Energy dissipation in dynamic fracture of brittle materials

Abstract

Dynamic crack growth in a plane strain strip is analysed using a cohesive surface fracture framework where the continuum is characterized by two constitutive relations: a material constitutive law that relates stress and strain, and a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation introduces a characteristic length into the formulation. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. Finite-strain transient analyses are carried out, with a focus on the relation between the increase in fracture energy with crack speed and the increase in surface area due to crack branching. The numerical results show that, even with a fixed work of separation per unit area, there is a substantial increase in fracture energy with increasing crack speed. This arises from an increase in fracture surface area due to crack branching. The computational results are in good agreement with experimental observations in Sharon et al (1996).