Stress-strain Curves Fro Diferents Material

7/25/2019 Stress-strain Curves Fro Diferents Material

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On the Strain Hardening Exponent

Definition and its influence

within SINTAP

UNIVERSITY OF CANTABRIA

Report/SINTAP/UC/07

April 1998

J. Ruiz OcejoF. Gutirrez-Solana

Departamento de Ciencia e Ingeniera del Terreno y de los MaterialesE.T.S. de Ingenieros de Caminos, Canales y Puertos

Universidad de CantabriaAvda de los Castros s/n39005, Santander (Spain)

Tel. 34-942-201819, Fax 34-942-201818


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University of CantabriaReport/SINTAP/UC/07

Page 1 of 26

1. INTRODUCTION

During the last months, a specific group formed by British Steel, GKSS and theUniversity of Cantabria has been working on different aspects of the SINTAP Procedure

related to the Y/T ratio as the following:

Estimation of Y/T from YS.

Definition of N and estimation from Y/T.

for L r 1. for L r > 1.

Treatment of yield plateau.

The University of Cantabria has carried out the analysis of the second point. During ameeting held in Paris in last February, the first results were presented (ref: ReportSINTAP/UC/06 ) about the treatment for L r 1. There, it was agreed that further work had to

be done on the different definitions of N.

2. WORK DONE

In order to clarify the use of N within SINTAP, the University of Cantabria was told toreanalyse stress-strain curves and to calculate the strain hardening exponent throughdifferent ways.

It was decided to perform the calculations by varying the last point considered in thestatistical fit. Therefore, four different intervals have been considered:

From YS up to UTS -noted in further figures as N (Y - U)-.

From YS up to the mean value of flow stress and UTS -noted in further figures as N (Y

- (F+U)/2)-.

From YS up to flow stress -noted in further figures as N (Y - F)-.

From YS up to the mean value of yield stress and flow stress -noted in further figuresas N (Y - (Y+F)/2)-.


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Page 2 of 26

Also, for all intervals, two types of fits have been done depending on whether or not

the yield point is fixed. Therefore, eight N values have been determined for each materialstudied.

The objective of such analysis is to evaluate the differences between these definitions

of N and to guarantee conservatism when it is predicted by means of the Y/T ratio in orderto be used in a FAD or in a CDF.

3. RESULTS

In the following pages (4 to 22), the results corresponding to the stress-strain curves of

the nineteen studied materials which follow are presented:

4Y14A2 S275 JR Steel -provided by British Steel-. 4Y17A2 S355 J2 Steel -provided by British Steel-.

Y6T8D 355 EMZ Steel -provided by British Steel-. Y6T26H 450 EMZ Steel -provided by British Steel-. 4Y18A2 450 EMZ Steel -provided by British Steel-. Microalloyed Steel E500. Y6A22D2C StE690 Steel -provided by British Steel-. Y6A4A4D StE690 Steel -provided by British Steel-. Microalloyed Steel E690 (1). Microalloyed Steel E690 (2). Microalloyed Steel E690 (3). Microalloyed Steel E690 (4). Microalloyed Steel E500. Normalised Steel 4135A (1). Normalised Steel 4135A (2).

Quenched Steel 4135B.


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Page 3 of 26

Austenitic Steel. Aged Stainless Steel. Stainless Weld Steel. Aluminium.4. ANALYSIS

In pages 23 to 25 different comparisons between the results are shown. The graphicson the left hand side of the page compare the values directly and a reference line (N=N) is

also plotted; the graphics on the right hand side compare the values relatively and thereference line drawn corresponds to (N/N=1).

Pages 23 and 24 present comparisons between N values where the difference is thelast point considered in the mathematical fit for both yield point fixed or not. All values arecompared to the N value calculated up to UTS which corresponds to the common use. It can

be seen that the less points considered, the higher the relative difference is, specially whenthe value is obtained only up to the mean value of YS and flow stress. Another remarkable

point could be that, for low N values, these different N definitions lead to lower N valuesthan the usual one, but for higher ones, it could lead to even higher figures. This change can

be placed at about 0.3.

In page 25, the comparison is between N values with the same points considered but

fixing or not the yield point. The graphics show that there are small differences betweenthem. It also can be seen that, generally, N values with yield point fixed are lower than Nvalues with yield point not fixed.

Finally, in page 26, a full diagram is presented where N is plotted versus Y/T ratio.Different reference lines are also drawn.

Within SINTAP, a lower bound with the simplest possible mathematical expressionhas been tried to be found in order to assure conservative assessment diagrams for L r >1.

Based on several studies, a very simple function has been suggested: 0.5*(1 - Y/T).

It can be seen through this figure and the following one (detail) that this line cannot be

considered anymore as it could lead to non-conservative results, specially when N is


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Page 5 of 26

4Y14A2 S275 JR Steel

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25

T r u e s t r e s s

True strain

Stress-strain curve

y YS (MPa) u (MPa) UTS (MPa) YS/UTS

367.9 730.7 576.8 0.6378

400

500

600

700

0.02 0.04 0.06 0.08 0.1

True values N (Y - U) N (Y - (F+U)/2) N (Y - F) N (Y - (Y+F)/2)

L o g

t r u e s t r e s s

Log true strain

400

500

600

700

0.02 0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain

Logarithmic least square fitsYield point not fixed

Logarithmic least square fitsYield point fixed


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Page 7 of 26

4Y17A2 S355 J2 Steel

0

100

200

300

400

500

600

700

800

0.00 0.05 0.10 0.15 0.20 0.25

T r u e s t r e s s

True strain

Stress-strain curve


423.9 795.9 625.9 0.6773

400

500

600

700

800

0.02 0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain

400

500

600

700

800

0.02 0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 8 of 26

Number Yield point not fixed Yield point fixedof points N r N r

y - u 17 0.26793 0.9972 0.25555 0.9958

y - +

u

212 0.28266 0.9955 0.25673 0.9899

y - 9 0.28505 0.9894 0.24839 0.9786

y -

y+

2 5 0.22290 0.9717 0.19893 0.9641


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Page 9 of 26

Y6T8D 355 EMZ Steel

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25

T r u e s t r e s s

True strain

Stress-strain curve


408.3 706.9 542.7 0.7524

400

500

600

700

0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain

400

500

600

700

0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 10 of 26


y - u 16 0.26052 0.9974 0.24013 0.9937

y - +

u

211 0.26094 0.9947 0.23514 0.9885

y - 7 0.25231 0.9866 0.22197 0.9771

y -

y+

2 4 0.19617 0.9728 0.17827 0.9670


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Page 11 of 26

Y6T26H 450 EMZ Steel

0

100

200

300

400

500

600

700

800

0.00 0.05 0.10 0.15

T r u e s t r e s s

True strain

Stress-strain curve


540.5 771.6 656.3 0.8236

500

600

700

800

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

500

600

700

800

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 12 of 26


y - u 21 0.15588 0.9889 0.13230 0.9751

y - +

u

214 0.13937 0.9848 0.11940 0.9720

y - 10 0.12201 0.9857 0.10687 0.9757

y -

y+

2 5 0.08932 0.9875 0.08150 0.9818


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Page 13 of 26

4Y18A2 450 EMZ Steel

0

100

200

300

400

500

600

700

800

0.00 0.05 0.10 0.15

T r u e s t r e s s

True strain

Stress-strain curve


572.6 802.7 670.7 0.8537

600

700

800

0.02 0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain

600

700

800

0.02 0.04 0.06 0.08 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 14 of 26


y - u 14 0.14848 0.9840 0.12067 0.9626

y - +

u

211 0.13778 0.9772 0.11154 0.9549

y - 7 0.10689 0.9663 0.08928 0.9492

y -

y+

2 5 0.08084 0.9694 0.07250 0.9625


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Page 15 of 26

Microalloyed Steel E500

0

100

200

300

400

500

600

700

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

T r u e s t r e s s

True strain

Stress-strain curve


540.0 676.5 636.0 0.8491

540

560

580

600

620

640

660

0.004 0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain

540

560

580

600

620

640

660

0.004 0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain




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Page 16 of 26


y - u 88 0.08995 0.9858 0.07622 0.9721

y - +

u

264 0.07944 0.9818 0.06951 0.9726

y - 46 0.06619 0.9858 0.06259 0.9841

y -

y+

2 23 0.05196 0.9915 0.05650 0.9868


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Page 17 of 26

Y6A22D2C StE690 Steel

0

200

400

600

800

1000

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

T r u e s t r e s s

True strain

Stress-strain curve


680.0 889.9 770.8 0.8822

700

800

900

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

700

800

900

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 18 of 26


y - u 17 0.10546 0.9755 0.08282 0.9485

y - +

u

212 0.09203 0.9679 0.07306 0.9424

y - 8 0.07217 0.9635 0.05949 0.9443

y -

y+

2 5 0.05171 0.9692 0.04554 0.9596


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Page 19 of 26

Y6A4A4D StE690 Steel

0

200

400

600

800

1000

0.00 0.02 0.04 0.06 0.08 0.10 0.12

T r u e s t r e s s

True strain

Stress-strain curve


734.6 946.5 841.0 0.8735

700

800

900

1000

0.01 0.1

True values N (Y -U) N (Y - (F+U)/2) N (Y - F) N (Y - (Y+F)/2)

L o g

t r u e s t r e s s

Log true strain

700

800

900

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 20 of 26


y - u 14 0.07153 0.9610 0.05847 0.9419

y - +

u

210 0.06079 0.9603 0.05160 0.9466

y - 6 0.04371 0.9772 0.04044 0.9735

y -

y+

2 4 0.03472 0.9939 0.03439 0.9939


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Page 21 of 26

Microalloyed Steel E690 (1)

0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

T r u e s t r e s s

True strain

Stress-strain curve


840.4 952.1 904.0 0.9296

840

860

880

900

920

940

0.006 0.008 0.01 0.02 0.04


L o g

t r u e s t r e s s

Log true strain

840

860

880

900

920

940

0.006 0.008 0.01 0.02 0.04


L o g

t r u e s t r e s s

Log true strain




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Page 22 of 26


y - u 68 0.05169 0.9837 0.04825 0.9801

y - +

u

256 0.04383 0.9829 0.04224 0.9818

y - 49 0.03689 0.9923 0.03759 0.9920

y -

y+

2 38 0.03449 0.9889 0.03710 0.9843


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Page 23 of 26


0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

T r u e s t r e s s

True strain

Stress-strain curve


809.0 937.3 874.0 0.9256

820

840

860

880

900

920

0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain

820

840

860

880

900

920

0.006 0.008 0.01 0.02 0.04 0.06

True values N (Y -U) N (Y - (F+U)/2) N (Y -F) N (Y - (Y+F)/2)

L o g

t r u e s t r e s s

Log true strain




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Page 25 of 26


0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

T r u e s t r e s s

True strain

Stress-strain curve


840.0 953.2 905.0 0.9282

840

860

880

900

920

940

0.006 0.008 0.01 0.02 0.04


L o g

t r u e s t r e s s

Log true strain

840

860

880

900

920

940

0.006 0.008 0.01 0.02 0.04


L o g

t r u e s t r e s s

Log true strain




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Page 26 of 26


y - u 67 0.05133 0.9833 0.04797 0.9797

y - +

u

256 0.04385 0.9830 0.04227 0.9818

y - 49 0.03691 0.9924 0.03763 0.9920

y -

y+

2 38 0.03451 0.9889 0.03715 0.9842


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Page 27 of 26


0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05 0.06

T r u e s t r e s s

True strain

Stress-strain curve


924.0 1051.8 994.0 0.9296

920

940

960

980

10001000

0.006 0.008 0.01 0.02 0.04


L o g

t r u e s t r e s s

Log true strain

920

940

960

980

10001000

0.006 0.008 0.01 0.02 0.04

True values N (Y - U) N (Y - (F+U)/2) N (Y - F) N (Y- (Y+F)/2)

L o g

t r u e s t r e s s

Log true strain




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Page 28 of 26


y - u 156 0.05953 0.9774 0.04821 0.9568

y - +

u

2108 0.05185 0.9741 0.04334 0.9584

y - 63 0.03891 0.9826 0.03581 0.9787

y -

y+

2 32 0.02939 0.9936 0.03089 0.9919


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Page 29 of 26

Normalised Steel 4135A (1)

0

200

400

600

800

1000

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

T r u e s t r e s s

True strain

Stress-strain curve


782.0 962.0 905.0 0.8641

800

900

0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain

800

900

0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain




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Page 30 of 26


y - u 107 0.09232 0.9939 0.08710 0.9920

y - +

u

267 0.08394 0.9916 0.08200 0.9913

y - 42 0.07221 0.9953 0.07613 0.9933

y -

y+

2 21 0.06676 0.9893 0.07821 0.9678


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Page 31 of 26

Normalised Steel 4135A (2)

0

200

400

600

800

1000

1200

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

T r u e s t r e s s

True strain

Stress-strain curve


690.0 1123.1 1042.0 0.6622

700

800

900

1000

0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain

700

800

900

1000

0.006 0.008 0.01 0.02 0.04 0.06


L o g

t r u e s t r e s s

Log true strain




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Page 33 of 26

Quenched Steel 4135B

0

400

800

1200

1600

2000

0.000 0.005 0.010 0.015 0.020 0.025 0.030

T r u e s t r e s s

True strain

Stress-strain curve


1245.0 2039.3 1981.9 0.6282

1200

1400

1600

1800

2000

0.008 0.01 0.02


L o g

t r u e s t r e s s

Log true strain

1200

1400

1600

1800

2000

0.008 0.01 0.02


L o g

t r u e s t r e s s

Log true strain




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Page 35 of 26

Austenitic Steel

0

200

400

600

800

1000

0.00 0.10 0.20 0.30 0.40 0.50

T r u e s t r e s s

True strain

Stress-strain curve


236.7 968.0 611.8 0.3869

200

400

600

800

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

200

400

600

800

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 36 of 26


y - u 19 0.27312 0.9753 0.23153 0.9599

y - +

u

217 0.24982 0.9768 0.21521 0.9639

y - 14 0.21247 0.9809 0.18973 0.9731

y -

y+

2 11 0.16724 0.9975 0.16269 0.9970


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Page 37 of 26

Aged Stainless Steel

0

200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20 0.25 0.30

T r u e s t r e s s

True strain

Stress-strain curve


335.0 934.9 712.0 0.4705

400

600

800

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

400

600

800

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 39 of 26

Stainless Weld Steel

0

200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

T r u e s t r e s s

True strain

Stress-strain curve


454.0 987.4 684.0 0.6637

500

600

700

800

900

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

500

600

700

800

900

1000

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 40 of 26


y - u 95 0.19908 0.9516 0.14552 0.9136

y - +

u

263 0.16607 0.9544 0.12891 0.9277

y - 37 0.12807 0.9668 0.10887 0.9542

y -

y+

2 17 0.08970 0.9926 0.08765 0.9923


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Page 41 of 26

Aluminium

0

50

100

150

200

250

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

T r u e s t r e s s

True strain

Stress-strain curve


82.6 257.2 224.0 0.3687

80

90

100

200

0.01 0.1


L o g

t r u e s t r e s s

Log true strain

80

90

100

200

0.01 0.1


L o g

t r u e s t r e s s

Log true strain




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Page 42 of 26


y - u 127 0.29646 0.9881 0.32501 0.9827

y - +

u

258 0.35820 0.9985 0.35863 0.9985

y - 31 0.37875 0.9997 0.36629 0.9990

y -

y+

2 17 0.36302 0.9993 0.34943 0.9983


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Internal Use OnlyPage 43 of 26

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (F+U)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - F)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - F) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (Y+F)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (Y+F)/2) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (F+U)/2) N (Y - F) N (Y - (Y+F)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2) / N (Y - U) N (Y - F) / N (Y - U) N (Y - (Y+F)/2) / N (Y - U)

N /

N

N (Y - U)

Comparisons between different N values as a function of the last point consideredYield point not fixed


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0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (F+U)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - F)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - F) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (Y+F)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (Y+F)/2) / N (Y - U)

N /

N

N (Y - U)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

N (Y - (F+U)/2) N (Y - F) N (Y - (Y+F)/2)

N

N (Y - U)

0.25

0.50

0.75

1.00

1.25

1.50

1.75

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2) / N (Y - U) N (Y - F) / N (Y - U) N (Y - (Y+F)/2) / N (Y - U)

N /

N

N (Y - U)

Comparisons between different N values as a function of the last point consideredYield point fixed


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0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - U)

N y

i e l d p o

i n t f i x e d

N yield point not fixed

0.7

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - U) / N (Y - U)

N y

i e l d p o

i n t f i x e d

/ N

y i e l d p o i n

t n o

t f i x e d


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2)

N y

i e l d p o

i n t f i x e d


0.7

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (F+U)/2) / N (Y - (F+U)/2)

N y

i e l d p o

i n t f i x e d

/ N y i e l d p o

i n t n o

t f i x e d


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - F)

N y

i e l d p o

i n t f i x e d


0.7

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - F) / N (Y - F)

N y

i e l d p o

i n t f i x e d

/ N

y i e l d p o

i n t n o

t f i x e d


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (Y+F)/2)

N y

i e l d p o

i n t f i x e d


0.7

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - (Y+F)/2) / N (Y - (Y+F)/2)

N y i e

l d p o

i n t f i x e d

/ N

y i e l d p o

i n t n o

t f i x e d


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - U) N (Y - (F+U)/2) N (Y - F) N (Y - (Y+F)/2)

N y

i e l d p o

i n t f i x e d


0.7

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

N (Y - U) / N (Y - U) N (Y - (F+U)/2) / N (Y - (F+U)/2) N (Y - F) / N (Y - F) N (Y - (Y+F)/2) / N (Y - (Y+F)/2) N

y i e l d p o

i n t f i x e d

/ N

y i e l d p o

i n t n o

t f i x e d


Comparisons between different N valuesas a function of whether or not the yield point is fixed


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0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N (Y - U) not fixed N (Y - (F+U)/2) not fixed N (Y - F) not fixed N (Y - (Y+F)/2) not fixed

N (Y - U) fixed N (Y - (F+U)/2) fixed N (Y - F) fixed N (Y - (Y+F)/2) fixed

N

Y/TAll different definitions of N versus Yield/Tensile Ratio

0 00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

N

Stress-strain Curves Fro Diferents Material

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