When and how do cracks propagate?

• Published in: Journal of the mechanics and physics of solids Vol. 57; no. 9; pp. 1614 - 1622
• Main Authors: Chambolle, A., Francfort, G.A., Marigo, J.-J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2009
• Subjects: Fracture mechanics; Stability; Variational methods; Variational methods; Fracture mechanics; Stability
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2009.05.009

Crack propagation in an isotropic 2d brittle material is widely viewed as the interplay between two separate criteria. Griffith's cap on the energy release rate along the crack path decides when the crack propagates, while the Principle of Local Symmetry PLS decides how, that is, in which direction, that crack propagates. The PLS, which essentially predicts mode I propagation, cannot possibly hold in an anisotropic setting. Further it disagrees with its competitor, the principle of maximal energy release, according to which the direction of propagation should coincide with that of maximal energy release. Also, continuity of the time propagation is always implicitly assumed. In the spirit of the rapidly growing variational theory of fracture, we revisit crack path in the light of an often used tool in physics, i.e. energetic meta-stability of the current state among suitable competing crack states. In so doing, we do not need to appeal to either isotropy, or continuity in time. Here, we illustrate the impact of meta-stability in a 2d setting. In a 2d isotropic setting, it recovers the PLS for smooth crack paths. In the anisotropic case, it gives rise to a new criterion. But, of more immediate concern to the community, it also demonstrates that 2d crack kinking in an isotropic setting is incompatible with continuity in time of the propagation. Consequently, if viewing time continuity as non-negotiable, our work implies that the classical view of crack kinking along a single crack branch is not correct and that a change in crack direction necessarily involves more subtle geometries or evolutions.