Large-strain cyclic response and martensitic transformation of austenitic stainless steel at elevated temperatures

Cyclic tension-compression tests were carried out for austenitic stainless steel (SUS304) at elevated temperatures. The significant Bauschinger effect was found in the obtained stress-strain curve. In addition, stagnation of deformation induced martensitic transformation was observed just after stress reversal until the equivalent stress reached the maximum value in the course of experiment. The constitutive model for SUS304 at room temperature was developed, in which homogenized stress of SUS304 was expressed by the weighed summation of stresses of austenite and martensite phases. The calculated stress-strain curves and predicted martensite volume fraction were well correlated with those experimental results.


Introduction
Austenitic stainless steel shows extensive workhardening even at large strain owing to the precipitation of hard α′-martensite phase by plastic deformation. The constitutive equations (e.g. Stringfellow et al [1]. and Geijselares et al. [2]) for an austenitic stainless steel with which martensitic transformation kinetics are incorporated were suggested. In the present study, large cyclic tension compression tests for an austenitic stainless steel (SUS304) were conducted at various temperatures (from 293 to 473K). The stress-strain curves as well as martensite volume fraction were measured during the deformation. From the obtained results, it was found that austenite phase show extensive workhardening at high temperature even though martensitic transformation did not take place. Additionally, stagnation of martensitic transformation due to the Bauschinger effect was found. The macroscopic constitutive model for the present material was proposed and it was found that the calculation results well predicted the stress-strain curves and martensitic volume fraction observed by the experiment at 293K.

Cyclic tension-compression test of austenitic stainless steel at elevated temperature
The material used for this study is an austenitic stainless steel type SUS304. The material was machined in the shape of tension-compression test specimen shown in Figure 1(a), and solution treated at 1223K for 5 minutes. Cyclic tension-compression apparatus is shown in Figure 1(b). A specimen was covered by the thermostatic chamber and specimen was warmed by the heaters installed in the

Constitutive model for austenitic stainless steel
Let us assume the stress of austenitic stainless steel σ is expressed by the following rule of mixture; ( 1 ) where subscripts m and a denote martensite and austenite, respectively, and f m is the volume fraction of martensite. The objective rates of martensite and austenite stresses are given as; where C e and C ep are the elastic and epasto-plastic tangent moduli, and  is the strain rate tensor.
A linear isotropic hardening model was assumed for martensite as; where m  and p m  are the equivalent stress and equivalent plastic strain of martensite, respectively, and Y m and H m are the material constants. By assuming the von Mises yield criteria and associative flow rule, one can have the constitutive relationship of martensite as the following equation.
On the other hand, we assumed Yoshida-Uemori kinematic hardening rule [3] for austenite phase since the strong Bauschinger effect was observed in cyclic test results. Similar to the case of martensite phase, von Mises yield criteria and associative flow rule were assumed then constitutive equation of austenite phase was derived as the following equation. ( 1 0 ) where α oc , β oc and n oc are material constants. It should be mentioned that the equation (10) is the empirical equation just to approximate the relationship between the martensite volume fraction and austenite stress obtained by the experiment. For an accurate model applicable to multiaxial stress state, further investigation such as biaxial tension with variety of stress ratio are essential. In addition to that, it was observed from the experiments that parameters in equation (10) could be different in tension and compression, therefore, α oc , β oc and n oc were determined from monotonic tension and compression tests separately, and the following assumptions were used for the subsequent calculations: i) when starting from tension, parameters for tension were used throughout calculation ii) when starting from compression, parameters for compression were used throughout calculation iii) for cyclic test with ±5% of strain, parameters for tension were used throughout calculation Material parameters used for the calculation are shown in Table 1 and 2.  Figure 2(a) and (b) are the experimentally obtained stress-strain curves and f m vs. plastic strain curves for each temperatures. The martensitic transformation becomes moderate with increase of test temperature. Since stress are almost the same below 8% of strain at any temperature, stress was not affected by temperature up to 353K. Therefore, one can conclude that the decrease in stress at large strain as the increase of temperature was caused by less precipitation of martensite which supposed to be harder than the austenite phase. Figure 3(a) and (b) are the comparisons of stress-strain and f m vs. plastic strain curves at 293K between experiment and simulation results, respectively. It is clear that the proposed model successfully predicted both stress-strain curve and martensite volume fraction, especially stagnation of martensitic transformation, were well predicted.

Conclusions
From the cyclic tension-compression tests for an austenitic stainless steel, we obtained the following findings: (i) deformation induced martensitic transformation would be minor at higher temperature, (ii) martensitic transformation stagnates due to the Bauschinger effect even if plastic strain accumulated. Based on the experimental observations, constitutive model for austenitic stainless steel was proposed. The calculated results well predicted both cyclic stress-strain curves and fm vs. plastic strain curves obtained from experiments.