Theory of dynamic crack branching in brittle materials

TL;DR

This paper presents a continuum mechanics model predicting the critical speed, branching angle, and subsequent crack path geometry during dynamic crack branching in brittle materials, aligning well with experimental observations.

Contribution

It introduces a new dynamic crack branching model based on energy criteria and local symmetry, explaining key features of crack instabilities in brittle materials.

Findings

Critical branching speed matches experiments

Branching angles are accurately predicted

Sign of stress T influences branch divergence or convergence

Abstract

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.