Origin of instability in dynamic fracture

TL;DR

This paper explains the origins of instability in dynamic fracture by modeling the cracked body as a temporary layer-like material, revealing how stress distribution and crack velocity lead to rough surfaces and branching.

Contribution

It introduces a novel model treating the cracked body as a temporary layer-like material, providing a unified explanation for crack roughness and branching phenomena.

Findings

Cracked body behaves as a TLLM with a growing 'brittle layer'.

Single crack causes stress reduction at small velocities.

Crack branching occurs when the 'brittle layer' is large enough.

Abstract

Unstable growth of cracks (rough crack surface and crack branching) in dynamic fracture has long been observed in various materials. Until now, there was no universally agreed upon explanation for these instabilities. Here, we demonstrate that: 1) Due to the non-uniform stress distribution in the cracked body and the expansion of high stress region as the crack velocity increases, a force-bearing cracked body can be treated as a temporary layer-like material (TLLM) with a "brittle layer" that the area of its automatically increases. 2) For this TLLM, it takes only one crack for the stress in its "brittle layer" to fall below a certain value at small velocities. Coupled with the asymmetry of the whole system, this results in a rough crack surface. 3) The "brittle layer" is large enough when the crack velocity reaches a certain value. Two cracks must be formed, or else the stress cannot be reduced below the certain value, resulting in crack branching. Crack propagation can be compared to cars traveling on a road: the high stress region in the cracked body provides a "road" to let cracks "pass ."