UNIVERSITY OF CALIFORNIA Establishing Correlations for Predicting Tensile Properties Based on the...

UNIVERSITY OF CALIFORNIA

Santa Barbara

Establishing Correlations for Predicting Tensile Properties Based on the Shear Punch

Test and Vickers Microhardness data

A Thesis submitted in partial satisfaction of the

requirements for the degree Master of Science

in Mechanical Engineering

by

Timothy S. Milot

Committee in charge:

Professor Robert Odette, Chair

Professor Matt Begley

Professor Keith Kedward

March 2013

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The thesis of Timothy S. Milot is approved.

_____________________________________________ Keith Kedward

_____________________________________________ Matthew Begley

_____________________________________________ Robert Odette, Committee Chair

November 2012

iii

ACKNOWLEDGEMENTS

I wish to thank my advisor, Professor G.R. Odette, whose advice has been

invaluable in my work toward becoming a better engineer, and who afforded me the

freedom to pursue my research, while providing insightful and constructive feedback. I

would also like to thank my other committee members, Professor K. Kedward and

Professor M. Begley, for their patience and assistance in reviewing this work.

I also gratefully acknowledge the Advanced Test Reactor National Scientific

User Facility (ATR NSUF) Program at the Idaho National Laboratory (INL) for tuition,

salary and other support during my entire graduate program at UCSB, and visits to INL

and the Center for Advanced Energy Studies. The help I received from Ms. Mary

Catherine Thelen at NSUF was invaluable. INL researchers Dr. J. Cole, Dr. B. Sencer,

Dr. C. Knight and, especially, Dr. B. Miller, were critically important to my work. Mr.

Tim Williams and Dr. Kieth Wilford of Rolls Royce provided the large set of steel

alloys characterized in this study, and the major support for the testing program at

UCSB. Dr. Randy Nanstad at Oak Ridge National Laboratory also assisted in the

procurement and qualification of the Rolls Royce alloys.

This work was also made possible by assistance I received from colleagues at

UCSB, particularly those in the Odette research group. Thanks go to Dr. T. Yamamoto

for always being available to answer scientific questions, and to both Mr. D. Gragg and

Mr. D. Klingensmith, for providing incredibly knowledgeable advice on experimental

methods, as well as assistance on all aspects of my research. Thanks also go to K.

iv

Fields, whose mechanical testing expertise and assistance was of great benefit and who

provided the tensile test data.

Special thanks go out to my friends and family for their love and support.

v

ABSTRACT

Establishing Correlations for Predicting Tensile Properties Based on the Shear Punch

Test and Vickers Microhardness data

Timothy S. Milot

A series of mechanical tests was performed on a matrix of pressure vessel alloys to

establish correlations between shear punch tests (SPT), microhardness (Hv), and tensile

data. The purpose is to estimate tensile properties from SPT and Hv data. Small

specimen testing is central to characterization of irradiation-induced changes in alloys

used for nuclear applications. SPT have the potential for estimating tensile yield and

ultimate strengths, strain hardening and ductility data, by using TEM disks, for

example. Additional insight into SPT was gained by performing finite element analysis

(FEA) simulations.

vi

CONTENTS

LIST OF TABLES ..................................................................................................... viii

LIST OF FIGURES ..................................................................................................... ix

NOMENCLATURE .................................................................................................... xi

Chapter 1 Introduction ...................................................................................................1

Chapter 2 Background ...................................................................................................2

Shear Punch Testing and Previous Research ...............................................2

Vickers Microhardness ..............................................................................10

Chapter 3 Materials ......................................................................................................12

Shear Punch Testing ..................................................................................14

Microhardness Testing ...............................................................................15

Tensile Testing ...........................................................................................16

Chapter 4 Data Analysis ..............................................................................................17

Shear Punch Testing ..................................................................................17

Tensile Testing ...........................................................................................29

Chapter 5 Results .........................................................................................................32

Chapter 6 Establishing Predictive Relationships Between SPT, Tensile Test and

Microhardness Properties .............................................................................................38

Chapter 7 Finite Element Analysis (FEA) of the SPT .................................................48

Finite Element Model and Boundary Conditions ......................................50

SPT P-d Fits ...............................................................................................52

Results ........................................................................................................53

vii

Chapter 8 Discussion and Conclusions ........................................................................64

Chapter 9 Future Work ................................................................................................65

References ....................................................................................................................68

Appendix A ..................................................................................................................71

Appendix B ..................................................................................................................73

viii

LIST OF TABLES

Table 1 Observed Relations Between τy and σy. .........................................................5

Table 2 Summary of the Test Data Statistics (MPa). ................................................32

Table 3 Summary of the Tensile Data.* *Stress units are in MPa. ..........................33

Table 4 Summary of the SPT Data.* ........................................................................35

Table 5 Summary of the Microhardness Data.* .......................................................37

Table 6 UTS estimation based on nτ and Sm, as UTS = Sm/sf. ..................................45

Table 7 Correlation averages, standard deviations and average deviations. .............65

Table 8 Flow Stress and H measured and predicted values ......................................72

ix

LIST OF FIGURES

Figure 1 Schematic illustration of shear punch test fixture. .......................................2

Figure 2 A typical SPT curve ......................................................................................4

Figure 3 Tensile yield strength (σy) by material. ......................................................13

Figure 4 Shear punch test fixture diagram ................................................................14

Figure 5 SS-J2 tensile specimen drawing. ................................................................16

Figure 6 Typical SPT τ−d/t (or P-d) curve ...............................................................19

Figure 7 Enlarged SPT P-d curve .............................................................................20

Figure 8 τsp(εsp) and σf(εt) true-stress strain for RR1 alloy. ......................................22

Figure 9 Flow geometry during punching. ...............................................................23

Figure 10 Deformation during uniform shear. ..........................................................23

Figure 11 The Cy = σy/τy ratios versus the SPT offset (%). .....................................25

Figure 12 τy vs. punch-die clearance, wg, for selected alloys. ..................................27

Figure 13 SPT Sm vs. punch-die clearance, wg, for selected alloys. ........................28

Figure 14 Tensile engineering stress-strain curve for RR7 alloy. ............................29

Figure 15 Tensile Plastic flow stress vs. true plastic strain for RR7 alloy. ..............30

Figure 16 Tensile σy versus shear SPT shear yield stress τy measurements and the

corresponding LSF line through the 0,0 origin. One SD error bars are shown for

the individual data points. ....................................................................................39

Figure 17 σy vs. Vickers microhardness. ..................................................................41

Figure 18 Tensile UTS vs. Vickers microhardness. .................................................42

Figure 19 The tensile UTS versus SPT Sm and corresponding LSF line. .................43

x

Figure 20 Flow stress vs. H. .....................................................................................45

Figure 21 UTS predicted using sf and UTS vs. UTS. ...............................................47

Figure 22 The finite element model of the SPT and mesh. ......................................48

Figure 23 True stress-strain σfl(εp) curves used in the FEA simulation of the SPT P-d

curves: RR1 εf = 0.625, RR19 εf = 1, RR27 εf = 0.75. .......................................50

Figure 24 Linear fit to the lower fixture compliance. Typical SPT Py ≈ 1.5-2KN. .51

Figure 25 Map of the εpe at small d. ..........................................................................53

Figure 26 FEA and experimental Se (MPa) versus d/t curves for RR1. ....................54

Figure 27 FEA and experimental Se (MPa) versus d/t curves for RR19. ..................55

Figure 28 FEA and experimental Se (MPa) versus d/t curves for RR27. ..................56

Figure 29 FEA elements used for averaging εpe evaluated as a function of d/t. .......57

Figure 30 The engineering Se and average 〈εpe〉 vs. d/t for RR1. ..............................57

Figure 31 Maps of 〈εpe〉 for two d/t: a) soon after the initial element failure; and, b)

near Sm. ................................................................................................................58

Figure 32 The εe(Ramaekars) and 〈εpe〉 (FEA) as a function of d/t. εe is about two

times the 〈εpe〉 for RR1. ........................................................................................59

Figure 33 Comparison of the Ramaekars Se(t/d) model with the experimental and

FEA simulation results. ........................................................................................61

Figure 34 The tensile σfl(εp) and 1.77*τ(εp) vs. εp for RR1. ....................................62

xi

NOMENCLATURE

SP Shear Punch

SPT Shear Punch Test

Se Engineering Shear Stress

σy Tensile yield

UTS Ultimate tensile strength

d SPT displacement

df SPT Displacement at maximum load

t SP specimen thickness

P Punch load

D Average of punch and die diameter (Dp and Dd respectively)

τy SPT yield

SPM SPT maximum load

Sm SPT maximum engineering stress

LDC Load displacement curve

Hv Vicker’s microhardness

n Strain hardening coefficient

εu Uniform strain at UTS

εpl Plastic strain

1

Chapter 1 Introduction

Development of materials for nuclear applications requires testing in fission

reactors and high-energy neutron sources. Due to the large number of specimens

needed and post-irradiation handling limitations, efficient small test specimen

techniques are essential to characterizing these materials and minimizing irradiated

volumes. Small specimen size also facilitates better temperature control associated

with less nuclear heating as well as lower fluence gradients in accelerator based

neutron irradiations [4].

Shear punch test (SPT) techniques have been developed to compliment

microhardness and tensile tests. The SPT measures a load-displacement (P-d) curve

(LDC) analogous to that measured in tensile testing using simple disks or sheet

coupons typically ≈ 0.25~0.5mm thick. SPT and microhardness test data can be used

to estimate equivalent tensile yield and ultimate tensile stress, and strain hardening

rates.

The objective of this research is to establish correlations for predicting tensile

properties based on the SPT and Vickers microhardness data. A series of 56 so-called

Rolls Royce alloys were used to establish this correlation.

2

Chapter 2 Background

Shear Punch Testing and Previous Research

SP testing is a blanking operation wherein a cylindrical punch is driven through a

flat test material into a die at constant speed, typically in a screw-driven or hydraulic

load frame. A typical shear punch fixture is schematically illustrated in Figure 1.

The fixture is comprised of an upper guide assembly with precisely aligned pins and a

lower base assembly with a receiver die into which the test material is punched.

Displacement is typically measured either by measurement of: a) movement of the

lower surface of the disk; b) the load frame cross head; c) a proximity sensor attached

to the punch measuring displacement relative to lower fixture assembly.

Figure 1 Schematic illustration of shear punch test fixture.

SPT data is used to estimate tensile test yield and ultimate stress, strain hardening,

and ductility [1-9]. SPT samples can be obtained from existing thin sheet coupons,

such as TEM discs, large coupons typically used to punch TEM discs, the end tabs of

3

tensile specimens, or, for example, slices cut from Charpy V-Notched (CVN) or other

fracture specimens commonly used in reactor surveillance programs. During SPT

plastic deformation occurs primarily in a cylindrical zone between punch and die [1-

9]. Since this volume is larger than the volume deformed in microhardness testing,

the effects of non-uniform microstructure and grain size differences are mitigated. In

high-energy neutron irradiations there is typically a limited volume (<500 cm3),

motivating the development of miniaturized specimens [10].

The SPT load displacement curve has characteristics in common with a tensile

test, namely a linear elastic portion, onset of plasticity, a maximum stress, and

reduction of load with further displacement corresponding to a geometric plastic

instability and eventually damage development [1,2]. The SPT plastic instability

occurs at a maximum engineering shear stress, Sm, when the load on the remaining

ligament, t-d, decreases more rapidly than increases in load associated with flow

stress increases due to strain hardening. SPT displacement is normalized to specimen

thickness, d/t. Analogous to finding the 0.2% offset tensile yield strength, σy, an

offset line parallel to the linear portion of the SPT curve offset is used to determine

the yield stress, τy, as shown in Figure 2.

4

Figure 2 A typical SPT curve

The engineering shear stress Se is calculated based on punch load (P), the average

of punch and die diameter (D), and specimen thickness (t).

S! = !

!∗!∗! (1)

At small strains associated with shear yielding stress 𝜏! ≅ S!". For ideal shear

dominated conditions the theoretical relation between τy and the uniaxial yield stress,

σy, is given by:

σ! = τ! ∗ 3 (2)

5

where the Von Mises yield criteria Cst = √3.

Table 1 summarizes Cst found in previous studies with expressions in the form of:

σ! = C!"τ! + τ!" (3)

Here τyO represents deviations from ideal deformation conditions and in most

cases Cst ≈ √3 have been reported with τ!" ≈ 0. In two cases k was >2 accompanied

by a large negative τyO offset between -73 and -93 MPa. In one case k = 1.64 with

τ!" = 156.1MPa.

Table 1 Observed Relations Between τy and σy.

Cst τ!" Alloy class Tests Reference

1.85 0 Steel, SS, Cu, Al Alloys, Brass 24 [2]

2.6 -‐73 Aluminum – baseline and irradiated

8 [8],[9]

1.7 29 HT9 and SS316 10 [9]

1.76 0 Steel, SS, Cu, Al Alloys, Brass 13 [14]

1.73 0 Steel, SS, Cu, Al Alloys, Brass

14 [14]

1.73 Cu, Brass -‐ [15]

1.64 156.1 Inconel 718 -‐ [16]

2.06 -‐92.7 SS304 L -‐ [16]

1.73 0 Low Carbon Steel,

SS316, Model Alloys, Aluminum

-‐ [24]

6

During the SPT process the engineering plastic strain (esp) is:

𝑒!" =!!!!!

(4)

where d is the displacement, which at yield is d0, and thickness is t [2].

A nominal true plastic strain is defined as:

ε!" = 𝑙𝑛 !!!!!"

(5)

The true shear stress is defined as:

𝜏 = 𝑆!/(1− 𝑒!") (6)

Lucas et al. proposed [2] a power law model to estimate a strain hardening

coefficient, nτ, for a series of SPT on aluminum, brass, copper, steel and stainless as:

𝛆𝒔𝒑𝟎.𝟎𝟎𝟐

𝒏𝝉= 𝝉𝒎

𝝉𝒚 (7)

Here 𝜏! the maximum true shear stress and ε!" is the corresponding true shear strain.

Rearranged to solve for nτ:

𝑛! =!" !! !!"(!!)

!"(!!")!!!(!.!!") (8)

Later work by Hankin et al. found that the engineering uniform elongation strain

in tensile testing, eu, approximately equals the tensile strain hardening exponent nσ for

the materials tested in their study, qualitatively consistent with simple power law

strain hardening in Eq. 7. Further, the SPT strain hardening coefficient nτ (< 0.2) was

found to approximately linearly correlate with nσ [11]. Previous work by Lucas et al.

found ligament reduction at failure to have a 1:1 correlation with tensile reduction in

7

area [2]. Subsequently, Toloczko et al. investigated 316SS, HT9, Cu and Al based

alloys extending the upper range of strain hardening coefficient to ≈ 0.6.

Work by Ramaekers et al. introduced a relationship for maximum punch force for

a given ultimate tensile strength (UTS) and an equivalent tensile strain hardening

coefficient through a series of interrupted SPT and a microhardness based

characterization of nσ [27, 28]. This model estimates Sm from ultimate tensile

strength based on a shear factor (sf) determined by nσ [24]:

𝑆! = UTS ∗ 𝑠𝑓 (9)

𝑠𝑓 = !!∗ !

!

! (10)

Karthic et al. studied the relationship of UTS vs. Sm by using a simple linear fit as

well as the shear factor method. A linear fit of UTS = m * Sm yielded m = 1.29 with a

predicted UTS standard deviation of 45 MPa [24]. Estimation of UTS using shear

factor method based on Equations 9 and 10 resulted in a standard deviation of 14

MPa. This study noted the limitations of using the strain hardening approach because

the constitutive properties predicted by nσ from tensile tests do not involve large

deformations and strains incurred in the SPT.

SPT data are sensitive to fixture alignment and deformation. Previous work at

UCSB found that firmly clamping the shear specimen reduced the bending stresses

helping to ensure yielding is primarily shear stress [1-5,7]. Determination of

deviation from linearity in the LDC also depends both on a flat normal punch surface

and precise concentric alignment of the punch and die to facilitate precise alignment

of fixtures. Thus the previous UCSB studies used shims between the upper and lower

8

fixture to ensure parallelity of the upper and lower fixture face and uniform loading of

the SP specimen [1,2].

The flatness of the specimens obviously has strong affect on the accuracy of SPT.

Kullen et al found that wedged specimens (specimen edge thicknesses varied from

0.16-0.18mm, and from 0.21-0.24 mm over 3mm apart) resulted in 19% error in SPT

yield (τy) of 12Cr-1Mo specimens and 25% in 9Cr-1Mo specimens, since partial

penetration and yielding occurs at the thick side of the disk. The SPT fixture these

tests were performed on was unclamped, and the specimen average thicknesses were

between 0.15mm and 0.35mm. The τy for thinned specimens (t ≈ 0.15mm) deviated

from the others, possibly due to grain size effects, or the relatively large ratio of

punch to die clearance (wg) to thickness, wg/t, that varied by a factor of 2.33. Thus

gaining further insight on specimen thickness effects requires reducing gap in

proportion to thickness.

Load train compliance can affect the SPT results as well. Finite element analysis

(FEA) by Toloczko has shown that the compliance of the cross head has a significant

effect upon the measurement of τy[13]. This motivated efforts to develop a test

fixture capable of a more direct measurement of displacement to remove load train

cross head compliance from SPT load displacement curve data [14]. High

compliance generally requires a larger elastic curve offset to evaluate the τy. Guduru

et al. performed subsequent FEA simulations and proposed a linear offset

corresponding to the development of through thickness plasticity in the disk at d/t of

0.15% in simulations corresponding to d/t at 1% offset in their SPT data [21,23]. The

higher SPT experimental offset required to evaluate yield stress compared to FEA

9

was attributed to the rigid punch and die in the simulation, compared to the actual

compliant load train. The FEA results indicated that punch to die clearances of 5 µm

to 20 µm in 5 µm increments had little effect on τy.

Goyal et al. extended the FEA evaluation of punch-die clearance from 5 µm to 40

µm finding minimal effect on τy, note that wg falls in the lower range of clearances

[25]. The τy was found to be sensitive to the relatively large punch compliance. As a

result the fixture was modified to measure displacement from the lower disk surface,

effectively eliminating the load train compliance. The improved SPT fixture τy

results were found to best correlate to the theoretical Von Mises shear to tensile stress

relation σy = √3 τy, for a 0.15% offset.

The effects of die clearance, wg, have been studied in some depth in industrial

punching and blanking applications. Note in these cases there are other factors such

as impact energy, which do not apply to the SPT. Primary concerns in commercial

punching applications are burr height, the placement of the punched material and tool

life. In most commercial applications the coupon simply sits on top of the die.

Bowing of the punched plug can create a vacuum seal across the top section of the

disk, so some punches use an ejector pin to break this seal to avoid pulling the plug

back with the punch[17]. There are also significant dynamic effects due to the high

velocity punch loading.

10

Vickers Microhardness

Microhardness tests are a non-destructive measure of mechanical properties, in

that the plastically deformed area is small relative to the specimen. Vickers

microhardness test utilizes a diamond shaped indenter loaded to a constant load, 500g

in our measurements, driven into the material for 13 seconds.

Microhardness is calculated with P, the mass load in kilograms, and d the mean

diagonal length of the indentation, mm [26]:

H! = !.!"##∗!

!! ( !"

!!!) (11)

There is a significant body of literature on the relation between Hv and σy with

early work reported by Tabor [33]. The relationship is given by the general form:

σy = CHHv + σyo (12)

Here, the coefficient (CH) and intercept (σyo) are fitted or calculated. The reported

values range from about CH ≈ 2.7 to 3.6 for Hv in units of kg/mm2. Busby et al.

reviewed various experimental studies of both ferritic and martensitic steels. They

found average value CH ≈ 3.0 for unirradiated, irradiated and cold-worked austenitic

stainless steels, with substantial scatter and a large negative σyo averaging about -330.

These workers also reported the relation between ΔHv and Δσy due to irradiation.

They found for small

Δσy ≈ 3.63ΔHv for (ΔHv < 100 kg/mm2)

while

Δσy ≈ 2.13ΔHv+ 155 for (ΔHv > 100 kg/mm2)

11

The corresponding results for one unirradiated and 3 irradiated low alloy ferritic

steels showed scattered around CH ≈ 3 and scattered around and σyo average of ≈ 10

MPa. Note in two other irradiated low alloy steel cases CH was found to be much

lower (< 1). Odette et al. found for irradiation-induced Δσy assuming σyo ≈ 0, initially

CH ≈ 3.6 for a small data set and subsequently 3.3 for a larger data set.

These results are not very consistent and in part reflect the fact that hardness

probes a finite regime of plastic strain beyond yield. For example Tabor suggested

that hardness correlates more directly with flow stress at 8% strain.

Among other workers, Odette and He carried out extensive FEA simulations of

the indentation test using an extremely wide range of constitutive laws. The results

were analyzed to derive the most effective correlation between H (MPa units) and

Δσfl.

They found the best Hv correlation was for the average flow stress from 0% to 10%

plastic strain to Hv.

𝜎!"#$ = 𝜎! + ‹𝜎!!› (13)

where ‹𝜎!!› is the corresponding strain hardening. The FEA results could be fitted by

the expression:

𝐻 = 𝐶! 1+ 𝐶! ∗ 𝜎!"#$ 𝜎!"#$ (14)

Here H is in MPa and C1 = 4.05 and C2 = -34.6/E, where E is the modulus of

elasticity of 200 GPa. This can be inverted to predicted 𝜎!"#! as a function of H. A

fitted model for predicting flow stress given H = Hv * 9.81 m/s2 was proposed:

𝜎!"#$ = 𝐾! ∗ 𝐻! + 𝐾! ∗ 𝐻 (15)

Where K1 is 1.72*10-5 and K2 is 0.272.

12

Chapter 3 Materials

A series of 50 Rolls Royce RPV steels plus 6 heat treatment variations on a subset

of these alloys was provided in nominally 0.5mm sheet form to UCSB. Shear punch

tests, Vickers microhardness tests and tensile tests were performed on these alloys.

The alloy matrix covered a range of compositions including Ni (0-3.5%) and Mn (0-

2%). Six alloys with compositions close to SA 508 Class 3 and SA 508-4N were

selected for heat treatments. Material compositions are listed in the Appendix A.

Six heat treatments were performed at UCSB in a He environment:

• Alloy 22, (L2413) to be re-heat treated for 48 hours at 600°C.



• Alloy 27, (L2423 )to be re-heat treated for 48 hours at 600°C.

• Alloy 40 (L2428) to be re-heat treated for 5 hours at 625°C.

• Alloy 40 to be re-heat treated for 5 hours at 650°C.

Tensile test yield ordered from low to high is shown in Figure 3.

13

Figure 3 Tensile yield strength (σy) by material.

14

Shear Punch Testing

A shear punch test fixture was designed using commercially available punch,

dies, and bushings [17]. A section view of the SPT fixture is shown in Figure 4. The

upper and lower halves of the fixture are bolted together. The punch diameter is 2.95

mm, and die is 3.05 mm for a nominal 3mm punch. The load frame used in these

SPT is an MTS model 810 load frame with 2000 lb load cell. Displacements are

measured by a lever arm extensometer mounted on the fixture base assembly in

contact with the lower disk surface connected by a displacement pin.

Figure 4 Shear punch test fixture diagram

15

The sample thickness is measured 3 times around the disk surface with a ball

micrometer. Next the test material is centered over the die in the fixture. Typical

samples are either 8 mm disks or square coupons sheared from sheet, nominally

0.5mm thick. Three ¼-28 UNF bolts are torqued to 75 in-lbs around the perimeter of

the fixture. Alignment shims are placed between the upper and lower fixture that are

approximately 0.03mm thinner than the specimen to ensure flatness and uniform

loading. The SPT fixture is placed in the load frame and pre-loaded to 150-175N to

reduce set-in during the beginning of the load displacement curve. The punch is then

driven by the load frame at a rate of 0.25mm/minute. Force and displacement data

are sampled at ten times per second and recorded in computer data files. Force output

is monitored until loads have dropped significantly, indicating sample failure. Tests

were repeated at least three times for each material.

Microhardness Testing

Microhardness measurements were performed on an automated LECO 400 series

tester with digitized image analysis. Specimens were prepared by sanding and

polishing to create a flat surface for indentation. Five indents were taken per alloy at

a 500g load. If an indent occurred at a scratch or surface imperfection the

measurement was repeated.

16

Tensile Testing

Tensile tests were performed on the matrix of Rolls Royce alloys at room

temperature, with a minimum of three tests per alloy. Specimens were taken from the

nominally 0.5mm wafer, cut transverse to rolling direction in the normal plane, as

shown in Figure 5. They were displaced at 0.1mm/minute in a MTS model 810 load-

frame equipped with a 1000lb load cell. Displacement was recorded by internal

LVDT. A 0.2% offset was used to calculate yield stress. Tensile and SPT test

records are attached in Appendix B.

Figure 5 SS-J2 tensile specimen drawing.

17

Chapter 4 Data Analysis

Shear Punch Testing

Figure 6 shows a typical P-d curve, in this case for the RR7 alloy. The overall

sigmoidal shape of the curve is composed of a convex region upon initial loading, an

approximately linear (elastic) region, followed by a concave region signaling the

onset of plastic yielding. The detailed nature and extent of these regions vary from

material to material and from test to test. The linear region is assumed to represent a

true elastic response that can be fit to estimate the point of SP yielding. However,

SPT P-d curves manifest a much more gradual transition from fully elastic to fully

plastic deformation compared to tensile tests. Thus it is critical to use an accurate and

robust method to fit the linear P-d region and to establish an off-set to define a shear

yield stress that can account for the test data variations noted above. The fitting was

accomplished as follows. First, the P-d curves were smoothed using a five point

moving average. Next, an enlarged section of the linear elastic region of the P-d curve

was examined to establish upper and lower linear P (or stress) and normalized

displacement (d/t) to be linear least squares fit. The linear region typically fell

between 0.3 to .5 of the maximum load and d/t from 0.02 to 0.04, but this was fine-

tuned for each individual curve. An example of the fitting is shown in Figure 6. The

fit line was visually inspected for its fidelity to the linear region of the P-d curve.

The elastic fit line was then off-set by various prescribed d/t and the

corresponding intersection with the P-d curve was used to define the shear yield (τy)

and flow stress values (also illustrated this in the P-d curve). This is akin to the

standard process of defining the 0.2% off-set tensile yield stress, σy. However given

18

the gradual nature of the development of plasticity (hence, the corresponding more

gradual non-linear deviation of the plastic P-d curve), this procedure is more difficult

in the case of the SPT. In general larger off-sets have less scatter in the plastic flow

shear stresses, but do not define yielding as well, since the loads include a degree of

strain hardening that increases with the d/t off-set. The effect of strain hardening is

reflected in a lower value of the coefficient (Cst) relating the SP to tensile yield stress

as

𝜎! = 𝐶!"𝜏! (16)

Analysis of many P-d curves suggests that d/t offsets between 0.15 and 0.2%

represent the best compromise and, as shown below, yield a Cst close to the

theoretical value of √3. While a bit arbitrary, an offset of 0.2% was used in this work.

In cases when the σy/τy varied significantly from the best-fit value (again ≈ √3), the P-

d curve was re-examined to in order to assure that the fitting procedure was done

properly. If not, the P-d data were reanalyzed. In some cases the P-d curves are

simply anomalous and, for example, may not have an extended linear region. In this

case the test was typically repeated. The average SD of τy (0.2% off-set) for at least 3

valid SP tests per specimen is 12.8 MPa.

19

Figure 6 Typical SPT τ−d/t (or P-d) curve

20

Figure 7 Enlarged SPT P-d curve

21

The post yield SPT P-d curve shows a region of strain hardening up to a

maximum load that is qualitatively analogous to the P-d curve in a tensile test. In both

cases the maximum load, Pm at dm, is defined by a plastic instability, which may or

may not be accompanied by internal damage. SPT engineering flow stress, Se, and

nominal plastic strain, esp, are simply defined as:

S! = !

!∗!∗! (17)

𝑒!" =!!!!!

(18)

Here do is the displacement at the P-d curve at the 0.2% offset. The maximum

engineering shear stress, Sm that is analogous to the tensile UTS, is:

S! = !!!∗!∗!

(19)

The corresponding SPT engineering strain analogous to the tensile uniform

elongation, εtu is:

𝑒!" =!!!!!

! (20)

Corresponding SPT true shear flow stress, τf, and plastic strain εs geometrically

analogous to those found in a tensile test are defined as

𝜏!(ε!") = 𝑆!/(1 − 𝑒!") (21)

22

ε!" = 𝑙𝑛 !!!!!"

(22)

A typical SPT τsp(εsp) curve up to peak load is shown in Figure 8 along with a

corresponding tensile σf(εt) curve. Note that SPT τsp(εsp) is a plot of stress versus a

geometric parameter, and not a true strain. True-stress strain relations for SPT are

shown in Figure 33 and Figure 34 below.

Figure 8 τsp(εsp) and σf(εt) true-stress strain for RR1 alloy.

The reason that the apparent SPT strain hardening rate is much larger than in a

tensile test is that these εsp cited above are nominal plastic strains accounting only for

the increasing reduction in the intact ligament with increasing deformation, d. While a

qualitative measure of degree of deformation, the εsp is not equivalent to the actual

23

plastic shear strains in the ligament itself, εp, which depend on the punch-die gap

dimension, wg = Dd - Dp. Assuming pure uniform shear, as illustrated in Figure 10,

γl is

γl ≈ d/wg (23)

For polycrystals ε ≈ 3γ thus the equivalent esp

εl ≈ d/3wg (24)

In this case, the nominal wg ≈ 0.1 mm and t = 0.5 mm. Thus for d/t = 0.25, εl ≈ 0.77,

which is much larger than the nominal εsp = 0.29.

Figure 9 Flow geometry during punching.

Figure 10 Deformation during uniform shear.

More generally, the use of εsp based on d/t is not a good representation of the

physical shear strain. More rigorous treatments require FEA simulations. Thus any

procedures that treat strain hardening in terms of the SPT and tensile P-d curves, such

as in Equation 7, are not strictly physically valid. However, SPT versus tensile stress

and strain measures, and especially ratios of these measures, may empirically and

24

simply correlate with one another, while reflecting a more complex underlying

physical relation.

Ramaekers developed a simple plastic instability model of a ligament in pure

shear [29]. For simple power law hardening:

σ!" = σ!(ε/ε! + 1)! (25)

this work gives the effective strain in the shear zone:

ε! = !! ln !

!!! (26)

The strain hardening exponent, n, is estimated from hardness measurements

converted to σfl in the highly strained shear zone. The relation between the

engineering shear stress Se and n is:

S! =!!!

!! !"(

!!!!!"

)!!!

!!

!

(27)

The maximum engineering shear stress, Sm, for small ε0 is given by:

S! ≈ !!!

!.!"!!!

!!

!

(28)

Assuming n is equal to the uniform strain εu in a tensile test Sm can be related to

the UTS. The relation can be expressed in terms of a so-called shear factor (sf) as

𝑆! = UTS ∗ 𝑠𝑓, where sf is defined as:

𝑠𝑓 = !!∗ !

!

! (29)

UTS are estimated based on the SPT nominal strain hardening coefficient, nτ. Here nτ

is calculated from stress-strain ratios at SPT yield stress τy and maximum stress τm,

and the corresponding nominal representation of strain, ε = .002 and εsp :

𝑛! =!" !! !!"(!!)

!"(!!")!!"(!.!!") (30)

25

For the purpose of calculating the shear factor, nτ is considered analogous to the strain

hardening coefficient, although failure in SPT is not by necking as in a tensile test,

and εsp is a geometric parameter and not a true strain.

SPT τy and tensile σy are least squares fit in the form of σy = Cyτy for SPT

stresses at d/t linear offsets of 0.1%, 0.15%, 0.2%, 0.25%, 0.5% and 1%. Figure 11

shows that Cy decreases with increasing offset between 0.1 and 1%. This trend is due

to the fact that an increased offset measures an increasing flow stress at higher plastic

strains and magnitudes of strain hardening. At 0.2% offset The Cy = 1.77 coefficient

is close to the Von Mises uniaxial to shear (τy) yield stress relationship, σy = √3τy.

Figure 11 The Cy = σy/τy ratios versus the SPT offset (%).

26

Figure 12 and Figure 13 show the effect of the punch-die gap (wg) on the SPT

τy and maximum engineering shear stress, Sm, respectively, for four alloys

representing a range of low to high strength. The lines are least square fit polynomials

meant to highlight the trends. The τy decreases significantly between the smallest and

larger gaps in the two lower strength alloys while τy increases with the gap dimension

in the highest strength steel. The effect of the gap size is minimal for the steel with τy

≈ 280 MPa. Overall the nominal (0.1 mm) and larger (0.15 mm) gaps produce the

most consistent results. The smallest gap size may increase friction effects, especially

in the softer alloys, while bending versus shear is favored by larger gaps. The Sm

generally decreases with increasing gap dimension and is most consistent between the

smallest (0.05 mm) and nominal (0.1 mm) gap. Overall these results support the

nominal 0.1mm gap used in this work.

27

Figure 12 τy vs. punch-die clearance, wg, for selected alloys.

100

150

200

250

300

350

400

450

500

0.04 0.06 0.08 0.1 0.12 0.14 0.16

τy vs clearance, 0.5mm nominal thickness tests

RR1 0.2% SPTyRR3 .2% SPTyRR18 .2% SPTyRR19 .2% SPTy

τ y (0.1

5% o

ffset

) (M

Pa)

Punch-die clearance, wg (diametric, mm)

28

Figure 13 SPT Sm vs. punch-die clearance, wg, for selected alloys.

250

300

350

400

450

500

550

600

650

0.04 0.06 0.08 0.1 0.12 0.14 0.16

Sm vs clearance, 0.5mm nominal thickness tests

RR1 SmaxRR3 SmaxRR18 SmaxRR19 Smax

Sm (M

Pa)

Punch-die clearance, wg (diametric, mm)

29

Tensile Testing

Figure 14 shows a typical engineering s-e tensile curve, in this case for the RR7

alloy. The linear fit region typically falls between 0.25 to .6 of the maximum load but

is adjusted as necessary. The elastic fit line is offset by 0.2% to find the tensile yield

stress, σy. Note engineering and trues stress and strain are effectively equal at yield.

The UTS is taken as the maximum stress from the stress-strain curve.

Figure 14 Tensile engineering stress-strain curve for RR7 alloy.

30

Engineering stress defined in the standard way is converted to true stress as:

𝜎 = 𝑆 ∗ (1+ 𝑒) (31)

and standard engineering strain is converted to true strain as:

𝜖 = ln(1+ 𝑒) (32)

A model for estimation of hardness given average flow stress to 10% true plastic

strain was introduced in Equation (14). True stress is averaged from 0 to 10% true

plastic strain for each material in the alloy test matrix and tabulated in Table 8.

Figure 15 shows true plastic stress and the average flow stress from to 10% true

plastic strain for the RR7 alloy.

Figure 15 Tensile Plastic flow stress vs. true plastic strain for RR7 alloy.

31

The strain hardening coefficient was calculated by power fit of the true plastic

stress-strain curve. The strain hardening coefficient, n, is used in the shear factor

calculation correlating UTS and Sm. The uniform elongation, εu, is taken as the true

strain at UTS.

32

Chapter 5 Results

Table 2 summarizes the average, standard deviation and percent of the deviation

of the SPT, tensile, and microhardness data. The results are excellent, for example,

with SD of < 10 MPa for the SPT and tensile results. The SD in the microhardness is

relatively larger, but not atypical of the lower load (500g) range of such tests. As

noted previously the SPT σy SD decreases with increasing offset, but the scatter at

0.15 and 0.2% is low and very acceptable.

Table 2 Summary of the Test Data Statistics (MPa).

33

Table 3 and Table 4 summarize tensile and SPT data, respectively. The

hardness data are summarized in Table 5. The test records for the SPT and tensile

tests are included in Appendix B.

Table 3 Summary of the Tensile Data.*

*Stress units are in MPa.

34

Table 3 Summary of the Tensile Data. (continued)


35

Table 4 Summary of the SPT Data.*


36

Table 4 Summary of the SPT Data. (continued)


37

Table 5 Summary of the Microhardness Data.*

*Hardness units in kg/mm2.

38

Chapter 6 Establishing Predictive Relationships Between SPT, Tensile Test and Microhardness Properties

The basic objective of this work is to use SPT and microhardness data to estimate

the properties typically measured in a tensile test. Developing predictive expressions

for the tensile properties is based either directly on least square fits of the primary

data or applications of model based relationships.

Figure 16 plots the tensile yield stress (σy) versus SPT shear yield stress (τy), both

as defined by 0.2% off-set lines. A least square fit gives σy = Cstτy. The Cst = 1.77

coefficient is close to the Von Mises uniaxial to shear yield (τy) stress relationship, σy

= √3τy. The reason that Cst is slightly higher than √3 is not known, but this seems to

be an acceptably small difference. The SD between σy estimated from τy and the

measured value is 16.9 MPa. Average predicted minus measured deviation of 0.2

MPa. These results are considered to be excellent and show the potential for

estimating σy using SPT

39

Figure 16 Tensile σy versus shear SPT shear yield stress τy measurements and the

corresponding LSF line through the 0,0 origin. One SD error bars are shown for the

individual data points.

Figure 17 plots the microhardness, Hv (kg/mm2) versus the tensile yield stress,

σy. In this case the LSF line is expected to have a negative intercept since the Hv

contains a contribution from strain hardening, σy = CHyHv + CHyo. The LSF yields

CHy = 2.82 and CHyo = -114 MPa. The predicted σy based on Hv versus the measured

value has a standard deviation of 22.8 MPa and the average predicted minus

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500

σy =1.77τ

y

σy

(MP

a)

τy (MPa) (0.2% offset)

40

measured σy is -1.6 MPa. The SD is similar to that for the Hv measurements

themselves. The offset can be compared to the average strain hardening between 0

and 10% plastic strain, which is 136 MPa. The dashed line compares an earlier

correlation for other UCSB and RR steels to the current results, where it was

previously found that:

𝜎! = 9.56x10!!H!! + 2.85H! − 120. (33)

This correlation over-predicts the new data by ≈ 5-10%, but the agreement is not

unreasonable. Note the coefficients are influenced by the strain hardening variation

between different alloys, including irradiated conditions in the earlier data set. Note

there may also be small biases between the hardness data measured by different

people.

41

Figure 17 σy vs. Vickers microhardness.

Figure 18 plots the microhardness, Hv (kg/mm2) versus the ultimate tensile

strength, UTS. The LSF equation has the same form as for σy, as UTS = CHuHv +

CHuo. The LSF yields CHu = 2.95 and CHuo = 0.8 MPa. The predicted UTS based on

Hv versus the measured value has a standard deviation of 25.8 MPa and the average

predicted minus measured UTS is 3.7 MPa. Again, the UTS SD is similar to that for

0

200

400

600

800

1000

0 50 100 150 200 250 300 350

σy = 2.82*H

v - 114

σy (M

Pa)

Hv (kg/mm^2)

42

the Hv measurements. The dashed line shows the earlier UTS correlation for other

UCSB and RR steels, where it was previously found that:

𝑈𝑇𝑆 = 1.27x10!!H!! + 2.15H! + 86.1. The previous correlation under predicts

the tensile UTS for the higher strength steels. Coefficients in this case again do not

have a good physical basis and are also fit to steels in the irradiated condition.

Figure 18 Tensile UTS vs. Vickers microhardness.

Figure 19 plots the tensile UTS versus SPT Sm. The linear LSF line had a

slope of 1.75, intercept of -174 MPa. The predicted versus measured SD = 25.8 MPa

with an average deviation of -2.2 MPa. The slope is again close to √3, as expected

0

200

400

600

800

1000

0 50 100 150 200 250 300 350

UTS = 2.95*Hv +0.8

UTS

(MP

a)

Hv (kg/mm^2)

43

based on the uniaxial to shear yield stress relation. The large negative offset is due to

the higher strains and strain hardening flow stress level in the SPT compared to in a

tensile test.

Figure 19 The tensile UTS versus SPT Sm and corresponding LSF line.

Odette and He developed a model based on extensive FEM simulations to

relate microhardness to the tensile flow stress (σfl) for a very wide range of

constitutive laws with an expression with the form [20]:

0

200

400

600

800

1000

0 100 200 300 400 500 600 700

UTS = 1.85 Sm -174

UTS

(MP

a)

Sm (MPa)

44

σfl = K1H2 + K2H (34)

Here H is in units of MPa. These researchers also developed an extensive σfl - H

database to fine-tune the model. The FEM showed that the best universal fit was for

the average sfl between 0 and 10% plastic strain. Figure 20 plots the σfl versus H data

from the current study. The LSF to the data yielded K1 = 1.72x10-5 and K2 = 0.272.

Fits to the new data set yield 1.61x10-5 and K2 = 0.266, Thus the previous correlation

slightly over predicts σfl. The SD of σfl for the new of is 25 MPa with an average

deviation of -0.1 MPa.

45

Figure 20 Flow stress vs. H.

Table 6 summarizes UTS estimation based on SPT. Figure 21 shows UTS versus

UTS(Sm). The standard deviation for UTS from predicted was 22.8 MPa and the

average deviation of the estimation was -7.7 MPa. However, there is a systematic

bias with the UTS under predicted at lower stresses and over predicted at higher

stresses.

Table 6 UTS estimation based on nτ and Sm, as UTS = Sm/sf.

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000 3500

σ fl = 1.61*10 5 H 2 + 0.266 * H

Flow

Stre

ss (M

Pa)

H (MPa)

Published Correlation

47

Figure 21 UTS predicted using sf and UTS vs. UTS.

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

UTS = 1.09 * UTSPred -42.6U

TS (M

Pa)

UTS Predicted (MPa)

48

Chapter 7 Finite Element Analysis (FEA) of the SPT

Finite element analysis (FEA) simulations of shear punch testing (SPT) have been

carried out. Initial analysis used rigid body representations of the punch, die and

upper and lower fixtures. These exhibit a load displacement P-d curve with higher

slope than found in SPT data, in part due to the absence of load train compliance. In

the subsequent analysis the punch and die was modeled as elastic solids of tool steel

(E=205 GPa) and a clamping preload force was applied to the rigid upper fixture.

The compliance of the lower fixture and die was incorporated into the model by the

use of spring elements. The spring stiffness was based on a measured load-

displacement curve of the die and lower fixture up to near the peak load of a typical

SPT. The FEA model is shown in Figure 22.

Figure 22 The finite element model of the SPT and mesh.

49

The constitutive properties were derived from the tensile tests. The absolute units

are length in mm, force in N, and stress in MPa. An elastic modulus of 205 GPa is

used. The true-stress strain constitutive law was obtained fitting the flow stress (σfl)

up to the uniform elongation (typically εu ≈ 0.1) with the form:

𝜎!" = 𝜎!!!!! + 1

! (35)

Here, eo is the yield strain (0.002) and the n was found by linear fits to the

ln(σfl) vs. ln(ε) data. As shown in Figure 23, the fitted curve was extrapolated

assuming continuation of power law hardening up to a maximum saturation flow

stress at εp = 0.5. The subsequent flow stress is constant up to an assigned strain at

element failure (εf), nominally due to damage accumulation. Note the saturation σfl

and ductile damage parameter are relatively arbitrary and will be improved in the

future based on extended true stress strain curves derived from the tensile data

beyond necking using iterative FEA methods [30].

50

Figure 23 True stress-strain σfl(εp) curves used in the FEA simulation of the SPT

P-d curves: RR1 εf = 0.625, RR19 εf = 1, RR27 εf = 0.75.

Finite Element Model and Boundary Conditions

A 2D axisymmetric model of the shear punch tip, disk, die and upper clamping

assembly was created in Abaqus. The punch diameter is 2.95 mm, and die is 3.05

mm for a nominal 3mm punch. The punch and die are modeled as 0.5mm high linear

elastic elements. The upper surface of the punch is constrained to a single control

node, as is the lower surface of the die. The disk is 0.5mm thick disk and 8mm in

diameter.

51

The guide, punch and die were constrained both radially and against rotation. The

guide was connected to the lower fixture assembly by a spring element with the

compliance of three bolts. The lower fixture was connected to a fully constrained

node by a spring element with a compliance taken from measurement of the lower

fixture under load, as shown in Figure 24.

Figure 24 Linear fit to the lower fixture compliance. Typical SPT Py ≈ 1.5-2KN.

Contact elements were located between the punch and disk, guide and disk, and

die and disk. The elastic punch and die were modeled with relatively coarse elements

52

of 0.13mm length, since it was only necessary to incorporate their global stiffness.

The annular region in the disk between the punch and die, which is of prime interest,

was modeled with 12.5µm elements. The disk mesh coarsens away from this zone.

The FEA mesh is shown above in Figure 22.

SPT P-d Fits

The FEA SPT simulation was compared to the measured P-d or engineering stress

strain measurements. The only adjustable parameter in the simulation was the fracture

strain εf, found by iteration. The influence of εf occurs at a plastic equivalent strain εpe

near Sm and results in a peak load followed by a gradual decrease as observed in the

SPT. If the εf is not imposed the load continues to increase beyond Sm, up to a plastic

instability at a higher d/t. The stiffness of a material element increases to the

undamaged value over a small increment of elastic strain that it is very small

compared to the corresponding plastic strain, εpe. Note the elements do not reach a

highly distorted shape before their stiffness is significantly degraded. A color-coded

map of the plastic equivalent strain (εpe) is shown in Figure 25. Even at a small d the

shear zone is dominated by εpe > 0.2.

The FEA simulations were performed using Abaqus Explicit. A quasi-static

approach was used to minimize dynamic effects (inertia, vibrations) that are not

central to the study of the SPT simulation, and to enhance computational efficiency

[27]. This involved imposing the mass in the relatively fine disk elements to increase

the minimum time step required in the solution.

53

Figure 25 Map of the εpe at small d.

Results

Figure 26 through Figure 28 compare the FEA simulations with the experimental

results. Engineering shear stress, Se, was calculated from the simulation of the SPT

by tabulation of the reaction force at the master node of the elastic punch (P), and

calculated as:

S! = !

!∗!∗! (36)

The agreement up to Sm is excellent, although it is emphasized that the input σfl(εpe)

and εf data are not unique and will require further refinement and verification.

Figure 29 shows the elements selected in the annular area of plastic

deformation, which are used to correlate d/t with average equivalent strain. This

allows a true stress strain curve, τ vs. ε to be developed using SPT test data and the

ε to d/t relation from FEA. The LSF fit of FEA average PEEQ, 〈εpe〉, to d/t was found

as follows:

54

‹𝜀!"› = −3.4832 !!

!+ 4.0754 !

!

! + 1.7404 !

!− 0.0043 (37)

Figure 30 plots Se and 〈εpe〉 versus d/t for RR1 alloy.

Figure 26 FEA and experimental Se (MPa) versus d/t curves for RR1.

0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6

RR1 SPT Test DataRR1 SPT FEA

Se (M

Pa)

Normalized Displacement (d/t)

55


0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6


Se (M

Pa)


56


0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6


Se (M

Pa)


57

Figure 29 FEA elements used for averaging εpe evaluated as a function of d/t.

Figure 30 The engineering Se and average 〈εpe〉 vs. d/t for RR1.

58

Plastic equivalent strain maps for d shortly after initial failure of the top elements

and near Sm are shown in Figure 31, a) and b) respectively.

Figure 31 Maps of 〈εpe〉 for two d/t: a) soon after the initial element failure; and,

b) near Sm.

59

As described previously, Ramaekars et al. proposed a method to estimate a high

strain constitutive law based on hardness tests in the highly deformed shear zone in

interrupted tests with the equation below. The hardness was first converted to σfl as a

function of ln [d/(t-d)] and that was then fit to derive σy(εo) and n. The constitutive

law was then inverted to derive what was termed an effective maximum plastic

equivalent strain, εe, in the highly sheared ligament as:

ε! = !! ln !

!!! (38)

As shown in Figure 32 for RR1 εe(Ramaekars) as a function of d/t is about two

times the 〈εpe〉 (FEA).

Figure 32 The εe(Ramaekars) and 〈εpe〉 (FEA) as a function of d/t. εe is about two

times the 〈εpe〉 for RR1.

60

The Se(d/t) curve for Ramaekars is given by:

𝑆! =!!!

!! !"(

!!!!!"

)!!!

!!

!

(39)

The maximum shear stress, Sm, at a plastic instability was defined in an analogous

way to a tensile test: when the rate of decrease force with a decreasing ligament

exceeds the rate of increase in the force due to strain hardening. The relation for

maximum effective shear in the remaining ligament is:

S! ≈ !!!

!.!"!!!

!!

!

(40)

Figure 33 shows Se(d/t) for the Ramaekars model and both the experimental

curve and the FEA simulation. Note that instability occurs at lower d/t for Ramaekars

model than experimental and simulated SPT curves; this is likely due to an

overestimation of the strain in the ligament shifting the plastic instability point to

lower d/t. However, the Sm are similar for all 3 cases.

61

Figure 33 Comparison of the Ramaekars Se(t/d) model with the experimental and

FEA simulation results.

Figure 13a compares the σfl(εp) derived from the tensile test of RR1 to that from

the SPT using the εpe (d/t) derived in the FEA and the experimental τ Eq. (37)

converted to the equivalent σ using the empirical factor of 1.77. Figure 13b shows

the same plots on a ln-ln scale. While there are small differences in the magnitude of

the σfl, both curves can be fit with a power law model in the form of:

𝜎!" = 𝜎!!!!! + 1

! (41)

with similar nτ = 0.17 (SPT) and nσ = 0.18 (tensile test). While the values are not

expected to be identical, these results suggest a remarkable self-consistency between

62

the experiment and FEA simulations of at the high plastic strains in the

severelydeformed ligament.

Figure 34 The tensile σfl(εp) and 1.77*τ(εp) vs. εp for RR1.

63

Note there have been a number of in-depth modeling studies relating constitutive

and damage models in commercial blanking operations, based on various analytic

methods and FEA approaches [27,30,31] and further examination of the pure shear

constitutive models from Ramaeker et al. [32]. But detailed discussion of this

literature is beyond the scope of this work.

Since the objective of this work is to determine tensile properties from SPT data,

the n in the previous expressions must be estimated from the latter. This was done by

mapping the equivalent stress, in the form of σ = τ∗1.77, to the average equivalent

strain, 〈εpe〉, to d/t by the using relation found in FEA of the SPT. A LSF of the ln-ln

relation of true-stress to average effective strain plotted in Figure 34 b was performed

for the tensile and SPT test curve. It is noted that for the purpose of calculating the

shear factor that nτ is considered analogous to the strain hardening coefficient,

although failure in SPT is not by necking as in a tensile test.

64

Chapter 8 Discussion and Conclusions

The objective of this work is to use shear punch and microhardness tests to

estimate the constitutive properties typically measured in tensile tests: yield stress,

ultimate stress (or strength), post yield flow stress and strain hardening rate. Table 7

summarizes the results for the strength properties, demonstrating that the SPT and

microhardness provide excellent small specimen test methods for this purpose. While

correlations derived in this work are empirical, the basic form of the equations and

fitted parameters are generally well understood. For example the fitted σy/τy was

1.77, versus a theoretical Von Mises value of √3 ≈ 1.73. Further, it has been shown

that the relations can be further refined using FEA simulations of the SPT (and, as

previously shown, tensile and hardness tests). The SPT is particularly valuable for

estimating the tensile yield, σy. Indeed, the predicted σy derived from SPT data had a

standard deviation that was only 3.2% of the mean. The corresponding value was

3.9% for the UTS. While these uncertainties are larger than the direct tensile

measurements in this study, they are similar to those expected for tensile data for a

large number of materials with a wide range of properties. And the uncertainties are

certainly consistent with the requirements for robust post irradiation examinations

(PIE) and the development of high quality irradiation effects databases. Finally, it

should be noted that both microhardness and SPT methods can be semi-automated,

permitting very high throughput PIE.

Another property typically extracted from tensile tests is the uniform

elongation, εu at the UTS. By the establishing the true stress strain constitutive law

65

over a moderate range of strain with SPD by FEA simulations or correlations (like d/t

with εpe) and microhardness tests, physically based estimates of εu can be obtained.

The values of εu decrease to very low values in highly irradiated alloys due to plastic

instabilities, often accompanied by flow localization. Thus it will be interesting to see

how this behavior maps onto SPT P-d curves. However, differences in the stress-

strain states and deformation patterns in tensile versus SPT and microhardness tests

preclude using these tests to estimate tensile failure ductility parameters like

reduction in area.

Table 7 Correlation averages, standard deviations and average deviations.

Correlation Std.

Deviation

Avg.

Deviation

Std.

Deviation (%)

σy(τy) 15.9 0.2 3.2%

σy(Hv) 22.8 -1.6 4.3%

UTS(Sm ) 25.8 -2.2 3.9%

UTS(Hv ) 25.82 3.7 3.9%

UTS(Sm , sf) 22.83 -7.7 3.9%

Chapter 9 Future Work

The results of this study are very encouraging. However, there is a long list of

needs and opportunities that remain. The following is a partial list that derives from

the experience of the research reported here:

66

1. More work should be done on the semi-empirical SPT-microhardness versus

tensile correlations. For example, combinations of both SPT and microhardness data

in fitting models guided by physical insight might provide better predictions of the

tensile properties that the correlations reported here.

2. Perform extensive FEA, especially for the SPT and to extend tensile test results to

higher post necking strains [34]. The FEA can be used to simulate the tests

themselves as well as to derive physical correlations between true stresses and strains

and test observables, again like that between d/t and εpe (and other measures of plastic

strain, like shear and principal strains). FEA should also be used to simulate the

effects of numerous test variables, such as the punch die gap, the flatness of the

coupon, clamping stresses, concentricity and so on. Finally, the role of damage

controlled failure parameters needs to be systematically evaluated.

3. Perform complementary experiments based on interrupted tests to experimentally

characterize and clarify details of the SPT, such as deformation patterns and strain

distributions in the shear zone and corresponding true flow stress values at high

strains based on hardness tests. These experiments should also characterize damage

development and failure mechanisms in SPT. Finally, experiments should

complement modeling of the test variables cited in item 1 above.

4. Apply and extend the combined testing to many more metals and alloys with a

wide range of σy and strain hardening behavior. This will include highly irradiated

materials consisting of various model alloys, RPV steels, tempered martensitic (8-

12Cr) steels, ODS steels and austenitic stainless steels.

67

5. Further develop a test protocols for SPT, including use of a set reference-

calibration alloys with uniform properties that are measured at the beginning and end

of a set of actual measurements on materials of interest. This is analogous to using

reference alloys for tensile tests [34] and calibrated test blocks for hardness testing.

Develop metrics for clamping-shimming, including the effects of alloy strength, as

well as coupon flatness. Further, it will be important to carefully assess individual

operator bias in hardness tests based on calibration materials. Finally, develop

procedures to measure and inspect punch die wear and its effect on SPT results, and

methods to qualify and calibrate replacement punch-die sets.

6. Extend the SPT method to smaller punch sizes of order 1 mm that can be used on

specimens such as 3 mm TEM discs.

7. Further optimize the SPT method, including:

a. Eliminate die set in loading displacements that result in an initial non-linear portion

of the P-d curves

b. Evaluate the effect of using a loaded follower pin below the punched disc to further

minimize bending and to enhance the flatness and overall shape of the punched disc.

c. Further examine the effects of the gap size and gap to coupon thickness ratio.

d. Develop and implement methods to minimize contamination and facilitate

decontamination in testing irradiated alloys.

8. Design, construct and qualify a stand-alone table-top automated SPT instrument for

high throughput PIE (underway).

9. Create a consensus ASTM standard for the SPT.

68

References

[1] LUCAS G.E. 1983. The development of Small specimen mechanical test techniques. Journal of Nuclear Materials 117: 323-332.

[2] G. E. Lucas, J. W. Sheckherd, G. R. Odette. Shear Punch and Microhardness Tests for Strength and Ductility Measurements. ASTM STP 888, American Society for Testing and Materials (1986) pp. 112-140.

[3] LUCAS G.E., SHECKHERD J.W., ODETTE G.R. & PANCHANADEESWARAN S. 1984. Shear punch tests for mechanical property measurements in TEM disc-sized specimens. Journal of Nuclear Materials 122: 429-434.

[4] LUCAS G.E. & ODETTE G.R. 1985. Methods for forecasting performance limits of fusion reactor structural materials. Nuclear Engineering and Design. Fusion 2: 145-173.

[5] W.R. Corwin and G.E. Lucas, ed., The Use of Small-Scale

Specimens for Testing Irradiated Material, ASTM-STP 888 (1986).

[6] P.S. Kullen, H.H. Smith, D.J. Michel, J. Nucl. Mater. 158 (1988) 57.

[7] LUCAS G. 1990. Review of Small specimen test techniques for irradiation testing. Metallurgical and Materials Transactions A 21: 1105-1119.

[8] HAMILTON M.L., TOLOCZKO M.B. & LUCAS G.E. 1994. Recent progress in shear punch testing. osti.gov

[9] HAMILTON M.L. & TOLOCZKO M.B. 1996. Correlation between shear punch and tensile data for neutron-irradiated aluminum alloys. ASTM special technical publication 11.

[10] P. J.A., A. HISHINUMA B, G.E. LUCAS C H. ULLMAIER 1996. Recommendation of miniaturized techniques for mechanical testing of fusion materials in an intense neutron source. Journal of Nuclear Materials 232: 196-205.

[11] HANKIN G.L., TOLOCZKO M.B., HAMILTON M.L. & FAULKNER R.G. 1998. Validation of the shear punch‚ correlation technique using irradiated materials. Journal of Nuclear Materials 258‚-263, Part 2: 1651-1656.

[12] TOLOCZKO M.B., HAMILTON M.L. & LUCAS G.E. 2000. Ductility correlations between shear punch and uniaxial tensile test data. Journal of Nuclear Materials 283-287, Part 2: 987-991.

69

[13] TOLOCZKO M.B., ABE K., HAMILTON M.L. & GARNER… F.A. 2000. The effect of test machine compliance on the measured shear punch yield stress as predicted using finite element analysis. Materials Transactions, JIM Vol. 41, No. 10. pp 1356-1359.

[14] TOLOCZKO M.B., KURTZ R.J., HASEGAWA A. & ABE K. 2002. Shear punch tests performed using a new low compliance test fixture. Journal of Nuclear Materials 307-311, Part 2: 1619-1623.

[15] DREW R.A.L. 2002. Small punch testing for assessing the tensile strength of gradient Al/NiSiC composites. Materials Letters 56: 812-816.

[16] HAMILTON M.L., GARNER F.A., TOLOCZKO M.B., MALOY S.A., SOMMER W.F., JAMES M.R., FERGUSON P.D. & LOUTHAN J., M.R 2000. Shear punch and tensile measurements of mechanical property changes induced in various austenitic alloys by high-energy mixed proton and neutron irradiation at low temperatures. Journal of Nuclear Materials 283‚-287, Part 1: 418-422.

[17] Dayton Progress Corporation, 500 Progress Rd. P.O. Box 39, Dayton, OH., 45449.

[18] G. R. ODETTE T.M.K.F., D. KLINGENSMITH 2012. Characterization of Rolls Royce Alloys in the UCSB National Scientific University Facility ATR-II Program: A High Fluence Embrittlement Database and ATR Irradiation Facility for Light Water Reactor Vessel-Life Extension. University of California, Santa Barbara

[19] JOHNSON K.L. 1970. The correlation of indentation experiments. Journal of the Mechanics and Physics of Solids 18: 115-126.

[20] HE M.Y., ODETTE G.R., YAMAMOTO T. & KLINGENSMITH D. 2007. A universal relationship between indentation hardness and flow stress. Journal of Nuclear Materials 367‚-370, Part A: 556-560.

[21] GUDURU R.K., DARLING K.A., KISHORE R., SCATTERGOOD R.O., KOCH C.C. & MURTY K.L. 2005. Evaluation of mechanical properties using shear punch testing. Materials Science and Engineering: A 395: 307-314.

[22] STEWART G.R., ELWAZRI A.M., VARANO R., POKUTYLOWICZ N., YUE S. & JONAS J.J. 2006. Shear punch testing of welded pipeline steel. Materials Science and Engineering: A 420: 115-121.

[23] GUDURU R.K., NAGASEKHAR A.V., SCATTERGOOD R.O., KOCH C.C. & MURTY K.L. 2007. Thickness and Clearance Effects in Shear Punch Testing. Advanced Engineering Materials Adv. Eng. Mater. 9: 157-160.

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[24] KARTHIK V., VISWESWARAN P., VIJAYRAGHAVAN A., KASIVISWANATHAN K.V. & RAJ B. 2009. Tensile‚ shear correlations obtained from shear punch test technique using a modified experimental approach. Journal of Nuclear Materials 393: 425-432.

[25] GOYAL S., KARTHIK V., KASIVISWANATHAN K.V., VALSAN M., RAO K.B.S. & RAJ B. 2010. Finite element analysis of shear punch testing and experimental validation. Materials & Design 31: 2546-2552.

[26] LECO CORPORATION. 2006. INSTRUCTION MANUAL. LM-100, LM-300 and LM-700 DIGITAL MICROINDENTATION TESTER.

[27] TEKKAYA A.E. 2000. State-of-the-art of simulation of sheet metal forming. Journal of Materials Processing Technology 103: 14-22.

[28] J.A.H. Ramaekars, J.A.G. Kals, Strain, stresses and forces in blanking, in: Proceedings of the IMC Conference Galway, 1986, pp. 126–138.

[29] J.A.H. Ramaekers, P.C. Veenstra, The relation between effective deformation and microhardness in a state of large plastic deformation. Annals of the C.I.R.P., 18 (1970), p. 541

[30] NAHSHON K. & HUTCHINSON J.W. 2008. Modification of the Gurson Model for shear failure. European Journal of Mechanics - A/Solids 27: 1-17.

[31] XUE Z., PONTIN M.G., ZOK F.W. & HUTCHINSON J.W. 2010. Calibration procedures for a computational model of ductile fracture. Engineering Fracture Mechanics 77: 492-509.

[32] KLINGENBERG W. & SINGH U.P. 2005. Comparison of two analytical models of blanking and proposal of a new model. International Journal of Machine Tools and Manufacture 45: 519-527. [33] TABOR D. 1951. The hardness of metals. Clarendon Press. [34] T. Yamamoto, G. R. Odette, Y. Wu. 2011. Constitutive, Damage and Plasticity Laws for Candidate Fusion Alloys. DOE/ER-0313/51 Semiannual Progress Report 51:78-84.

71

Appendix A

72

Table 8 Flow Stress and H measured and predicted values

Shear Punch Test Records

73

Appendix B

0 0.1 0.20

100

200

300

400

500

600

700

rr01 YSP = 181.1 Smax = 387.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 176.4 Smax = 379.9

Strain (mm/mm)0 0.1 0.2

0

100

200

300

400

500

600

700

YSP = 206 Smax = 397.7

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr01 YSP = 188 offset=0.002 Smax = 388 spty SD=16 Smax SD=9

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


74

0 0.1 0.20

100

200

300

400

500

600

700

rr02 YSP = 155.3 Smax = 337.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 158.9 Smax = 324.9


0

100

200

300

400

500

600

700

YSP = 150.9 Smax = 346.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr02 YSP = 155 offset=0.002 Smax = 336 spty SD=4 Smax SD=1e+001

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


75

0 0.1 0.20

100

200

300

400

500

600

700

rr03 YSP = 133.8 Smax = 312St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 119.3 Smax = 315.8


0

100

200

300

400

500

600

700

YSP = 139.4 Smax = 304.7

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


76

0 0.1 0.20

100

200

300

400

500

600

700

rr04 YSP = 200.7 Smax = 410.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 208.8 Smax = 418.3


0

100

200

300

400

500

600

700

YSP = 206 Smax = 426.6

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr04 YSP = 205 offset=0.002 Smax = 418 spty SD=4.1 Smax SD=8

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


77

0 0.1 0.20

100

200

300

400

500

600

700

rr05 YSP = 205.1 Smax = 371.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 199.7 Smax = 375.2


0

100

200

300

400

500

600

700

YSP = 213.1 Smax = 369.6

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


78

0 0.1 0.20

100

200

300

400

500

600

700

rr06 YSP = 243.2 Smax = 394.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 230.1 Smax = 390.6


0

100

200

300

400

500

600

700

YSP = 221.7 Smax = 398.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


79

0 0.1 0.20

100

200

300

400

500

600

700

rr07 YSP = 253.5 Smax = 426.5St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 237.4 Smax = 423.9


0

100

200

300

400

500

600

700

YSP = 243.2 Smax = 426.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


80

0 0.1 0.20

100

200

300

400

500

600

700

rr08 YSP = 204.5 Smax = 405.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 186 Smax = 404.1


0

100

200

300

400

500

600

700

YSP = 192.4 Smax = 404.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr08 YSP = 194 offset=0.002 Smax = 405 spty SD=9.4 Smax SD=0.8

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


81

0 0.1 0.20

100

200

300

400

500

600

700

rr09 YSP = 215.9 Smax = 418.9St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 227.6 Smax = 423.9


0

100

200

300

400

500

600

700

YSP = 225.7 Smax = 423

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


82

0 0.1 0.20

100

200

300

400

500

600

700

rr10 YSP = 418.5 Smax = 608.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 409.7 Smax = 606.8


0

100

200

300

400

500

600

700

YSP = 418.4 Smax = 598.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


83

0 0.1 0.20

100

200

300

400

500

600

700

rr11 YSP = 365.3 Smax = 535.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 365 Smax = 526.5


0

100

200

300

400

500

600

700

YSP = 357.4 Smax = 533.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


84

0 0.1 0.20

100

200

300

400

500

600

700

rr12 YSP = 295.8 Smax = 473.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 284 Smax = 460.6


0

100

200

300

400

500

600

700

YSP = 285.4 Smax = 473.6

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


85

0 0.1 0.20

100

200

300

400

500

600

700

rr13 YSP = 392.8 Smax = 618.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 414.4 Smax = 615.4


0

100

200

300

400

500

600

700

YSP = 402.3 Smax = 620.2

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


86

0 0.1 0.20

100

200

300

400

500

600

700

rr14 YSP = 364.9 Smax = 540.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 354.1 Smax = 529.9


0

100

200

300

400

500

600

700

YSP = 368.3 Smax = 536.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


87

0 0.1 0.20

100

200

300

400

500

600

700

rr15 YSP = 402.6 Smax = 589.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 407.5 Smax = 586


0

100

200

300

400

500

600

700

YSP = 404.8 Smax = 582.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


88

0 0.1 0.20

100

200

300

400

500

600

700

rr16 YSP = 413.8 Smax = 588.5St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 420.6 Smax = 591.2


0

100

200

300

400

500

600

700

YSP = 422.6 Smax = 589.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


89

0 0.1 0.20

100

200

300

400

500

600

700

rr17 YSP = 394.2 Smax = 583.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 410.8 Smax = 579.5


0

100

200

300

400

500

600

700

YSP = 420.8 Smax = 588.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


90

0 0.1 0.20

100

200

300

400

500

600

700

rr18 YSP = 420.1 Smax = 618.9St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 437.5 Smax = 628.6


0

100

200

300

400

500

600

700

YSP = 430.1 Smax = 611.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


91

0 0.1 0.20

100

200

300

400

500

600

700

rr19 YSP = 283.3 Smax = 458.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 278.7 Smax = 463.4


0

100

200

300

400

500

600

700

YSP = 269.1 Smax = 458.2

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


92

0 0.1 0.20

100

200

300

400

500

600

700

rr20 YSP = 210.9 Smax = 377.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 232.2 Smax = 378.2


0

100

200

300

400

500

600

700

YSP = 209.1 Smax = 374.6

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


93

0 0.1 0.20

100

200

300

400

500

600

700

rr21 YSP = 279.3 Smax = 442.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 280.5 Smax = 444.8


0

100

200

300

400

500

600

700

YSP = 274.7 Smax = 444.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


94

0 0.1 0.20

100

200

300

400

500

600

700

rr22 YSP = 349.2 Smax = 538St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 346.5 Smax = 532.7


0

100

200

300

400

500

600

700

YSP = 335.4 Smax = 527.4

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


95

0 0.1 0.20

100

200

300

400

500

600

700

rr23 YSP = 256.6 Smax = 418.3St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 260.4 Smax = 420.9


0

100

200

300

400

500

600

700

YSP = 263.1 Smax = 423.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


96

0 0.1 0.20

100

200

300

400

500

600

700

rr24 YSP = 366 Smax = 560.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 370.1 Smax = 569


0

100

200

300

400

500

600

700

YSP = 371.1 Smax = 565.7

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


97

0 0.1 0.20

100

200

300

400

500

600

700

rr25 YSP = 280.1 Smax = 461.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 292.5 Smax = 460


0

100

200

300

400

500

600

700

YSP = 279.4 Smax = 452.4

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


98

0 0.1 0.20

100

200

300

400

500

600

700

rr26 YSP = 358 Smax = 564.7St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 368.7 Smax = 560.6


0

100

200

300

400

500

600

700

YSP = 370.5 Smax = 570

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


99

0 0.1 0.20

100

200

300

400

500

600

700

rr27 YSP = 277.4 Smax = 418.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 267.6 Smax = 419.5


0

100

200

300

400

500

600

700

YSP = 270 Smax = 418.4

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


100

0 0.1 0.20

100

200

300

400

500

600

700

rr28 YSP = 347 Smax = 551.7St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 337.3 Smax = 545.7


0

100

200

300

400

500

600

700

YSP = 332.2 Smax = 551.7

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


101

0 0.1 0.20

100

200

300

400

500

600

700

rr29 YSP = 277.2 Smax = 450.7St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 294.2 Smax = 450


0

100

200

300

400

500

600

700

YSP = 278.2 Smax = 447.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


102

0 0.1 0.20

100

200

300

400

500

600

700

rr30 YSP = 302.1 Smax = 474.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 293.8 Smax = 464.8


0

100

200

300

400

500

600

700

YSP = 293.3 Smax = 471.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


103

0 0.1 0.20

100

200

300

400

500

600

700

rr31b YSP = 362.9 Smax = 534St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 359 Smax = 530.2


0

100

200

300

400

500

600

700

YSP = 371.2 Smax = 535.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr31b YSP = 364 offset=0.002 Smax = 533 spty SD=6.2 Smax SD=3

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


104

0 0.1 0.20

100

200

300

400

500

600

700

rr32 YSP = 421.2 Smax = 578.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 416.7 Smax = 574


0

100

200

300

400

500

600

700

YSP = 394.9 Smax = 590.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


105

0 0.1 0.20

100

200

300

400

500

600

700

rr33 YSP = 298.2 Smax = 490.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 305 Smax = 485.7


0

100

200

300

400

500

600

700

YSP = 298.9 Smax = 489.2

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


106

0 0.1 0.20

100

200

300

400

500

600

700

rr34 YSP = 309.2 Smax = 473.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 290.4 Smax = 471.7


0

100

200

300

400

500

600

700

YSP = 305.9 Smax = 480.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


107

0 0.1 0.20

100

200

300

400

500

600

700

rr35 YSP = 275.4 Smax = 475.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 280.8 Smax = 477.8


0

100

200

300

400

500

600

700

YSP = 278.3 Smax = 479.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


108

0 0.1 0.20

100

200

300

400

500

600

700

rr36 YSP = 231.3 Smax = 386.9St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 233.9 Smax = 387.6


0

100

200

300

400

500

600

700

YSP = 234.3 Smax = 388

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


109

0 0.1 0.20

100

200

300

400

500

600

700

rr37 YSP = 311.4 Smax = 513.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 325.6 Smax = 526.1


0

100

200

300

400

500

600

700

YSP = 326 Smax = 520.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


110

0 0.1 0.20

100

200

300

400

500

600

700

rr38 YSP = 243.3 Smax = 408.7St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 246.2 Smax = 407.7


0

100

200

300

400

500

600

700

YSP = 249.7 Smax = 415.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


111

0 0.1 0.20

100

200

300

400

500

600

700

rr39 YSP = 285.4 Smax = 448.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 272.7 Smax = 444.6


0

100

200

300

400

500

600

700

YSP = 260.2 Smax = 441.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


112

0 0.1 0.20

100

200

300

400

500

600

700

rr40 YSP = 296.7 Smax = 482.4St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 295.8 Smax = 478.6


0

100

200

300

400

500

600

700

YSP = 302.6 Smax = 489.3

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


113

0 0.1 0.20

100

200

300

400

500

600

700

rr41 YSP = 278.4 Smax = 477.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 282.6 Smax = 469


0

100

200

300

400

500

600

700

YSP = 288.4 Smax = 477.9

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


114

0 0.1 0.20

100

200

300

400

500

600

700

rr42 YSP = 301.6 Smax = 487.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 314.3 Smax = 480.1


0

100

200

300

400

500

600

700

YSP = 304.9 Smax = 476.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


115

0 0.1 0.20

100

200

300

400

500

600

700

rr43 YSP = 314 Smax = 488.5St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 325.1 Smax = 493.1


0

100

200

300

400

500

600

700

YSP = 306.3 Smax = 481.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


116

0 0.1 0.20

100

200

300

400

500

600

700

rr44 YSP = 327.7 Smax = 495St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 323.5 Smax = 493.1


0

100

200

300

400

500

600

700

YSP = 323.5 Smax = 495.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


117

0 0.1 0.20

100

200

300

400

500

600

700

rr45 YSP = 353.2 Smax = 511.7St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 357.1 Smax = 516


0

100

200

300

400

500

600

700

YSP = 385.4 Smax = 520.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


118

0 0.1 0.20

100

200

300

400

500

600

700

rr46b YSP = 431.9 Smax = 618.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 406.6 Smax = 629.7


0

100

200

300

400

500

600

700

YSP = 442.8 Smax = 630

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr46b YSP = 427 offset=0.002 Smax = 626 spty SD=19 Smax SD=6

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


119

0 0.1 0.20

100

200

300

400

500

600

700

rr47 YSP = 308.1 Smax = 492.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 317.5 Smax = 490.3


0

100

200

300

400

500

600

700

YSP = 288.1 Smax = 490.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


120

0 0.1 0.20

100

200

300

400

500

600

700

rr48 YSP = 367.7 Smax = 552.2St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 370.8 Smax = 545.9


0

100

200

300

400

500

600

700

YSP = 384.8 Smax = 545.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


121

0 0.1 0.20

100

200

300

400

500

600

700

rr49 YSP = 376.1 Smax = 526.1St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 334.5 Smax = 518.2


0

100

200

300

400

500

600

700

YSP = 343.3 Smax = 523.4

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700


Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


122

0 0.1 0.20

100

200

300

400

500

600

700

rr50b YSP = 382.1 Smax = 553.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 380.8 Smax = 548.6


0

100

200

300

400

500

600

700

YSP = 371 Smax = 547.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

rr50b YSP = 378 offset=0.002 Smax = 550 spty SD=6.1 Smax SD=3

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


123

0 0.1 0.20

100

200

300

400

500

600

700

xrha YSP = 265.4 Smax = 445.6St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 268.4 Smax = 447


0

100

200

300

400

500

600

700

YSP = 265.4 Smax = 444.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrha YSP = 266 offset=0.002 Smax = 446 spty SD=1.7 Smax SD=1

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


124

0 0.1 0.20

100

200

300

400

500

600

700

xrhb YSP = 270.5 Smax = 459.9St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 273.8 Smax = 459.5


0

100

200

300

400

500

600

700

YSP = 286.6 Smax = 463.8

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrhb YSP = 277 offset=0.002 Smax = 461 spty SD=8.5 Smax SD=2

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


125

0 0.1 0.20

100

200

300

400

500

600

700

xrhc YSP = 279.5 Smax = 454.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 278.9 Smax = 448.1


0

100

200

300

400

500

600

700

YSP = 296.5 Smax = 449.1

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrhc YSP = 285 offset=0.002 Smax = 451 spty SD=10 Smax SD=4

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


126

0 0.1 0.20

100

200

300

400

500

600

700

xrhdb YSP = 217.3 Smax = 352.5St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 216.7 Smax = 344.2


0

100

200

300

400

500

600

700

YSP = 209.4 Smax = 341.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrhdb YSP = 214 offset=0.002 Smax = 346 spty SD=4.4 Smax SD=6

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


127

0 0.1 0.20

100

200

300

400

500

600

700

xrhe YSP = 296 Smax = 436.8St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 281.8 Smax = 430.5


0

100

200

300

400

500

600

700

YSP = 284.7 Smax = 425.5

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrhe YSP = 287 offset=0.002 Smax = 431 spty SD=7.5 Smax SD=6

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700


128

0 0.1 0.20

100

200

300

400

500

600

700

xrhfb YSP = 210.7 Smax = 356.5St

ress

(MPa

)

0 0.1 0.20

100

200

300

400

500

600

700

YSP = 237.5 Smax = 355.8


0

100

200

300

400

500

600

700

YSP = 230.7 Smax = 348.6

0 0.50

100

200

300

400

500

600

700

Stre

ss (M

Pa)

0 0.50

100

200

300

400

500

600

700

xrhfb YSP = 226 offset=0.002 Smax = 354 spty SD=14 Smax SD=4

Strain (mm/mm)0 0.5

0

100

200

300

400

500

600

700

Tensile Test Records

129

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR01 ys = 352.7 UTS = 512.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 353.3 UTS = 506.8


0

100

200

300

400

500

600

700

800

900

1000 ys = 340.2 UTS = 506.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR01 yflow avg = 479.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 473.2

True Plastic Strain (mm/mm)0 0.05 0.1

0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 471.6


130

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR02 ys = 267.4 UTS = 413.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 273.3 UTS = 416.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 273.7 UTS = 416.5

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR02 yflow avg = 365.7

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 370.6


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 368.1


131

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR03 ys = 232.9 UTS = 360.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 236.4 UTS = 361.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 235.2 UTS = 361.5

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR03 yflow avg = 305.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 311.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 309.7


132

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR04 ys = 339.9 UTS = 506.6

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 336.4 UTS = 511.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 340.1 UTS = 504.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR04 yflow avg = 467.7

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 473.6


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 468.4


133

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR05 ys = 321.7 UTS = 471.6

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 332.5 UTS = 480


0

100

200

300

400

500

600

700

800

900

1000 ys = 318.3 UTS = 475.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR05 yflow avg = 444.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 454.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 451.1


134

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR06 ys = 377.6 UTS = 536.6

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 387.4 UTS = 540.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 392.5 UTS = 543.3

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR06 yflow avg = 520.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 521.9


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 527.1


135

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR07 ys = 424.3 UTS = 577.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 411.7 UTS = 567.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 414.6 UTS = 577.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR07 yflow avg = 567.4

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 558.1


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 568.4


136

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR08 ys = 308.2 UTS = 491

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 339.3 UTS = 501.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 328.9 UTS = 493.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR08 yflow avg = 448.6

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 453.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 446.8


137

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR09 ys = 393.3 UTS = 550

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 391.3 UTS = 550.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 388.2 UTS = 553.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR09 yflow avg = 523.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 522.4


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 527.3


138

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR10 ys = 757.3 UTS = 879.9

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 765.3 UTS = 895.4


0

100

200

300

400

500

600

700

800

900

1000 ys = 782.5 UTS = 895.8

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR10 yflow avg = 907.1

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 919.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 920.2


139

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR11 ys = 638.8 UTS = 757.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 634.4 UTS = 751.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 622.3 UTS = 744.2

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR11 yflow avg = 771.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 765.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 764


140

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR12 ys = 510.8 UTS = 646.2

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 499.5 UTS = 642.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 511.2 UTS = 646.8

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR12 yflow avg = 653.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 651.4


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 656.1


141

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR13 ys = 703 UTS = 874.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 676.8 UTS = 874.4


0

100

200

300

400

500

600

700

800

900

1000 ys = 662.4 UTS = 877.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR13 yflow avg = 894.3

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 892.1


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 896.3


142

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR14 ys = 617 UTS = 788.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 626.6 UTS = 782.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 586.5 UTS = 781.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR14 yflow avg = 801.4

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 797.7


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 795.2


143

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR15 ys = 721.3 UTS = 859.2

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 721.9 UTS = 861.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 716.2 UTS = 857.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR15 yflow avg = 892

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 899.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 891.8


144

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR16 ys = 758.8 UTS = 869.2

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 721.3 UTS = 871


0

100

200

300

400

500

600

700

800

900

1000 ys = 743.3 UTS = 863.8

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR16 yflow avg = 935.7

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 912.8


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 932.2


145

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR17 ys = 768.7 UTS = 895

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 756.6 UTS = 884.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 751.4 UTS = 878.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR17 yflow avg = 921.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 922.1


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 899.9


146

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR18 ys = 797.3 UTS = 893.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 774.4 UTS = 897


0

100

200

300

400

500

600

700

800

900

1000 ys = 775.6 UTS = 895.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR18 yflow avg = 936.7

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 939.3


0

100

200

300

400

500

600

700

800

900



147

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR19 ys = 519 UTS = 643

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 517.6 UTS = 642.7


0

100

200

300

400

500

600

700

800

900

1000 ys = 517.3 UTS = 642.5

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR19 yflow avg = 676.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 676.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 675.7


148

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR20 ys = 386.5 UTS = 481.7

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 391.5 UTS = 484.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 390.3 UTS = 482.6

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 510.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 509.7


149

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR21 ys = 457.2 UTS = 596.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 463.8 UTS = 598.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 462.5 UTS = 603.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 601.8


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 603.9


150

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR22 ys = 591.1 UTS = 761

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 585.6 UTS = 753.5


0

100

200

300

400

500

600

700

800

900

1000 ys = 567.5 UTS = 757.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR22 yflow avg = 779.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 766.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 767.4


151

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR23 ys = 433.9 UTS = 579.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 432.2 UTS = 553


0

100

200

300

400

500

600

700

800

900

1000 ys = 445.4 UTS = 553

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR23 yflow avg = 550.1

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900



0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 556.2


152

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR24 ys = 632.5 UTS = 831.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 650.6 UTS = 843.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 652.5 UTS = 845.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR24 yflow avg = 853.6

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 864.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 865.8


153

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR25 ys = 463.6 UTS = 620.4

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 462.1 UTS = 622.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 458.6 UTS = 624.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR25 yflow avg = 623.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 622.9


0

100

200

300

400

500

600

700

800

900



154

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR26 ys = 629.2 UTS = 785

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 627.2 UTS = 784.4


0

100

200

300

400

500

600

700

800

900

1000 ys = 579.4 UTS = 724.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR26 yflow avg = 802.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 803.1


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 739.5


155

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR27 ys = 457.5 UTS = 560.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 459.4 UTS = 563.5


0

100

200

300

400

500

600

700

800

900

1000 ys = 453.6 UTS = 559.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR27 yflow avg = 568.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 572.1


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 569.5


156

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR28 ys = 584.6 UTS = 775

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 584.7 UTS = 777


0

100

200

300

400

500

600

700

800

900

1000 ys = 561 UTS = 769.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR28 yflow avg = 787.1

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 790.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 783.9


157

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR29 ys = 495.1 UTS = 625

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 486.9 UTS = 623.5


0

100

200

300

400

500

600

700

800

900

1000 ys = 486.1 UTS = 630.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR29 yflow avg = 633.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 632.8


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 639.3


158

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR30 ys = 507.2 UTS = 650.9

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 500.8 UTS = 645.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 503.5 UTS = 640.6

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR30 yflow avg = 651.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900



0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 648.9


159

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR31 ys = 645.6 UTS = 783.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 635.4 UTS = 779.5


0

100

200

300

400

500

600

700

800

900

1000 ys = 646 UTS = 785

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 791.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 799.9


160

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR32 ys = 698.5 UTS = 839.2

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 718.1 UTS = 840.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 709.8 UTS = 842.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR32 yflow avg = 856.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 859.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 860.5


161

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR33 ys = 515.2 UTS = 665.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 519.5 UTS = 663.4


0

100

200

300

400

500

600

700

800

900

1000 ys = 515 UTS = 658.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR33 yflow avg = 674.3

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 669.9


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 664.2


162

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR34 ys = 517.5 UTS = 663

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 520.7 UTS = 659.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 529.2 UTS = 664.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR34 yflow avg = 669.4

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 672.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 672.9


163

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR35 ys = 508.7 UTS = 672.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 506.8 UTS = 667.3


0

100

200

300

400

500

600

700

800

900

1000 ys = 505 UTS = 672.5

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 671.9


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 679.6


164

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR36 ys = 419 UTS = 526.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 407.4 UTS = 521.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 422.3 UTS = 529.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR36 yflow avg = 523.2

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 516.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 525.7


165

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR37 ys = 526.3 UTS = 725.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 520.7 UTS = 716.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 515.2 UTS = 709.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR37 yflow avg = 725.3

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 720.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 714.1


166

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR38 ys = 408.8 UTS = 556.4

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 405 UTS = 549.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 422.6 UTS = 563.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR38 yflow avg = 548.4

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 537.6


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 554.3


167

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR39 ys = 488.8 UTS = 636.6

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 486.1 UTS = 627.3


0

100

200

300

400

500

600

700

800

900

1000 ys = 485.6 UTS = 627.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR39 yflow avg = 642.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 633.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 630.7


168

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR40 ys = 506.3 UTS = 652.6

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 505.9 UTS = 654.5


0

100

200

300

400

500

600

700

800

900

1000 ys = 509.9 UTS = 652.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900



0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 651.6


169

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR41 ys = 497.8 UTS = 654

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 494.5 UTS = 642.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 489.3 UTS = 643.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR41 yflow avg = 655.2

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 644.8


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 647.3


170

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR42 ys = 534.6 UTS = 685.9

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 533.1 UTS = 670.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 540.1 UTS = 680.8

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR42 yflow avg = 692.7

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 679.7


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 689.3


171

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR43 ys = 539 UTS = 687.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 547.1 UTS = 683.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 552.6 UTS = 685.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR43 yflow avg = 692.2

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 692.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 693.3


172

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR44 ys = 560.5 UTS = 696.8

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 562.1 UTS = 689


0

100

200

300

400

500

600

700

800

900

1000 ys = 552 UTS = 686.3

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR44 yflow avg = 705.5

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 702.7


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 697.5


173

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR45 ys = 645.3 UTS = 785.4

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 646.5 UTS = 779.8


0

100

200

300

400

500

600

700

800

900

1000 ys = 649.1 UTS = 781.9

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR45 yflow avg = 813.3

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 805.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 806.1


174

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR46 ys = 710.5 UTS = 947.2

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 705.9 UTS = 937.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 699.3 UTS = 936.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR46 yflow avg = 973.3

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 972.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 967.9


175

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR47 ys = 515.3 UTS = 683.5

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 513.9 UTS = 671.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 515.7 UTS = 673.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900


True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 673.5


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 675.1


176

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR48 ys = 627 UTS = 792.9

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 640 UTS = 806.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 646.7 UTS = 813.6

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR48 yflow avg = 805.6

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 817.9


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 823.9


177

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR49 ys = 622.2 UTS = 771.4

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 623.2 UTS = 767.1


0

100

200

300

400

500

600

700

800

900

1000 ys = 617.7 UTS = 755.6

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR49 yflow avg = 794.1

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 789.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 781.6


178

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000RR50 ys = 674.1 UTS = 813.7

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 671.8 UTS = 814.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 669.7 UTS = 813.2

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000RR50 yflow avg = 840.4

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900



0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 839.2


179

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTA ys = 454.5 UTS = 597.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 448.6 UTS = 594


0

100

200

300

400

500

600

700

800

900

1000 ys = 453 UTS = 595.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTA yflow avg = 589.1

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 583.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 587.9


180

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTB ys = 468.6 UTS = 610.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 465.4 UTS = 604.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 467.4 UTS = 605.7

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTB yflow avg = 604.9

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 599.6


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 603.2


181

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTC ys = 486.2 UTS = 586.3

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 497.9 UTS = 611.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 481.3 UTS = 581.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTC yflow avg = 589.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 614.6


0

100

200

300

400

500

600

700

800

900



182

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTD ys = 345 UTS = 435.1

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 342.3 UTS = 433.9


0

100

200

300

400

500

600

700

800

900

1000 ys = 354.6 UTS = 437.1

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTD yflow avg = 439.2

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 438.3


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 443.2


183

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTE ys = 513.5 UTS = 609.7

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 512.6 UTS = 605.6


0

100

200

300

400

500

600

700

800

900

1000 ys = 507.3 UTS = 605.8

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTE yflow avg = 621.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 616.2


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 616.5


184

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000XHTF ys = 369.9 UTS = 457.4

Stre

ss (M

Pa)

0 0.1 0.20

100

200

300

400

500

600

700

800

900

1000 ys = 375.9 UTS = 455.2


0

100

200

300

400

500

600

700

800

900

1000 ys = 372.1 UTS = 453.4

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000XHTF yflow avg = 455.8

True

Stre

ss (M

Pa)

0 0.05 0.10

100

200

300

400

500

600

700

800

900

1000 yflow avg = 455.9


0

100

200

300

400

500

600

700

800

900

1000 yflow avg = 454.1


185

UNIVERSITY OF CALIFORNIA Establishing Correlations for Predicting Tensile Properties Based on the...

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Transcript of UNIVERSITY OF CALIFORNIA Establishing Correlations for Predicting Tensile Properties Based on the...