend curvature. They are prone and

hence more exposed to different corrosion failure modes than straight pipes. Late detection of

such elbow damages can lead to different dangerous and emergency situations which cause

environmental disasters, pollution, substantial consumer losses and a serious threat to human life.

A comprehensive safety and reliability assessment of pipe elbows, including usage of prediction

models, can provide significant increases in the service life of pipelines. It is well known that the

limit pressure is an important parameter to assess the piping integrity. In this paper, the integrity

assessment of damaged pipeline elbows made of API 5L X52 steel was done within the

framework of numerical modeling using the finite element method (FEM) and finite element

analysis (FEA). The evaluation of numerically FEM modeled limit pressure in the corroded

elbow containing a rectangular parallelepiped-shaped corrosion defect with rounded corners at

the intrados section was done and compared to different codes for calculating limit pressure.

Moreover, the area with the corrosion defects with different relative defect depth to wall

thickness ratios was FEM modeled at the intrados section of the pipe elbow where the highest

hoop stress exists. The results showed that the codes for straight pipes could not be applied for

the pipe elbows due to the significantly higher error in the obtained limit pressure value compared

with numerically FEM obtained results. However, the results for modified codes, adapted for the

pipe elbow case using the Goodall formula for calculation of the hoop stress in pipe elbows with

defects are pretty consistent with the numerical FEA results. The notch failure assessment

diagram (NFAD) was also used for the straight pipe and pipe bends with different corrosion

defect depth ratios, while the obtained critical defect depth ratios further highlighted the

criticality of pipe elbows as an essential pipeline component.

Keywords: Pipe elbow, Corrosion, Limit pressure, Codes, FEA.

Journ

al Pre-pro

of

2

1. Introduction

In the hydrocarbons processing industry, pipelines are essential components to transport

energy in the safest way in large volumes over large distances. Consequently, the structural

integrity, high reliability, and effective maintenance of pipelines take the highest importance

due to the critical role of pipelines in global economic and environmental safety. In recent

decades, the use of crude oil and natural gas has increased faster which leads to the need for

modifications, implementation of improved maintenance strategies, and extension of existing

pipeline systems. This complicated network of pipelines includes the necessity for usage of

numerous and various pipe elbows (bends) and junctions for distribution, transportation, and

change of the fluid direction. The pipe elbows are prone to the various damage mechanisms

on both internal and external surfaces due to the exposure to fluids and external environments

such as corrosion, erosion, erosion-corrosion fatigue, and different other combined damages

[1-14]. Frequently this leads to the burst in critical parts of piping systems, forced outages,

and long term interruptions in operation. The corrosion of pipe elbows in natural gas

pipelines and various other industrial systems such as hydrocarbons industries and

desalination plants [15-19] was extensively examined and reported.

Extensive studies have been conducted related to the reliability and structural integrity

prediction, prevention of corrosion damages, and repair of corroded steel pipelines and pipe

elbows [20-37]. Different experimental approaches and tests, numerical analyses, and

analytical methods were used. Knowledge of limit pressure (PL) is an important issue in the

field of pipeline design, integrity assessment, and maintenance management to achieve

prolonged and reliable operation of pipelines [38,39]. Generally, failure pressure appears

when the internal pipeline pressure exceeds the limit pressure value [40,41]. NG-18 equation

was the first original formula and the semi-empirical failure criteria developed by Maxey et

al. [42] to calculate the residual strength of corroded straight pipes with cracks and defects.

However, there are various models, standards, codes, and plastic collapse failure criteria

based on NG-18 equations [42] such as ASME B31G [43], modified ASME B31G [44],

DNV-RP-F101 [45], Shell-92 [46], RSTRENG [47], and PCORRC [48] which were

developed to calculate the limit pressure according to the flow stress in the straight pipe.

However, these standards and codes for the fitness-for-purpose assessment of corroded

pipelines could not be applied to pipe elbows due to the effect of the elbow curvature that

leads to the increase of hoop stress [49].

Journ

al Pre-pro

of

3

S o m e r es e ar c h ers [ 2 3, 3 2, 3 3, 5 0] h a v e pr o p os e d n e w f or m ul as t o c al c ul at e t h e li mit

pr ess ur e f or a pi p e el b o w wit h t h e d ef e cts. G o o d all [ 5 1] h as pr o p os e d t h e first f or m ul a t o

c al c ul at e t h e cir c u mf er e nti al str ess i n pi p e el b o ws wit h d ef e cts. T his f or m ul a is pr es e nt e d

l at er i n s e cti o n 2. V ari o us a ut h ors h a v e p erf or m e d t h eir a n al ysis o n t h e pl asti c li mit pr ess ur e

of el b o ws a n d pr o p os e d diff er e nt m o d els b as e d o n t h e G o o d all f or m ul a [ 3 2, 4 9]. D u a n a n d

S h e n [ 3 2] h a v e pr o p os e d a n e m piri c al m o d el f or t h e c al c ul ati o n of t h e li mit l o a d i n pi p e

el b o ws at t h e e xtr a d os l o c ati o n a n d als o v ali d at e d b y e x p eri m e nts. Y a hi a o ui et al. [ 5 0] h a v e

st u di e d t h e el b o ws wit h a s h ort r a di us a n d cr a c ks b y usi n g F E M. Ki m et al. [ 5 2] h a v e

e x a mi n e d t h e i nt e grit y of a pi p e el b o w i n t h e pr es e n c e of d ef e cts at t h e i ntr a d os a n d e xtr a d os

s e cti o ns u n d er i nt er n al pr ess ur e a n d pl a n e- b e n di n g l o a d. T h e y h a v e c o n cl u d e d t h at t h e

i ntr a d os s e cti o n is m or e e n d a n g er e d a n d v ul n er a bl e t h a n t h e e xtr a d os s e cti o n a c c or di n g t o

t h eir e x p eri m e nts a n d o bt ai n e d r es ults. L e e et al. [ 3 3] h a v e st u di e d er osi o n- c orr osi o n

pr o v o k e d d ef e cts i n diff er e nt p ositi o ns of t h e pi p e el b o w usi n g m at h e m ati c al f or m ul as a n d

n u m eri c al a n al ysis. T h e y pr o p os e d a n e w m et h o d t o c al c ul at e b urst pr ess ur e usi n g i n d ustri al

c o d es a n d t h e L or e n z f a ct or [ 3 3]. Xi e et al. [ 2 3] h a v e pr o p os e d a n e w f or m ul a b y i ntr o d u ci n g

c ur v at ur e a n d w all t hi c k n ess f a ct ors t o c al c ul at e h o o p str ess i n t h e t hi c k- w all e d el b o w, w hi c h

w as a d diti o n all y v erifi e d a n d s u p p ort e d usi n g t h e F E M. T e e a n d W or d u [ 5 3] h a v e f o u n d t h at

t h e g e o m etri c al p ar a m et ers of t h e c orr osi o n d ef e ct (l e n gt h a n d d e pt h) h a v e a si g nifi c a nt

i nfl u e n c e o n t h e f ail ur e pr ess ur e. B esi d es, t h e s h a p e of t h e g o u g e h as m or e i m p a ct t h a n t h e

s h a p e of a c orr osi o n pit.

T h e fr a ct ur e m e c h a ni cs i s c o nsi d er e d as i m p ort a nt d uri n g t h e e v al u ati o n of t h e str u ct ur al

i nt e grit y of pi pi n g s yst e ms. B as e d o n t h e t h e or y of li n e ar el asti c fr a ct ur e m e c h a ni cs ( L E F M),

f ail ur e o c c urs w h e n t h e v al u e of t h e str ess i nt e nsit y f a ct or (K I) is hi g h er t h a n t h e criti c al v al u e

of pla n e str ai n fr a ct ur e t o u g h n ess f or m o d e I cr a c k dis pl a c e m e nt ( K I C), i. e., (K I ≥ KI C) [ 5 4].

T h e l o c ali z e d ( pitti n g) c orr osi o n g e n er all y c o nsi d er e d as a n ot c h i n t h e pi pi n g s yst e m. T h e

n ot c h h as a str o n g i nfl u e n c e o n t h e f ail ur e or b urst a n d t h e N ot c h Str e ss I nt e nsit y F a ct or

( N SI F) is us e d as a pr e di cti o n f or t h e fr a ct ur e c o n c e pt [ 5 5- 5 7]. D e p e n di n g o n t h e n ot c h t er m,

t h e f ail ur e o c c urs w h e n t h e str ess distri b uti o n e x c e e ds t h e criti c al v al u e at t h e n ot c h ti p (K ρ ≥

K ρ C ). T h e criti c al N SI F c o ul d b e c all e d fr a ct ur e t o u g h n ess (K ρ C

J our

n al

Pre-

pro of

) i n n ot c h ti ps. F urt h er m or e,

t h e c o nstr ai nt h as a si g nifi c a nt eff e ct o n t h e fr a ct ur e t o u g h n ess v al u e [ 5 8, 5 9]. T h e v ol u m etri c

m et h o d is us e d i n or d er t o c al c ul at e N SI F. It is c o nsi d er e d a s e mi-l o c al m et h o d f or n u m eri c al

a n al ysis [ 6 0- 6 2].

4

T h e N ot c h F ail ur e Ass es s m e nt Di a gr a m ( N F A D) is fr e q u e ntl y us e d t o st u d y t h e s af et y a n d

f or t h e fr a ct ur e ass ess m e nt of pi p eli n es or el b o ws wit h diff er e nt t y p es of d ef e cts [ 3 9, 4 1, 6 3-

7 6]. It d e p e n ds o n t h e fr a ct ur e t o u g h n ess ( K ρ C ), d ef e ct si z e, i. e., d ef e ct d e pt h r ati o ( d/t), a n d

t h e i nt er n al l o a di n g - pr ess ur e ( P) [ 6 9]. T h e N F A D m et h o d ol o g y s u bstit ut e d t h es e t hr e e

p ar a m et ers wit h o nl y t w o n o n- di m e nsi o n al p ar a m et ers K r a n d L r, w hi c h pr es e nt t h e a p pli e d

st r ess a n d t h e cr a c k dri vi n g f or c e, r es p e cti v el y, a n d b y i ntr o d u ci n g t h e c orr es p o n di n g

ass ess m e nt p oi nt c o or di n at es ( L r, Kr) o n t h e F A D a n d N F A D [ 6 9]. N u m er o us pr e vi o us

st u di es h a v e s h o w n t h at el b o ws ar e m or e v ul n er a bl e t h a n str ai g ht pi p es d u e t o t h e m or e

s e v er e str ess c o n diti o ns of el b o ws wit h a d ef e ct, w hil e ass ess m e nt p oi nts f or el b o ws ar e

t y pi c all y s hift e d i n c o m p aris o n wit h str ai g ht pi p es a n d l o c at e d i n t h e brittl e fr a ct ur e d o m ai n

of t h e F A D or N F A D (s e e s u bs e cti o n 3. 3.) [ 1 7, 5 2, 6 3- 6 5].

I n o ur pr e vi o us st u d y [ 1 2], t h e criti c al p ositi o n al o n g a pi p e el b o w m a d e of A PI 5 L X 5 2

st e el, a c c or di n g t o t h e eff e cts of t h e criti c al str e ss l o c ati o n, criti c al cr a c k ori e nt ati o n a n gl e,

a n d criti c al el b o w a n gl e o n SI F, w as i n v esti g at e d wit h t h e ai d of a m o difi e d F A D [ 1 2]. T h e

criti c al p ositi o n al o n g t h e el b o w wit h t h e m a xi m u m str ess w as l o c at e d at a c ur v at ur e a n gl e

α = 7 2 °. Als o, a s e mi- elli pti c al cr a c k w as cr e at e d at t hi s l o c ati o n, at t h e criti c al i ntr a d os

s e cti o n of pi p e el b o w [ 5 2], t a k e n i nt o a c c o u nt t h e i m p ort a n c e of e q ui v al e nt str ess i nt e nsit y

f a ct or (K e q ) as a f ail ur e crit eri o n t o d et er mi n e t h e criti c al s e mi- elli pti c al cr a c k a n gl e

ori e nt ati o n. T h e cr a c k ori e nt ati o n a n gl e of 9 0 ° w a s f o u n d t o b e criti c al f or a pi p e el b o w [ 1 2].

It w as als o o bs er v e d t h at d u e t o str ess i nt e nsifi c ati o n a n d hi g h er c o nstr ai nt i n pi p e el b o ws, t h e

c orr es p o n di n g ass ess m e nt p oi nt f or t h e s a m e r el ati v e d ef e ct si z e l o c at e d at t h e i ntr a d os

s e cti o n of pi p e el b o w h as a hi g h er v al u e of b ot h c o or di n at es ( L r, Kr) t h e n f or t h e str ai g ht pi p e.

In t his w or k, t h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e cts wit h r o u n d e d c or n ers

wit h o ut cr a c k a n d wit h diff er e nt r el ati v e d ef e ct d e pt h t o w all t hi c k n ess r ati os ( d/t = 0. 1 - 0. 8,

s e e Fi g. 1 c) at t h e mi d dl e of t h e criti c al [ 5 2] i ntr a d os s e cti o n of a pi p e el b o w ( A PI 5 L X 5 2

st e el) w er e cr e at e d t o e x a mi n e t h e eff e cts of c orr osi o n d ef e cts o n t h e i nt e grit y ass ess m e nt of

pi p e el b o ws. T h e li mit pr ess ur e pr e di cti o n f or a pi p e el b o w c o nt ai ni n g c orr osi o n d ef e cts at

t h e i ntr a d os s e cti o n is i n v esti g at e d usi n g F E A. F or li mit pr ess ur e c al c ul ati o n i n t h e pi p e

el b o w wit h diff er e nt d ef e ct d e pt h r ati os a n d t o c h e c k t h e a p pli c a bilit y of m o difi e d c o d es, t h e

G o o d all f or m ul a [ 5 2] f or c al c ul ati o n of t h e h o o p str ess ( σ θ )

J our

n al

Pre-

pro of

i n pi p e el b o w w as us e d i n v ari o us

c o d es. T h e o bt ai n e d r es ults w er e f urt h er c o m p ar e d wit h t h e n u m eri c al F E A r es ults, a n d

c o ns e q u e ntl y, t h e a p pli c a bilit y of diff er e nt m o difi e d c o d es ( a d a pt e d f or t h e pi p e el b o w c as e)

f or t h e c al c ul ati o n of t h e li mit pr ess ur e i n t h e pi p e el b o w w as als o c h e c k e d. T h e n ot c h f ail ur e

5

as s ess m e nt di a gr a m ( N F A D) is us e d f or t h e str ai g ht pi p e a n d pi p e b e n ds f or t h e s af et y f a ct or

c al c ul ati o n a n d t o e v al u at e t h e criti c al d et e ct d e pt h r ati os. Fi n all y, t h e o bt ai n e d r es ults of t h e

str u ct ur al i nt e grit y ass es s m e nt f or pi p e el b o ws wit h diff er e nt r el ati v e c orr osi o n d ef e ct d e pt h

r ati os pr es e nt e d i n t his st u d y ar e c o m p ar e d wit h o ur pr e vi o usl y p u blis h e d r es ults [ 1 2] f or a

pi p e el b o w wit h diff er e nt s e mi- elli pti c al r el ati v e cr a c k d e pt h r ati os.

2. Li mit p r ess u r e st a n d a r d s a n d pi p e el b o w h o o p st r ess

I n t h e lit er at ur e, s e v er al c o d es h a v e b e e n s u c c e ssf ull y us e d as f ail ur e crit eri a f or t h e

r eli a bilit y ass ess m e nt of c orr o d e d pi p eli n es [ 4 3- 4 8, 7 5]. C os h a m et al. [ 7 5] h a v e p oi nt e d o ut

t h at t h e a p pli c a bilit y of a p arti c ul ar c o d e str o n gl y d e p e n ds o n t h e t o u g h n es s v al u e of diff er e nt

pi p eli n e st e els. T h e ol d er m o d els, li k e A S M E B 3 1 G [ 4 3], m o difi e d A S M E B 3 1 G [ 4 4], a n d

t h e r e m ai ni n g str e n gt h f or m ul a - R S T R E N G [ 4 7], w er e d e v el o p e d a n d v ali d at e d t hr o u g h t ests

o n ol d er pi p eli n e st e els wit h r el ati v el y l o w er t o u g h n ess. O n t h e ot h er h a n d, t h e n e w m o d els,

li k e D N V- R P- F 1 0 1 [ 4 5], a n d P C O R R C [ 4 8], ar e m ostl y b as e d o n e q u ati o ns f oll o wi n g b ot h

n u m eri c al - fi nit e el e m e nt a n al ys es ( F E A) a n d e x p eri m e nt al d at a. T h es e " n e w " m o d els w er e

d e v el o p e d a n d v ali d at e d f or hi g h t o u g h n ess pi p eli n e st e els, a n d h e n c e s uit a bl e a n d a p pli c a bl e

m ostl y f or t h es e m o d er n st e els [ 7 5]. Als o, C os h a m et al. [ 7 5] e m p h asi z e d t h at s o m e of t h e

m et h o ds f or ass essi n g c orr osi o n b as e d o n t h e N G- 1 8 e q u ati o ns [ 4 2], p arti c ul arl y ol d er A S M E

B 3 1 G [ 4 3] a n d m o difi e d B 3 1 G [ 4 4], ar e r at h er c o ns er v ati v e i n t h e c as e of bl u nt, p art- w all

d ef e cts.

V ari o us c o d es a n d st a n d ar ds f or t h e str ai g ht pi p e h a v e a d et ail e d f or m a n d st yl e f or t h eir

f or m ul as a n d a p pli e d d et er mi nisti c a p pr o a c h e s, T a bl e 1. T h e m ai n str ess es (str es s

c o m p o n e nts) f or t h e str ai g ht pi p e s u bj e ct e d t o i nt er n al pr ess ur e ar e e x pr ess e d b y t h e

f oll o wi n g e q u ati o ns [ 7 7]:

P r

tθσ = , 0. 5

2l

P r

tθσ σ= = , 0rσ ≈ ( 1)

w h er e, σ θ , σ l, σ r, P , r , a n d t ar e h o o p str es s, l o n git u di n al str es s, r a di al str es s, i nt er n al

pr es s ur e, a v er a g e r a di u s a n d w all t hi c k n es s of pi p eli n e, r es p e cti v el y. A c c or di n g t o t h e

d et er mi ni sti c as s es s m e nt m o d el s, b ot h ol d er a n d c o nt e m p or ar y m o d el s m e nti o n e d a b o v e, t h e

i nt er n al pr es s ur e (P ) m u st b e l es s t h a n t h e li mit pr es s ur e (P L ): (P < P L

J our

n al

Pre-

pro of

) t o pr e v e nt t h e pi p e

b u rst, T a bl e 1. F or c orr o d e d pi p es m a d e of ol d st e el s wit h l o w er t o u g h n es s, li mit pr es s ur e c a n

b e c al c ul at e d u si n g o n e of t h e st a n d ar d b ut ol d er m o d el s ( A S M E B 3 1 G, M o difi e d A S M E

6

B 3 1 G, a n d R S T R E N G). F or t h e m o d er n st e el s wit h hi g h er t o u g h n es s, li mit pr es s ur e c a n b e

c al c ul at e d u si n g o n e of t h e c o nt e m p or ar y m o d el s ( D N V R P- F 1 0 1 a n d P C O R R C) [ 7 8, 7 9].

T a bl e 1 C o d e s f or c al c ul ati n g li mit pr es s ur e P L of t h e str ai g ht pi p e.

T h e p ar a m et ers pr es e nt e d i n T a bl e 1: P L , D , d, t, M, σ y , σ ult , a n d L ar e t h e li mit pr es s ur e,

p i p e o ut er di a m et er, cr a c k d e pt h, w all t hi c k n es s, F oli as f a ct or, yi el d str e n gt h, ulti m at e t e n sil e

str e n gt h, a n d l o n git u di n al c orr o si o n d ef e ct l e n gt h, r es p e cti v el y. H o o p str e s s i s t h e d o mi n a nt

str es s f or pi p eli n es s u bj e ct e d t o i nt er n al pr es s ur e, a n d t h e p ar a m et ers d a n d L ar e i m p ort a nt

i n p ut p ar a m et ers f or t h e li mit pr es s ur e - P L b as e d m o d el s. T h e m ai n diff er e n c e b et w e e n c o d es

p r ese nt e d i n T a bl e 1 i s t h e d efi niti o n of t h e fl o w str es s σ 0 ( b as e d o n σ y or σ ult ) a n d t h e d ef e ct

s h a p e [ 7 5]. A S M E B 3 1 G [ 4 3] c o d e i s u s e d f or t h e p ar a b oli c s h a p e c orr o si o n d ef e ct s, w hil e

t h e m a xi m u m h o o p str es s c a n n ot e x c e e d t h e yi el d str e n gt h of t h e m at eri al σ θ ≤ σ y . T h e

m o difi e d A S M E B 3 1 G [ 4 4] m o d el i s u s e d f or t h e i d e ali z e d, r e ct a n g ul ar i n s h a p e c orr o si o n

d ef e ct s w hil e t h e t ot al d ef e ct d e pt h s h o ul d n ot e x c e e d 8 0 % of t h e w all t hi c k n es s [ 3 3]. S h ell-

9 2 [ 4 6], P C O R R C [ 4 7], a n d D N V R P- F 1 0 1 [ 4 5] m o d el s ar e al s o u s e d f or t h e r e ct a n g ul ar

s h a p e d ef e ct s a n d t h e y ar e a p pli c a bl e i n t h e c as e of bl u nt d ef e ct s i n t o u g h m at eri al s [ 7 8, 7 9].

T h e h o o p str es s i n t h e pi p eli n es s u bj e ct e d t o i nt er n al pr es s ur e i s diff er e nt fr o m t h at of t h e

pi p e el b o w. It o c c urs i n a cir c u mf er e nti al dir e cti o n. O n t h e c o ntr ar y, t h e l o n git u di n al str es s i s

t h e s a m e f or b ot h str ai g ht pi p e a n d pi p e el b o w, h e n c e t h e pr es e n c e of c ur v at ur e of t h e el b o w

d o es n ot i nfl u e n c e t h e l o n git u di n al str es s [ 8 0]. T h e h o o p str es s at t h e e xtr a d o s s e cti o n of t h e

pi p e el b o w i s t h e l o w est, w hil e t h e i ntr a d o s s e cti o n i s t h e z o n e of t h e hi g h est h o o p str es s [ 8 0].

T h e i n cr e as e of b e n d r a di u s c a u s es a n i n cr e as e i n t h e h o o p str es s at t h e e xtr a d o s s e cti o n,

w hil e at t h e i ntr a d o s s e cti o n t h e h o o p str es s i s di mi ni s hi n g [ 2 5]. T h e diff er e nt h o o p str es s

e q u ati o n s w er e pr o p o s e d i n t h e lit er at ur e f or a pr es s uri z e d pi p e el b o w a n d pr es e nt e d b y

G o o d all [ 5 1] - E q. ( 2), Li et al. [ 2 5] - E q. ( 3), a n d Xi e et al. [ 2 3] - E q. ( 4), r es p e cti v el y:

1 / 2

1 /

Pr r R

t r Rθσ

−= ×

− ( 2)

2 si n

2 si n

P r R r

t R rθ

θσ

θ

+= ×

+ ( 3)

2 21

0. 5 1 1 122

2 1si n

t R

P r P r D tC C

Rt t r D

D

θσ

θ

= × × = × × + × − × −

+

J our

n al

Pre-

pro of

( 4)

7

w h er e, P , r , t, R , D , C t, C R , a n d (r , θ ) ar e t h e i nt er n al pr es s ur e, m e a n r a di u s, w all t hi c k n es s,

b e n d r a di u s, o ut er di a m et er, w all t hi c k n es s f a ct or, c ur v at ur e f a ct or of pi p e el b o w, a n d

c o or di n at es of c al c ul at e d p oi nt s, r es p e cti v el y. E q u ati o n ( 4), pr o p o s e d b y Xi e et al. [ 2 3] al s o

i n cl u d e d t w o a d diti o n al c orr e cti o n f a ct ors, i. e., t h e w all t hi c k n es s f a ct or C t a n d c ur v at ur e

f act or C R . Mill er [ 8 1] p oi nt e d o ut t h e c o n s er v ati s m r el at e d t o t h e G o o d all f or m ul a ( E q. ( 2)),

p re d o mi n a ntl y d u e t o t h e a b s e n c e of e x p eri m e nt al v ali d ati o n.

3. R es ults a n d dis c u ssi o n s

T hi s r es e ar c h r e pr es e nt s a c o nti n u ati o n a n d f urt h er a d v a n c e m e nt r e g ar di n g o ur pr e vi o u s

s tu di es a n d c o n cl u si o n s a b o ut t h e i nt e grit y as s es s m e nt of d a m a g e d pi p eli n e el b o w s. I n o ur

pr e vi o u s r es e ar c h [ 1 6], t h e c o m pr e h e n si v e c as e st u d y of c orr o d e d pi p e el b o w s d u e t o t h e

fl ui d-s oli d i nt er a cti o n u n d er t h e c o m pl e x o p er ati n g c o n diti o n s a n d t h e pr es e n c e of sili c o n e

p arti cl es w as d o n e. I n r e c e nt w or k, t h e n u m eri c al F E A st u d y of s e mi- elli pti c al cr a c k s i n t h e

criti c al p o siti o n at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w w as c o n d u ct e d [ 1 2]. T h e

a p pli c a bilit y of diff er e nt c o d es f or c al c ul ati o n s of t h e li mit pr es s ur e i n t h e c orr o d e d str ai g ht

pi p es i n t h e pr es e n c e of v ari o u s fl ui d fl o w c o n diti o n s ( p ur e n at ur al g a s a n d n at ur al g as-

h y dr o g e n mi x tr a n s p ort) w er e al s o e x a mi n e d a n d c o m p ar e d wit h t h e F E A r es ult s

[ 4 1, 6 6, 6 7, 7 0, 7 6].

T hi s st u d y i s c arri e d o ut b y u si n g a fi nit e el e m e nt a n al ysi s ( F E A) t o si m ul at e a pi p e el b o w

wit h t h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct s wit h r o u n d e d c or n ers a n d wit h

d iff er e nt r el ati v e d ef e ct d e pt h t o w all t hi c k n es s r ati o s (d/t = 0. 1 - 0. 8, s e e Fi g. 1 c) at t h e

criti c al i ntr a d o s s e cti o n of t h e pi p e el b o w. T h e n u m eri c al F E A r es ult s w er e al s o c o m p ar e d

wit h r es ult s o bt ai n e d b y c o d es t o m o dif y t h e li mit pr es s ur e e q u ati o n s of c o d es ( A S M E B 3 1 G,

m o difi e d A S M E B 3 1 G, a n d D N V R P- F 1 0 1), pr e s e nt e d i n T a bl e 1. T h e m o difi c ati o n i n cl u d es

t h e i m pl e m e nt ati o n of t h e G o o d all f or m ul a ( E q. ( 2)) f or t h e h o o p str es s σ θ i n t h e pi p e el b o w

d uri n g t h e c al c ul ati o n of t h e li mit pr es s ur e P L a c c or di n g t o t hr e e c o d es ori gi n all y d e v el o p e d

f or t h e str ai g ht pi p e.

F or t hi s r e as o n, all r es ult s a n d di s c u s si o n s ar e pr es e nt e d i n t hr e e s u b s e cti o n s. First, i n

s u b s e cti o n 3. 1, t h e h o o p str es s at t h e i ntr a d o s l o c ati o n of t h e pi p e el b o w wit h o ut d ef e ct w as

e x a mi n e d a n d c al c ul at e d u si n g t h e e q u ati o n s s u g g est e d i n t h e lit er at ur e f or t h e str ai g ht pi p e

( E q. ( 1)) a n d G o o d all f or m ul a f or t h e pi p e el b o w ( E q. ( 2)). Al s o, t h es e r e s ult s ar e c o m p ar e d

wit h t h e r es ult s f or t h e di stri b uti o n of h o o p str es s o n t h e i ntr a d o s ( φ

J our

n al

Pre-

pro of

= 0 °) s e cti o n s of t h e pi p e

el b o w o bt ai n e d b y n u m eri c al F E A. I n t h e n e xt s u b s e cti o n 3. 2, t h e r es ult s of t h e li mit pr es s ur e

8

c a l c ul ati o n f or diff er e nt c orr o si o n d ef e ct d e pt h r ati o s u si n g t hr e e m o difi e d c o d es ( A S M E

B 3 1 G, m o difi e d A S M E B 3 1 G, a n d D N V R P- F 1 0 1), a n d t h e G o o d all f or m ul a [ 5 1] f or

c al c ul ati o n of t h e h o o p str es s ( σ θ ) i n t h e pi p e el b o w, i s pr es e nt e d a n d c o m p ar e d wit h

n u m eri c al F E A r es ult s. Al s o, t h e N F A D f or t h e str ai g ht pi p e a n d pi p e b e n d s wit h c orr o si o n

d ef e ct s f or t h e s af et y f a ct or c al c ul ati o n i s pr es e nt e d a n d f urt h er a n al y z e d i n t h e fi n al

s u b s e cti o n 3. 3.

3. 1. H o o p st r es s at i nt r a d o s s e cti o n of t h e pi p e el b o w wit h o ut d ef e ct, m o d el s a n d F E A r es ult s

T h e n u m eri c al st u d y w a s c o n d u ct e d u si n g t h e F E A s oft w ar e A N S Y S [ 8 2]. A pi p e el b o w

m a d e of A PI X 5 2 pi p eli n e st e el w as u s e d i n t hi s w or k a n d it s di m e n si o n s ar e s h o w n i n Fi g. 1.

T a bl e 2 pr es e nt s t h e m e c h a ni c al pr o p erti es of t h e pi p e el b o w m a d e of A PI 5 L X 5 2 st e el.

Fi g. 1. A PI X 5 2 pi p eli n e el b o w: ( a) m a nif ol d s e p ar ati o n s yst e m; ( b) c orr o d e d pi p e

e lb o w; ( c) pi p e el b o w di m e n si o n s.

Fi gs. 1 a a n d 1 b s h o w t h e i nt a k e m a nif ol d el b o w s c o n n e ct e d wit h t h e h ori z o nt al t hr e e-

p h as e s e p ar at ors. T h e g e o m etri c al c h ar a ct eri sti c s of t h e pi p e el b o w ar e t h e i nt er n al r a di u s

r = 2 8 5. 7 5 m m, w all t hi c k n es s t= 1 2. 7 m m, t h e l e n gt h L = 1 0 0 0 m m, a n d t h e b e n di n g r a di u s

R = 7 9 8. 4 5 m m, Fi gs. 1 b a n d 1 c.

T a bl e 2 M e c h a ni c al pr o p erti es of A PI 5 L X 5 2 pi p eli n e st e el.

A pi p e el b o w i s s u bj e ct e d t o t h e i nt er n al - s er vi c e pr es s ur e P s= 7 M P a. T h e F E M r es ult s

a re s h o w n i n Fi g. 2. Fi g. 2 a s h o w s t h e 9 0 ° pi p e el b o w g e o m etr y. Fi g. 2 b s h o w s t h e m es h

c o n str u ct e d wit h a 1 6- n o d e q u a dril at er al el e m e nt a v ail a bl e i n A N S Y S s oft w ar e. Fi g. 2 c

ill u str at es t h e h o o p str es s di stri b uti o n al o n g t h e pi p e el b o w. Fi g. 3 a pr es e nt s t h e di stri b uti o n

of h o o p str es s es at diff er e nt a n gl es al o n g t h e pi p e el b o w, as ill u str at e d i n Fi g. 3 b.

Fi g. 2. Pi p e el b o w wit h o ut c orr o si o n d ef e ct s s u bj e ct e d t o t h e i nt er n al - s er vi c e pr es s ur e

P s= 7 M P a, g e o m etr y, m es hi n g, a n d h o o p str es s di stri b uti o n.

Fi g. 3. Pi p e el b o w wit h o ut c orr o si o n d ef e ct s: ( a) di stri b uti o n of t h e h o o p str es s; ( b) diff er e nt

p a t h s a n gl es al o n g t h e pi p e el b o w.

It i s cl e ar t h at t h e m a xi m al v al u e of h o o p str es s i s l o c at e d at t h e i ntr a d o s s e cti o n of t h e

pi p e el b o w, as s h o w n i n Fi gs. 2 a n d 3. Fi gs. 3 a a n d 3 b pr es e nt t h e di stri b uti o n of h o o p str es s

at t h e i ntr a d o s ( φ = 0 °), e xtr a d o s ( φ = 1 8 0 °) a n d cr o w n ( φ

J our

n al

Pre-

pro of

= 9 0 °) s e cti o n s of t h e pi p e el b o w.

9

M o r e o v er, r es ult s c o nfir m t h e criti c al i nfl u e n c e of t h e i ntr a d o s s e cti o n of t h e pi p e el b o w

b as e d o n t h e o bt ai n e d hi g h h o o p str es s v al u e t h at e q u al s σ θ = 2 1 2. 4 M P a. T h e v al u e of h o o p

str es s d e cr e as es at t h e cr o w n s e cti o n of t h e pi p e el b o w, a n d it i s cl o s e t o t h e v al u e f or t h e

str ai g ht pi p e ( σ θ = 1 6 4. 5 M P a).

T a bl e 3 H o o p str es s σ θ at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w wit h o ut c orr o si o n d ef e ct s.

T a bl e 3 s h o w s t h e m a xi m al h o o p str es s v al u es o bt ai n e d b y t h e n u m eri c al F E A m o d el

t o g et h er wit h v al u es o bt ai n e d u si n g t h e G o o d all f or m ul a ( E q. ( 2)), a n d t h e f or m ul a f or t h e

str ai g ht pi p e ( E q. ( 1)). It i s cl e ar t h at t h e h o o p str es s v al u e o bt ai n e d u si n g t h e G o o d all

f or m ul a - E q. ( 2) (σ θ = 2 0 1. 3 9 M P a) i s cl o s e t o t h e v al u e o bt ai n e d b y t h e n u m eri c al F E A

m o d el, Fi g. 3 ( σ θ = 2 1 2. 6 9 M P a), wit h t h e s m all err or of 5. 3 2 %, T a bl e 3. T h e err or i s

c al c ul at e d u si n g t h e f oll o wi n g f or m ul a: err or ( %) = ( σ θ ( F E A) - σ θ ( E q. 1, 2)) / σ θ ( F E A) x 1 0 0 %,

w h er e σ θ ( F E A), a n d σ θ ( E q. 1, 2) ar e t h e h o o p str es s v al u es o bt ai n e d b y F E M m o d el, e q u ati o n ( 1),

a n d E q. ( 2), r es p e cti v el y. O n t h e ot h er h a n d, a m u c h hi g h er err or ( 2 5. 9 4 %) i s o bt ai n e d u si n g

t h e str ai g ht pi p e f or m ul a ( E q. ( 1)) f or c al c ul ati o n of t h e h o o p str es s (σ θ = 1 5 7. 5 0 M P a), T a bl e

3. S u c h a l ar g e di s cr e p a n c y b et w e e n h o o p str es s v al u es at t h e i ntr a d o s s e cti o n of t h e pi p e

el b o w, o bt ai n e d b y b ot h F E A a n d t h e G o o d all f or m ul a, a n d t h e v al u e o bt ai n e d u si n g t h e

f or m ul a f or t h e str ai g ht pi p es i n di c at e t h e hi g h criti c alit y of t hi s s e cti o n of pi p e el b o w s. A

g o o d a gr e e m e nt b et w e e n t h e h o o p str es s v al u e o bt ai n e d u si n g t h e G o o d all f or m ul a [ 5 1] f or

c al c ul ati o n of t h e h o o p str es s ( σ θ ) i n a pi p e el b o w, a n d t h e v al u e o bt ai n e d b y n u m eri c al F E A

m o d el (s e e T a bl e 3, err or = 5. 3 2 %), pr o vi d es a s oli d b a c k gr o u n d f or c h e c ki n g t h e li mit

pr es s ur e c al c ul ati o n s r es ult s u si n g t hr e e m o difi e d c o d es. Al s o, t h e o bt ai n e d n u m eri c al F E A

v al u e f or t h e h o o p str es s ( σ θ ( F E A)= 2 1 2. 6 9 M P a) as w ell as t h e err or i n c o m p ari s o n wit h t h e

G o o d all f or m ul a [ 5 1] r es ult s ( 5. 3 2 %) ar e i n cl o s e a gr e e m e nt wit h t h e m a xi m u m err or of 6. 5 8

% r e p ort e d b y D u a n a n d S h e n [ 3 2]. O n c e a g ai n, t h e h o o p str es s v al u e o bt ai n e d b y t h e

G o o d all f or m ul a i s s o m e w h at hi g h er t h a n t h at o bt ai n e d b y t h e n u m eri c al F E A. T h e

c o m p ari s o n of r es ult s o bt ai n e d u si n g m o difi e d c o d es a n d t h e F E A r es ult s i s t h e t o pi c of t h e

n e xt s u b s e cti o n 3. 2.

3. 2. T h e li mit p r es s u r e c al c ul ati o n u si n g m o difi e d c o d es a n d F E A r es ult s

J our

n al

Pre-

pro of

I n t hi s s u b s e cti o n, t h e c orr o d e d pi p e el b o w as s es s m e nt i s st u di e d t o pr e v e nt t h eir b urst a n d

t h e r es ult s of t h e li mit pr es s ur e c al c ul ati o n u si n g m o difi e d c o d es ar e c o m p ar e d wit h t h e F E A

r es ult s. Pr e vi o u s r es e ar c h i n di c at es t h at t h er e i s a s eri o u s n e e d t o d et er mi n e a p erf e ct f or m ul a

1 0

t o c al c ul at e a li mit pr ess ur e at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w [ 2 3, 2 5, 3 2, 3 3, 5 0- 5 2].

T h er ef or e, t h e li mit pr es s ur e of t h e c orr o d e d pi p e el b o w i s a n al y z e d u si n g F E A a n d A N S Y S

s oft w ar e, as s h o w n i n Fi gs. 4 a n d 5. T h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct

w it h r o u n d e d c or n ers i s si m ul at e d at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w. T h e pi p e el b o w

wi t h a l e n gt h (L = 1 7 4 m m), wi dt h ( W = 2 0 8 m m), a n d wit h diff er e nt g e o m etri c al r el ati v e

c orr o si o n d ef e ct d e pt h t o w all t hi c k n es s r ati o s ( d/t = 0. 1 - 0. 8, s e e Fi g. 1 c) i s i n v esti g at e d,

Fi g. 4. T h e c orr o si o n d ef e ct s wit h diff er e nt d/t d e pt h r ati o s w er e m o d el e d at t h e i ntr a d o s

s e cti o n of t h e 9 0 ° pi p e el b o w, Fi gs. 4 a a n d 4 b. T h e h o o p str es s di stri b uti o n f or d/t = 0. 5 i s

s h o w n i n Fi g. 4 c.

Fi g. 4. Pi p e el b o w wit h t h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct wit h r o u n d e d

c or n ers at t h e i ntr a d o s s e cti o n s u bj e ct e d t o t h e i nt er n al - s er vi c e pr es s ur e P s= 7 M P a: pi p e

el b o w a n d t h e g e o m etr y of r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct wit h r o u n d e d

c or n ers , m es hi n g, a n d h o o p str es s di stri b uti o n (d/ t= 0. 5).

I n c o n d u ct e d F E A, f or e a c h d ef e ct d e pt h (d/t = 0. 1 - 0. 8, s e e Fi g. 1 c), t h e a p pli e d pr es s ur e

i s i n cr e as e d wit h a n i n cr e m e nt of 1 M P a, fr o m 1 M P a t o t h e m a xi m al 1 6 M P a. T h e h o o p

str es s t h at i s e q u al t o t h e yi el d or ulti m at e str e n gt h c a n b e c o n si d er e d as a li mit pr es s ur e, as

i n di c at e d i n Fi g. 5 a. T h e eff e ct s of d ef e ct d e pt h r ati o s (d/t = 0. 1 - 0. 8) o n t h e h o o p str es s w er e

a n al y z e d at diff er e nt i nt er n al pr es s ur es. B el o w t h e yi el d str e n gt h v al u e ( σ y = 4 1 0 M P a), a

t ypi c al li n e ar i n cr e as e of t h e h o o p str es s c a n b e o b s er v e d, Fi g 5 a [ 7 6]. D u e t o t h e e nt eri n g

i nt o t h e pl asti c r e gi m e, a b o v e σ y w hil e a p pr o a c hi n g t h e ulti m at e str e n gt h v al u e

(σ ult = 5 2 0 M P a), n o nli n e arit y i n t h e h o o p str es s i n cr e as e w as o b s er v e d, Fi g 5 a. Fi g. 5 b

ill u str at es t h e n u m eri c al F E A o bt ai n e d li mit pr es s ur es b as e d o n t h e yi el d σ y a n d ulti m at e

st r e n gt h σ ult v al u es f or A PI 5 L X 5 2 st e el wit h diff er e nt d ef e ct d e pt h r ati o s (d/ t= 0. 1 - 0. 8, s e e

Fi g. 1 c) at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w.

Fi g. 5. N u m eri c al a n al ysi s of el b o w d ef e ct s wit h diff er e nt d e pt h r ati o s d/ t at t h e i ntr a d o s

s e cti o n: ( a) h o o p str es s v ers u s i nt er n al pr es s ur e; ( b) li mit pr es s ur e P L a c c or di n g t o t h e yi el d

a n d ulti m at e str e n gt h.

A s pr e vi o u sl y di s c u s s e d, t h e li mit pr es s ur e d et er mi n es t h e pi p e b urst. It d e p e n d s o n t w o

m ai n m e c h a ni c al pr o p erti es (i) yi el d str e n gt h σ y a n d (ii) ulti m at e str e n gt h σ ult . A s i n di c at e d i n

F igs. 5 a a n d 5 b, t h e li mit pr es s ur e f or t h e pi p e el b o w m a d e of A PI 5 L X 5 2 st e el wit h d ef e ct

d e pt h r ati o d/t

J our

n al

Pre-

pro of

= 0. 1 i s al m o st 1 6 M P a b as e d o n t h e ulti m at e str e n gt h a n d 1 2 M P a b as e d o n t h e

11

yield strength. While the limit pressure for defected pipe elbow with defect depth ratio

d/t= 0.8 is much lower, approximately 8 MPa based on the ultimate strength and only

4.5 MPa based on the yield strength. The reduction of the internal - service pressure

Ps= 7 MPa (Fig. 5b) in the pipe elbow is necessary when a critical defect depth reaches

d/t= 0.65, based on the yield strength �y= 410 MPa for API 5L X52 steel. In this study of pipe

elbows, the presented numerical FEA results (Figs. 5b and 6) indicate that the use of yield

strength as a limit value for the limit pressure determination does not represent a conservative

solution as it was in the case of straight pipe made of the same steel [76]. It is also important

to note that in our previous study [66,76] the oval-shaped corrosion defects were introduced

with the same defect depth ratios range (d/t= 0.1 - 0.8), while in this study more stress

intensive rectangular parallelepiped-shaped corrosion defects with rounded corners are

investigated. Nevertheless, during comparison of the suitability for application of the ultimate

strength or yield strength as a limit value for the limit pressure determination and the

conservatism estimation, it is necessary to take into account other important factors. These

factors are (i) the pipeline component: straight pipe or a pipe elbow, (ii) the type of the

defect: cracks (the stress intensity factor - SIF) or corrosion defects without the crack, (iii)

geometrical characteristics of the corrosion defect (the degree of stress intensification), and

(iv) the relative defect depth to wall thickness ratio d/t [12,16,38,39,41,66,69,72,76].

Finally, it is important to reduce the internal pressure when the defect size is increasing to

maintain the reliable operation of pipelines. It is always advisable to make a comparison

between the deterministic and probabilistic approaches because of the confirmed trend of a

decrease in the reliability index with an increase of the defect depth to wall thickness ratio

[76]. It is clear based on the presented results that pipe elbows represent critical components

and hence endangered mostly the reliability of pipelines.

The comparison between the numerical FEA results for the limit pressure, and results

obtained using three modified codes (ASME B31G, modified ASME B31G, and DNV RP-

F101) for different corrosion defect depth ratios are presented in Fig. 6. The decrease of the

limit pressure in API 5L X52 made steel pipeline is compared for the straight pipe case, using

three standard codes, and for the pipe elbow case, using both modified codes together with

the Goodall formula for calculation of the hoop stress in the pipe elbow and FEA results. The

numerical FEA results for the limit pressure based on both yield strength and ultimate

strength are presented in Fig. 6. The rectangular parallelepiped-shaped corrosion defects with

rounded corners and with different corrosion defect depth ratios (d/t= 0.1 - 0.8) are located at

Journ

al Pre-pro

of

1 2

t he str ai g ht pi p e, a n d at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w ( Fi g. 4), r es p e cti v el y. A s

e x p e ct e d, t h e li mit pr es s ur e v al u es i n t h e str ai g ht pi p e, o bt ai n e d u si n g all t hr e e c o d es, ar e

si g nifi c a ntl y hi g h er t h a n f or t h e pi p e el b o w. T hi s i n di c at es t h at t h e a p pli c ati o n of u n m o difi e d

- ori gi n al c o d es d e v el o p e d f or t h e str ai g ht pi p e i n t h e c as e of t h e pi p e el b o w i s n ot a d vi s a bl e

a n d j u stifi e d b e c a u s e of t h e si g nifi c a nt o v er esti m ati o n of t h e all o w a bl e li mit pr es s ur e.

C o ntr ar y, t h e r es ult s f or t h e m o difi e d c o d es t h at t a k e i nt o a c c o u nt t h e pi p e el b o w g e o m etr y

b y u si n g t h e G o o d all f or m ul a f or c al c ul ati o n of t h e h o o p str es s i n t h e pi p e el b o w ar e f o u n d t o

b e i n cl o s e a gr e e m e nt wit h t h e n u m eri c al F E A r e s ult s. W h e n t h e ulti m at e str e n gt h i s u s e d t o

d et er mi n e t h e li mit pr es s ur e i n t h e n u m eri c al F E A ( P L σ ult( F E A) ), a m u c h b ett er a gr e e m e nt wit h

r es ult s f or all t hr e e m o difi e d st a n d ar d s ar e c o nfir m e d, T a bl e 4. T h e m a xi m al err or wit hi n t h e

r a n g e 1 0. 5 6 % (d/t = 0. 1) - 1 7. 9 3 % ( d/t = 0. 8), ( err or ( %) = ( P L ( B 3 1 G) - P L σ ult( F E A) ) / P L σ ult( F E A)

x 1 0 0 %) i s o bt ai n e d u si n g A S M E B 3 1 G c o d e f or all d ef e ct d e pt h r ati o s, T a bl e 4. F or d ef e ct

d e pt h r ati o s d/t b el o w 0. 5 (d/t ≤ 0. 5), t h e A S M E B 3 1 G c o d e c al c ul ati o n r es ult s ar e

c o n s er v ati v e ( err or: 1. 4 0 % ( d/t = 0. 5) u p t o 1 0. 5 6 % ( d/t = 0. 1)), a n d t h e g a p b et w e e n t h e F E A

a n d A S M E B 3 1 G r es ult s i s di mi ni s hi n g w hil e a p pr o a c hi n g t h e d ef e ct d e pt h r ati o of 0. 5. At

d ef e ct d e pt h r ati o s hi g h er t h a n 0. 5 ( d/t > 0. 5), t h e A S M E B 3 1 G r es ult s f or t h e li mit pr es s ur e

ar e hi g h er t h a n t h o s e o bt ai n e d b y t h e F E A ( err or: 4. 3 9 % ( d/t = 0. 6) - 1 7. 9 3 % ( d/t = 0. 8)), a n d

t h e g a p ( err or) b e c o m es hi g h er wit h f urt h er d ef e ct d e pt h r ati o i n cr e as e u p t o d/t = 0. 8, T a bl e 4.

A si mil ar c o n s er v ati v e tr e n d w h e n u si n g t h e A S M E B 3 1 G c o d e w as al s o o b s er v e d b y L e e et

al . [ 3 3] a n d A m a n di et al. [ 8 3]. T h e r es ult s f or t h e li mit pr es s ur e (P L ( M o d. B 3 1 G) a n d P L ( D N V) )

o b t ai n e d u si n g ot h er t w o m o difi e d st a n d ar d s ( m o difi e d A S M E B 3 1 G, a n d D N V R P- F 1 0 1)

ar e l es s c o n s er v ati v e, hi g h er t h a n t h o s e o bt ai n e d b y t h e F E A, a n d i n b ett er a gr e e m e nt s wit h

t h e n u m eri c al F E A r es ult s b as e d o n t h e ulti m at e str e n gt h (P L σ ult( F E A) ), s e e Fi g. 6 a n d T a bl e 4.

T h e c ur v at ur e of t h e F E A r es ult s a n d f or b ot h A S M E B 3 1 G a n d D N V R P- F 1 0 1 c o d es f oll o w

a si mil ar tr e n d. T h e r es ult s f or b ot h m o difi e d st a n d ar d s ar e sli g htl y l es s c o n s er v ati v e t h a n

F E A r es ult s a n d si mil arl y f or all d ef e ct d e pt h r ati o s. A si mil ar tr e n d of t h e b urst pr es s ur es

v al u es of t h e d a m a g e d pi p e el b o w s o bt ai n e d u si n g A S M E B 3 1 G a n d D N V R P- F 1 0 1 c o d es

w as al s o o b s er v e d b y L e e et al. [ 3 3], al b eit t h eir st u d y i n di c at es t h at b ot h m o d el s h a v e s h o w n

m o r e c o n s er v ati s m t h a n t h e F E A.

T h e r es ult s o bt ai n e d i n t hi s st u d y u si n g t h e m o difi e d A S M E B 3 1 G st a n d ar d ( P L ( M o d. B 3 1 G) )

ar e cl o s est t o t h e n u m eri c al F E A r es ult s ( P L σ ult( F E A)

J our

n al

Pre-

pro of

) f or all d ef e ct d e pt h r ati o s, Fi g. 6. T h e

er r or i s r el ati v el y s m all f or all d e pt h r ati o s a n d wit hi n t h e r a n g e 2. 4 9 - 1 0. 2 7 %, T a bl e 4. O n

t h e ot h er h a n d, t h e n u m eri c al F E A r es ult s f or t h e li mit pr es s ur e i n t h e pi p e el b o w u si n g t h e

1 3

yi el d str e n gt h ( P L σ y( F E A) ) f or diff er e nt d ef e ct d e pt h r ati o s ar e c o n si st e ntl y m u c h m or e

c o n s er v ati v e, Fi g. 6. T h e s e n u m eri c al m o d el r es ult s o bt ai n e d u si n g t h e G o o d all f or m ul a f or

c al c ul ati o n of t h e h o o p str es s i n t h e pi p e el b o w ar e i n g o o d a gr e e m e nt wit h r es ult s r e p ort e d

b y D u a n a n d S h e n [ 3 2] f or t h e c as e w h e n t h e m a xi m u m str ai n is l o c at e d i n t h e i n n er w all at

t h e i ntr a d o s of t h e pi p e el b o w.

Fi g. 6. C o m p ari s o n b et w e e n t h e li mit pr es s ur e v al u es i n t h e str ai g ht pi p e ( A PI 5 L X 5 2) a n d

th e pi p e el b o w ( at t h e i ntr a d o s s e cti o n) f or diff er e nt d e pt h r ati o s ( d/t = 0. 1 - 0. 8) of t h e

r ect a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct s wit h r o u n d e d c or n ers , o bt ai n e d n u m eri c all y

b y F E A, a n d a n al yti c all y u si n g st a n d ar d (str ai g ht pi p e) a n d m o difi e d ( pi p e el b o w) c o d es.

T a bl e 4 T h e diff er e n c e i n t h e li mit pr es s ur e P L v al u es f or t h e pi p e el b o w b as e d o n t h e

ul ti m at e str e n gt h (P L σ ult( F E A) ) o bt ai n e d b y F E A, a n d b y m o difi e d c o d es ( B 3 1 G, m o difi e d

B 3 1 G, a n d D N V R P- F 1 0 1) u si n g t h e G o o d all f or m ul a f or c al c ul ati o n of t h e h o o p str es s i n t h e

pi p e el b o w.

3. 3. T h e n ot c h f ail u r e a s s es s m e nt di a g r a m ( N F A D) f o r t h e st r ai g ht pi p e a n d pi p e b e n d s wit h

c o r r o si o n d ef e ct s

I n t hi s fi n al s u b s e cti o n, t h e n ot c h f ail ur e as s es s m e nt di a gr a m ( N F A D) f or t h e str ai g ht pi p e

a n d pi p e b e n d s wit h c orr o si o n d ef e ct s i s pr es e nt e d a n d a n al y z e d. T h e as s es s m e nt p oi nt i n

N F A D i s d efi n e d wit h t w o n o n- di m e n si o n al p ar a m et ers - c o or di n at es ( L r, K r), w h er e L r i s

a p pli e d str es s (l o a d), a n d K r i s a dri vi n g f or c e. A s m e nti o n e d i n t h e i ntr o d u cti o n s e cti o n, t h es e

t wo p ar a m et ers - c o or di n at es i n t h e N F A D s u b stit ut e t hr e e i nfl u e n ci n g p ar a m et ers, t h e

fr a ct ur e t o u g h n es s (K ρ C ), d ef e ct d e pt h r ati o ( d/t), a n d t h e i nt er n al pr es s ur e ( P). I n t hi s st u d y,

t h e N F A D w as m o difi e d u si n g t h e pi p e el b o w h o o p str es s σ θ i n t h e e q u ati o n f or c al c ul ati o n

of a n o n- di m e n si o n al l o a d L r a c c or di n g t o t h e f oll o wi n g e q u ati o n L r= σ θ /σ ο , w h er e σ θ a n d

σ ο ar e t h e h o o p str es s ( m a xi m u m cir c u mf er e nti al str es s), a n d fl o w str es s, r es p e cti v el y [ 1 2].

T h e fl o w str es s σ ο i s e x pr es s e d b y t h e f oll o wi n g e q u ati o n σ ο = ( σ y + σ ult ) / 2, wh er e σ y a n d σ ult

ar e t h e yi el d str e n gt h a n d ulti m at e str e n gt h, r es p e cti v el y [ 1 2, 8 4] . T h e v al u es of σ y a n d σ ult f or

A P I 5 L X 5 2 st e el u s e d i n t hi s st u d y ar e s h o w n i n T a bl e 2. Al s o, f or t h e c al c ul ati o n of a n o n-

di m e n si o n al cr a c k dri vi n g f or c e K r i n t h e pi p e el b o w, a m a xi m u m e q ui v al e nt n ot c h str es s

i nt e n sit y f a ct or (K ρ e q

J our

n al

Pre-

pro of

) i s u s e d a n d c o m p ut e d b e c a u s e of t h e el b o w c ur v at ur e w hi c h pr o v o k e d

1 4

t he m or e c o m pl e x mi x e d m o d e of l o a di n g ( K Iρ , K IIρ , a n d K IIIρ , Kρ e q = f ( K Iρ , K IIρ , a n d K IIIρ ))

a c c or di n g t o t h e f oll o wi n g e q u ati o n K r= K ρ e q / K ρ C [ 1 2]. C al c ul at e d fr a ct ur e t o u g h n es s v al u e s

fo r t h e pi p e el b o w (K ρ C = 9 5 M P a. m 0 . 5) a n d str ai g ht pi p e (K ΙC = 1 1 6. 6 M P a. m 0 . 5) m a d e of t h e

s am e m at eri al ( A PI 5 L X 5 2 st e el), a n d wit h t h e s a m e di m e n si o n s a n d g e o m etr y, ar e t a k e n

fr o m o ur pr e vi o u s st u d y (s e e T a bl e 2) [ 1 2]. Al s o, t h e fr a ct ur e t o u g h n es s v al u e f or t h e pi p e

el b o w i s l es s t h a n f or t h e str ai g ht pi p e d u e t o a hi g h er c o n str ai nt [ 1 2]. T h e N F A D i s b as e d o n

t h e i nt er p ol ati o n c ur v e K r= f ( L r) a n d it i s t y pi c all y pr es e nt e d i n p ol ar c o or di n at es (r, θ ) [ 8 4].

A s c h e m ati c r e pr es e nt ati o n of a t y pi c al N F A D wit h t w o c h ar a ct eri sti c p ol ar a n gl e v al u es ( θ 1

a n d θ 2 ) t h at d efi n e d t hr e e t y pi c al d o m ai n s (θ > θ 1 - brittl e fr a ct ur e, θ 1 > θ > θ 2 - el ast o- pl asti c

fr a ct ur e, a n d θ < θ 2 - pl a sti c c oll a p s e) i s s h o w n i n Fi g. 7. F ail ur e h a p p e n s if t h e as s es s m e nt

p o i nt (L r, Kr) i s a b o v e t h e i nt er p ol ati o n - f ail ur e c ur v e K r= f ( L r) [ 8 4]. M or e d et ail s a b o ut

p o l ar a n gl es d efi niti o n, t hr e e t y pi c al d o m ai n s, a n d t h e a p pli c ati o n of t h e N F A D ar e pr es e nt e d

i n n u m er o u s pr e vi o u sl y p u bli s h e d w or k s [ 1 2, 3 9, 4 1, 6 4- 7 5, 8 4, 8 6].

Fi g ur e 8 s h o w s t h e N F A D f or t h e str ai g ht pi p e a n d pi p e el b o w wit h diff er e nt d e pt h r ati o s

(d/t = 0. 1 - 0. 8) of t h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct s wit h r o u n d e d c or n ers

at t h e i ntr a d o s s e cti o n. E v ol uti o n s of t h e f u n cti o n p oi nt c o or di n at es, w hi c h d efi n e t h e

as s es s m e nt p oi nt o n t h e N F A D, i n di c at e t h at t h e pi p e el b o w i s a m or e e n d a n g er e d c o m p o n e nt

of t h e pi p eli n e. F or all c orr o si o n d ef e ct d e pt h r ati o s, t h e as s es s m e nt p oi nt s f or t h e pi p e el b o w

h a v e a hi g h er v al u e of b ot h c o or di n at es ( L r, Kr) t h a n f or t h e str ai g ht pi p e d u e t o t h e str es s

a m plifi c ati o n a n d hi g h er c o n str ai nt i n pi p e el b o w s. P arti c ul arl y, t h e n o n- di m e n si o n al a p pli e d

cr a c k dri vi n g f or c e Kr c o or di n at es f or all c orr o si o n d ef e ct d e pt h r ati o s ar e hi g h er f or t h e pi p e

e l b o w s. T h e diff er e n c e b et w e e n t h e K r c o or di n at e f or t h e pi p e el b o w a n d str ai g ht pi p e

in cr e as es si g nifi c a ntl y wit h a n i n cr e as e of t h e c orr o si o n d ef e ct d e pt h r ati o d/t fr o m 0. 1 t o 0. 8.

T h er ef or e, o nl y at t h e l o w est c orr o si o n d ef e ct d e pt h r ati o ( d/t = 0. 1), t h e pi p e el b o w

as s es s m e nt p oi nt i s i n t h e el ast o- pl asti c f ail ur e d o m ai n of t h e N F A D. A f urt h er si g nifi c a nt

ri s e of t h e K r c o or di n at es at s o m e w h at hi g h er d/ t r ati o s ( 0. 1 < d/t ≤ 0. 3 8), pr o v o k es c o n diti o n s

f or t h e pi p e el b o w as s es s m e nt p oi nt s t o b e s hift e d i nt o t h e brittl e z o n e of t h e N F A D, b ut still

wit hi n t h e s af et y z o n e. T h e l o a di n g p at h i n cr e as es i n a m or e n o n-li n e arl y w a y wit h t h e ri s e of

cr a c k d e pt h r ati o d/t ( 0. 3 8 < d/t ≤ 0. 8) at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w. Al s o, f or t h e

c o rr o si o n d e pt h r ati o s hi g h er t h a n t h e criti c al (d/t > 0. 3 8), all as s es s m e nt p oi nt s ar e l o c at e d i n

t h e f ail ur e z o n e of t h e N F A D, Fi g. 8. T h e o bt ai n e d criti c al d e pt h r ati o (d /t= 0. 3 8) of t h e

r ect a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct wit h r o u n d e d c or n ers

J our

n al

Pre-

pro of

f or t h e pi p e el b o w i s

15

somewhat higher than the critical semi-elliptical relative crack depth ratio (d/t= 0.28) in the

pipe elbow obtained in our previous study [12].

The loading path increases in a more linear way for the straight pipe with different

corrosion defect depth ratio. More linear behavior is mainly the consequence of the lower

increments of the corresponding Kr coordinates for the straight pipe with the increase of d/t.

The obtained critical depth ratio (d/t= 0.69) of the rectangular parallelepiped-shaped corrosion

defect with rounded corners for the straight pipe is significantly higher than for the pipe elbow

(d/t= 0.38). Moreover, all assessment points for the straight pipe with corrosion defect depth

ratios below the critical (0.1 < d/t � 0.69) are located in the least dangerous plastic collapse

fracture domain of the NFAD, as shown in Fig. 8. The obtained critical depth ratio (d/t= 0.69)

of the rectangular parallelepiped-shaped corrosion defect with rounded corners for the straight

pipe, Fig. 8, is slightly higher than for the critical semi-elliptical relative crack depth ratio

(d/t= 0.66) in the straight pipe obtained in our previous study [12]. Also, for the crack depth

ratios lower than the critical (0.1 < d/t � 0.66), investigated in our previous study [12], all

assessment points were located in the more dangerous elasto-plastic fracture domain of the

NFAD. Contrary, in this study of the rectangular parallelepiped-shaped corrosion defects with

rounded corners in the straight pipe, for all defect depth ratios lower than the critical (0.1 < d/t

� 0.69), the assessment points are located in the less dangerous plastic collapse fracture

domain of the NFAD, as shown in Fig. 8.

It can be concluded that due to more pronounced stress intensification provoked by the

semi-elliptical cracks with different relative depth rations [12], the structural integrity and

reliability of both straight pipe and pipe elbow is more threatened than in the case of a

rectangular parallelepiped-shaped corrosion defect with rounded corners. The results presented

in this study indicate further that the more severe stress conditions in pipe elbows with

corrosion defect at the intrados section in comparison to the straight pipe lead to the shift of

assessment points into the brittle zone of the modified NFAD. According to the codes,

previously analyzed in subsection 3.2, the straight pipe can resist the defect depths which

reach 80 - 85 % of pipe wall thickness [33,81,85]. The results presented in this study and the

NFAD for the straight pipe indicate that such a criterion is overly optimistic and hence not

universally applicable. The presented results are proving the applicability and practical

benefits of the modified NFAD. The NFAD is useful for the reliability assessment of

corroded pipes and particularly critical pipe elbows taking into account the different shapes

and depth of defects and the significant stress intensification in pipe elbows.

Journ

al Pre-pro

of

1 6

Fi g. 7. T h e s c h e m ati c vi e w of t h e n ot c h f ail ur e as s es s m e nt di a gr a m ( N F A D) a n d t hr e e t y pi c al

d o m ai n s. A d a pt e d a n d m o difi e d fr o m [ 8 4].

Fi g. 8. N ot c h f ail ur e as s e s s m e nt di a gr a m ( N F A D) f or t h e str ai g ht pi p e a n d pi p e el b o w wit h

di ff er e nt d e pt h r ati o s (d/t = 0. 1 - 0. 8) of t h e r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct s

wi t h r o u n d e d c or n ers at t h e i ntr a d o s s e cti o n.

4. C o n cl u si o n s

A c o m pr e h e n si v e st u d y of s af et y a n d r eli a bilit y as s es s m e nt of t h e c orr o d e d pi p e el b o w a n d

th e str ai g ht pi p e m a d e of A PI 5 L X 5 2 pi p eli n e st e el u si n g t h e n u m eri c al F E A, i n cl u di n g t h e

a p pli c a bilit y of t h e m o difi e d c o d es a d a pt e d f or t h e pi p e el b o w, i s pr es e nt e d i n t hi s p a p er.

R e g ar di n g t h e r es ult s of t h e li mit pr es s ur e c al c ul ati o n a n d t h e h o o p str es s v al u es i n t h e pi p e

el b o w wit h a n d wit h o ut diff er e nt r e ct a n g ul ar p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct d e pt h

r ati o s (d/t = 0. 1 - 0. 8) a n d t h e a p pli c a bilit y of t h e m o difi e d c o d es u si n g t h e G o o d all f or m ul a

f or c al c ul ati o n of t h e h o o p str es s, t h e f oll o wi n g c o n cl u si o n s c a n b e dr a w n.

• T h er e i s a g o o d a gr e e m e nt b et w e e n t h e h o o p str e s s v al u e o bt ai n e d u si n g t h e G o o d all

f or m ul a f or c al c ul ati o n of t h e h o o p str es s at t h e i ntr a d o s s e cti o n of a pi p e el b o w

wit h o ut c orr o si o n d ef e ct s a n d t h e v al u e o bt ai n e d b y t h e F E A wit h t h e s m all err or of

5. 3 2 %.

• T h e m u c h hi g h er err or ( 2 5. 9 4 %) i s o bt ai n e d u si n g t h e str ai g ht pi p e f or m ul a f or t h e

c a l c ul ati o n of t h e h o o p str es s i n t h e pi p e el b o w.

• T h e r es ult s of t h e li mit pr es s ur e c al c ul ati o n s u si n g t h e m o difi e d c o d es t h at t a k e i nt o

a c c o u nt t h e pi p e el b o w g e o m etr y b y u si n g t h e G o o d all f or m ul a f or c al c ul ati o n of t h e

h o o p str es s i n t h e pi p e el b o w ar e i n cl o s e a gr e e m e nt wit h t h e n u m eri c al F E A r es ult s.

• B ot h c o n s er v ati v e tr e n d a n d o v er esti m ati o n i n t h e li mit pr es s ur e v al u es o bt ai n e d u si n g

A S M E B 3 1 G c o d e wit h t h e hi g h est err ors (fr o m 1 0. 5 6 u p t o 1 7. 9 3 %) of all t hr e e

u s e d m o d el s i n c o m p ari s o n wit h t h e n u m eri c al F E A r es ult s f or a n al y z e d d ef e ct d e pt h

r ati o s (d/t

J our

n al

Pre-

pro of

= 0. 1 - 0. 8) ar e o b s er v e d.

1 7

• T h e r es ult s f or t h e li mit pr es s ur e o bt ai n e d u si n g t h e ot h er t w o m o difi e d st a n d ar d s

(m o difi e d A S M E B 3 1 G, a n d D N V R P- F 1 0 1) ar e l es s c o n s er v ati v e a n d i n m u c h b ett er

a gr e e m e nt wit h t h e n u m eri c al F E A r es ult s b as e d o n t h e ulti m at e str e n gt h.

• T h e r es ult s f or t h e li mit pr es s ur e o bt ai n e d u si n g t h e m o difi e d A S M E B 3 1 G st a n d ar d

ar e cl o s est t o t h e n u m eri c al F E A r es ult s f or all d ef e ct d e pt h r ati o s ( err or: 2. 4 9 -

1 0. 2 7 %).

• T h e n u m eri c al F E A r es ult s f or t h e li mit pr es s ur e i n t h e pi p e el b o w u si n g t h e yi el d

st r e n gt h f or diff er e nt d ef e ct d e pt h r ati o s ar e c o n si st e ntl y m u c h m or e c o n s er v ati v e a n d

h e n c e n ot a p pli c a bl e i n t hi s st u d y.

T h e r es ult s o bt ai n e d i n t h e pr e vi o u s r es e ar c h h a v e pr o v e d t h e pr a cti c al b e n efit s of t h e

m o difi e d n ot c h f ail ur e as s es s m e nt di a gr a m ( N F A D) f or t h e as s es s m e nt of t h e str u ct ur al

i nt e grit y a n d r eli a bilit y of str ai g ht pi p es a n d pi p e el b o w s wit h diff er e nt c orr o si o n d ef e ct s.

B as e d o n t h e c o m pr e h e n si v e r eli a bilit y a n al ysi s u si n g t h e N F A D f or t h e str ai g ht pi p e a n d

pi p e b e n d s ( A PI 5 L X 5 2) wit h diff er e nt d e pt h r ati o s (d /t= 0. 1 - 0. 8) of t h e r e ct a n g ul ar

p ar all el e pi p e d-s h a p e d c orr osi o n d ef e ct wit h r o u n d e d c or n ers at t h e i ntr a d o s s e cti o n t h e

f oll o wi n g c o n cl u si o n s c a n b e dr a w n.

• F or t h e c al c ul ati o n of a n o n- di m e n si o n al cr a c k dri vi n g f or c e K r i n t h e pi p e el b o w, a

m a xi m u m e q ui v al e nt n ot c h str es s i nt e n sit y f a ct or ( K ρ e q ) s h o ul d b e c o m p ut e d a n d u s e d

si n c e t h e el b o w c ur v at ur e pr o v o k e d t h e c o m pl e x mi x e d m o d e of l o a di n g. T h e

o bt ai n e d fr a ct ur e t o u g h n es s v al u e f or t h e pi p e el b o w i s l es s t h a n f or t h e str ai g ht pi p e

d u e t o a hi g h er c o n str ai nt.

• T h e as s es s m e nt p oi nt s f or t h e pi p e el b o w h a v e a hi g h er v al u e of b ot h c o or di n at es ( L r,

K r) f or all c orr o si o n d ef e ct d e pt h r ati o s t h a n f or t h e str ai g ht pi p e, d u e t o t h e str es s

in t e n sifi c ati o n a n d hi g h er c o n str ai n i n t h e pi p e el b o w s.

• F or t h e c orr o si o n d ef e ct d e pt h r ati o s hi g h er t h a n 0. 2 ( d/ t> 0. 2), t h e pi p e el b o w

as s es s m e nt p oi nt s ar e l o c at e d i n t h e brittl e z o n e of t h e N F A D, w hil e t h e criti c al

c orr o si o n d ef e ct d e pt h r ati o (i n t h e f ail ur e z o n e of t h e N F A D) i s d/t = 0. 3 8.

• T h e o bt ai n e d criti c al c orr o si o n d ef e ct d e pt h r ati o ( d/ t= 0. 6 9) f or t h e str ai g ht pi p e i s

si g nifi c a ntl y hi g h er t h a n f or t h e pi p e el b o w ( d/t

J our

n al

Pre-

pro of

= 0. 3 8). Al s o, all as s es s m e nt p oi nt s f or

c orr o si o n d ef e ct d e pt h r ati o s b el o w t h e criti c al ar e l o c at e d i n t h e l e ast d a n g er o u s

pl asti c c oll a p s e fr a ct ur e d o m ai n of t h e N F A D.

18

This study confirms that the pipe elbow is a critical part of piping systems. Moreover, the

stresses at the intrados section of the pipe elbow are higher than at extrados or crown

sections. Due to these facts, unmodified codes developed for the straight pipes are not

applicable for pipe elbows. Further investigation of modified codes for the limit pressure

calculation in the pipe elbow, taking into account the application of different contemporary

formulas for the calculation of the hoop stress, is envisaged in our future research.

Journ

al Pre-pro

of

19

References

[1] Djukic, M.B., Zeravcic, V.S., Bakic, G.M., Sedmak. A. and Rajicic B., 2015. Hydrogen damage of steels: A case study and hydrogen embrittlement model. Engineering Failure Analysis, 58, pp.485-498, https://doi.org/10.1016/j.engfailanal.2015.05.017

[2] Popov, B.N., Lee, J.W., and Djukic, M.B., 2018. Hydrogen permeation and hydrogen-induced cracking. In Myer Kutz, editor. Handbook of Environmental Degradation of Materials, Third Edition. William Andrew Publishing, pp.133-162,

https://doi.org/10.1016/B978-0-323-52472-8.00007-1

[3] Wasim, M. and Djukic, M.B., 2020. Hydrogen embrittlement of low carbon structural steel at macro-, micro- and nano-levels. International Journal of Hydrogen Energy, 45(3), pp.2145-2156, https://doi.org/10.1016/j.ijhydene.2019.11.070

[4] Djukic, M.B., Bakic, G.M., Zeravcic, V.S., Sedmak, A. and Rajicic, B., 2019. The synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: Localized plasticity and decohesion. Engineering Fracture Mechanics, 216, p.106528, https://doi.org/10.1016/j.engfracmech.2019.106528

[5] Wasim, M. and Djukic, M.B., 2020. Long-term external microbiologically influenced corrosion of buried cast iron pipes in the presence of sulfate-reducing bacteria (SRB). Engineering Failure Analysis, 115, p.104657,

https://doi.org/10.1016/j.engfailanal.2020.104657

[6] Bakic, G.M., Djukic, M.B., Rajicic, B., Zeravcic, V.S., Maslarevic, A. and Milosevic, N., 2016. Oxidation behavior during prolonged service of boiler tubes made of 2.25Cr1Mo and 12Cr1Mo0.3V heat resistance steels. Procedia Structural Integrity, 2, pp.3647-3653, https://doi.org/10.1016/j.prostr.2016.06.453

[7] Baki�, G.M., Šija�kiŽerav�i�, V.M., Djuki�, M.B., Maksimovi�, S.M., Plešinac, D.S. and Raji�i�, B.M., 2011. Thermal history and stress state of a fresh steam-pipeline influencing its remaining service life. Thermal Science, 15(3), pp.691-704,

https://doi.org/10.2298/TSCI110509050B

[8] Meriem-Benziane, M., Bou-Saïd, B. and Boudouani, N., 2017. The effect of crude oil in the pipeline corrosion by the naphthenic acid and the sulfur: A numerical approach. Journal of Petroleum Science and Engineering, 158, pp.672-679,

https://doi.org/10.1016/j.petrol.2017.08.073

[9] Soudani, M., Bouledroua, O., Hadj Meliani, M., El-Miloudi, K., Muthanna, B.G.N., Khelil, A., Elhoud, A., Matvienko, Y.G. and Pluvinage, G., 2018. Corrosion inspection and recommendation on the internal wall degradation caused rupture of 6” gas line pipe. Journal of Bio-and Tribo-Corrosion, 4(2), p.28, https://doi.org/10.1007/s40735-018-0145-0

[10] Amara, M., Bouledroua, O., Hadj Meliani, M., Muthanna, B.G.N., Tahar Abbes, M. and Pluvinage, G., 2018. Assessment of pipe for CO2 transportation using a constraint modified ctod failure assessment diagram. Structural Integrity and Life, 18(2), pp.149-153,

Journ

al Pre-pro

of

20

http://divk.inovacionicentar.rs/ivk/ivk18/149-IVK2-2018-MA-OB-MHM-BGNM-MTA-GP.pdf

[11] Yu, W., Fede, P., Climent, E. and Sanders, S., 2019. Multi-fluid approach for the numerical prediction of wall erosion in an elbow. Powder Technology, 354, pp.561-583, https://doi.org/10.1016/j.powtec.2019.06.007

[12] Muthanna, B.G.N., Bouledroua, O., Meriem-Benziane, M., Hadj Meliani, M., Pluvinage, G. and Suleiman, R.K., 2019. Numerical study of semi-elliptical cracks in the critical position of pipe elbow. Frattura ed Integrità Strutturale, 13(49), pp.463-477,

https://doi.org/10.3221/IGF-ESIS.49.44

[13] Peng, W., Cao, X., Hou, J., Xu, K., Fan, Y. and Xing, S., 2020. Experiment and numerical simulation of sand particle erosion under slug flow condition in a horizontal pipe bend. Journal of Natural Gas Science and Engineering, 76, p.103175,

https://doi.org/10.1016/j.jngse.2020.103175

[14] Amara, M., Muthanna, B.G.N., Tahar Abbes, M. and Hadj Meliani, M., 2018. Effect of sand particles on the Erosion-corrosion for a different locations of carbon steel pipe elbow. Procedia Structural Integrity, 13, pp.2137-2142,

https://doi.org/10.1016/j.prostr.2018.12.151

[15] Tawancy, H.M., Al-Hadhrami, L.M. and Al-Yousef, F.K., 2013. Analysis of corroded elbow section of carbon steel piping system of an oil–gas separator vessel. Case Studies in Engineering Failure Analysis, 1(1), pp.6-14,

https://doi.org/10.1016/j.csefa.2012.11.001

[16] Muthanna, B.G.N., Amara, M., Hadj Meliani, M., Mettai, B., Boži�, Ž., Suleiman, R. and Sorour, A.A., 2019. Inspection of internal erosion-corrosion of elbow pipe in the desalination station. Engineering Failure Analysis, 102, pp.293-302, https://doi.org/10.1016/j.engfailanal.2019.04.062

[17] Kusmono and Khasani, 2017. Analysis of a failed pipe elbow in geothermal production facility. Case Studies in Engineering Failure Analysis, 9, pp. 71-77,

https://doi.org/10.1016/j.csefa.2017.08.001

[18] Qiao, Q., Cheng, G., Li, Y., Wu, W., Hu, H. and Huang, H., 2017. Corrosion failure analyses of an elbow and an elbow-to-pipe weld in a natural gas gathering pipeline. Engineering Failure Analysis, 82, pp. 599-616,

https://doi.org/10.1016/j.engfailanal.2017.04.016

[19] Ilman, M.N., 2014. Analysis of internal corrosion in subsea oil pipeline. case studies in Engineering Failure Analysis, 2(1), pp.1-8, https://doi.org/10.1016/j.csefa.2013.12.003

[20] Li, L., Li, C.Q. and Mahmoodian, M., 2019. Prediction of fatigue failure of steel beams subjected to simultaneous corrosion and cyclic loading. Structures, 19, pp. 386-393, https://doi.org/10.1016/j.istruc.2019.02.003

Journ

al Pre-pro

of

21

[21] Kim, J.W., Na, Y.S. and Lee, S.H., 2009. Experimental evaluation of the bending load effect on the failure pressure of wall-thinned elbows. Journal of Pressure Vessel Technology, 131(3), p.031210, https://doi.org/10.1115/1.3122032

[22] Li, Y., Zhao, J.H., Zhu, Q. and Cao, X.Y., 2015. Unified Solution of Burst Pressure for Defect-Free Thin Walled Elbows. Journal of Pressure Vessel Technology, 137(2), p.021203, https://doi.org/10.1115/1.4028068

[23] Xie, Y.J., Zhang, H., Liu, S., Yang, P. and Luo, X., 2013. A Study on Stress Corrosion Crack of Thick-Walled Elbow in Manifold for Acid Fracturing. Journal of Pressure Vessel Technology, 135(2), p.021207, https://doi.org/10.1115/1.4023420

[24] Zhang, S.H., Gao, C.R., Zhao, D.W. and Wang, G.D., 2013. Limit analysis of defect-free pipe elbow under internal pressure with mean yield criterion. Journal of Iron and Steel Research, International, 20(4), pp.11-15, https://doi.org/10.1016/S1006-706X(13)60075-8

[25] Li, Z., Yinpei, W., Jin, C. and Cengdian, L., 2001. Evaluation of local thinned pressurized elbows. International Journal of Pressure Vessels and Piping, 78(10), pp.697-703, https://doi.org/10.1016/S0308-0161(01)00125-9

[26] Lee, G.H., Seo, J.K. and Paik, J.K., 2017. Condition assessment of damaged elbow in subsea pipelines. Ships and Offshore Structures, 12(1), pp.135-151,

https://doi.org/10.1080/17445302.2015.1116245

[27] Kim, Y.J. and Oh, C.S., 2006. Limit loads for pipe bends under combined pressure and in-plane bending based on finite element limit analysis. International Journal of Pressure Vessels and Piping, 83(2), pp.148-153, https://doi.org/10.1016/j.ijpvp.2005.11.001

[28] Khalajestani, M.K., Bahaari, M.R., Salehi, A. and Shahbazi, S., 2015. Predicting the limit pressure capacity of pipe elbows containing single defects. Applied Ocean Research, 53, pp.15-22, https://doi.org/10.1016/j.apor.2015.07.002

[29] Khalajestani, M.K. and Bahaari, M.R., 2014. Investigation of pressurized elbows containing interacting corrosion defects. International Journal of Pressure Vessels and Piping, 123, pp.77-85, https://doi.org/10.1016/j.ijpvp.2014.08.002

[30] Hong, S.P., Kim, J.H. and Kim, Y.J., 2009. Limit pressures of 90 elbows with circumferential surface cracks. Engineering Fracture Mechanics, 76(14), pp.2202-2216, https://doi.org/10.1016/j.engfracmech.2009.07.005

[31] Chattopadhyay, J. and Tomar, A.K.S., 2006. New plastic collapse moment equations of defect-free and throughwall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment. Engineering Fracture Mechanics, 73(7), pp.829-854, https://doi.org/10.1016/j.engfracmech.2005.12.002

[32] Duan, Z.X. and Shen, S.M., 2006. Analysis and experiments on the plastic limit pressure of elbows. International journal of pressure vessels and piping, 83(10), pp.707-713, https://doi.org/10.1016/j.ijpvp.2006.08.003

[33] Lee, G.H., Pouraria, H., Seo, J.K. and Paik, J.K., 2015. Burst strength behaviour of an aging subsea gas pipeline elbow in different external and internal corrosion-damaged

Journ

al Pre-pro

of

22

positions. International Journal of Naval Architecture and Ocean Engineering, 7(3), pp.435-451, https://doi.org/10.1515/ijnaoe-2015-0031

[34] Mahdi, R.S. and Zahiraniza, M., 2019. Rehabilitation of Corroded Circular Hollow Sectional Steel Beam by CFRP Patch. Steel and Composite Structures, 32(1), pp.127-139, https://doi.org/10.12989/scs.2019.32.1.127

[35] Mahdi, R.S., Zahiraniza, M., Biramarta, I., Nasir, S., Zubair I.S. and Do Kyan, K., 2016 Meso-Scale Numerical Study of Composite Patch Repaired Hole Drilled Steel Plate. ARPN Journal of Engineering and Applied Sciences, 11(3), pp.1724-1728,

http://www.arpnjournals.org/jeas/research_papers/rp_2016/jeas_0216_3557.pdf

[36] Mahdi R.S., Zahiraniza M., Nasir S., BiramartaI. and ZubairI. S., Finite Element Modeling of Wet Lay-up CFRP Patch Repaired Corroded Offshore Steel Jacket Member. Offshore Technology Conference (OTC) Asia, Malaysia, 2016,

https://doi.org/10.4043/26737-MS

[37] Firoozabad, E.S., Jeon, B.G., Choi, H.S. and Kim, N.S., 2016. Failure criterion for steel pipe elbows under cyclic loading. Engineering Failure Analysis, 66, pp.515-525, https://doi.org/10.1016/j.engfailanal.2016.05.012

[38] Zelmati, D., Ghelloudj, O. and Amirat, A., 2017. Reliability estimation of pressurized API 5L X70 pipeline steel under longitudinal elliptical corrosion defect. The International Journal of Advanced Manufacturing Technology, 90(9-12), pp.2777-2783,

https://doi.org/10.1007/s00170-016-9580-6

[39] Zelmati, D., Ghelloudj, O. and Amirat, A., 2017. Correlation between defect depth and defect length through a reliability index when evaluating of the remaining life of steel pipeline under corrosion and crack defects. Engineering Failure Analysis, 79, pp.171-185, https://doi.org/10.1016/j.engfailanal.2017.04.025

[40] Zhou, W., 2010. System reliability of corroding pipelines. International Journal of Pressure Vessels and Piping, 87(10), pp.587-595, https://doi.org/10.1016/j.ijpvp.2010.07.011

[41] Bouledroua, O., Zelmati, D. and Hassani, M., 2019. Inspections, statistical and reliability assessment study of corroded pipeline. Engineering failure analysis, 100, pp.1-10, https://doi.org/10.1016/j.engfailanal.2019.02.012

[42] Maxey, W.A., Kiefner, J.F., Eiber, R.J. and Duffy, A.R., 1972. Ductile fracture initiation, propagation, and arrest in cylindrical vessels. In Fracture Toughness: Part II, ed. H. Corten (West Conshohocken, PA: ASTM International, 1972), pp.70-81,

https://doi.org/10.1520/STP38819S

[43] ASME, Manual for Determining the Remaining Strength of Corroded Pipelines- a Supplement to ASME B31 Code for Pressure Piping, The American Society of Mechanical Engineers, New York, 1991.

Journ

al Pre-pro

of

23

[44] Kiefner, J. and Vieth, P., A Modified Criterion for Evaluating the Remaining Strength of Corroded Pipe, Final Report on Project PR 3-805, Battelle Memorial Institute, Columbus, OH, 1989, 1989.

[45] DNV Recommended Practice, RP-F101. Corroded pipelines. Det Norske Veritas; 2004

[46] Ritchie, D. and Last, S., 1995, April. Burst criteria of corroded pipelines-defect acceptance criteria. In Proceedings of the EPRG/PRC 10th biennial joint technical meeting on line pipe research.

[47] Kiefner, J.F. and Vieth, P.H., PC program speeds new criterion for evaluating corroded pipe, Oil Gas J. (1990) 91–93. August 20, 1990.

[48] Stephens, D.R. and Leis, B.N., Development of an alternative criterion for residual strength of corrosion defects in moderate-to high-toughness pipe, In: 2000 3rd International Pipeline Conference, October 1–5, 2000, Calgary, Alberta, Canada American Society of Mechanical Engineers, 2000, p.IPC2000-192, https://doi.org/10.1115/IPC2000-192

[49] Wang, Q. and Zhou, W., 2019. A new burst pressure model for thin-walled pipe elbows containing metal-loss corrosion defects. Engineering Structures, 200, p.109720, https://doi.org/10.1016/j.engstruct.2019.109720

[50] Yahiaoui, K., Moffat, D.G. and Moreton, D.N., 2000. Piping elbows with cracks Part 2: global finite element and experimental plastic loads under opening bending. The Journal of Strain Analysis for Engineering Design, 35(1), pp.47-57,

https://doi.org/10.1243/0309324001514008

[51] Goodall, I.W., 1978. Lower bound limit analysis of curved tubes loaded by combined internal pressure and in-plane bending moment. Research Division Report RD/B N, 4360, p.14.

[52] Kim, J.W., Yoon, M.S. and Park, C.Y., 2013. The effect of load-controlled bending load on the failure pressure of wall-thinned pipe elbows. Nuclear Engineering and Design, 265, pp.174-183, https://doi.org/10.1016/j.nucengdes.2013.07.027

[53] Tee, K.F. and Wordu, A.H., 2020. Burst strength analysis of pressurized steel pipelines with corrosion and gouge defects. Engineering Failure Analysis, 108, p.104347, https://doi.org/10.1016/j.engfailanal.2019.104347

[54] Yang, S., Li, C.Q. and Yang, W., 2016. Analytical model of elastic fracture toughness for steel pipes with internal cracks. Engineering Fracture Mechanics, 153, pp.50-60, https://doi.org/10.1016/j.engfracmech.2015.11.014

[55] Pluvinage, G., 1998. Fatigue and fracture emanating from notch; the use of the notch stress intensity factor. Nuclear Engineering and Design, 185(2-3), pp.173-184, https://doi.org/10.1016/S0029-5493(98)00183-6

[56] Adib, H., Jallouf, S., Schmitt, C., Carmasol, A. and Pluvinage, G., 2007. Evaluation of the effect of corrosion defects on the structural integrity of X52 gas pipelines using the SINTAP procedure and notch theory. International journal of pressure vessels and piping, 84(3), pp.123-131, https://doi.org/10.1016/j.ijpvp.2006.10.005

Journ

al Pre-pro

of

24

[57] Hadj Meliani, M., Pluvinage, G. and Capelle, J., 2009. Gouge assessment for pipes and associated transferability problem. In Defect and Diffusion Forum (Vol. 294, pp.15-25). Trans Tech Publications Ltd, https://doi.org/10.1016/j.engfailanal.2010.01.007

[58] Pluvinage, G., Capelle, J. and Hadj Meliani, M., 2019. Pipe networks transporting hydrogen pure or blended with natural gas, design and maintenance. Engineering Failure Analysis, 106, pp.104-164, https://doi.org/10.1016/j.engfailanal.2019.104164

[59] Hadj Meliani, M., Azari, Z., Pluvinage, G. and Capelle, J., 2010. Gouge assessment for pipes and associated transferability problem. Engineering Failure Analysis, 5(17), pp.1117-1126, https://doi.org/10.1016/j.engfailanal.2010.01.007

[60] Moustabchir, H., Zitouni, A., Hariri, S., Gilgert, J. and Pruncu, C.I., 2018. Experimental–numerical characterization of the fracture behaviour of P264GH steel notched pipes subject to internal pressure. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 42(2), pp.107-115, https://doi.org/10.1007/s40997-017-0086-0

[61] Adib, H. and Pluvinage, G., 2003. Theoretical and numerical aspects of the volumetric approach for fatigue life prediction in notched components. International Journal of fatigue, 25(1), pp.67-76, https://doi.org/10.1016/S0142-1123(02)00040-3

[62] Adib-Ramezani, H., Jeong, J. and Pluvinage, G., 2006. Structural integrity evaluation of X52 gas pipes subjected to external corrosion defects using the SINTAP procedure. International Journal of Pressure Vessels and Piping, 83(6), pp.420-432, https://doi.org/10.1016/j.ijpvp.2006.02.023

[63] Chattopadhyay, J., Pavankumar, T.V., Dutta, B.K. and Kushwaha, H.S., 2005. Fracture experiments on through wall cracked elbows under in-plane bending moment: Test results and theoretical/numerical analyses. Engineering fracture mechanics, 72(10), pp.1461-1497, https://doi.org/10.1016/j.engfracmech.2004.11.005

[64] Ainsworth, R.A., Gintalas, M., Sahu, M.K., Chattopadhyay, J. and Dutta, B.K., 2016. Application of failure assessment diagram methods to cracked straight pipes and elbows. International Journal of Pressure Vessels and Piping, 148, pp.26-35, https://doi.org/10.1016/j.ijpvp.2016.10.005

[65] Ainsworth, R.A., Gintalas, M., Sahu, M.K., Chattopadhyay, J. and Dutta, B.K., 2015. Failure Assessment Diagram Assessments of Large-Scale Cracked Straight Pipes and Elbows. Transactions, SMiRT-23 Manchester, United Kingdom - August 10-14, 2015.

http://www.lib.ncsu.edu/resolver/1840.20/33859

[66] Bouledroua, O., Hafsi, Z., Djukic, M.B. and Elaoud, S., 2020. The synergistic effects of hydrogen embrittlement and transient gas flow conditions on integrity assessment of a precracked steel pipeline. International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.04.262

[67] Boukortt, H., Amara, M., Hadj Meliani, M., Bouledroua, O., Muthanna, B.G.N., Suleiman, R.K., Sorour, A.A. and Pluvinage, G., 2018. Hydrogen embrittlement effect on the

Journ

al Pre-pro

of

25

structural integrity of API 5L X52 steel pipeline. International Journal of Hydrogen Energy, 43(42), pp.19615-19624, https://doi.org/10.1016/j.ijhydene.2018.08.149

[68] Meriem-Benziane, M., Abdul-Wahab, S.A., Zahloul, H., Babaziane, B., Hadj-Meliani, M. and Pluvinage, G., 2015. Finite element analysis of the integrity of an API X65 pipeline with a longitudinal crack repaired with single-and double-bonded composites. Composites Part B: Engineering, 77, pp.431-439, https://doi.org/10.1016/j.compositesb.2015.03.008

[69] Bouledroua, O., Hadj Meliani, M. and Pluvinage, G., 2017. Assessment of pipe defects using a constraint-modified failure assessment diagram. Journal of Failure Analysis and Prevention, 17(1), pp.144-153, https://doi.org/10.1007/s11668-016-0221-z

[70] Pluvinage, G., Bouledroua, O., Hadj Meliani, M. and Suleiman, R., 2018. Corrosion defect analysis using domain failure assessment diagram. International Journal of Pressure Vessels and Piping, 165, pp.126-134, https://doi.org/10.1016/j.ijpvp.2018.06.005

[71] Zhang, F., Rosenfeld, M. and Gustafson, J., 2018. Fitness for Service Analysis of the Circumferential Extent of Corrosion in Pipelines. In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, p.IPC2018-78338, V001T03A030, https://doi.org/10.1115/IPC2018-78338

[72] Amara, M., Bouledroua, O., Hadj Meliani, M., Azari, Z., Abbess, M.T., Pluvinage, G. and Bozic, Z., 2019. Effect of corrosion damage on a pipeline burst pressure and repairing methods. Archive of Applied Mechanics, 89(5), pp.939-951, https://doi.org/10.1007/s00419-019-01518-z

[73] Larrosa, N.O., Ainsworth, R.A., Akid, R., Budden, P.J., Davies, C.M., Hadley, I., Tice, D.R., Turnbull, A. and Zhou, S., 2017. ‘Mind the gap’in fitness-for-service assessment procedures-review and summary of a recent workshop. International Journal of Pressure Vessels and Piping, 158, pp.1-19, https://doi.org/10.1016/j.ijpvp.2017.09.004

[74] Pluvinage, G., Bouledroua, O. and Meliani, M.H., 2018. Corrosion defect harmfulness by domain failure assessment diagram. Pipeline Science and Technology, 2(3), pp.163-177, https://doi.org/10.28999/2514-541X-2018-2-3-163-177

[75] Cosham, A., Hopkins, P. and Macdonald, K.A., 2007. Best practice for the assessment of defects in pipelines–Corrosion. Engineering Failure Analysis, 14(7), pp.1245-1265,

https://doi.org/10.1016/j.engfailanal.2006.11.035�

[76] Zelmati, D., Bouledroua, O., Hafsi, Z. and Djukic, M.B., 2020. Probabilistic analysis of corroded pipeline under localized corrosion defects based on the intelligent inspection tool. Engineering Failure Analysis, 115, p.104683,

https://doi.org/10.1016/j.engfailanal.2020.104683

[77] Escoe, A.K., 2006. Piping and Pipelines Assessment Guide. Gulf Professional Publishing, Burlington, MA, https://doi.org/10.1016/B978-0-7506-7880-3.X5000-4

[78] BjØrnØy, O.H. and Marley, M.J., 2001. Assessment of corroded pipelines: past, present and future. In The Eleventh International Offshore and Polar Engineering Conference, 17-22 June, Stavanger, Norway. https://www.onepetro.org/conference-paper/ISOPE-I-01-138

Journ

al Pre-pro

of

26

[79] Stephens, D.R. and Francini, R.B., 2000. A review and evaluation of remaining strength criteria for corrosion defects in transmission pipelines. In Proceedings of ETCE/OMAE 2000 Joint Conference on Energy for the New Millennium, New Orleans, LA, USA (pp. 14-17).

[80] Zhang, S.H., Gao, C.R., Zhao, D.W. and Wang, G.D., 2013. Limit analysis of defect-free pipe elbow under internal pressure with mean yield criterion. Journal of Iron and Steel Research, International, 20(4), pp.11-15, https://doi.org/10.1016/S1006-706X(13)60075-8

[81] Miller, A.G., 1988. Review of limit loads of structures containing defects. International Journal of Pressure Vessels and Piping, 32(1-4), pp.197-327, https://doi.org/10.1016/0308-0161(88)90073-7

[82] Ansys® Academic Research Mechanical, Release 19.1

[83] Amandi, K.U., Diemuodeke, E.O. and Briggs T.A., 2019. Model for remaining strength estimation of a corroded pipeline with interacting defects for oil and gas operations. Cogent Engineering, 6(1), p.1663682, https://doi.org/10.1080/23311916.2019.1663682

[84] Hadj Meliani, M., Matvienko, Y.G., Pluvinage, G., 2011. Corrosion defect assessment on pipes using limit analysis and notch fracture mechanics. Engineering Failure Analysis, 18(1), pp.271-283, https://doi.org/10.1016/j.engfailanal.2010.09.006�

[85] Amaya-Gómezac, R., Sánchez-Silva, M., Bastidas-Arteaga, M., Schoefs, F. and Muñoza, F., 2019. Reliability assessments of corroded pipelines based on internal pressure – A review. Engineering Failure Analysis, 98, pp.190-214,

https://doi.org/10.1016/j.engfailanal.2019.01.064

[86] Zareei, A. and Nabavi, S.M., 2016. Weight function for circumferential semi-elliptical cracks in cylinders due to residual stress fields induced by welding. Archive of Applied Mechanics, 86(7), pp.1219-1230, https://doi.org/10.1007/s00419-015-1087-3

Journ

al Pre-pro

of

2 7

L I S T O F T A B L E S

T a b l e 1 C o d es f or c al c ul ati n g li mit pr es s ur e P L of t h e str ai g ht pi p e.

T a bl e 2 M e c h a ni c al pr o p erti es of A PI 5 L X 5 2 pi p eli n e st e el.

T a bl e 3 H o o p str es s σ θ at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w wit h o ut c orr o si o n d ef e ct s.

T a bl e 4 T h e diff er e n c e i n t h e li mit pr es s ur e P L v al u es f or t h e pi p e el b o w b as e d o n t h e

u lti m at e str e n gt h (P L σ ult( F E A) ) o bt ai n e d b y F E A, a n d b y m o difi e d c o d es ( B 3 1 G, m o difi e d

B 3 1 G, a n d D N V R P- F 1 0 1) u si n g t h e G o o d all f or m ul a f or c al c ul ati o n of t h e h o o p str es s i n t h e

pi p e el b o w.

T a bl e 1 C o d es f or c al c ul ati n g li mit pr es s ur e P L of t h e str ai g ht pi p e.

C o d e Li mit pr ess ur e, P L St r e n gt h r e d u cti o n

f a ct or, f( d/t) F oli as F a ct or, M G e o m etri c al c o n diti o ns

A S M E B 3 1 G [ 4 3]

( )2 1. 1 y t df

D t

σ

Mtd

td

/)/()3/2(1

)/()3/2(1

×−

×− 0. 52

1 0. 8L

Dt

+ ×

48.0

5.02

≤

×

Dt

L

t

d−1 ∞ 48.0

5.02

>

×

Dt

L

M o difi e d A S M E B 3 1 G [ 4 4]

( )2 1. 1 6 9y t df

D t

σ +

Mtd

td

/)/(8 5.01

)/(8 5.01

×−

×− 0. 522 2

1 0. 6 2 7 5 0. 0 0 3 3 7 5L L

D t Dt

+ × − ×

5 0

2

≤

Dt

L

Mtd

td

/)/(8 5.01

)/(8 5.01

×−

×− 0. 52

1 0. 3 1L

Dt

+

5 02

>

Dt

L

D N V R P-F 1 0 1 [ 4 5]

( )2 ult t df

D t t

σ

−

Mtd

td

/)/(1

)/(1

−

− 0. 52

1 0. 3 1L

Dt

+

S h ell- 9 2 [ 4 6]

1. 8.ult t df

D t

σ

1 ( / )

1 ( / ) /

d t

d t M

−

−

0. 52

1 0. 8L

Dt

+

R S T R E N G [ 4 7]

2.ult t df

D t

σ

1 ( / ) /d t M−

0. 522 2

1 0. 6 2 7 5 0. 0 0 3 3 7 5L L

D t Dt

+ × − ×

P C O R R C [ 4 8]

2.ult t df

D t

σ

1 ( / ) *d t M−

1 e x p 0. 1 5 7( ) / 2

L

D t d

− − −

J our

n al

Pre-

pro of

2 8

T a bl e 2 M e c h a ni c al pr o p erti es of A PI 5 L X 5 2 pi p eli n e st e el.

Y iel d str e n gt h, σ y ( MP a)

Ulti m at e str e n gt h, σ ult ( M P a)

El o n g ati o n, A ( %)

Fr a ct ur e t o u g h n es s, K I C

( M P a.m 0. 5 )

4 1 0 5 2 8 3 2 str ai g ht pi p e: 1 1 6. 6 [ 1 2]

pi p e el b o w: 9 5 [ 1 2]

J our

n al

Pre-

pro of

2 9

T a bl e 3 H o o p str es s σ θ at t h e i ntr a d o s s e cti o n of t h e pi p e el b o w wit h o ut c orr o si o n d ef e ct s.

M et h o d of c al c ul ati o n H o o p str es s, σ θ ( M P a)

Err or ( %) = (σ θ ( F E A ) -σ θ ( E q. 1, 2)) /σ θ ( F E A) x 1 0 0 %

N u m eri c al F E A m o d el ( Fi g. 3) σ θ ( F E A)= 2 1 2. 6 9

-

G o o d all f or m ul a [ 5 1] ( E q. ( 2)) σ θ ( E q. 2)=

2 0 1. 3 9 5. 3 2

Str ai g ht pi p e f or m ul a ( E q. ( 1)) σ θ ( E q. 1)=

1 5 7. 5 0 2 5 . 9 4

J our

n al

Pre-

pro of

3 0

T a bl e 4 T h e diff er e n c e i n t h e li mit pr es s ur e P L v al u es f or t h e pi p e el b o w b as e d o n t h e

u lti m at e str e n gt h (P L σ ult( F E A) ) o bt ai n e d b y F E A, a n d b y m o difi e d c o d es ( B 3 1 G, m o difi e d

B 3 1 G, a n d D N V R P- F 1 0 1) u si n g t h e G o o d all f or m ul a f or c al c ul ati o n of t h e h o o p str es s i n t h e

pi p e el b o w.

D ef e ct d e pt h r ati o, d/t

P L ( M P a), s e e Fi g. 6, a n d Err or ( %) = ( P L ( B 3 1 G, M o d. B 3 1 G, a n d D N V) - P L σ ult( F E A) ) / P L σ ult( F E A) x 1 0 0 %

P L σ ult( F E A) ( MP a)

P L ( B 3 1 G)

( M P a) Err or ( %)

P L ( M o d. B 3 1 G)

( M P a) Err or ( %)

P L ( D N V) ( M P a)

Err or ( %)

0. 1 1 6. 1 9 1 4. 4 8 1 0. 5 6 1 6. 5 9 2. 4 9 1 7. 3 2 6. 9 5

0. 2 1 5. 3 7 1 3. 9 1 9. 4 8 1 5. 8 1 2. 8 6 1 6. 5 8 7. 8 7

0. 3 1 4. 4 5 1 3. 3 1 7. 9 1 1 4. 9 4 3. 4 1 1 5. 7 2 8. 7 9

0. 4 1 3. 3 5 1 2. 6 5 5. 2 1 1 3. 9 8 4. 7 2 1 4. 7 0 1 0. 1 4

0. 5 1 2. 1 2 1 1. 9 5 1. 4 0 1 2. 9 0 6. 4 5 1 3. 4 8 1 1. 2 5

0. 6 1 0. 7 2 1 1. 1 9 4. 3 9 1 1. 6 9 9. 0 3 1 1. 9 9 1 1. 8 5

0. 7 9. 3 5 1 0. 3 7 1 0. 8 7 1 0. 3 1 1 0. 2 7 1 0. 1 2 8. 2 6

0. 8 8. 0 3 9. 4 7 1 7. 9 3 8. 7 3 8. 7 7 7. 7 2 3. 8 9

J our

n al

Pre-

pro of

31

LIST OF FIGURES

Fig. 1. API X52 pipeline elbow: (a) manifold separation system; (b) corroded pipe elbow;

(c) pipe elbow dimensions.

Fig. 2. Pipe elbow without corrosion defects subjected to the internal - service pressure Ps=

7 MPa, geometry, meshing, and hoop stress distribution.

Fig. 3. Pipe elbow without corrosion defects: (a) distribution of the hoop stress; (b) different

angles along the pipe elbow.

Fig. 4. Pipe elbow with the rectangular parallelepiped-shaped corrosion defect with rounded

corners at the intrados section subjected to the internal - service pressure Ps= 7 MPa: pipe

elbow and the geometry of rectangular parallelepiped-shaped corrosion defect with rounded

corners, meshing, and hoop stress distribution (d/t= 0.5).

Fig. 5. Numerical analysis of elbow defects with different depth ratios d/t at the intrados

section: (a) hoop stress versus internal pressure; (b) limit pressure PL according to the yield

and ultimate strength.

Fig. 6. Comparison between the limit pressure values in the straight pipe (API 5L X52) and

the pipe elbow (at the intrados section) for different depth ratios (d/t= 0.1 - 0.8) of the

rectangular parallelepiped-shaped corrosion defects with rounded corners, obtained numerically

by FEA, and analytically using standard (straight pipe) and modified (pipe elbow) codes.

Fig. 7. The schematic view of the notch failure assessment diagram (NFAD) and three typical

domains. Adapted and modified from [84].

Fig. 8. Notch failure assessment diagram (NFAD) for the straight pipe and pipe elbow with

different depth ratios (d/t= 0.1 - 0.8) of the rectangular parallelepiped-shaped corrosion defects

with rounded corners at the intrados section.

Journ

al Pre-pro

of

32

Fig. 1. API X52 pipeline elbow: (a) manifold separation system; (b) corroded pipe elbow;

(c) pipe elbow dimensions.

�

(b)�(a)� (c)�

Journ

al Pre-pro

of

33

Fig. 2. Pipe elbow without corrosion defects subjected to the internal - service pressure

Ps = 7 MPa, geometry, meshing, and hoop stress distribution.

Journ

al Pre-pro

of

3 4

F ig. 3. Pi p e el b o w wit h o ut c orr o si o n d ef e ct s: ( a) di stri b uti o n of t h e h o o p str es s; ( b) diff er e nt

p a t h s a n gl es al o n g t h e pi p e el b o w.

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

Str ai g ht pi p e σθ= 1 6 4. 5 M P a

Pi p e el b o w σθ [ 1, 2 a n d 3]

= 2 1 2. 4 M P a

Hoop

str

ess,

σθ (

MPa

)

A n gl e p ositi o n, θ (°)

φ = 0 ° φ = 4 5 ° φ = 9 0 ° φ = 1 3 5 ° φ = 1 8 0 °

θ

0

9 0

1 8 0

4 5 1 3 5

φ

( a) ( b)

J our

n al

Pre-

pro of

35

Fig. 4. Pipe elbow with rectangular parallelepiped-shaped corrosion defect with rounded corners

at the intrados section subjected to the internal - service pressure Ps= 7 MPa: pipe elbow and

the geometry of rectangular parallelepiped-shaped corrosion defect with rounded corners,

meshing, and hoop stress distribution (d/t= 0.5).

Journ

al Pre-pro

of

3 6

( a)

( b)

F ig. 5. N u m eri c al a n al ysi s of el b o w d ef e ct s wit h diff er e nt d e pt h r ati o s d/ t at t h e i ntr a d o s

s e cti o n: ( a) h o o p str es s v ers u s i nt er n al pr es s ur e; ( b) li mit pr es s ur e P L a c c or di n g t o t h e yi el d

a n d ulti m at e str e n gt h.

0 2 4 6 8 1 0 1 2 1 4 1 6

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

P = 4. 5 9 M P a P = 1 2. 3 2 M P a

P = 8. 3 2 M P a P = 1 6. 2 6 M P aUlti m at e str e n gt h σ

ult= 5 2 8 M P a

Yi el d str e n gt h σ

y= 4 1 0 M P a

Hoop

str

ess,

σθ (

MPa

)

A p pli e d pr ess ur e, P ( M P a)

d/t = 0. 1 d/t = 0. 2 d/t = 0. 3 d/t = 0. 4 d/t = 0. 5 d/t = 0. 6 d/t = 0. 7 d/t = 0. 8

L = 1 7 4 m m W = 2 0 8 m m

0, 1 0, 2 0, 3 0, 4 0, 5 0, 6 0, 7 0, 8

4

6

8

1 0

1 2

1 4

1 6

S er vi c e pr ess ur e P

s= 7 M P a

Limit

pres

sure

, P

L (

MPa

)

D ef e ct d e pt h r ati o, d/t

Yi el d str e n gt h

J our

n al

Pre-

pro of

Ulti m at e str e n gt h

37

Fig. 6. Comparison between the limit pressure values in the straight pipe (API 5L X52) and

the pipe elbow (at the intrados section) for different depth ratios (d/t= 0.1 - 0.8) of the

rectangular parallelepiped-shaped corrosion defects with rounded corners, obtained numerically

by FEA, and analytically using standard (straight pipe) and modified (pipe elbow) codes.

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,80

2

4

6

8

10

12

14

16

18

20

22

Pipe elbow (numerical analysis) Yield strength Ultimate strength

Straight pipe standards B31G Mod B31G DNV

Lim

it pr

essu

re, P

L (MPa

)

Defect depth ratio, d/t

Pipe elbow (modified standards) B31G Mod B31G DNV

Journ

al Pre-pro

of

38

Fig. 7. The schematic view of the notch failure assessment diagram (NFAD) and three typical

domains. Adapted and modified from [84].

Journ

al Pre-pro

of

39

Fig. 8. Notch failure assessment diagram (NFAD) for the straight pipe and pipe elbow with

different depth ratios (d/t= 0.1 - 0.8) of the rectangular parallelepiped-shaped corrosion defects

with rounded corners at the intrados section.

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,80,0

0,2

0,4

0,6

0,8

1,0

1,2

Plastic collapse fracture

Elasto-plastic fracture

Brittle fracture

d/t=0.8

d/t=0.7d/t=0.6

d/t=0.5d/t=0.4

d/t=0.3

d/t=0.2

d/t=0.1

d/t=0.1d/t=0.2

d/t=0.3d/t=0.4

d/t=0.5 d/t=0.6 d/t=0.7 d/t=0.8Security zone

Safety zone

Failure zone

Kr

Lr

Straight pipe Pipe elbow

d/t=0.1 to 0.8 P=7 MPa

Journ

al Pre-pro

of

Hi g hli g hts

• I nt e grit y of c orr o d e d pi p e el b o w w as i n v esti g at e d b as e d o n t h e li mit pr ess ur e.

• A p ar all el e pi p e d r o u n d e d b or d ers c orr osi o n d ef e ct w as cr e at e d i n t h e i ntr a d os s e cti o n.

• T h e n u m eri c al fi nit e el e m e nt a n al ys es ( F E A) w er e d o n e t o m o dif y t h e c o d es.

• T w o m o d els ( m o difi e d B 3 1 G a n d D N V R P- F 1 0 1) a gr e es w ell wit h F E A r e s ults.

•

J our

n al

Pre-

pro of

T h e n ot c h f ail ur e ass ess m e nt di a gr a m ( N F A D) c o nfir ms t h e pi p e el b o w criti c alit y.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships

that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered

as potential competing interests:

Journ

al Pre-pro

of