Topological defects govern crack front motion and facet formation on broken surfaces

Cracks develop intricate patterns on the surfaces that they create. As faceted fracture surfaces are commonly formed by slow tensile cracks in both crystalline and amorphous materials, facet formation and structure cannot reflect microscopic order. Although 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. Here we show that these steps are topological defects of crack fronts and that crack front separation into disconnected overlapping segments provides the condition for step stability. Real-time imaging of propagating crack fronts combined with surface measurements shows that crack dynamics are governed by localized steps that 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 study how three-dimensional topology couples to two-dimensional fracture dynamics to provide a fundamental picture of how patterned surfaces are generated.