Super-austenitic Various constitutive models viz. physically based

Super-austenitic stainless steels are special grades of austenitic stainless steels alloyed with higher concentrations of chromium and nickel in addition to the presence of relatively higher contents of nitrogen, molybdenum, and copper 1–3.  Due to its excellent combination of alloying elements, these steels often possess superior mechanical properties and greater corrosion resistance compared to ordinary grades of austenitic stainless steels which facilitates its broad applicability in thermonuclear and chemical industries. 4–7. Thermo-mechanical processing is widely employed for manufacturing of complex parts and shapes of the alloy that are used for various industrial applications 8–11. The evaluation of forming load has cardinal importance in forming industries for designing various forming components. The forming load often depends upon flow behavior, geometry of the deformation and friction between workpiece and die interface 12–16. Therefore, development of constitutive relations for predicting elevated temperature flow behavior is important.  The constitutive flow behavior of polycrystalline alloys is often found to be very complex and largely depends on various processing parameters like temperature, strain, strain-rate 17–20. Various constitutive models viz. physically based 12,21–30, phenomenological 13,19,31–39 and empirical/semi-empirical 2,40–42 models have been developed by researchers in the past for predicting flow behaviour of different grades of metals and alloys following hot deformation. Amongst the physically based/phenomenological relationships, Johnson-Cook (JC) 31 and Zerilli-Armstrong (ZA) 21 models are widely employed in various commercial metal forming simulation software.  The JC model considers only the individual effect of processing parameters viz. isotropic hardening, strain rate hardening and thermal softening 31. Although, JC model has been widely employed in the flow prediction, it often fails when there is a change in flow mechanism 32,43,44. On the other hand, ZA model was often preferred for low-temperature deformation below 0.6 Tm , where Tm is the melting temperature of the alloy 45,46. ZA model is often giving better prediction than JC model as couples the effect of processing parameters such as temperature and strain-rates 12,32,44. However, this model is predominantly not suitable for prediction of flow stress at higher temperatures (i.e. >0.6Tm) and lower strain rates 47. In view of this, a modified ZA (M-ZA) model was proposed by Samantaray et al. 32 to make it suitable for predicting flow behavior in high temperatures and wide strain-rate domain. This was accomplished by neglecting athermal part of flow-stress and incorporating coupled effects of strain-rate and temperature as well as strain and temperature 32. The M-ZA model has been successfully applied by various researchers for a various grades of materials 48–50.The objective of the present work is to formulate a suitable phenomenological constitutive model to predict high temperature flow behaviour of a super-austenitic stainless steel in a wide range of TMP domain with good accuracy and reliability. Before contemplating on developing a new model, we have first assessed the applicability of the JC and M-ZA model to predict the flow behaviour of the studied alloy. The individual and coupled effects of various process parameters viz. strain, strain rate and temperature on the flow behaviour of the alloy under investigation have been carefully evaluated. Based on this observation and evaluation, a novel revised ZA (R-ZA) model has been proposed and the predictability of the proposed model has been critically compared with the existing JC and M-ZA models