A crystal plasticity-damage coupled finite element framework for predicting mechanical behavior and ductility limits of thin metal sheets

Abstract

A new crystal plasticity finite element (CPFE) approach is developed to predict the mechanical behavior and ductility limits of thin metal sheets. Within this approach, a representative volume element (RVE) is chosen to accurately capture the mechanical characteristics of these metal sheets. This approach uses the periodic homogenization multiscale scheme to ensure the transition between the RVE and single crystal scales. At the single crystal scale, the mechanical behavior is modeled as elastoplastic within the finite strain framework. The plastic flow is governed by a modified version of the Schmid law, which incorporates the effects of damage on the evolution of microscopic mechanical variables. The damage behavior is modeled using the framework of Continuum Damage Mechanics (CDM), introducing a scalar microscopic damage variable at the level of each crystallographic slip system (CSS). The evolution law of this damage variable is derived from thermodynamic forces, resulting in deviations from the normality rule in microscopic plastic flow. This coupling of damage and elastoplastic behavior leads to a highly nonlinear set of constitutive equations. To solve these equations, an efficient return-mapping algorithm is developed and implemented in the ABAQUS/Standard finite element software via a user-defined material subroutine (UMAT). At the macroscopic scale, the onset of localized necking is predicted by the Rice bifurcation theory. The proposed damage-coupled single crystal model and its integration scheme are validated through several numerical simulations. The analysis extensively explores the impact of microstructural and damage parameters on the mechanical behavior and ductility limits of both single crystals and polycrystalline aggregates. The numerical results indicate that both of the mechanical behavior and ductility limits are significantly influenced by the microscopic damage and deviations from normal plastic flow rule.