Continuum multiscale modeling of finite deformation plasticity and anisotropic damage in polycrystals

Abstract

A framework for describing the deformation and failure responses of multi-phase polycrystalline microstructures is developed from micromechanical considerations and volume averaging techniques. Contributions from damage (i.e., displacement discontinuities such as cracks, voids, and shear bands) are captured explicitly in the framework’s kinematics and balance relations through additive decompositions of the total deformation gradient and nominal stress, respectively. These additive decompositions—which notably enable description of arbitrarily anisotropic deformations and stresses induced by damage—are derived following the generalized theorem of Gauss, i.e., a version of the divergence theorem of vector calculus. A specific rendition of the general framework is applied to study the response of a dual-phase tungsten (W) alloy consisting of relatively stiff pure W grains embedded in a more ductile metallic binder material. In the present implementation, a Taylor scheme is invoked to average grain responses within each phase, with the local behavior of individual grains modeled with finite deformation crystal plasticity theory. The framework distinguishes between the effects of intergranular damage at grain and phase boundaries and transgranular damage (e.g., cleavage fracture of individual crystals). Strength reduction is induced by the evolving volume fraction of damage (i.e., porosity) and microcrack densities. Model predictions are compared with experimental data and observations for the W alloy subjected to various loading conditions.