The Topology and Mechanics of Fracture Surface Pattern Formation

Fracture of brittle materials often results in the formation of structure on crack faces whose origin has long remained obscured. The difficulty lies in seeing how microscopic structures are formed by rapid cracks. To overcome this difficulty, we study soft brittle gels where crack speeds are much lower than in hard materials. Much below the shear wave speed, cracks form facetted surfaces deliniated by steps. At higher speeds, facets give way to micro-branches, frustrated cracks that branch off the main crack. We directly visualize the leading edge of the crack, the crack front, as it forms surface structure. In the faceting regime, steps induce long-ranged deformation along the crack front. Since surface formation costs energy, steps imply locally increased dissipation. We show that steps persist due to topological defects of the crack front, that quantitatively link local dissipation increases at steps to crack front deformation. We also show that crack front curvature may feed back to deflect step paths via nonlinear focusing of crack fronts, causing steps to converge to form a micro-branch. Thus, our results supply the basis for a unified picture of pattern formation on fracture surfaces.