Quenched disorder and instability control dynamic fracture in three dimensions

Abstract

Materials failure in 3D still poses basic challenges. We study 3D brittle crack dynamics using a phase-field approach, where Gaussian quenched disorder in the fracture energy is incorporated. Disorder is characterized by a correlation length R and strength σ. We find that the mean crack velocity v is bounded by a limiting velocity, which is smaller than the homogeneous material's prediction and decreases with σ. It emerges from a dynamic renormalization of the fracture energy with increasing crack driving force G, resembling a critical point, due to an interplay between a 2D branching instability and disorder. At small G, the probability of localized branching on a scale R is super-exponentially small. With increasing G, this probability quickly increases, leading to misty fracture surfaces, yet the associated extra dissipation remains small. As G is further increased, branching-related lengthscales become dynamic and persistently increase, leading to hackle-like structures and a macroscopic contribution to the fracture surface. The latter dynamically renormalizes the actual fracture energy until, eventually, any increase in G is balanced by extra fracture surface, with no accompanying increase in v. Finally, branching width reaches the system's thickness such that 2D symmetry is statistically restored. Our findings are consistent with a broad range of experimental observations.