UC San Diego

High-rate deformation processes of metals such as explosive welding and cold spray additive manufacturing entail intense grain refinement. The multi-field variational formulation and the associated computational method capable of modeling the evolution of microstructures with sharp solution transition near the grain boundaries remain challenging in achieving high accuracy, stability, and computational efficiency. In this work, a new computational formulation for coupling Cosserat crystal plasticity and phase field is developed. The conventional approach by penalizing the kinematic incompatibility between lattice orientation and displacement-based elastic rotation leads to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed under a multi-field variational framework. The associated Galerkin formulation incorporated with a weak inf-sup-based skew-symmetric stress projection is introduced to ensure coercivity for stability in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. It is shown that under this formulation, the equal order displacement-rotation-phase field approximations are stable, which allows efficient construction of approximation functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the conventional penalty-based approach and successfully captures the dominant rotational recrystallization mechanisms that exist in the block dislocation structures and grain boundary migration.Modeling the sharp transition in the phase field near the grain boundaries associated with the lattice orientation often requires highly refined discretization for sufficient accuracy, which significantly increases the computational cost. While adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh-based methods to perform adaptive model refinement. In this work, neural network-enhanced reproducing kernel particle method (NN-RKPM) is proposed, where the location, orientation, and the shape of the solution transition is automatically captured by the NN approximation by the minimization of total potential energy. The standard RK approximation is then utilized to approximate the smooth part of the solution to permit a much coarser discretization than the high-resolution discretization needed to capture sharp solution transition with the conventional methods. The proposed NN-RKPM is first verified by solving the standard damage evolution problems. The proposed computational framework is then applied to modeling grain refinement mechanisms, including the migration of grain boundaries at a triple junction, for validating the effectiveness of the proposed methods.