Multi-Scale Energy Release Rate in Dynamic Crack Growth of Strain-Softening Materials

Abstract

Dynamic crack growth in an elastic-plastic solid containing damage has been studied under mode-I plane strain conditions from a multi-scale viewpoint. A modified Dugdale model is used to define the transition from stable to spontaneous fracture. The non-linear zone consists of two parts: a specified plastic zone and a fracture process zone (FPZ) resulting from two distinct mechanisms due to strain hardening and strain softening, respectively. The length ratio between the FPZ and the whole cohesive zone determines the crack growth stability. In the softening FPZ zone, a rate-dependent power-law traction-separation relationship, expressed in terms of the ultimate tensile strength, softening index and viscosity, controls the constitutive relationship of the damaged material. The governing integral equation and the auxiliary conditions are given. Numerical solutions for fracture toughness are obtained based on a critical crack-tip opening angle criterion. The results show that the fracture toughness increases at high crack velocities and low crack-tip constraints. But it is insensitive to the size of the damage zone and the strain-softening index. The constraint effect due to specimen geometry and crack speed can influence significantly the toughness and the length ratio.