Physically-based constitutive equation for prediction of the flow stress of microalloyed steel during hot deformation

The constitutive equations based on the dislocation mechanics are applicable at relatively low temperatures. Nevertheless, considering the diffusion processes is necessary for modeling the hot flow stress. In other words, the softening effects of dynamic recovery and recrystallization should be taken into account. In the present work, a modified Zerilli–Armstrong constitutive equation for predicting the hot flow stress of a microalloyed steel was proposed, in which the effects of hardening and softening phenomena were contemplated. It was shown that the original equation is not able to model the softening part of flow curves related to dynamic recrystallization and it was clarified that the constants of the model should be modified for appropriate consideration of the effects of dynamic recovery. On the other hand, it was found that the hardening and softening stages should be separated and the peak strain can be utilized into the flow stress formula. While retaining the general form of the original Zerilli–Armstrong model, the developed constitutive relation was able to appropriately predict the hot flow stress. Conclusively, this constitutive model can be considered as a simple and viable one for modeling the flow stress of steels.