UNIVERSITY OF CANTABRIAUniversity 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

On the Strain Hardening Exponent

Definition and its influence

within SINTAP

UNIVERSITY OF CANTABRIA

Report/SINTAP/UC/07

April 1998

J. Ruiz OcejoF. Gutiérrez-Solana

Departamento de Ciencia e Ingeniería 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

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 the

University 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 Lr � 1.

∗ for Lr > 1.

• Treatment of yield plateau.

The University of Cantabria has carried out the analysis of the second point. During a

meeting held in Paris in last February, the first results were presented (ref: Report

SINTAP/UC/06) about the treatment for Lr � 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 to

reanalyse stress-strain curves and to calculate the strain hardening exponent through

different ways.

It was decided to perform the calculations by varying the last point considered in the

statistical 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 figures

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


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 material

studied.

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 order

to 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 E500.

• Normalised Steel 4135A (1).

• Normalised Steel 4135A (2).

• Quenched Steel 4135B.


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 graphics

on 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 the

reference line drawn corresponds to (N/N=1).

Pages 23 and 24 present comparisons between N values where the difference is the

last point considered in the mathematical fit for both yield point fixed or not. All values are

compared 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 when

the 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 values

than 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 between

them. It also can be seen that, generally, N values with yield point fixed are lower than N

values 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 expression

has been tried to be found in order to assure conservative assessment diagrams for Lr >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


Page 4 of 26

analysed by fixing the yield point and only up to the flow stress or the average between this

and the yield stress.

These values recommend a lower bound between 0.3 and 0.4 times (1 - Y/T). Then, a

final function should be defined within Consortium.


Page 5 of 26

4Y14A2 S275 JR Steel

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σσσσy ≈≈≈≈ YS (MPa) σσσσu (MPa) UTS (MPa) YS/UTS

367.9 730.7 576.8 0.6378

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Page 6 of 26

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

σy - σu 20 0.29888 0.9958 0.27654 0.9924

σy - σ + σu

214 0.31022 0.9921 0.27345 0.9836

σy - σ 10 0.30366 0.9834 0.26148 0.9717

σy -

σy + σ 2

4 0.21853 0.9658 0.19559 0.9580


Page 7 of 26

4Y17A2 S355 J2 Steel

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423.9 795.9 625.9 0.6773

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Page 8 of 26


σy - σu 17 0.26793 0.9972 0.25555 0.9958

σy - σ + σu

212 0.28266 0.9955 0.25673 0.9899

σy - σ 9 0.28505 0.9894 0.24839 0.9786

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5 0.22290 0.9717 0.19893 0.9641


Page 9 of 26

Y6T8D 355 EMZ Steel

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408.3 706.9 542.7 0.7524

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Page 10 of 26


σy - σu 16 0.26052 0.9974 0.24013 0.9937

σy - σ + σu

211 0.26094 0.9947 0.23514 0.9885

σy - σ 7 0.25231 0.9866 0.22197 0.9771

σy -

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4 0.19617 0.9728 0.17827 0.9670


Page 11 of 26

Y6T26H 450 EMZ Steel

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540.5 771.6 656.3 0.8236

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Page 12 of 26


σy - σu 21 0.15588 0.9889 0.13230 0.9751

σy - σ + σu

214 0.13937 0.9848 0.11940 0.9720

σy - σ 10 0.12201 0.9857 0.10687 0.9757

σy -

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5 0.08932 0.9875 0.08150 0.9818


Page 13 of 26

4Y18A2 450 EMZ Steel

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572.6 802.7 670.7 0.8537

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Page 14 of 26


σy - σu 14 0.14848 0.9840 0.12067 0.9626

σy - σ + σu

211 0.13778 0.9772 0.11154 0.9549

σy - σ 7 0.10689 0.9663 0.08928 0.9492

σy -

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5 0.08084 0.9694 0.07250 0.9625


Page 15 of 26

Microalloyed Steel E500

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540.0 676.5 636.0 0.8491

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Page 16 of 26


σy - σu 88 0.08995 0.9858 0.07622 0.9721

σy - σ + σu

264 0.07944 0.9818 0.06951 0.9726

σy - σ 46 0.06619 0.9858 0.06259 0.9841

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23 0.05196 0.9915 0.05650 0.9868


Page 17 of 26

Y6A22D2C StE690 Steel

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680.0 889.9 770.8 0.8822

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Page 18 of 26


σy - σu 17 0.10546 0.9755 0.08282 0.9485

σy - σ + σu

212 0.09203 0.9679 0.07306 0.9424

σy - σ 8 0.07217 0.9635 0.05949 0.9443

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5 0.05171 0.9692 0.04554 0.9596


Page 19 of 26

Y6A4A4D StE690 Steel

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734.6 946.5 841.0 0.8735

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Page 20 of 26


σy - σu 14 0.07153 0.9610 0.05847 0.9419

σy - σ + σu

210 0.06079 0.9603 0.05160 0.9466

σy - σ 6 0.04371 0.9772 0.04044 0.9735

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4 0.03472 0.9939 0.03439 0.9939


Page 21 of 26

Microalloyed Steel E690 (1)

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Page 22 of 26


σy - σu 68 0.05169 0.9837 0.04825 0.9801

σy - σ + σu

256 0.04383 0.9829 0.04224 0.9818

σy - σ 49 0.03689 0.9923 0.03759 0.9920

σy -

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38 0.03449 0.9889 0.03710 0.9843


Page 23 of 26


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809.0 937.3 874.0 0.9256

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Page 24 of 26


σy - σu 122 0.06488 0.9703 0.04866 0.9357

σy - σ + σu

281 0.05361 0.9633 0.04214 0.9378

σy - σ 51 0.04055 0.9728 0.03521 0.9629

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23 0.02806 0.9929 0.02884 0.9925


Page 25 of 26


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Page 26 of 26


σy - σu 67 0.05133 0.9833 0.04797 0.9797

σy - σ + σu

256 0.04385 0.9830 0.04227 0.9818

σy - σ 49 0.03691 0.9924 0.03763 0.9920

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Page 27 of 26


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Page 28 of 26


σy - σu 156 0.05953 0.9774 0.04821 0.9568

σy - σ + σu

2108 0.05185 0.9741 0.04334 0.9584

σy - σ 63 0.03891 0.9826 0.03581 0.9787

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Page 29 of 26

Normalised Steel 4135A (1)

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Page 30 of 26


σy - σu 107 0.09232 0.9939 0.08710 0.9920

σy - σ + σu

267 0.08394 0.9916 0.08200 0.9913

σy - σ 42 0.07221 0.9953 0.07613 0.9933

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Page 31 of 26

Normalised Steel 4135A (2)

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Page 32 of 26


σy - σu 95 0.18575 0.9901 0.22388 0.9641

σy - σ + σu

266 0.20777 0.9931 0.24229 0.9761

σy - σ 31 0.24804 0.9938 0.27957 0.9832

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Page 33 of 26

Quenched Steel 4135B

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Page 34 of 26


σy - σu 54 0.39377 0.9890 0.44835 0.9767

σy - σ + σu

233 0.47407 0.9970 0.50530 0.9941

σy - σ 20 0.52602 0.9992 0.54161 0.9986

σy -

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Page 35 of 26

Austenitic Steel

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236.7 968.0 611.8 0.3869

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Page 36 of 26


σy - σu 19 0.27312 0.9753 0.23153 0.9599

σy - σ + σu

217 0.24982 0.9768 0.21521 0.9639

σy - σ 14 0.21247 0.9809 0.18973 0.9731

σy -

σy + σ 2

11 0.16724 0.9975 0.16269 0.9970


Page 37 of 26

Aged Stainless Steel

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200

400

600

800

1000

0.00 0.05 0.10 0.15 0.20 0.25 0.30

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True strain

Stress-strain curve


335.0 934.9 712.0 0.4705

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Page 38 of 26


σy - σu 65 0.24793 0.9953 0.23898 0.9945

σy - σ + σu

241 0.22953 0.9975 0.22840 0.9975

σy - σ 25 0.21337 0.9993 0.22022 0.9986

σy -

σy + σ 2

14 0.21991 0.9984 0.22967 0.9970


Page 39 of 26

Stainless Weld Steel

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Stress-strain curve


454.0 987.4 684.0 0.6637

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Page 40 of 26


σy - σu 95 0.19908 0.9516 0.14552 0.9136

σy - σ + σu

263 0.16607 0.9544 0.12891 0.9277

σy - σ 37 0.12807 0.9668 0.10887 0.9542

σy -

σy + σ 2

17 0.08970 0.9926 0.08765 0.9923


Page 41 of 26

Aluminium

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82.6 257.2 224.0 0.3687

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Page 42 of 26


σy - σu 127 0.29646 0.9881 0.32501 0.9827

σy - σ + σu

258 0.35820 0.9985 0.35863 0.9985

σy - σ 31 0.37875 0.9997 0.36629 0.9990

σy -

σy + σ 2

17 0.36302 0.9993 0.34943 0.9983


Internal Use Only

Page 43 of 26

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N

N (Y - U)

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

N /

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N (Y - U)

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


Internal Use Only

Page 44 of 26

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N /

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


Internal Use Only

Page 45 of 26

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poi

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N y

ield

poi

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ixed

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yie

ld p

oint

not

fix

ed


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


Internal Use Only

Page 46 of 26

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

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

N

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

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0.08

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0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

N

Y/T

Detail of the previous figure

Documents

UNIVERSITY OF CANTABRIAUniversity 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