Dual Role for Heterogeneity in Dynamic Fracture

We approach the problem of heterogeneous dynamic fracture by considering spatiotemporal perturbations to planar crack fronts. Front propagation is governed by local energy balance between the elastic energy per unit area available to fracture G and the dissipation in creating new surfaces. G is known analytically as a perturbation series in the crack front fluctuation. For dissipation that monotonically increases with the crack speed, we derive an equation of motion for crack fronts that is second-order accurate. In the linear order, heterogeneity does not change the net speed of fracture. In the second order, nonlinear interactions of the front and the heterogeneous landscape populate an intermediate-scale fluctuation spectrum. We find that, when dissipation weakly grows with velocity, nonlinearities globally amplify dissipation and reduce the crack speed. Strong velocity dependence, however, mitigates toughening effects and may facilitate fracture.