Fig. 1. True stress-true strain experimental data of the quasi-static tests at different temperature
Then, still assuming a multiplicative hardening function like eq. (2) but now discarding any assumption about uncoupling of variables, the experimental values of the thermal softening are derived at different instants of the tests by calculating\({S=\sigma}_{\text{Eq}}\left(\varepsilon_{\text{True}},T\right)/\sigma_{\text{Eq}}\left(\varepsilon_{\text{True}},T_{\text{Room}}\right)\). The resulting softening values are then related to the corresponding current values of strain and temperature, so that a general two-variables function \(S\left(T,\varepsilon\right)\) is then derived as a best-fit of such experimental data associated in triplets of the kind \(T,\varepsilon,S\).
The equivalent stress-strain functions at all temperatures, for calculating the above softening values, are derived from each experiment by correcting the respective true curve through the MLR function15.
The bestfit function\(\text{\ S}\left(T,\varepsilon\right)\) is plotted in Fig. 2 and clearly shows a remarkable dependence of \(S\) on both \(T\) and \(\varepsilon\). The coupling of temperature and strain is frequently neglected in the literature, but for materials like the A2-70 steel it is clear that it cannot be neglected.