Conditions for Consistent Implementation of Flow Stress Models Incorporating Dynamic Recrystallization into Finite Element Simulation Codes

Abstract

Dynamic recrystallization (DRX) is widely used in industrial hot working processes to control the microstructure and properties of the workpiece and to keep the forming forces low. For the analysis and design of metal forming processes powerful simulation methods, must notably the Finite Element (FE) method, have been developed. Various models are available that consider the coupled evolution of microstructure and flow stress during hot deformation processes. Some of these models have been implemented into FE codes and are widely available now. However, for the implementation of flow stress models incorporating DRX into an FE formulation, special smoothness requirements exist that are not automatically fulfilled by the available flow stress models. This work reviews some conditions that a flow stress model incorporating DRX has to fulfill in order to be consistently embedded into an FE code for large plastic deformation. A specific Sellars-type model is analyzed for consistency with these conditions. It is shown that the use of a classical JMAK equation for the DRX kinetics within these models is problematic for Avrami exponents smaller than or equal to 3, for which the flow stress model is not sufficiently smooth. DRX kinetics based on the work of Cahn are proposed to remedy the differentiability issues.