A strain-damage coupled model and its application to near crack tip localization analysis

Three-dimensional equations of a strain-damage coupled model for ductile deformation processes in solids are presented in an attempt to find approaches for study of the anisotropic damage effect on the perfect plastic flow. Damage state is represented by a symmetric damage tensor. A modified Tresca yielding condition, associated flow and damage rules are used to formulate the strain-damage coupled constitutive equations, thus allowing to take account of that effect. The principal axes of stresses are chosen as a local frame for representing the static, kinematic and constitutive equations of the coupled model. The closed system of equations represented in the local principal frame needed for formulation of the strain-damage coupled model is obtained. This system is shown belong to the hyperbolic type. Theory of characteristic lines of the strain-damage coupled equations is developed. A numerical solution of the plane strain problem of the strain-damage localization near a mode I crack tip is obtained. It shows the marked effect of damage induced anisotropy on the localization of plastic strains near a crack tip and allows to estimate an extension of the damaged zone ahead of the crack tip. Gradual distortion of the slip line geometry is also determined thus demonstrating how the anisotropic damage affects plastic flow.