An Elastic-plastic Constitutive Law Embedding Cohesive Cracks with Plasticity-induced Damage to Realize Degradation of Strength and Toughness under Cyclic Loading

An elastic-plastic constitutive law embedding cohesive cracks with plasticity-induced damage is proposed to realize degradation of strength and toughness under cyclic loading. A conventional elastic-plastic constitutive law with isotropic and kinematic hardening is combined with our cohesive-force embedding damage model to realize plastic deformation and fracture behavior under monotonic and cyclic loading by solving two kinds of conditional equations. One of them is local balance equation between cohesive traction and principal stress and the other is yield function with nonlinear isotropic and kinematic hardening law. The relationship between the cohesive traction and the crack opening displacement is determined by a cohesive zone model associated with energy release rate to represent process of stress release due to formation of crack surface. In addition, a new plasticity-induced damage is introduced into the cohesive zone model to realize the degradation of the tensile strength and the energy release rate caused by the accumulated plastic strain. On the other hand, the difference of the plastic deformation under various ranges of cyclic loading is represented by additional hardening law depending on a memory surface that is corresponding to plastic strain range. After the material parameters are identified from three experimental results under monotonic and cyclic loading, the capability of our proposed constitutive law is demonstrated by prediction of residual tensile strength and breaking strain of a metal after cyclic loading.