Crystal Plasticity Phase-Field Model with Crack Tip Enhancement Through a Concurrent Atomistic-Continuum Model

This paper develops a method for physics-based augmentation of the Helmholtz free energy density functionals, used in coupled crystal plasticity phase-field finite element (CP-PF FE) models of fracture in crystalline metallic materials. Specifically, the defect and crack surface energy components are enhanced with terms that mechanistically account for the presence of atomic-scale, crack-tip nucleated dislocations. The additional terms in the free energy representation are motivated and calibrated by energy equivalence between a concurrent atomistic-continuum scale model and the CP-PF FE model. The atomistic domain of the concurrent model incorporates a time-accelerated, molecular dynamics (MD) LAMMPS code, while the continuum domain is modeled by a dislocation-density crystal plasticity FE model. The concurrent model transfers and transforms discrete dislocations in the atomistic domain to dislocation densities in the crystal plasticity domain. Dislocation densities are transported in the continuum domain by solving the advection equation using a particle-based reproducing kernel particle method with collocation. A new form of the defect energy density is proposed by considering the effect of crack-tip nucleated dislocations. Parameters in the augmented defect and surface energies are evaluated by comparing with the concurrent model results. A comparison of crack propagation with and without contributions from the nucleated dislocations demonstrates a significant effect of nucleated dislocations on the evolution of the crack.

Automated summary

This paper presents a method for enhancing the Helmholtz free energy density functionals in coupled crystal plasticity phase-field finite element models of fracture by considering the influence of atomic-scale, crack-tip nucleated dislocations. The proposed approach is motivated and calibrated by energy equivalence between atomistic-continuum scale models, demonstrating the significant effect of nucleated dislocations on crack evolution.