Implications from the Poliak–Jonas criterion for the construction of flow stress models incorporating dynamic recrystallization

Dynamic recrystallization (DRX) processes are widely used in industrial hot working operations, not only to keep the forming forces low, but also to control the microstructure and final properties of the workpiece. According to Poliak and Jonas, the onset of DRX can be detected from an inflection point in the strain hardening rate as a function of flow stress. Various models are available that predict the evolution of flow stress from incipient plastic flow to steady-state deformation in the presence of DRX, but their consistency with the criterion of Poliak and Jonas has not been investigated. This work analyzes the conditions that a flow stress model incorporating DRX has to fulfill to be consistent with the criterion of Poliak and Jonas. As the most important inconsistency, it is found that a model might suffer from insufficient differentiability at the critical point. For all models that use a classical JMAK equation for the DRX kinetics, it is shown that the Avrami exponent must exceed a value of 3. If the Avrami exponent is at most 3, a kink may develop in the strain hardening rate, and the second derivative criterion is violated. For DRX kinetics based on nucleation and growth rates that are functions of time, criteria are derived that ensure consistency with the criterion of Poliak and Jonas. DRX kinetics that are consistent with the second derivative criterion are put forward, drawing upon kinetics proposed by Cahn for transformations that originate at grain boundaries. Finally, a minimal model that is consistent with the second derivative criterion is formulated.