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.