Heterogeneous Dynamic Fracture: Amplitude Scaling of Crack Front Deformations

We study numerically the deformation of a dynamic crack propagating through a planar heterogeneous interface. We investigate the evolution of the front shape due to variations of fracture toughness, represented by weak and strong stripes parallel to the rupture direction. When going from homogeneous to heterogeneous properties, the crack enters a transient regime during which the front evolves from a straight configuration to a sinusoidal shape. This process is governed by crack front waves that decay with time. Following this regime, the front reaches a stationary shape whose amplitude is determined by the heterogeneity size, the toughness variation between heterogeneities, the relative contraction of the process zone, and the process zone elasticity. We propose a unique scaling relation for the front amplitude that we support with an extensive parametric study.