ABSTRACT
Consider a two-stage thermomechanical loading, as illustrated schematically in Figure 19.3. Let SI, SII, SIII denote the principal values of the 2nd Piola-Kirchhoff stress, and suppose that SIII=0. In the first stage, with the temperature held fixed at T0, the stresses are applied proportionally well into the plastic range. The center of the yield surface moves along a line in the (S1, S2) plane, and the yield surface expands as it moves. In the second stage, suppose that the stresses S1 and S2 are fixed, but that the temperature increases to T1 and then to T2 and T3. The plastic strain must increase, thus, the center of the yield surface moves. In addition, strain hardening tends to cause the yield surface to expand, while the increased temperature tends to make it contract. However, in this case, thermal softening must dominate strain hardening, and contraction must occur since the center of the yield surface must move further along the path shown even as the yield surface continues to “kiss” the fixed stresses SI and SII.
