Coupling of a crystal plasticity finite-element model with a probabilisticcellular automaton for simulating primary static recrystallization in aluminium

The paper presents a two-dimensional approach for simulating primary static recrystallization, which is based on coupling a viscoplastic crystal plast icity finite-element model with a probabilistic kinetic cellular automaton. The crystal plasticity finite-element model accounts for crystallographic slip and for the rotation of the crystal lattice during plastic deformation . The model uses space and time as independent variables and the crystal or ientation and the accumulated slip as dependent variables. The ambiguity in the selection of the active slip systems is avoided by using a viscoplasti c formulation that assumes that the slip rate on a slip system is related t o the resolved shear stress through a power-law relation. The equations are cast in an updated Lagrangian framework. The model has been implemented as a user subroutine in the commercial finite-element code Abaqus. The cellul ar automaton uses a switching rule that is formulated as a probabilistic an alogue of the Linearized symmetric Turnbull kinetic equation for the motion of sharp grain boundaries. The actual decision about a switching event is made using a simple sampling nonMetropolis Monte Carlo step. The automaton uses space and rime as independent variables and the crystal orientation an d a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through the mesh size, the grain boundar y mobility, and the driving force data. The coupling of the two models is r ealized by: translating the state variables used in the finite-element plas ticity model into state variables used in the cellular automaton; mapping t he finite-element integration point locations on the quadratic cellular aut omaton mesh; using the resulting cell size, maximum driving force, and maxi mum grain boundary mobility occurring in the region for determining the len gth scale, time step, and local switching probabilities in the automaton; a nd identifying an appropriate nucleation criterion. The coupling method is applied to the two-dimensional simulation of texture and microstructure evo lution in a heterogeneously deformed, high-purity aluminium polycrystal dur ing static primary recrystallization, considering local grain boundary mobi lities and driving forces.