The classical fracture mechanics approach describes only partially the fracture process in heterogeneous brittle materials-such as rocks, ceramics or concrete for example. The study of crack growth in weakly heterogeneous solids where fracture behaviors can be seen as a perturbation from the response of homogeneous media is a fruitful approach that provides rich insights on the role of heterogeneities on crack propagation.
In this work, we focus on the path followed by cracks, and study whether a crack previously disturbed by some heterogeneities recovers a straight trajectory or instead departs from it. To address this question, we build on the work of Cotterell and Rice [1] enriched by the one of Movchan et al. [2] to derive a path equation for a slightly perturbed crack under macroscopic mode I loading. This path equation is then used to investigate the stability of straight crack trajectories. Three regimes corresponding to different loading conditions that can be parametrized through two length scales emerging from the geometry of the fracturing sample and the loading conditions can be evidenced: (i) a stable regime where path perturbations rapidly decay (ii) an unstable regime with an exponential growth of the geometrical crack perturbations (iii) a marginally stable regime that displays oscillatory crack solutions.
These predictions are compared with experimental fracture tests in various geometries where crack path disturbances are manually introduced. We find that our approach accounts for the stability of straight trajectory as observed experimentally. The conditions required to observe oscillatory crack paths are finally discussed.