The Topology and Mechanics of the Formation of Fracture Surface Patterns*

How and why are patterns formed on broken surfaces? Faceted fracture surfaces are commonly formed by slow tensile cracks in amorphous materials; hence their formation cannot reflect microscopic order. While fracture mechanics predict that slow crack fronts should be straight and form mirror-like surfaces, facet-forming fronts propagate simultaneously within different planes separated by steps. Why are steps stable, what determines their path and how do they couple to crack front dynamics? By integrating real-time imaging of propagating crack fronts with surface measurements, we demonstrate that steps are topological defects; crack front separation into disconnected overlapping segments provides the condition for step stability. Crack dynamics are enslaved to steps; steps drift at a constant angle to the local front propagation direction while their increased dissipation couples to long-ranged elasticity to determine front shapes. We see how 3D topology couples to 2D fracture dynamics to provide a fundamental picture of how patterned surfaces are generated. 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.