Crack Front Dynamics in Disordered Solids

Rapid cracks are the cause of catastrophic material failure. The continuum theory of cracks, Linear Elastic Fracture Mechanics (LEFM), is widely used to predict fracture in homogeneous solids. For heterogeneous materials, a comprehensive framework for describing the propagation of fast cracks is missing. Predicting fracture propagation in disordered solids is challenging because the overall energy cost of driving the crack becomes a function of its dynamics rather than a ‘static’ material property. I will show how we modify LEFM to incorporate the dynamics of crack fronts, following the pioneering works of Willis and Movchan (JMPS, 1995) and Ramanathan and Fisher (PRL, 1997). By expanding the theory to nonlinear perturbations, we derive an energy-balance-based equation of motion for the crack front. By solving for the crack motion, we obtain the energetic cost to drive a crack in disordered solids. I will discuss how disorder results in increased dissipation in some materials, while lowering dissipation in others.