A strain gradient plasticity model of porous single crystal ductile fracture

Abstract

A strain gradient void-driven ductile fracture model of single crystals is proposed and applied to simulate crack propagation in single and oligo-crystal specimens. The model is based on a thermodynamical framework for homogenized porous solids unifying and generalizing existing thermodynamical formulations. This porous single crystal ductile fracture model relies on a multi-surface representation of porous crystal plasticity in which the standard Schmid law is enhanced to account for porosity, including void growth and void coalescence mechanisms. A new criterion to detect the onset of void coalescence in porous single crystals is proposed and validated by comparison to porous single crystal unit-cell simulations. This criterion can either be used as an additional yield surface or it can be used to follow the well established Gurson–Tvergaard–Needleman approach based on an effective porosity to model void coalescence. The strain gradient formulation relies on a Lagrange multiplier based relaxation of strain gradient plasticity. Material points simulations are performed in order to depict the elementary features of the porous single crystal ductile fracture model without strain gradient effects. The model is then applied to the simulation of plane strain single crystal specimen loaded in tension up to failure. The regularization ability and convergence with mesh refinement are demonstrated. Finally two- and three-dimensional simulations of ductile fracture of single and oligo-crystal specimens are presented. The significant influence of plastic anisotropy on the crack path, ductility and fracture toughness is highlighted.