Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm

Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified Metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions.