Why planar cracks fragment into echelon cracks

Abstract

Predicting the path and shape of growing cracks is fundamental to understanding of fracture. Under out-of-plane shear loading, an initially planar crack may spontaneously fragment into multiple cracks, forming a striking echelon crack pattern. Explaining this crack morphogenesis in brittle materials has been a long-standing open problem essential to developing a complete theory of crack growth. Here, through comparison with classical experiments, we show that a strength-constrained minimization of the sum of elastic and surface energies explains echelon crack formation. Results are presented for both soft and hard materials, confirming the model's general applicability to any brittle material. As a corollary, we show that, contrary to prevailing views, a purely energetic minimization model is insufficient to predict the growth of large cracks. We identify two key non-dimensional parameters governing crack fragmentation and orientation, and demonstrate that these reconcile the various energy-based and stress-based empirical criteria proposed in the literature for crack path.