Theory of dynamic crack branching in brittle materials

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.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

Thermal fracture as a framework for quasi-static crack propagation

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.Comment: 19 pages, 8 figure