Constitutive analysis in hot working

Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.