The University of Sydney Department of Civil Engineering Sydney NSW 2006 AUSTRALIA.

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1 Sydney NSW 26 AUSTRALIA Centre for Advanced Strctral Engineering Fll-range Stress-strain Crves for Stainless Steel Alloys By Kim JR Rasmssen MScEng, PhD November 21

2 Centre for Advanced Strctral Engineering Fll-range Stress-strain Crves for Stainless Steel Alloys Kim JR Rasmssen, MScEng, PhD November 21 Abstract: The report develops an expression for the stress-strain crves for stainless steel alloys which is valid over the fll strain range. The expression is sefl for the design and nmerical modelling of stainless steel members and elements which reach stresses beyond the.2% proof stress in their ltimate limit state. In this stress range, crrent stress-strain crves based on the Ramberg-Osgood expression become seriosly inaccrate principally becase they are extrapolations of crve fits to stresses lower than the.2% proof stress. The extrapolation becomes particlarly inaccrate for alloys with prononced strain hardening. The report also develops expressions for determining the ltimate tensile strength ( ) and strain ( ) for given vales of the Ramberg-Osgood parameters (E,.2,n). The expressions are compared with a wide range of experimental data and shown to be reasonably accrate for all strctral classes of stainless steel alloys. Based on the expressions for ( ) and ( ), it is possible to constrct the entire stressstrain crve from the Ramberg-Osgood parameters (E,.2,n). Keywords: Stainless steel, stress-strain crves, Ramberg-Osgood crve, tests.

3 Copyright Notice, Research Report R811 Fll-range Stress-strain Crves for Stainless Steel Alloys 21 Kim JR Rasmssen This pblication may be redistribted freely in its entirety and in its original form withot the consent of the copyright owner. Use of material contained in this pblication in any other pblished works mst be appropriately referenced, and, if necessary, permission soght from the athor. Pblished by: Sydney, NSW, 26 AUSTRALIA November

4 Introdction Stainless steel alloys have low proportionality limits and extended strain-hardening capability. The prononced yield platea familiar from strctral steel is nonexistent and so an eqivalent yield stress is sed in strctral design, sally chosen as a sitable proof stress. The nonlinear stress-strain behavior is acknowledged in the American (ASCE, 1991), Astralian (AS/NZS 4673, 21) and Soth African (SABS 1997) standards for cold-formed stainless steel strctres which define the stress-strain crve in terms of the Ramberg-Osgood expression (Ramberg and Osgood, 1941), p. E = + (1) p Eqation 1 was originally developed for alminim alloys bt has proven sitable for other nonlinear metals inclding stainless steel alloys. It involves the initial Yong s modls (E ), the proof stress ( p ) corresponding to the plastic strain p, and a parameter (n) which determines the sharpness of the knee of the stress-strain crve. In the design of alminim and stainless steel strctres, it has become indstry practice to se the.2% proof stress (.2 ) as the eqivalent yield stress. For this proof stress, the stress-strain relationship takes the form,.2. E = + (2).2 It has also become standard practice to determine the parameter (n) sing the.1% and.2% proof stresses which leads to the following expression, ln(2) n =. (3) ln(.2 /.1) Eqation 3 ensres that the Ramberg-Osgood approximation matches exactly the measred stress-strain crve at the.1% and.2% proof stresses. It generally provides close approximations to measred stress-strain crves for stresses p to the.2% proof stress. In concentrically loaded colmns, the strains are small when reaching the ltimate load for all practical ranges of length. It is therefore possible to base the design on the Ramberg- Osgood crve and achieve close agreement with experimental strengths, e.g. see Rasmssen and Hancock (1993) and Rhodes et al. (2). Rasmssen and Rondal (1997) sed this reslt to develop a direct relationship between the colmn strength and the parameters n and e, where e is the nondimensional proof stress,.2 e =. (4) E However, strctral components which ndergo significant straining before reaching their ltimate capacity, sch as plates in compression or shear, compact beams failing by in-plane bending and tension members, may develop stresses beyond the.2% proof stress and strains well in excess of the.2% total strain, n n.2.2 = +.2. (5) E When the strains exceed the.2% total strain (.2 ), the Ramberg-Osgood crve obtained on the basis of the.1% and.2% proof stresses may become seriosly inaccrate, tending to 3

5 prodce too high stresses, as shown in Fig. 1. This particlarly applies to alloys with low vales of n. In this strain range, it is necessary to se a refined expression for the stress-strain crve with wider applicability range. This report aims to develop sch an expression within the following constraints: 1. Crrent vales of n, sch as those given in the American, Astralian and Soth African standards for stainless steel strctres, shall remain applicable. This implies that the stress-strain crve can be accrately determined sing the Ramberg-Osgood expression for stresses p to the.2% proof stress. 2. In the stress range between the.2% proof stress and the ltimate tensile strength ( ), the stress-strain crve shall be defined in terms of a minimm of additional parameters. These constraints ensre simplicity in the stress-strain crve formlation. It will be demonstrated that it is possible to obtain agreement with measred stress-strain crves within tolerances that wold be deemed acceptable for a wide range of applications. Recent approaches MacDonald et al. (2) reported a series of tests on astenitic UNS34 (AISI34) stainless steel channel colmns. Ramberg-Osgood crves were fitted to stress-strain crves obtained from stb colmn and tension copon testing by sing the.1% and.2% proof stresses to determine the n-parameter. The fitted Ramberg-Osgood crves were shown to err significantly at strains exceeding the.2% total strain (.2 ) and a modified expression was sggested in the form k i+ j 1 = +.2 (6) E 1 where the constants i, j and k took vales ranging from 2.5 to 6 depending on the thickness of the material tested. While this expression proved very accrate, it was limited in applicability to the particlar alloy and thicknesses tested. Olsson (21) stdied advanced plasticity models for stainless steel alloys and performed a large nmber of tests on niaxially and biaxially loaded copons. He plotted the stressstrain crves as tre stress ( t ) vs engineering strain () and observed experimentally that the stress-strain crve approached a straight line at large strains. He proposed that the tre-stress vs engineering strain crve be approximated by a Ramberg-Osgood crve for strains p to a total strain of 2% and a straight line from this point onwards, as shown in Fig. 2. The straight line was chosen as an average fit to the measred stress-strain crve. It was not reqired to eqal the tre ltimate tensile strength ( t ) at the ltimate total strain ( ). Acknowledging the relationship between the tre and engineering stresses, t = ( 1 + ) and observing that d/d for, it is apparent that as the tre stress vs engineering strain crve asymptotes to the line, t ( 1 + ). = Evidently, the slope of this line and the intercept of the line with the stress axis both eqal, as shown in Fig. 2. The slope of the line is different from the slope of the line throgh the tre 2% proof stress and tre ltimate tensile strength. (7) (8) 4

6 While Olsson s approach is attractive becase of its theoretical jstification, it lacks accracy at small strains since it assmes the Ramberg-Osgood crve is valid for total strains p to 2%. Olsson determined the n-parameter by se of the.2% and 1% proof stresses which implies compromised accracy in the important strain range <.2. In view of Constraint #1 stated in the Introdction, Olsson s approach has not been adopted in this report. However, it may prove appropriate for applications concerned mainly with large strains. data A wide range of tests has been sed to develop the fll-range stress-strain relation, inclding copon tests on astenitic, dplex and ferritic stainless steel alloys. To cover the practical range of proof stress and n-vales, the test data incldes copons ct from annealed plate as well as cold-formed sections (rectanglar hollow sections (RHS), circlar hollow sections (CHS) and channels sections). The data is smmarised in Table 1. Thirteen tests were performed on astenitic alloys (UNS34, UNS343, UNS3163), for on dplex alloys (UNS3183), and two on ferritic alloys (UNS43, 3Cr12). The vales of n range from 4.45 to 12.2, as shown in Table 1. The vales of nondimensional proof stress (e=.2 /E ) range from.14 to.37. Several references sed for the experimental data did not inclde vales of initial modls (E ) or proportionality stress (.1 ). In these cases, the vales were determined from the stress-strain crves. In cases where the n-parameter was not presented, the vale was calclated sing Eqn. 3. Stress-strain crve expression In view of Constraint #1 mentioned in the Introdction, the stress-strain crve is chosen as a standard Ramberg-Osgood crve for stresses p to the.2% proof stress, = +.2 for. 2. (9) E.2 In developing a model for the part of the stress-strain crve between the.2% proof stress and the ltimate tensile strength ( ), it is noted that the stress-strain crve in this range is similar in shape to the initial part of the stress-strain crve p to the.2% proof stress, as shown in Fig. 3. This observation sggests a linear transformation of the stress and strain and the se of the Ramberg-Osgood expression (Eqn. 1) in the following form, = + for >.2.2 E p where and are the transformed strain and stress (see Fig. 3b), defined as.2 n m (1) = (11) =.2. (12) The initial modls to the crve (E.2 ) is also the tangent modls of the stress-strain crve at the.2% proof stress, as shown in Fig. 3. By reqiring continity in slope at.2, E.2 is obtained from Eqn. 9 as d / d, =.2 5

7 E E.2 =. (13) 1 +.2n / e In adopting Eqn. 1, the proof stress ( p ) is taken as the transformed ltimate tensile strength ), ( =.2 (14) and accordingly, the plastic strain (p) is the transformed ltimate plastic strain ( ), p = /. (15).2 E Stainless steel alloys are generally dctile and so negligible error is made by approximating the transformed ltimate plastic strain by the total ltimate strain, p. (16) The exponent (m) is obtained by trial and error sing the stress-strain crves reported in the references smmarised in note (b) of Table 1. Recognising that the exponent is dependent on the ltimate tensile strength in relation to the.2% proof stress, the following expression was obtained,. 2 m = (17) The fll-range stress-strain crve can be written ot in fll as follows: n +.2 for.2 E.2 = m (18) for >.2 E.2.2 where E.2 and m are given by Eqns 13 and 17 respectively. Figres 4, 5 and 6 show typical comparisons of the stress-stain crves obtained sing Eqn. 18 with experimental data for astenitic, dplex and ferritic alloys respectively. The complete set of crves for the 19 tests listed in Table 1 are contained in Appendix A. The agreement between the test and proposed fll-range stress-strain crves is generally excellent, while the Ramberg-Osgood crves extended past the.2% proof stress become increasingly inaccrate with strain, as shown in Figs 4-6. The agreement is particlarly good for the UNS343 alloy, as shown in Fig. 4. The copon test on UNS43 alloy condcted by Korvink and van den Berg (1993) was only reported for strains p to.7, as shown in Fig. 6. The agreement is good in this strain range. The agreement for the (dplex) UNS3183 is reasonable althogh the proposed crve is higher than the test crve immediately after the.2% proof stress, as shown in Fig. 5. The discrepancy is a conseqence of the slope (E.2 ) of the Ramberg-Osgood crve determined at the.2% proof stress which is too high. p Expressions for and The expression for the fll-range stress-strain crve (Eqn. 18) involves three parameters (E,n,.2 ) for.2 and two additional parameters (, ) for >.2. In many sitations, the vales of and may not be available or may not be achievable experimentally, as in the testing of compression copons. To cater for these sitations, eqations are developed in this section for the determination of and in terms of n and e, where e is the nondimensional eqivalent yield stress given by Eqn. 4. 6

8 The experimental data is that contained in Table 1 agmented by the reslts given in a report by the Steel Constrction Institte (SCI, 1991) and reports by the Rand African University (van der Merwe et al. 1986, van der Merwe and van den Berg 1987). These reports do not contain complete stress-strain crves and cold not be sed for deriving a fllrange expression for the stress-strain crves, as described in Section 4. The SCI report details 227 tension and compression copon tests on astenitic (UNS343, UNS3163) and dplex (UNS3183) alloys, while the Soth African reports detail tension and compression tests on ferritic UNS43 stainless steel and weldable 12% chromim containing corrosion resisting steel, poplarly know as 3Cr12, which is closely related to the ferritic alloy class. 288 tests are contained in the Soth African reports for varios thicknesses and direction of loading (longitdinal and transverse). Only the mean vales of the reslts for each alloy, thickness and direction of loading have been sed in this report, adding a frther 12 tests to the database. The British and Soth African experimental data is smmarised in Appendix B. Evidently, the.2% proof stress approaches the ltimate tensile strength when increased by cold-forming, as is commonly fond in astenitic alloys. This sggests that a relationship may exist between the ratio.2 / and the.2% proof stress. Accordingly, the ratio (.2 / ) is plotted against the nondimensional proof stress (e), as shown in Fig. 7. The graph indicates a linear relationship when exclding the ferritic alloys. A line of best fit throgh the test data for astenitic and dplex alloys prodces the following eqation,.2 = e (astenitic and dplex alloys). (19) The ferritic alloys (inclding 3Cr12) generally have larger n-vales than astenitic and dplex alloys. Hence, their stress-strain crves have sharper knees which explain the higher vales of (.2 / ) for given vale of e, as shown in Fig. 7. To accont for the inflence of n, the following expression for.2 / has been obtained, e = (all alloys). (2) 1.375( n 5) Figre 8 shows the experimental vales of (.2 / ) plotted against the approximate vales given by Eqn. 2. The data points are shown with solid markers and are not biased towards a particlar alloy. However, they have greater scatter compared to the data points based on Eqn. 19 which are shown with open markers in Fig. 8. Eqation 2 is therefore less accrate than Eqn. 19 for astenitic and dplex alloys bt is more generally applicable. Finally, an expression is soght for determining the ltimate tensile total strain ( ). Recognising that for.2, the ltimate tensile strain is plotted against the ratio of.2% proof stress to ltimate tensile strength, as shown in Fig. 9. There is significant scatter in the plot, as cold be expected given the generally large variability in vales of ltimate tensile strain. It is also not clear whether the ltimate tensile strain qoted in the references were the niform elongation at the ltimate tensile strength, as has been assmed, or the total strain after fractre inclding local elongation in the area of necking. The line of best fit can be closely approximated by,. 2 = 1. (21) as shown with a solid line in Fig. 9. The data points are not biased towards a particlar alloy and no attempt has been made to explore a possible relationship between and the n- parameter. 7

9 With Eqns 2 and 21 at hand for determining and, the fll-range stress-strain crves can be obtained from Eqn. 18 for given vales of E,.2 and n. To assess the effect of the variability associated with Eqns 2 and 21, stress-strain crves have been determined for the combinations of and shown in Tables 2 and 3 respectively. In all cases, the Ramberg-Osgood parameters were taken as (E =2 GPa,.2 =4 MPa, n=6), and the reference vales of ( =675 MPa, =.48) were determined sing Eqns (2,21). In Table 2, the ltimate tensile strength ( ) is changed by ±1% and ±2% while keeping =.48 constant. Conversely, in Table 3, the ltimate tensile strain ( ) is changed by ±2% and ±4% while keeping =675MPa constant. These changes in ltimate tensile strength and strain are representative of the largest differences between test data and the vales of and determined sing Eqns 19 and 2 respectively, as shown in Figs 8 and 9. The stress-strain crves reslting from the vales of and given in Tables 2 and 3 are shown in Figs 1 and 11 respectively. The changes in stress at a strain of 2% are shown in the 4 th colmns of Tables 2 and 3. It follows from Table 2 that for the chosen vales of (E,.2,n), a redction of 2% in leads to a 7.1% decrease in (=2%). According to Table 3, a redction of 4% in leads to a 2.7% increase in (=2%). Since these deviations in and represent the maximm deviations of the test data, it can be conclded that the expressions given by Eqns 2 and 21 are likely to prodce stress-strain crves with a maximm error of abot 7% in stress at a strain of 2%, which for many applications is a likely pper bond to the ltimate limit state strains. Conclsions An expression has been derived (Eqn. 18) for the complete stress-strain crve for stainless steel alloys. The expression involves the conventional Ramberg-Osgood parameters (E,.2, n) as well as the ltimate tensile strength ( ) and strain ( ). It has been shown to prodce stress-strain crves which are in good agreement with tests over the fll range of strains p to the ltimate tensile strain. Expressions are also derived for the ltimate tensile strength ( ) and strain ( ) in terms of the Ramberg-Osgood parameters, see Eqns 2 and 21. The expressions are generally in reasonable agreement with experimental data. The maximm deviations observed are of the order of 2% for the ltimate tensile strength ( ) and 4% for the ltimate tensile strain ( ). It is shown that a deviation in of 2% prodces a maximm error in stress of 7.1% at a strain of 2% for a typical stainless steel alloy. Likewise, a deviation in of 4% prodces a maximm error in stress of 2.7% at a strain of 2%. It can be conclded that the maximm variability associated with sing Eqns 2 and 21 leads to a maximm error on the stress of the order of 7% at a strain of 2%. By sing Eqns 2 and 21 to determine ( ) and ( ), the fll-range stress-strain crve can be obtained directly from the Ramberg-Osgood parameters (E,.2, n). This reslt is particlarly sefl for the design and nmerical modelling of stainless steel strctral members and elements where the stress-strain crve is specified in terms of the Ramberg- Osgood parameters, sch as in the Astralian, American and Soth African specifications for stainless steel strctres. 8

10 References ASCE, (1991), Specification for Cold-formed Stainless Steel Strctral Members, ANSI/ASCE-8, American Society of Civil Engineers, New York. AS/NZS4673, (21), Cold-formed Stainless Steel Strctres, Standards Astralia, Sydney. Brns, T and Bezkorovainy, P, (21), Bckling of Stiffened Stainless Steel Plates, BE (Honors) Thesis,, University of Sydney. Korvink, SA and van den Berg, GJ, (1993), Web Crippling of Stainless Steel Cold-formed Beams, Proceedings, SSRC Annal Technical Session. MacDonald, M, Rhodes, J and Taylor, GT, (2), Mechanical Properties of Stainless Steel Lipped Channels, Proceedings, 15 th International Specialty Conference on Cold-formed Steel Strctres. Eds RA LaBobe and W-W Y, University of Missori-Rolla, p Olsson, A., (21), Stainless Steel Plasticity Material Modelling and Strctral Applications, PhD thesis, Department of Civil and Mining Engineering, Lleå University of Technology, Sweden. Ramberg, W and Osgood, WR, (1941), Determination of Stress-strain Crves by Three Parameters, Technical Note No. 53, National Advisory Committee on Aeronatics, (NACA). Rasmssen, KJR and Hancock, GJ, (1993), Design of Cold-formed Stainless Steel Tblar Members. I: Colmns, Jornal of Strctral Engineering, ASCE, 119(8), p Rasmssen, KJR and Rondal, J, (1997), Strength Crves for Metal Colmns, Jornal of Strctral Engineering, ASCE, 123(6), p Rhodes, J, MacDonald, M and McNiff, W, (2), Bckling of Stainless Steel Colmns nder Concentric and Eccentric Loading, Proceedings, 15 th International Specialty Conference on Cold-formed Steel Strctres. Eds RA LaBobe and W-W Y, University of Missori-Rolla, p SABS, (1997), Strctral Use of Steel. Part 4: The Design of Cold-formed Stainless Steel Strctral Members, The Soth African Brea of Standards, Pretoria. SCI, (1991), s on Stainless Steel Materials, Report No. SCI-RT-251, Steel Constrction Institte, London. Talja, A and Salmi, P, (1995), Design of Stainless Steel RHS Beams, Colmns and Beamcolmns, VTT Research Note 1619, Technical Research Centre of Finland, Espoo. Van der Merwe, P, van den Berg, GJ, and Marshall, V, (1986), Experimental Stress-strain Crves for Cold-rolled 3Cr12 Steel Sheets, Internal Report No. MD-21, Department of Civil Engineering, Rand Afrikaans University, Jly. Van der Merwe, P, and van den Berg, GJ, (1987), Experimental Stress-strain Crves for Cold-rolled Type 43 Steel Sheets, Internal Report No. MD-36, Department of Civil Engineering, Rand Afrikaans University, Agst. 9

11 Alloy a Sorce b Form c E.1.2 e n m f GPa MPa MPa MPa 1 UNS34 1 RHS UNS34 1 RHS UNS34 1 RHS UNS34 1 RHS UNS34 1 RHS UNS34 1 RHS UNS34 2 Ch e UNS34 3 P UNS343 4 RHS g.51 g UNS343 4 RHS UNS343 4 CHS g.51 g UNS343 4 CHS UNS P UNS P UNS P UNS P UNS P UNS43 6 P d.48 e Cr12 6 P d.38 e a) UNS34 AISI34 ENV1.431; UNS343 AISI34L ENV1.436; UNS3163 AISI316L ENV1.4436; UNS3183 ENV Dplex 225; UNS43 AISI43 ENV1.416; UNS415 3Cr12 ENV1.43 b) 1 Talja & Salmi (1995); 2 McDonald et al. (2); 3 Olsson (21); 4 Rasmssen & Hancock (1993); 5 Brns & Bezkorovainy (21); 6 Korvink & van den Berg (1993) c) RHS rectanglar hollow section; CHS circlar hollow section; Ch channel section; P plate or sheet d) Ultimate tensile strength estimated sing Eqn. 2. e) Ultimate total strain estimated sing Eqn. 21. f) The parameter m is obtained sing Eqn. 17. g) Compression test. The vales of and are assmed eqal to the vales for the corresponding tensile tests. Table 1. Mechanical properties 1

12 % change in (=2%) % change in (=2%) (MPa) (MPa) =.48, E =2 GPa,.2 =4 MPa, n=6 Table 2: Effect of change in % change in (=2%) % change in (=2%) (MPa) =675 MPa, E =2 GPa,.2 =4 MPa, n=6 Table 3: Effect of change in 11

13 E Ramberg-Osgood Crve Figre 1. Typical stress-strain crve for stainless steel and Ramberg-Osgood approximation. (, t ) t ) ( 1 Tre Stress 2 ( 2, 2 t ) 2 Engineering Strain () Figre 2. Stress-strain crve in terms of tre stress, and comparison with Olsson s model. 12

14 E.2 (, ) 1 E.2 1 (.2,.2 ) 1 E (a).2 (b) a) initial - crve b) fll - crve Figre 3. Initial and fll stress-strain crves. 1 ( ) 8 (MPa) Figre 4. Stress-strain crves for UNS343 alloy. #9, see Table 1 for sorce. 13

15 1 8 (MPa) Figre 5. Stress-strain crves for UNS3183 alloy. #15, see Table 1 for sorce. 6 4 (MPa) Figre 6. Stress-strain crves for UNS43 alloy. #18, see Table 1 for sorce. 14

16 = (n-5) Astenitic Dplex Ferritic e Figre 7..2 / vs e. (The ferritic alloy test reslts are not inclded in the regression fit shown). (.2 ) test = e = e (n-5) +1% +2% -2% -1%.2 (.2 ) = ( test.2 ) theoretical (.2 ) theoretical Figre 8. (.2 / ) test vs (.2 / ) theoretical 15

17 % +2%.6.4 = Astenitic Dplex Ferritic -4% -2% Figre 9: vs (.2 / ) 16

18 6 Ramberg-Osgood (MPa) 81 (+2%) 743 (+1%) (-1%) 54 (-2%) Figre 1: Effect of change in 6 Ramberg-Osgood (-4%).326 (-2%) (+2%).571 (+4%) Figre 11: Effect of change in 17

19 Appendix A: Fll-range Stress-strain Crves This appendix contains comparisons of measred stress strain crves with stress-strain crves obtained sing Eqn. 18. The test nmbers given in the figre captions refer to Table 1. Where the fll or large parts of the stress-strain crve was reported, comparisons are shown for the fll and initial parts of the crve. The first six measred stress-strain crves (Figs A.1-A.6) are obtained from Talja and Salmi (1995). The proposed crves in the same figres have been prodced sing the Ramberg-Osgood parameters (E,.2, n) also given in Talja and Salmi (1995). However, for s #3, 4 and 5, the Ramberg-Osgood parameters and stress-strain crves were not obtained from the same tests (althogh from nominally identical specimens) which probably explains the discrepancies seen in Figs A.3 and A.4. There is also some dobts abot the Ramberg- Osgood parameters given in Talja and Salmi (1995) for s #1 and 2 in that the stress-strain crves do not intercept the.2% proof stress as reqired. However, despite these ncertainties, the shape of the proposed crves generally matches well the measred stressstrain crves, as shown in Figs A.1-A.6. 18

20 8 6.2 (MPa) Figre A.1. Stress-strain crves for UNS34 alloy. #1, (Talja & Salmi (1995), copon RHS 1a-ST-1N). 8 6 (MPa) Figre A.2. Stress-strain crves for UNS34 alloy. #2, (Talja & Salmi (1995), copon RHS 1a-ST-1W). 19

21 6 4 (MPa) Figre A.3. Stress-strain crves for UNS34 alloy. #3, (Talja & Salmi (1995), copon RHS 2-ST-3N). 6 4 (MPa) Figre A.4. Stress-strain crves for UNS34 alloy. #4, (Talja & Salmi (1995), copon RHS 2-ST-3W). 2

22 6 4 (MPa) Figre A.5. Stress-strain crves for UNS34 alloy. #5, (Talja & Salmi (1995), copon RHS 3a-ST-2N). 6 4 (MPa) Figre A.6. Stress-strain crves for UNS34 alloy. #6, (Talja & Salmi (1995), copon RHS 3a-ST-2W). 21

23 1 8 (MPa) Figre A.7. Stress-strain crves for UNS34 alloy. #7, (McDonald et al (2), copon W). 8 ( ( )) 6 (MPa) Figre A.8. Initial stress-strain crves for UNS34 alloy. #7, (McDonald et al (2), copon W). 22

24 6 4 (MPa) Figre A.9. Stress-strain crves for UNS34 alloy. #8, (Olsson (21), pp. 122 Fig. 5.6 ). 6 ( ) 4 (MPa) Figre A.1. Initial stress-strain crves for UNS34 alloy. #8, (Olsson (21), pp. 122 Fig. 5.6 ). 23

25 1 8 (MPa) Figre A.11. Stress-strain crves for UNS343 alloy. #9, (Rasmssen & Hancock (1993), Copon T1-SHS ). 8 ( ) 6 (MPa) Figre A.12. Initial stress-strain crves for UNS343 alloy. #9, (Rasmssen & Hancock (1993), Copon T1-SHS ). 24

26 8 6 (MPa) Figre A.13. Initial stress-strain crves for UNS343 alloy. #1, (Rasmssen & Hancock (1993), Copon C1-SHS ). 25

27 8 6 (MPa) Figre A.14. Stress-strain crves for UNS343 alloy. #11, (Rasmssen & Hancock (1993), Copon T1-CHS ). 6 4 (MPa) Figre A.15. Initial stress-strain crves for UNS343 alloy. #11, (Rasmssen & Hancock (1993), Copon T1-CHS ). 26

28 8 6 (MPa) Figre A.16. Initial stress-strain crves for UNS343 alloy. #12, (Rasmssen & Hancock (1993), Copon C1-CHS ). 27

29 6 ( ) 4 (MPa) Figre A.17. Stress-strain crves for UNS316 alloy. #13, (Olsson (21), pp. 123, Fig. 5.7 ). 6 (MPa) Figre A.18. Initial stress-strain crves for UNS316 alloy. #13, (Olsson (21), pp. 123, Fig. 5.7 ). 28

30 1 ( ) 8 (MPa) Figre A.19. Stress-strain crves for UNS3183 alloy. #14, (Olsson (21), pp. 123, Fig. 5.8 ). 1 8 (MPa) Figre A.2. Initial stress-strain crves for UNS3183 alloy. #14, (Olsson (21), pp. 123, Fig. 5.8 ). 29

31 1 8 (MPa) Figre A.21. Stress-strain crves for UNS3183 alloy. #15, (Brns & Bezkorovainy (21), copon LT2 ). 1 8 (MPa) Figre A.22. Initial stress-strain crves for UNS3183 alloy. #15, (Brns & Bezkorovainy (21), copon LT2 ). 3

32 12 ( ) 1 8 (MPa) Figre A.23. Stress-strain crves for UNS3183 alloy. #16, (Brns & Bezkorovainy (21), copon TT1 ). 1 8 (MPa) Figre A.24. Initial stress-strain crves for UNS3183 alloy. #16, (Brns & Bezkorovainy (21), copon TT1 ). 31

33 12 ( ) 1 8 (MPa) Figre A.25. Stress-strain crves for UNS3183 alloy. #17, (Brns & Bezkorovainy (21), copon TT2 ). 1 8 (MPa) Figre A.26. Initial stress-strain crves for UNS3183 alloy. #17, (Brns & Bezkorovainy (21), copon TT2 ). 32

34 6 4 (MPa) Figre A.27. Stress-strain crves for UNS43 alloy. #18, (Korvink & van den Berg (1993), Copon Type 43 ). 4 3 (MPa) Figre A.28. Stress-strain crves for UNS43 alloy. #19, (Korvink & van den Berg (1993), Copon Type 3Cr12 ). 33

35 Appendix B: Copon Data Appendix B.1 smmarises the test data contained in the report by the Steel Constrction Institte (SCI, 1991). Appendix B.2 smmarises the test data contained in the reports by van der Merwe et al. (1986) and van der Merwe & van den Berg (1987) from Rand Afrikaans University. The data are the mean vales given in the reports. 34

36 Alloy: 34L Longitdinal Tension (LT) Appendix B.1: SCI Copon Data Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LT LT LT LT1R LT4R LT1R LT2R LT3R LT4R LT5R LT6R LT LT LT Average Standard deviation Coefficient of variation Transverse Tension (TT) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm2/s) MPa MPa MPa % GPa TT TT TT TT TT TT TT TT1R TT3R TT4R TT TT TT TT TT TT TT Average Standard deviation Coefficient of variation

37 Alloy: 34L Longitdinal Compression (LC) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC Average Standard deviation Coefficient of variation Transverse Compression (TC) Specimen t l. rate s.2 s1. s elong. E n s.1/s.2 (mm) (N/mm2/s) MPa MPa MPa % GPa TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC Average Standard deviation Coefficient of variation

38 Alloy: 316L Longitdinal Tension (LT) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LT LT LT LT LT1R LT4R LT LT LT1R LT2R LT3R LT4R LT5R LT6R LT7R Average Standard deviation Coefficient of variation Transverse Tension (TT) Specimen t l. rate s.2 s1. s elong. E n s.1/s.2 (mm) (N/mm2/s) MPa MPa MPa % GPa TT TT TT TT TT TT TT TT TT1R TT4R TT TT TT1R TT2R TT3R TT5R Average Standard deviation Coefficient of variation

39 Alloy: 316L Longitdinal Compression (LC) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LC LC LC LC LC LC LC LC LC LC1R LC2R LC LC LC LC LC LC LC LC LC LC Average Standard deviation Coefficient of variation

40 Alloy: 316L Transverse Compression (TC) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC Average Standard deviation Coefficient of variation

41 Alloy: 225 Longitdinal Tension (LT) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LT LT LT LT LT LT LT LT LT LT LT LT LT LT LT LT LT1R LT4R LT7R Average Standard deviation Coefficient of variation

42 Alloy: 225 Transverse Tension (TT) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT1R TT4R TT7R Average Standard deviation Coefficient of variation

43 Alloy: 225 Transverse Compression (TC) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC Average Standard deviation Coefficient of variation

44 Alloy: 225 Longitdinal Compression (LC) Specimen t l. rate s.2 s 1. s elong. E n s.1 /s.2 (mm) (N/mm 2 /s) MPa MPa MPa % GPa LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC LC Average Standard deviation Coefficient of variation

45 Appendix B.2: Soth African Copon Data Alloy a Sorce b Form c E.1.2 e n m d GPa MPa MPa MPa P P P P P P P P Cr12 8 P Cr12 8 P Cr12 8 P Cr12 8 P a) UNS43 AISI43 ENV1.416, UNS415 3Cr12 ENV1.43 b) 7 van der Merwe & van den Berg (1987); 8 van der Merwe et al. (1986) c) P plate or sheet d) The parameter m is obtained sing Eqn