Evaluation of Plasticity and Creep Parameters From Tensile Stress–Strain Data for a Range of Strain Rates S. Ooi1,2 | R. P. Thompson2 | T. W. Clyne2 1Ovako Corporate R&D, Hofors, Sweden | 2Department of Materials Science, University of Cambridge, Cambridge, UK Correspondence: T. W. Clyne (twc10@cam.ac.uk) Received: 29 December 2025 | Revised: 26 February 2026 | Accepted: 3 March 2026 Keywords: creep | stainless steel | tensile testing ABSTRACT A novel methodology is presented for evaluation of plasticity and creep parameters via analysis of experimental data obtained during tensile testing with several different strain rates. This offers a number of advantages over conventional creep testing. It involves the use of a simple numerical model, which can be implemented using a spreadsheet. The procedure has been applied to a standard stainless steel (SS301) at 700°C. At this temperature, the tensile response of this alloy (within the ‘quasi-static’ range of strain rate) is ‘creep-affected’. In addition, conventional creep testing has been carried out, with different fixed loads (correspond- ing to nominal stresses around and above the yield stress). Using the Miller–Norton equation to capture creep strain histories, the outcomes of these tests have been converted so that they correspond to those expected with a fixed true stress. Very close agreement is observed between the creep parameter values obtained with the two approaches. 1 | Introduction This section provides background to the work, including an over- view of plasticity (time-independent) and creep (time-dependent) permanent deformation of metals, how they are characterised and how they may affect tensile testing. 1.1 | Analytical Representation of Plasticity and Creep Several analytical expressions (‘constitutive laws’) have been pro- posed for representation of the (instantaneous) progression of plastic deformation. The Voce equation [1] is used in the current work. A set of (3) Voce parameter values defines a true stress – true (plastic) strain relationship, although this is readily converted to a ‘nominal’ (or ‘engineering’) stress–strain curve, using the standard relationships. This can only be done up to the peak in this nominal curve (at the Ultimate Tensile Stress, UTS), which is where necking is expected to start. Several representations have also been proposed for the time- dependent progression of straining under a sustained load (creep). There is often an initial period during which the creep rate is higher – usually referred to as ‘primary’ creep. This is commonly taken to correspond to a period during which rear- rangement and motion of dislocations occurs (as a prelude to the establishment of a steady state). Such primary creep is likely to be more significant in the ‘high stress/short time’ regime. Constitutive laws have been proposed that capture primary creep and its transition towards a steady state [2, 3]. The one used in the current work is that of Miller–Norton: εc = Cσnt m+ 1ð Þ m+ 1 (1) in which C is a constant (MPa−n s−(m+ 1)) and m is a dimension- less constant (that captures the time dependence). The creep strain rate after any given time is given by differentiation: dεc dt =Cσntm (2) This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2026 The Author(s). Advanced Engineering Materials published by Wiley-VCH GmbH. Advanced Engineering Materials, 2026; e70775 1 of 9 https://doi.org/10.1002/adem.70775 Advanced Engineering Materials www.aem-journal.com RESEARCH ARTICLE https://orcid.org/0000-0001-8415-0214 https://orcid.org/0000-0003-2163-1840 mailto:twc10@cam.ac.uk http://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1002/adem.70775 http://www.aem-journal.com https://doi.org/10.1002/adem.70775 The value ofm is typically around −0.7: the strain rate thus tends to approach a constant value after prolonged periods – for example, 1000−0.7 has a value of about 8 10−3, while 2000−0.7 is about 5 10−3 and 3000−0.7 is about 3.7 10−3. Such behaviour is often exhibited experimentally. As with all constitutive laws, these are empirical relationships. Real experimental data are unlikely to conform exactly to them. Nevertheless, with suitable selection of parameter values, agreement may be very good. It is a common observation that the creep strain rate exhibits an exponential dependence on the stress. The value of the exponent (n) is often taken to provide information about the operative creep mechanism. A low value (�1–2) is expected if this is primar- ily the diffusive redistribution of atoms. This is common when the creep takes place over long periods, with the stress being rela- tively low. However, if dislocations are involved, with the time dependence arising from climb, then higher values of n (�3–10) are likely to be obtained. This is more likely in the ‘high stress/short time’ regime (in which tensile testing commonly occurs). Some more general observations should perhaps be made regard- ing the links between analytical representation of the behaviour, the mechanisms responsible and the microstructure of the metal. Under the conditions of interest – i.e. at relatively high temper- atures and over timescales that are at least not instantaneous, several micro-mechanisms are likely to be operative. These include dislocation glide, diffusion, dislocation climb, dislocation cross-slip, grain boundary sliding, etc. They all have their own sensitivities to temperature and time, and they are likely to contribute to the overall straining on different timescales. Various microstructural features, such as grain size, fine scale precipitates, grain boundary structures, crystallographic texture, and impurity content, are likely to affect the response. Many publications [4–8] cover such issues. However, while separating these various effects, and their roles in the overall response, is virtually impossible, this is not necessary. All that is needed is for the behaviour of the case (metal/temperature combination) concerned to be reliably represented via a combination of two expressions, one with and one without a dependence on time. As noted above, it is possible that the values of certain parameters in these expressions, such as the stress exponent in Equation (2), could provide pointers about the operative mechanisms. In gen- eral, however, their complexity is such that this is likely to be quite limited in scope. True values of stress, strain and strain rate must be used in all such constitutive laws. The difference between nominal (or engineering) and true values is thus important when accurately quantifying and modelling the behaviour. The term nominal (rather than engineering) is used in the current work. Conversion between true and nominal values of stress and strain is carried out via standard equations, which are based on conservation of volume. 1.2 | Creep Testing Many reviews of creep are available [9–14]. It is conventionally characterised by measuring the strain as a function of time, using a range of values for applied load (nominal stress), which remains constant throughout the test. Such tests present several difficulties. One is that, as deformation proceeds, and the sec- tional area reduces, the true stress rises. It is possible to maintain a constant true stress (by continually adjusting the load), but this is not common. Furthermore, the behaviour may become unstable during such tests (‘tertiary creep’ [15–20]), leading to localised damage such as cavitation, necking and rupture. Other approaches to obtaining creep characteristics have been employed. These include uniaxial loading in compression [21, 22], avoiding problems of necking and rupture. However, other types of dimensional instability can occur. Also, the effects of friction between platens and sample can introduce uncertainty. 1.3 | Creep-Affected Tensile Testing Rapid creep can affect conventional tensile testing. The main out- come is a nominal stress–nominal strain relationship. Ideally, this is independent of time, which does not usually figure in reported outcomes. In practice, if creep is significant, the stress–strain curve may depend on the strain rate (within the ‘quasi-static’ strain rate regime). This term indicates that ‘dynamic’ effects (at very high strain rates) are not expected to occur. There is no clear definition of the quasi-static regime, but it broadly covers the range from, say, 10−6 s1 to 10−1 s−1. The strain might be taken up to around 10%, so the correspond- ing test duration ranges from 1 s up to 100,000 s (almost 30 h). It is difficult (with standard tensile testing equipment) to complete a tensile test in less than 1 s, while test durations of many hours or days are also unusual. If creep is significant, stress levels will tend to be lower with slower imposed strain rates, since longer periods are available during which creep straining can take place. For such ‘creep- affected’ tests, a stress–strain curve may be tagged with the strain rate that was used. However, this is far from satisfactory, since it neither represents a genuine (time-independent) plasticity relationship nor does it give any clear indication of the creep characteristics. This remains true even if several stress–strain curves are obtained, each with an associated strain rate. The effect of creep on tensile stress–strain curves (for metals) can vary considerably. Two recent publications cover this, one [23] concerning ‘creep-affected’ cases and the other [24] ‘creep-dominated’ conditions. For the former, the nominal stress–strain curve retains its conventional shape. It usually exhibits a yield stress, followed by work hardening and neck for- mation (expected to initiate at the peak in a nominal stress–strain plot). Imposing a slower strain rate may cause a slight reduction in the apparent yield stress and also reduce the work hardening rate, often pushing the peak to higher strains. Necking is still likely to initiate at the (nominal) strain level of the peak. However, for the latter category (rapid creep), the effect may be more substantial [24], with the nominal stress–strain curve having a peak at low strain, followed by a progressive fall in stress. This early peak does not correspond to the onset of necking and indeed the sample may not neck until much higher strains are reached (if at all). Moreover, the stress level at the peak may be considerably lower with slower strain rates. The real (time-independent) yield stress may never be reached during such tests, with all of the permanent straining arising from creep. Incorporation of creep into simulation of a tensile test is in principle straightforward. Moreover, provided there is no interest in the onset of necking, it can be carried out for a single volume element. It can thus be implemented using a standard 2 of 9 Advanced Engineering Materials, 2026 spreadsheet, rather than requiring a commercial finite element model. A schematic presented in a previous publication [23] shows how the three contributions to the strain (elastic, plastic and creep) develop as the test progresses (with a given strain rate). With a slower strain rate, more time is spent at all stress levels, giving higher creep strains at those levels. The elastic and plastic strain contributions, on the other hand, are independent of time, and hence of strain rate. However, such a model must be implemented numerically. While the Voce equation gives the (creep-free) stress–strain curve directly, the increments of creep strain (in a given time interval) predicted by the Miller–Norton equation increase progressively as the stress rises. Many experimental studies [23, 25–38] have investigated how creep affects outcomes of tensile tests carried out with different strain rates. It is widely recognised that it should be possible to extract creep characteristics from such sets of tests. This is attractive, since they are in general easier to carry out than conventional constant load creep tests, which must be done with several different loads, are often complicated by the true stress changing throughout the test and may become unstable and be terminated prematurely by rupture. However, as outlined above, there are two effects that are rarely incorporated into such treatments. One is that primary creep is often important, rather than just secondary (steady state) creep. The other is that creep at and above the yield stress is likely to strongly affect the stress–strain curve. Conventional creep testing is carried out with the stress kept below the yield stress, so information about (primary) creep rates at higher stress levels is rarely available. Furthermore, many such investigations have not taken into account the need to work in true levels of stress, strain and strain rate. 2 | Materials and Test Procedures In this section, the experimental procedures involved in the work are briefly described. 2.1 | Material The testing programme is based on a single well-established material–301 stainless steel, which has been tested at a single temperature. Since this material is single phase over the complete range of temperature, with no precipitate formation, there should be no complications from properties changing significantly with time during holding at high temperature. Also, oxide formation is expected to be minimal. 2.2 | Tensile Testing The 301 stainless steel, supplied in the cold-rolled condition, had the following measured composition (wt%): 0.12C, 1.26Si, 1.12Mn, 0.03P, 0.003S, 16.5Cr, 0.03Mo, 6.6Ni, and 0.084N. It was solution-annealed at 1060°C for 30min, followed by water quenching. The tensile specimens were prepared by electric discharge machining. The gauge surfaces were ground to 600 grit. The sample dimensions and grip arrangement are shown in Figure 1. The testing set-up was based on an Instron 8800 Series servo- hydraulic machine, with an 8800MT Controller and a 100 kN load capacity. Strains within the gauge length were measured with a clip gauge having an initial separation between the knife edges of 12 mm. Displacement speeds of 10 mm/min, 1 mm/min, 0.1 mm/min and 0.03 mm/min were used. The nominal strain rate does not scale exactly with the displacement speed, since straining outside of the gauge length varied between cases. In fact, the strain rate during a particular test is not quite constant (due to creep effects). However, corresponding nominal strain rates (from clip gauge readings as a function of time) were approximately 7 10−3 s1, 7 10−4 s1, 6 10−5 s1 and 2 105 s1. Tests were run up to about 15%-20% strain, so their durations varied between about 15 s and 45 minutes. Tensile testing was carried out at 700°C. A resistance furnace was used for heating, with the temperature measured and controlled FIGURE 1 | Sample dimensions and tensile testing setup. Advanced Engineering Materials, 2026 3 of 9 by a thermocouple in contact with the specimen gauge length. The specimen temperature was maintained within ±2°C. A pre- load of 400 N was applied prior to heating, to prevent buckling and accommodate the thermal expansion of specimen and grips. The target temperature was typically reached within 1 h, after which tensile testing was started once thermal stabilisation had been achieved. 2.3 | Creep Testing Tests were also carried out, using the same temperature, loading arrangement and sample dimensions as for the tensile testing, aimed at obtaining information more directly about the creep characteristics. These involved a short initial period during which the test was carried out as for a tensile test, followed by an extended period (about 6 h) with a fixed load (after it had reached a prede- termined level under displacement control). Four (nominal) stress levels were employed in each case, around and above the notional yield stress. The main objective was to capture the behaviour using an analytical law (covering both primary creep and the tran- sition towards a steady state). The Miller–Norton formulation was employed for this purpose – see §1.1. However, there is an important issue when using such fixed load testing with this objective, particularly when the work is oriented towards the early parts of the strain–time curves –, i.e. towards primary creep – and interest centres on the behaviour at rela- tively high stresses. The true stress increases progressively during such testing. For example, if the nominal stress is set at 100MPa, the true stress will have risen to 110MPa by the point where the nominal strain has reached 10%. If the creep stress exponent (n) has a value of, say, 5, then the creep strain rate would be expected to be higher than it ‘should be’ at this point, by a factor of (1.1)5 –, i.e. about 1.61. Large errors are thus expected to arise in attempt- ing to fit a creep law to such curves (unless the operation is confined to very low levels of strain, which will clearly make it inaccurate). This problem was tackled by converting each experimental strain–time curve (for a fixed nominal stresses) to one that would have been obtained if the true stress level had been held constant. Details are given in §4.2. 3 | Outcomes of Tensile Testing In this section, experimental results are presented for the tensile tests carried out over a range of strain rates. The model for these tests and the methodology for using it to obtain both plasticity and creep parameter values are described and applied to the experimental data. 3.1 | Tensile Testing with Several Strain Rates The plots in Figure 2 show stress–strain curves for the 4 displace- ment speeds used. (Corresponding nominal strain rates are noted in §2.2.) Repeat runs gave a high level of reproducibility. Rather than attempting to distil “averaged” curves from a set of such repeats, single curves are used in these figures and for compari- son (below) with corresponding modelled data. The nominal stress–strain curves are also shown as true values, with conversion having been carried out using the standard equations. This was only done up to the peak in the nominal curves (where the onset of necking is expected). It may be noted that neither nominal nor true strain rates were constant during these tests. As described in §2.2, nominal strain rates are affected by creep, while the true strain rate falls as the gauge length increases. However, this is not a problem when comparing exper- imental stress–strain curves with modelled ones, since the model simply mimics the conditions during the experiment. Regarding the curves in Figure 2, first, the strain rate clearly does have a significant effect, over this (supposedly quasi-static) range. Second, for this range of strain, the differences between true and nominal plots are substantial. (In general, only for strains up to about 2% can the two be regarded as very similar.) Finally, the onset of necking (expected around the peak in the nominal curve) has largely been avoided in these runs (and indeed it was not physically apparent in any of the samples). These curves were used to guide the choice of stress levels for the creep tests, with the aim of studying the behaviour over a stress range that extends above the notional yield stress. 3.2 | Modelling of Tensile Testing to Obtain Plasticity and Creep Parameters The procedure for predicting tensile stress–strain curves involves stepping in time and reading in the experimental nominal stress (load) and nominal strain (clip gauge reading). The Voce equation is used to establish the plastic strain (from the true stress, after it reaches the yield stress). The Miller– Norton equation is used to calculate the increments of creep strain that arise during each time increment. The elastic strain is also calculated after each step (as the ratio of the true stress to the Young’s modulus, E). The algorithm is shown as a flow chart in Figure 3. (This is similar to, but not the same, as one in a previous publication [23]). Extraction of the best fit Voce and M-N parameter values was carried out by systematically varying them so as to optimise FIGURE 2 | Tensile stress–strain curves obtained using with four different strain rates, each plotted as nominal stress v. nominal strain and as true stress v. true strain. 4 of 9 Advanced Engineering Materials, 2026 the agreement between model and experiment (for all of the strain rates). A goodness of fit parameter is needed to direct this convergence operation. The one used here was similar to one defined in a previous publication [39]. It was the (normalised) sum of the squares of the residuals, S. This was obtained by step- ping in (experimental) increments of true stress and summing the differences between corresponding measured and modelled true strains. S= P N i= 1 εi,TM − εi,TE � � 2 Nε2av,E (3) where εi,TM is the ith value of the modeled strain, εi,TE is the corresponding experimental (target) value and εav,E is the average experimental value. The value of N was the number of experi- mental data points for the run concerned. This varied between runs, but was typically of the order of a hundred up to a few thou- sand. A value of S was obtained for each of the runs (strain rates) and the average (Sav) taken as the overall goodness of fit for the set of parameter values concerned. Convergence can be implemented in various ways, such as via an automated Nelder–Mead procedure [39–41]. However, in the present work, it was carried out via simple manual sweeps, utilising the characteristics of changes in features of the stress–strain curves that result from altering individual Voce and M-N parameter values. For example, the predicted rate of creep increases on raising both C and n, but a larger value of n accelerates creep to a greater extent at higher stress levels. Since each simulation was implemented via a spreadsheet, the overall computation time was very short each time and conver- gence typically required something like 10–20 iterations. The parameter S is a positive dimensionless number, with a value that ranges upwards from 0 (corresponding to perfect fit). As a generalisation, modelling that captures the material response reasonably well (over the range of strain rates) should lead to a solution (set of parameter values) for which Sav is no greater than, say, about 10−2. This effectively constitutes a health check on the solution – if, for example, no solution can be found giving a value smaller than, say, 10−1, then this suggests that there can only be limited confidence in the inferred set of values. This could be due to experimental deficiencies and/or an inability to capture the behaviour well with the constitutive laws being used. The outcome of this operation is shown in Figure 4. Agreement between the experimental stress–strain curves (converted to true) and those obtained via this simple model is quite close, with the value of Sav being 1.3 10−2. The optimised sets of parameter val- ues are shown in the figure. The pure Voce plot (no creep) con- stitutes an upper envelope for the set of curves and is shown for information. It is noticeable that some creep is occurring even with the fastest strain rate, particularly at the higher levels of stress. The sensitivity of the modelled curves to the parameter values is high. For example, it’s estimated that the inferred value of n is accurate within ±�0.1. Progress of the convergence operation is illustrated in Figure 5, which shows the values of the 6 parameters after each iteration, and the corresponding values of Sav. 4 | Outcomes of Creep Testing Experimental results are presented here for creep testing with several fixed loads. These results were used to obtain the creep characteristics in a standard way, although, as described in the introduction, cases in which primary creep is important can present complications, as can the need to work with true values of stress and strain. FIGURE 3 | Flow chart for obtaining a predicted (true) stress–strain relationship for a tensile test carried out at a fixed displacement rate, using specified Voce and Miller–Norton parameter sets. (The experimen- tal outcome is the nominal stress and nominal strain values after a series of time increments, i.e. σN(t) and εN(t)). FIGURE 4 | Comparison between experimental tensile stress–strain curves (with 4 different strain rates) and corresponding modelled curves (obtained using the optimised sets of Voce and M-N parameter values shown). A plot of the Voce equation alone, for these parameter values, is also shown. Advanced Engineering Materials, 2026 5 of 9 4.1 | Raw Strain-Time Data Constant load tests were carried out using four different load levels. As described above, these loads were designed to cover a stress range extending above the yield stress (as indicated approximately by the outcomes of the tensile tests). This is unusual for conventional creep testing, during which the stress is not normally allowed to exceed the yield stress, but it is essen- tial to understand how creep affects tensile testing. Ideally, creep tests are carried out with the true stress held constant, but this requires continued real time interactive control over the applied load and in practice is rarely done. However, the current work is focussed on a regime in which the changing value of the true stress is likely to introduce large errors into the operation of fitting the data to a creep law, unless a ‘correction’ of some sort is carried out. This correction has been described previously [23], but for completeness it is also outlined below. 4.2 | Correction of Creep Strain History Data As noted above, it is important for present purposes to fit Miller– Norton curves to experimental plots that are based on a fixed true stress. These were derived from the experimental data (obtained with fixed nominal stress) by using Equation (2) for the strain rate as a function of time. At any point along a strain–time curve, the relationship between the measured strain rate with a stress σ1 and what it would have been if the stress had been σ2 is thus dεc dt � � 2 = dεc dt � � 1 σ2 σ1 � � n (4) Applying this to the relationship between the measured strain rate with an applied nominal stress and the corresponding (‘corrected’) strain rate, which would have been produced if the true stress had been held at the same value, leads to FIGURE 5 | Progression of the convergence operation, showing (a) the Voce parameter values, (b) theM-N parameter values and (c) the values of the goodness of fit parameter. FIGURE 6 | Measured nominal strain history for a fixed nominal stress of 225MPa, together with ‘corrected’ curves obtained as described in §4.2, for two different values of n. These curves represent the true strain histories expected if the true stress had been held at 225MPa. FIGURE 7 | Comparison between experimental (‘corrected’) strain histories, with 4 different stress levels, and corresponding (best-fit) Miller–Norton curves (obtained using the set of parameter values shown). 6 of 9 Advanced Engineering Materials, 2026 dεc dt � � corr = dεc dt � � meas σN σT � � n (5) The value of σT at any point in time is obtained from the nominal stress, σN, and the nominal strain, εN, at that point, using the standard relationships. Since this will lead to σT being greater than σN, Equation (5) will give a corrected strain rate that is lower than the measured one. The overall procedure is thus to step in time, use the measured strain rate to obtain the corrected one and then obtain the complete (true) strain as a function of time by cumulatively adding these increments of strain created during each time interval. This is a straightforward operation, which was carried out using a standard spreadsheet. It does require a value for n, so an iterative procedure is needed between this operation and that of fitting the curves to a Miller–Norton set. This approach to ‘correcting’ a nominal strain history obtained with a fixed nominal stress (to a true strain history with fixed true stress) is quite general, although it does depend on the creep behaviour conforming to a Miller–Norton relationship. An outcome is shown in Figure 6 (for σN= 225MPa). Relatively high strains were created almost throughout this test, so the ‘correction’ creates a substantial change. The corrected curves shown in this figure correspond to two different values of n. As expected, the corrections are more significant for the larger value. It may, however, be noted that a relatively high value (perhaps� 10) may be appropriate in the ‘high stress’ regime. Furthermore, even for the lower value (of 5), attempting to fit Miller–Norton parameter values to the original curve, or even to the curve created by simply converting the strains to true values, would differ signifi- cantly from the set that would emerge using the ‘corrected’ curve. A point to note about the nominal curve (and also the directly converted true curve) in Figure 6 is that the gradient (strain rate) rises towards the end of the test. Such an increase is often seen in strain–time curves and is commonly referred to as ‘tertiary creep’. It can arise from damage development, such as internal cavitation. However, it may be due solely to the rise in true stress. In this particular case, the fact that the n= 5 ‘corrected’ curve (which turned out to be approximately the appropriate case – see below) does show a slight increase in gradient towards the end may be indicative of some genuine ‘tertiary’ behaviour. This would be con- sistent with the fact that this sample ruptured at the end (�7,500 s), whereas no rupture or necking occurred with the tests conducted at lower stress levels. In such a case, it may be appropriate to discard the latter part of the curve when making comparisons with Miller–Norton plots, although this was not actually done here. 4.3 | Derivation of Creep Parameters The procedure used to obtain a set of Miller–Norton parameter values was thus to convert the experimental strain histories (for the set of stress levels concerned) to ‘corrected’ ones, and then iteratively converge on a best-fit M-N set (using a similar procedure to that applied to the tensile test data). The outcome is shown in Figure 7, where a comparison is made between (corrected) experimental strain histories and those corresponding to the best fit set of M-N parameter values. The value of n giving optimal consistency with the observed dependence on stress level is 4.6 in this case. The agreement is good, across the range of stress levels, with the value of the goodness of fit parameter (Equation (3)) being about 1.3 10−2. The creep characteristics are thus being well captured with this formulation. A comparison is shown in Table 1 between the val- ues obtained with the two types of test. While the sets of M-N parameters giving optimal fit are not quite identical, they are very similar. In particular, the two values of n are close (�4.6, within an error that appears to be about ±0.1). It is certainly unrealistic to aim for a precision any better than this. The main practical interest often lies in evaluating n, and it is expected to apply throughout such testing, even during long duration runs (in which the primary regime may be of limited interest). Obtaining its value from a series of short tests that is easier and simpler to carry out than those of conventional creep testing is an attractive prospect. The data presented here relate only to a single alloy and test temperature. Much more comprehensive testing of this type is evidently needed to explore capabilities and limitations of the methodology. Development of an automated convergence proce- dure is also likely to be helpful, perhaps leading to a software package that simply requires input of the sets of experimental (nominal) stress–strain curves. Creating a useful mainstream test methodology based on the work presented here would thus require a comprehensive research and development programme. 5 | Conclusions This study presents a novel procedure for obtaining both creep and plasticity characteristics via analysis of tensile test data for a range of (nominal) strain rates. Its usage is illustrated using data obtained for a standard stainless steel at a single tempera- ture (at which rates of creep are significant). The following conclusions can be drawn: 1. The experimental stress–strain curves have been well captured in a simple numerical model based on represen- tation of both plasticity (time-independent) and creep char- acteristics. This has been done using established constitutive laws – those of Voce and Miller-Norton, with the latter capturing both primary and secondary creep regimes. The model can be implemented using a standard spreadsheet, with very short computation times. TABLE 1 | Optimised sets of Miller–Norton and Voce parameters from the two types of test. Test type Miller–Norton parameter Voce parameter Goodness of fit parameter, Sav (-) C, MPa−n s−(m+ 1) n (-) m (-) σY, MPa σs, MPa ε0 (-) Tensile 3 10−14 4.7 −0.72 130 560 0.125 1.3 10−2 Creep 3.5 10−14 4.6 −0.73 — — — 1.3 10−2 Advanced Engineering Materials, 2026 7 of 9 2. Values of the parameters in the Voce and Miller–Norton formulations have been obtained by iteratively running the model until optimum agreement is reached between measured and modelled stress–strain curves. This can be done very quickly, with good levels of agreement being obtainable. The sensitivity of the predicted curves to the inferred parameter values is relatively high. Such an evaluation would normally be difficult to obtain for the plasticity characteristics and would require testing that is more time-consuming and problematic for the creep characteristics. 3. For the alloy and temperature concerned, conventional creep testing has also been carried out, using a set of fixed (nominal) stress levels around and above the yield stress. Values of the Miller–Norton parameters have been obtained using a similar approach to that applied to the ten- sile testing, although in this case there is no need for a numerical model (since the Miller–Norton formulation immediately gives the experimental outcome –, i.e. the creep strain as a function of time). It was, however, still necessary to iteratively change the values of the parameters until optimum agreement was reached. The set of parameter values obtained in this way was very similar to that from the tensile testing. 4. A key issue in carrying out these tests and modelling procedures concerns differences between nominal and true levels of stress and strain, which tend to be significant for most such testing. Analytical representations of plasticity and creep are always formulated in terms of true values, so experimental data must also be obtained in this form. Creep tests are normally carried out with fixed levels of nominal stress (i.e. constant load), so a procedure has been used here to convert the resulting strain histories to a form corresponding to conditions of constant true stress. Author Contributions S. Ooi: investigation, writing – review & editing, methodology, data curation, resources. R. P. Thompson: writing – review & editing, resources, software. T. W. Clyne: conceptualisation, writing – original draft, data curation, supervision, software, methodology. Acknowledgments Financial support for TWC has been provided by EPSRC, via Grant No. EP/I038691/1. Relevant support has also been received from the Leverhulme Trust, in the form of an Emeritus Fellowship (EM/2019- 038/4). The authors would like to thank Theodore Vassi (Outokumpu) for supplying the 301 stainless steel used in this study. SO acknowledges the cooperation of Dr. David Collins for hosting him at the Department of Materials Science and Metallurgy, University of Cambridge. Funding This study was supported by Engineering and Physical Sciences Research Council (grant EP/I038691/1), Leverhulme Trust (grant EM/2019-038/4). Conflicts of Interest The authors declare no conflicts of interest. Data Availability Statement Data will be made available on request. References 1. E. Voce, “The Relationship between Stress and Strain for Homogeneous Deformation,” Journal of the Institute of Metals 74 (1948): 537–562. 2. J. K. Solberg, “A Semi-Empirical Model for Stress-Relaxation including Primary and Secondary Creep Stages,” Journal of Materials Science 21 (1986): 630–636, https://doi.org/10.1007/bf01145534. 3. R. Sandström, “BasicModel for Primary and SecondaryCreep inCopper,”Acta Materialia 60 (2012): 314–322, https://doi.org/10.1016/j.actamat.2011.09.052. 4. S. Karthikeyan, G. B. Viswanathan, P. I. Gouma, V. K. 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Introduction 1.1. Analytical Representation of Plasticity and Creep 1.2. Creep Testing 1.3. Creep-Affected Tensile Testing 2. Materials and Test Procedures 2.1. Material 2.2. Tensile Testing 2.3. Creep Testing 3. Outcomes of Tensile Testing 3.1. Tensile Testing with Several Strain Rates 3.2. Modelling of Tensile Testing to Obtain Plasticity and Creep Parameters 4. Outcomes of Creep Testing 4.1. Raw Strain-Time Data 4.2. Correction of Creep Strain History Data 4.3. Derivation of Creep Parameters 5. Conclusions