Scaling and patterns in surface fragmentation processes

We model the failure of inhomogeneous surface layers under expansion. The quenched disorder is accounted for by a probability distribution (PD) of local breakdown strengths. The ensuing crack patterns range from percolation-like defect aggregates to well-defined polygons. Since no load sharing takes place in surface fragmentation, the effects governing crack propagation are local: the defects interact only within some correlation length. Fragmentation can be viewed as anisotropic, correlated percolation, where the formation of a new defect depends on the defects already present. Both the overall picture and the scaling of the fragment sizes depend strongly on the PD.