A three-dimensional multi-physics model of grain microstructure evolution with dislocation induced spontaneous grain nucleation

RWTH Publications (RWTH Aachen)

Abstract

The granular microstructure of metals evolves significantly during thermomechanical processing, driven by concurrent physical mechanisms such as viscoplastic deformation and recrystallization. Severe plastic deformation can result in texture formation, fragmentation of grains, and localized deformation bands. Microstructural features such as grain boundaries, subgrains, and non-uniform dislocation distributions critically influence the evolution throughout subsequent heat treatment, where grain boundaries migrate at elevated temperatures due to increased mobility and new dislocation-free grains nucleate forming a recrystallized microstructure. Grain nucleation, growth and plastic deformation concurrently alter the lattice orientation at any given material point, posing a major challenge for consistent numerical simulations. Traditionally, modeling this coupled evolution is mostly handled using separate, specialized frameworks for mechanical deformation and microstructural kinetics, typically used in a staggered manner where nucleation is incorporated as an intermediate step. Defects such as grain boundaries, triple-junctions and second-phase particles are preferred nucleation sites. The nuclei are planted at predefined sites in an ad-hoc manner based on trigger criteria such as critical dislocation density, stress or strain. This is a consequence of the inherent limitations of the staggered approach, where newly formed grain boundaries or grains have to be incorporated with additional processing. In this work, we propose a unified, thermodynamically consistent field theory that naturally enables spontaneous nucleation driven by stored dislocations at grain boundaries. Significant progress was made recognizing that the Cosserat continuum represents an ideal framework for the coupling between different mechanisms causing lattice reorientation, since rotations are native degrees of freedom in this setting. Thus, the proposed model integrates Cosserat crystal plasticity with the Henry-Mellenthin-Plapp (HMP) orientation phase field approach, allowing the simulation of key microstructural defects, as well as curvature- and stored energy-driven grain boundary migration. Compared to models based on the Kobayashi-Warren-Carter phase-field, the HMP formulation removes the term linear in the gradient of orientation from the free energy density, thus eliminating long-range interactions between grain boundaries. Further, HMP orientation phase field can account for inclination-dependent grain boundary energies. The unified approach enables seamless identification of grain boundaries that emerge from deformation and nucleation. Nucleation is activated through a coupling function that links dislocation-related free energy contributions to the phase field. Dislocation recovery occurs both at newly formed nuclei and behind migrating grain boundaries. We demonstrate the model’s capabilities and numerical performance within a two- and three-dimensional small deformation framework, implemented using the finite element method. Mechanisms such as strain-induced boundary migration, subgrain growth and coalescence are captured. The spontaneous nucleation mechanism offers a novel addition to the capabilities of phase field models for recrystallization simulation. The proposed framework enables physically consistent simulation of recrystallization, offering predictive capability for microstructure evolution in metals.

Authors 1

1. İzzet Tarik Tandoğan corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen