Crack tip enhanced phase-field model for crack evolution in crystalline Ti6Al from concurrent crystal plasticity FE-molecular dynamics simulations

KA Nair and S Ghosh, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 100, 104983 (2023).

DOI: 10.1016/j.euromechsol.2023.104983

Dislocations nucleating from a crack-tip contribute to the plasticity evolution in the vicinity of crack, as well as to the crack propagation process. This paper systematically develops a method for enhancing the defect energy, accounting for crack-tip nucleated dislocations in the Helmholtz free energy density functional, associated with the phase- field formulation of crack evolution, in a coupled crystal plasticity finite element phase field (CPFE-PF) model. A concurrent crystal plasticity FE-hyper-dynamics accelerated molecular dynamics (CPFEMD) model is created. The model that identifies, transfers, and propagates dislocations from the atomistic to continuum domain, is used to generate a dataset of crack tip dislocation density evolution along with different state variables. The paper focuses on crack tip plasticity mechanisms for the crystalline alloy Ti6Al. Using a Bayesian inference approach the critical state variables that affect the evolution of crack tip nucleated dislocation density are inferred. A functional form of the evolution of dislocation density in terms of the state variables is derived by employing a genetic programming based symbolic regression (GPSR) approach. The contribution of nucleated dislocation densities to effective plastic strain evolution at the crack tip is validated using the CPFE-MD model simulations. A comparison of the crack path and other state variables in the vicinity of the crack with and without contributions from the nucleated dislocations shows the importance of this augmentation on crack evolution.

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