  Patterns on broken surfaces are well-known from everyday experience, but
surprisingly, how and why they form are very much open questions. Well-defined
facets are commonly observed1-4 along fracture surfaces which are created by
slow tensile cracks. As facets appear in amorphous materials5-7, their
formation does not reflect microscopic order. Fracture mechanics, however,
predict that slow crack fronts should be straight, creating mirror-like
surfaces8-13. In contrast, facet-forming fronts propagate simultaneously within
different planes separated by steps. It is therefore unclear why steps are
stable, what determines their path and how they couple to crack front dynamics.
Here we show, by integrating real-time imaging of propagating crack fronts with
surface measurements, that steps are topological defects of crack fronts; crack
front separation into discontinuous overlapping segments provides the condition
for step stability. Steps drift at a constant angle to the local front
propagation direction and the increased local dissipation due to step formation
couples to the long-range deformation of the surrounding crack fronts. Slow
crack front dynamics are enslaved to changes in step heights and positions.
These observations show how 3D topology couples to 2D fracture dynamics to
provide a fundamental picture of how patterned surfaces are generated.
