On the development of stage IV hardening using a model based on the mechanical threshold

A two state variable hardening law is developed that is capable of simulating stage IV hardening. It is based on a physically motivated dislocation density evolution equation originally intended for use in a detailed FEM analysis, where individual grains are modeled with numerous finite elements. The evolution equation contains a contribution from geometrically necessary dislocations (net/excess dislocations), which can be associated with the slip plane lattice incompatibility. FEM analyses show that slip plane lattice incompatibility evolves linearly with accumulated slip. This observation forms the basis for the evolution equation of the second state variable. Compression and tension of copper are simulated with a rate and temperature dependent viscoplastic polycrystal model, in which the developed hardening law is embedded. The model is capable of predicting the experimentally observed enhanced hardening of small grain sized materials. The material parameter estimates and the state variable initial conditions are obtained by solving an identification problem.