Dissipative Visco-plastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals “fracture energy” $\mathrm{\Gamma }$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $\mathrm{\Gamma }=\mathrm{\Gamma }(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of $\mathrm{\Gamma }$ and its velocity dependence.