Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming

Construction metallic materials combine strength with formability. These features are obtained for heterogeneous microstructures with hard constituents dispersed in a soft matrix. On the other hand, sharp gradients of properties between phases cause a local fracture. Advanced models are needed to design microstructures with smoother gradients of their features. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness to equations describing the evolution of dislocations and grain size. The idea of the internal variable model with dislocation density and grain size being stochastic variables is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model. The loads as a function of time during compression and histograms of the grain size after deformation were measured in each test. Identification and validation of the model were performed. Finally, the developed model was applied to simulate selected industrial hot forming processes.