L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL 57–64 STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL [TUDIJ EV ALUACIJSKE METODE ZA SUPER-PLASTI^NO DUPLEKS NERJA VNO JEKLO Li Jia 1 , Xueping Ren 1* , Kaifeng Zhang 2 1 School of Materials Science and Engineering, University of Science and Technology Beijing, 30 College Road, Haidian District, Beijing 100083, China 2 National Key Laboratory for Precision Heat Processing of Metals, Harbin Institute of Technology, 92 Xidazhi Street, Nangang District, Harbin 150001, China Prejem rokopisa – received: 2019-03-13; sprejem za objavo – accepted for publication: 2019-09-18 doi:10.17222/mit.2019.055 Aiming at the problem of long duration of superplastic tensile tests for materials with a large elongation, a new method for evaluating the superplastic properties of duplex stainless steel (DSS) is proposed. In this paper, relative values of stress difference D and stress variation factor f are introduced to predict the elongation, . Elongation can be predicted with the relational expression between D and as long as the specimen is stretched only by 500 % during the superplastic uniaxial tensile test. Factors affecting elongation include the thermo-mechanical treatment and superplastic-deformation conditions. For DSS2205, the change trend of f and influencing factors is similar to that of elongation and influencing factors. Keywords: duplex stainless steel, superplastic tension, evaluation method, stress variation factor Avtorji prispevka so, glede na te`ave z dolgotrajnim preizku{anjem super-plasti~nih materialov pod natezno obremenitvijo, predlagali novo metodo za ovrednotenje super-plasti~nih dupleks nerjavnih jekel (DSS). V tem ~lanku uvajajo relativne vrednosti napetostne diference D in faktor variiranja napetosti f za napoved raztezka . Raztezek se lahko napoveduje z izrazom med D in tako dolgo dokler se raztezek preizku{anca ne pove~a za 500 % med dolgotrajnim super-plasti~nim enoosnim nateznim preizkusom. Faktorja, ki vplivata na raztezek sta termomehanska obdelava in pogoji super-plasti~ne deformacije. Pri jeklu DSS 2205 je sprememba trenda f podobna trendu raztezka in vplivnim faktorjem. Klju~ne besede: dupleks nerjavno jeklo, super-plasti~no natezanje, evaluacijska metoda, faktor variiranja napetosti 1 INTRODUCTION Superplasticity has been formally defined as the capability of a fine-grained polycrystalline solid to exhibit a notable ductility over hundreds of percent of elongation at a high temperature and/or low strain rate. 1,2 The high ductility achieved through superplastic ma- terials bears industrial significance as it forms the basis for fabrication methods for producing complex shapes. The main parameters to evaluate superplasticity include elongation to failure, strain-rate sensitivity index, defor- mation homogeneity and activation energy. 3–5 Among these parameters, elongation and strain-rate sensitivity index, m, are the most important. 4 In general, elongation shows a monotonic increase with an increasing m-value. 6–10 However, several pa - pers 11–13 concerned with superplastic materials reported that the peak ductility does not necessarily occur at maximum m. G. Rai and N. J. Grant 11 elaborated that the maximum value of m ( 0.9) occurs at a strain rate of 10 –3 s –1 whereas elongation to fracture totals 700 %, in contrast to 1200 % obtained at a lower strain rate when the initial m is 0.08. H. Miyamoto et al. 12 showed that the total elongation of Fe-25Cr-7Ni-3Mo-0.14Ni reaches the maximum at an intermediate strain rate, whereas the m-value increases monotonously with an increasing strain rate. H. Zhang 13 concluded that "higher m-values alone do not necessarily lead to higher elongations." For different materials, errors in the monotonic increase of the m-value with the increasing elongation often occur. In ultrahigh-strength steels, martensite and carbides may cause internal-stress concentrations or cavities during a deformation, thus limiting the superplastic elongation at high m-values. 13 For example, the average m-value of 1.3CMnSiCr steels of AC (air cooled) samples equals 0.44 at 1023 K, whereas the average elongation amounts to 233 %. 13 However, duplex stainless steel (DSS) exhibits excellent superplasticity, and an elongation of more than 1000 % can be obtained under certain circumstances 14–17 at a low m-value. The maximum elongation value of 25Cr-6.5Ni-3Mo-0.14N 17 goes above 2000 %, whereas the calculated m-value is ~0.46. The peak elongation of Fe-24Cr-7Ni-3Mo-0.14N 18 of 750 % is obtained, where- as the strain-rate sensitivity is 0.37. Other researchers pointed out that m is strain dependent, thus a function of strain. 19,20 A. K. Ghosh 19 suggested that the terminal m, i.e., m near fracture, not the initial yield, would be expected to control the elongation at fracture. In Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 57 UDK 620.1:691.714.018.8:67.017 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 54(1)57(2020) *Corresponding author's e-mail: rxp33@ustb.edu.cn (Xueping Ren) addition, the measurements of this parameter are challenging, and varied results are observed from different test procedures. 10 Thereby, the m-value alone proves insufficient for evaluating the superplastic behaviour. Elongation is one of the most commonly used measures for characterizing superplastic properties. As most of the superplastic uniaxial-tension experiments are conducted at a constant crosshead speed, the test time is notably long for the materials with a high elongation. For a tensile specimen with a gage length of 10 mm, the test time is 10 4 s when the initial strain rate is 10 –3 s –1 , and the elongation is 1000 %; it reaches 10 5 s when the strain rate is 10 –4 s –1 . In addition, only the difference in the gage dimension results in a different elongation. Taking a Zn-22%Al alloy as an example, after the same treat- ment, the elongation of the alloy with a gage diameter of 5.994 mm ( 400 %) becomes much higher than that with a 0.1524-mm gage diameter ( 30 %) under the same deformation condition. 21 In the empirical sense, differences in the material preparation, test machine state, operation level and control capability influence superplastic elongation. Under the same deformation conditions, superplastic elongation still varies sub- stantially. Therefore, evaluation of the superplastic properties of materials based on elongation is subject to certain limitations. In view of the abovementioned problems, the para- meter that can reduce the time consumed and efforts devoted and enhance the accuracy and completeness needed for predicting the superplastic property of a given metal alloy is still required. For this purpose, our paper proposes relative values of stress difference at two points after the peak strain, D, to evaluate the superplasticity. The reciprocal of D, the stress variation factor, f,i s introduced. In addition, the relationships between f and elongations under different thermo-mechanical treat- ments and deformation conditions of DSS2205 are discussed. In this work, the stress–strain curve of the superplastic uniaxial tension with a fixed displacement rate is explored to determine D and f under different conditions. Elongation can be predicted based on f or D by stretching the samples only to a given elongation of 500 %, which greatly shortens the experimental time. 2 EXPERIMENTAL PART Table 1 lists the types and chemical composition of DSSs used in this study. Among these DSSs, 2205 and 2906 are used as experimental steels by the author of this paper. S1, S2, D1 and D2 were used by the Japanese scholar Y. Maehara. 22 Industrially cast, hot-rolled and solution-treated strips were laboratory cold-rolled to 2 mm. To examine the effect of the thermo-mechanical- treatment conditions on superplasticity, the solution treatment temperature and cold-rolled reduction ratio were varied. The as-received hot-rolled steel was solution treated at a temperature range of 1050–1350 °C for 30 min, followed by water quenching. The hot-rolled steel of different thicknesses was then cold rolled to 2-mm sheets with different reduction ratios ranging from 0 % to 85 %. Dog-bone-shaped tension specimens with a gage length of 10 mm, width of 6 mm and thickness of 2 mm were cut parallel to the rolling direction, using spark cutting, from the cold-rolled sheets. The specimens were strained isothermally at a constant crosshead speed. Tensile tests were carried out in a temperature interval of 850–1000 °C, at strain rates ranging from 5×10 – s –1 to 1.5×10 –3 s –1 . After reaching the selected testing tem- perature, the specimens were homogenized for (1, 2, 3, 5, 7, 10, 15, 20 and 30) min prior to applying the load in order to study the effect of the holding time on the superplasticity. 3 RESULTS AND DISCUSSION 3.1 Stress–strain curves of DSS The stress–strain curve for superplastic axial tension generally involves two forms, i.e., the true stress–strain curve and the engineering stress–strain curve. Figure 1 shows the two kinds of stress–strain curves for the super- plastic tension of DSS2205 at a solution temperature of 1200 °C, deformation temperature of 950 °C, strain rate of 1.5×10 –3 s –1 and cold-rolling reduction ranging from 0 % to 85 %. In the stress–strain curve, after the peak stress, the flow stress decreases until the final fracture. The inflection point mathematically refers to the point that changes the curve in the upward or downward direction. Intuitively speaking, the inflection point is the concave–convex boundary point of the curve. As ob- served on Figure 1, the largest difference between the two kinds of curves is the fact that the engineering stress–strain curves show the inflection point after the L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL 58 Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 Table 1: Types and chemical compositions of DSSs, (w/%) Steel Cr Ni Mo N C Si Mn Cu P S W Fe 2205 22.05 5.37 3.22 0.15 0.017 0.42 1.10 0.043 0.024 0.006 – Bal 2906 30.06 7.26 2.86 0.47 0.0064 0.25 0.53 0.52 – – – Bal S1 18.52 4.06 – 0.0094 0.0015 1.69 3.22 1.18 0.005 0.002 – Bal S2 18.77 3.96 – 0.00928 0.0015 1.73 3.42 1.20 0.005 0.002 – Bal D1 24.66 6.82 2.79 0.143 0.0017 0.48 0.85 0.46 0.025 0.001 0.28 Bal D2 22.88 10.52 – 0.0912 0.0005 3.22 0.79 – 0.003 0.001 – Bal peak strain, whereas the true stress-strain curves exhibit otherwise. This finding coincides with the uniaxial ten- sion of most superplastic DSSs; however, an inflection point also exists after the peak strain in certain true stress–strain curves. 23 Experience has shown that if an inflection point occurs on the stress–strain curve, the flow stress after the peak stress decreases slowly; otherwise, it drops rapidly. For a material without an inflection point on the engi- neering stress–strain curve, elongation is usually less than 200 %. Figure 2 shows examples of flow stress–strain curves of various steels cited in 22 . Figure 2 shows the absence of inflection points on the curves of S2 and D2 and their presence on the curves of S1 and D1. After passing the peak stress, the flow stress de- creases gradually until the final fracture of steels S1 and D1. However, a sudden stress decrease corresponding to the local necking is observed in steels S2 and D2. S1 and S2 exhibit poor ductility and can be regarded as non- superplastic materials under this condition. It can be used to assess whether a DSS is a superplastic material according to the inflection point after the peak strain on an engineering stress–strain curve; that is, if an inflection point exists on the curve, the DSS is superplastic; otherwise it can be regarded as a conventional one. Figures 1 and 2 reveal that the stress after the in- flection point decreases more slowly with a higher elongation than with a lower elongation. To describe the change rule of stress with strain more intuitively, the first derivative d /d is obtained for the stress–strain curve of Figure 1, and the obtained result is shown in Figure 3. The peak point appears where d /d = 0 and the inflec- tion point appears where d 2 /d 2 = 0, i.e., the first derivative is the extreme value. Figure 3a illustrates that for the true stress–strain curve, the first derivative d /d decreases with the L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 59 Figure 2: Engineering stress–strain curves of four DDSs (original data of DDS superplastic materials from Y. Maehara 22 ) Figure 1: Stress–strain curves of DSS2205 during superplastic uni- axial tension: a) true stress–strain curve, b) engineering stress–strain curve Figure 3: First-order derivative diagrams of stress–strain curves corresponding to Figure 1 (note: s.t. stands for solution treatment; d.c. stands for deformation condition; holding time is 5 min unless otherwise stated; the same below) increasing strain, whereas the slope of the curve varies notably under different conditions. When the elongation is higher, the curve after the peak strain decreases more slowly, indicating a better superplasticity of the material. After the peak strain, the discrimination degree of the d /d - curve under different cold-rolling reduction ratios becomes more notable with the increasing strain. This condition provides the possibility to evaluate the superplasticity of the material using the first derivative d /d at a certain strain after the peak strain. Given the lack of inflection point for the true stress–strain curve used, no extreme value exists on the first derivative curve. For the inflection point in the engineering stress–strain curve corresponding to Figure 1b,a ne x - treme value exists in the first derivative diagram shown in Figure 3b. The first derivative value first decreases with the strain and then increases, whereas the first derivative at the inflection point has its minimum value. A larger first derivative (i.e., a smaller absolute value) indicates a higher elongation. After the inflection-point strain, the discrimination degree of the d /d - curve under different cold-rolling reduction conditions also becomes notable. Owing to uncertain factors during superplastic uniaxial stretching, elongations differ under the same conditions as shown in Figure 4. Figure 4a depicts the two engineering stress–strain curves of DSS2205 deformed at 950 °C and an the initial strain rate of 1.5 × 10 –3 s –1 with the solution at 1200 °C and a cold-rolled reduction ratio of 85 %; Figure 4b depicts the two engineering stress–strain curves of DSS2205 deformed at 950 °C and the initial strain rate of 7.5 × 10 –4 s –1 with the solution at 1200 °C and a cold-rolled reduction ratio of 85 %. As observed from Figure 4, the elongations differ under the same thermo-mechanical treatment and deformation conditions, but the slope of the stress–strain curve d /d is roughly the same between the inflec- tion-point strain and 400 %. When the strain is higher than 400–500 %, the slope of the curve begins to change. In addition, for the samples with a high elongation, the peak stress is high, which may be related to the difference in the length of the uniform deformation zone; that is, a longer length of the uniform deformation zone denotes a higher superplastic elongation. 3.2 Evaluation of superplasticity with the stress diffe- rence Theoretically, the superplasticity of a material can be evaluated using d /d at a certain strain after the peak strain. However, in practical applications, the smooth- ness degree of stress–strain curves must be particularly high when obtaining the d /d - curve. Numerous factors affect the curve vibration during a tension test. Excessively artificial smoothing distorts the curve, thus increasing the accumulative error of d /d . Therefore, this paper proposes to evaluate the superplasticity by adopting a relative value of the stress difference, D, which can lower the standards for the smoothness of a curve and reduce the error caused by curve fluctuation. The Backofen equation is the most commonly used constitutive equation for describing superplastic flow characteristics: 16 = K m (1) where refers to the superplastic flow stress; denotes the strain rate; m represents the strain-rate sensitivity index; and K is a material constant. For the superplastic tension with a constant strain rate, the tensile speed (i.e., tester chuck speed) increases with the increasing strain. This condition requires precise control of the tensile speed of the testing machine, which is slightly more complex than the one under a constant tensile speed. Therefore, most of the superplastic tensile tests are carried out under constant tensile-speed con- ditions, and the strain rate decreases gradually during a deformation. According to the plasticity theory, the relation bet- ween the strain rate and the tensile speed under a con- stant tensile speed is given by the following Equation (2): L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL 60 Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 Figure 4: Engineering stress–strain curves with different elongations of DSS2205 under the same precondition and deformation condition (note: h represents the cold-rolling reduction ratio; the same below) () = + = + u l 0 0 11 (2) where corresponds to the strain; stands for the initial strain rate; l 0 signifies the original length of gage segment; and u 0 is the tensile rate. Substituting Equation (2) into Equation (1) and Equation (3) becomes obtainable: = + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ K m 1 (3) In the engineering stress–strain curve, two points (A and B) after the peak stress are selected: A and A , B and B are set to the engineering stress and engineering strain of points A and B, respectively. When the strain difference between points A and B is small, the m-value is assumed to change minimally within this range. According to Equation 3, the relative values of the stress difference between A and B , that is D (A,B) , can be expressed by Equation 4: D m () A, B AB A = − =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 1 1 (4) The stress–strain curves show that a smaller relative value of stress difference results in a higher superplastic elongation of the material. Equation 4 indicates that a larger m implies a larger relative value of the allowable stress difference and vice versa. The discrimination degree of the d /d – curve under different conditions becomes more notable with the increasing strain (Figure 3). To reduce the test time, the selected cut-off strain is as small as possible. Thus, the most formable strain range must be determined to accurately characterize the superplasticity. Considering the peak strain p as the strain zero point, two points (A, B) of the strain difference are selected. For example, in the engineering strain–stress curve, p = 30 %, A =6 0%a n d B = 110 %. Then, under the above assumptions, p =0% , A = 30 % and B =8 0% .T h e corresponding D (A,B) -value can be obtained by analysing the stress–strain curves. In order to test and verify the feasibility of the proposed parameter, the relationship between under various conditions mentioned in the experimental part and D (A,B) corresponding to different strains was investigated. It is particularly important to choose the strain values of A and B. Figures 5a, 5b, 5c L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 61 Figure 5: Relationships between relative values of the engineering-stress difference and elongation of DSS2205: a) A =5 0% , B = 100 %, b) A = 150 %, B = 200 %, c) A = 250 %, B = 300 %, d) A = 300 %, B = 350 % and 5d show the relationships between and D (50,100) , D (150,200) , D (250,300) , and D (300,350) , respectively. When the selected strains of A and B are larger, the relationship between and D (A,B) is more relevant. When A = 300 % and B = 350 %, there is a good correspondence between and D (A,B) . To teremine the relative difference between the engineering stress and true stress, the superscript e is added, that is, D e (A, B) . The relationship can be expressed with Equation (5). D e (, .e x p 300 350 5526 = − = =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + !"#$ 300 350 300 453 0155 . exp . − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + !"$ (5) In general, the peak strain of the engineering stress–strain curve of DSSs is less than 50 %. When A = 300 % and B = 350 %, the total cut-off strain reaches less than 500 %. Therefore, the superplastic tension with a constant tensile speed can be stretched only to 500 % and elongation is predicted in accordance with Equation 5, whereby the test time can be remarkably shortened. The peak strain in the true stress–strain curve is generally greater than the one in the engineering stress–strain curve. For example, the peak true strain of DSS2205 studied in this paper generally appears at around 100 %. By adopting the method mentioned above and analysing the relationship between the relative values of the true-stress difference and elongation when A = 50 % and B = 100 %, after the peak true strain is selected, a good correspondence between them is achieved (Figure 6). The relationship can be expressed with Equation (6). D e (, .e x p 50 100 2698165 0 = − = =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + %! 50 100 50 . exp . 323 0 034 − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + $!#& (6) Figure 7 shows the relationship between the relative values of the engineering stress difference and elong- ation of DSS2906 at A = 300 % and B = 350 %. The corresponding fitting formula can be expressed with Equation (7): D e (, . exp . 300 350 6 081 1 = − = =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + %!$" 300 350 300 193 0121 exp . − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ’!% (7) Comparing Equations (5), (6), and (7), the forms of the fitting formulas are the same, but the corresponding coefficients differ. To determine these coefficients, se- veral sets of elongation values and corresponding stress differences are needed, and then obtained with the nonlinear-curve-fitting method in Origin Software. 3.3 Evaluation of superplasticity with stress-variation factors As D (A,B) decreases with the increasing ,1 / D (A,B) is proposed for the evaluation of superplasticity. Further- more, in the following description, 300 /( 300 - 350 )i s referred to as the stress-variation factor and it is represented by f. Figure 8 shows the variation rule of the stress-variation factor and measured elongation of DSS2205 with the solution temperature, cold-rolling reduction, deformation temperature, strain rate and holding time. With an increase in the deformation tem- perature, and f increase when deformed at a strain rate of 1.5×10 –3 s –1 with a solution temperature of 1300 °C and a rolling reduction of 85 % as seen on Figure 8a. Figure 8b shows that and f of DSS2205 with an 80-% rolling reduction first decrease and then increase with an increase in the solution temperature when tested at 950 °C with a strain rate of 1.5×10 –3 s –1 , and the mini- mum value is obtained at 1150 °C. Figure 8c shows that the relationships between , f and strain rate are para- bolic when the sample is deformed at 950 °C, with a solution temperature of 1200 °C and rolling reduction of 85 %. Figure 8d indicates that that the relationships between , f and holding time are wavy when the sample L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL 62 Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 Figure 7: Relationship between relative values of the engineer- ing-stress difference and elongation of DSS2906 Figure 6: Relationship between relative values of the true-stress difference and elongation of DSS2205 is deformed at 950 °C, with a strain rate of 1.5×10 –3 s –1 , solution temperature of 1300 °C and rolling reduction of 85 %. Figure 8e demonstrates that and f increase with an increase in the rolling reduction when the sample is deformed at 950 °C, with a strain rate of 1.5×10 –3 s –1 and solution temperature of 1200 °C. As depicted in Figure 8, the trends of f and , as a whole, are almost the same under pre-treatment and superplastic-deformation conditions. Therefore, f can be used to predict the change rule of elongation under specific deformation conditions. 4 CONCLUSIONS The stress–strain curves of DSS2205 and DSS2906 during a superplastic deformation are investigated. The main conclusions of the present study include the following: • Whether a material is superplastic can be assessed with respect to whether an inflection point occurs after the peak strain of the engineering stress–strain curve; that is, a superplastic material has an inflection point and a conventional one is without an inflection point. • When applying superplastic uniaxial tension with a constant tensile speed and the sample is stretched to 500 %, the material elongation can be predicted in accordance with the change rule of D e (,) 300 350 – . This condition may lead to a significant reduction in the total experiment time for a material with a high elon- gation. • For DSS2205, the stress-variation factor and elon- gation show a good consistency with the changes in the thermo-mechanical treatment and superplastic- deformation conditions. Acknowledgment This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 5 REFERENCES 1 W. Cao, C. Huang, C. Wang, H. Dong, Y . Weng, Dynamic reverse phase transformation induced high-strain-rate superplasticity in low carbon low alloy steels with commercial potential, Sci. Rep., 7 (2017) 1, 9199, doi:10.1038/s41598-017-09493-7 2 H. Masuda, T. Kanazawa, H. Tobe, E. Sato, Dynamic anisotropic grain growth during superplasticity in Al-Mg-Mn alloy, Scripta Mater., 149 (2018), 84–87, doi:10.1016/j.scriptamat.2018.02.021 3 D. H. Avery, W. A. Backofen, Structural basis for superplasticity, Trans. ASM, 58 (1965), 551 4 G. Kumaresan, K. Kalaichelvan, Multi-dome forming test for deter- mining the strain rate sensitivity index of a superplastic 7075Al alloy sheet, J. Alloys Compd., 583 (2014) 3, 226–230, doi:10.1016/ j.jallcom.2013.08.194 5 M. Sagradi, D. Pulino-Sagradi, R. E. Medrano, The effect of the microstructure on the superplasticity of a duplex stainless steel, Acta Mater., 46 (1998) 11, 3857–3862, doi:10.1016/S1359-6454(98) 00087-1 6 O. A. Kaibyshev, Superplasticity in Metals and Ceramics, Mater. Sci. Forum, 357–359 (2001), 73–82, doi:10.4028/www.scientific.net/ MSF.357-359.73 7 D. A. Woodford, Strain-rate sensitivity as a measure of ductility, Trans. ASM, 62 (1969), 291–293 8 G. J. Davies, J. W. Edington, C. P. Cutler, K. A. Padmanabhan, Superplasticity: a review, J. Mater. Sci., 5 (1970) 12, 1091–1102, doi:10.1007/BF00553897 9 T. G. Langdon, The mechanical properties of superplastic ma- terials, Metall. Trans. A, 13 (1982) 5, 689–701, doi:10.1007/ BF02642383 10 A. K. Ghosh, C. H. Hamilton, Influences of material parameters and microstructure on superplastic forming, Metall. Trans. A, 13 (1982) 5, 733–743, doi:10.1007/BF02642386 L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64 63 Figure 8: Variation rule for f and with different pre-treatment and deformation conditions for DSS2205 11 G. Rai, N. J. Grant, On the measurements of superplasticity in an Al-Cu alloy, Metall. Trans. A, 6 (1975) 2, 385–390, doi:10.1007/ BF02667294 12 H. Miyamoto, T. Mimaki, S. Hashimoto, Superplastic deformation of micro-specimens of duplex stainless steel, Mater. Sci. Eng. A, 319 (2001), 779–783, doi:10.1016/S0921-5093(01)01015-2 13 H. Zhang, B. Bai, D. Raabe, Superplastic martensitic Mn-Si-Cr-C steel with 900 % elongation, Acta Mater., 59 (2011) 14, 5787–5802, doi:10.1016/j.actamat.2011.05.055 14 H. W. Hayden, S. Floreen, P. D. Goodell, The deformation mecha- nisms of superplasticity, Metall. Trans., 3 (1972) 4, 833–842- 15 G. Frommeyer, H. Hofmann, J. Löhr, Structural superplasticity at high strain rates of super duplex stainless steel Fe-25Cr-7Ni-3Mo- 0.3N, Steel Res. Int., 74 (2003) 5, 338–344, doi:10.1002/srin. 200300195 16 S. X. Li, X. P. Ren, X. Ji, Y. Y. Gui, Effects of microstructure changes on the superplasticity of 2205 duplex stainless steel, Mater. Des., 55 (2014) 6, 146–151, doi:10.1016/j.matdes.2013.09.042 17 Y . Maehara, Y . Ohmori, Microstructural change during superplastic deformation of -ferrite/austenite duplex stainless steel, Metall. Mater. Trans. A, 18 (1987) 4, 663–672 18 S. H. Hong, Y . S. Han, Phenomena and mechanism of superplasticity of duplex stainless steels, Met. Mater., 6 (2000) 2, 161–167 19 A. K. Ghosh, R. A. Ayres, On reported anomalies in relating strain- rate sensitivity (m) to ductility, Metall. Trans. A, 7 (1976) 10, 1589–1591 20 Y . Maehara, High strain rate superplasticity of a 25 wt pct Cr-7 wt pct Ni-3 wt pct Mo-0.14 wt pct N duplex stainless steel, Metall. Trans. A, 22 (1991) 5, 1083–1091 21 W. A. Backofen, I. Turner, D. H. Avery, Superplasticity in an Al-Zn alloy, Trans. ASM, 57 (1964), 980–990 22 Y. Maehara, Superplastic deformation mechanism of / duplex stainless steels, Trans. ISIJ, 27 (1987) 9, 705–712 23 K. Tsuzaki, H. Matsuyama, M. Nagao, M. Tadashi, High-strain rate superplasticity and role of dynamic recrystallization in a superplastic duplex stainless steel, Mater. Trans. Jim., 31 (1990) 11, 983–994, doi:10.2320/matertrans1989.31.983 L. JIA et al.: STUDY ON THE EV ALUATION METHOD FOR SUPERPLASTICITY OF DUPLEX STAINLESS STEEL 64 Materiali in tehnologije / Materials and technology 54 (2020) 1, 57–64