Dissipative Viscoplastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals a “fracture energy” $\Gamma$ 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, $\Gamma =\Gamma (v)$. We show that a simple dynamical theory of viscoplasticity 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 $\Gamma$ and its velocity dependence.

Figure 1

Solutions for $\lambda s_y=1$. Left panel: The tip radius $R$ normalized by the first data point ($R_0=0.012c_s\tau$) as a function of the normalized velocity $v/c_s$. Right panel: The fracture energy $\Gamma$ normalized by the first data point (${\Gamma }_0=0.01s_y{c}_s\tau$) as a function of the normalized velocity $v/c_s$.