Quenched disorder and instability control dynamic fracture in three dimensions

TL;DR

This study uses a phase-field model to analyze how quenched disorder affects 3D brittle crack dynamics, revealing a velocity limit and complex branching behavior that aligns with experimental observations.

Contribution

It introduces a phase-field approach incorporating quenched disorder to understand 3D fracture dynamics and identifies a velocity bound influenced by disorder and instability.

Findings

Mean crack velocity is bounded and decreases with disorder strength.

Branching probability increases with driving force, leading to complex fracture surfaces.

Dynamic renormalization of fracture energy explains velocity limits and surface structures.

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 $\sigma$. 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 $\sigma$. 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 to 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.