PATTERNS AND SCALING IN SURFACE FRAGMENTATION PROCESSES

We consider a finite-element model for the fragmentation of a coating covering a bulk material. The coating breaks under a quasistatical, sl owly increasing strain (induced, e.g., by temperature changes, by desi ccation, or by mechanical deformations). We model the coating through an array of springs and account for its statistical inhomogeneities by assigning each spring a breakdown threshold taken from a given probab ility distribution (PD). The adhesion to the bulk is modeled through o ther springs, which connect the coating to the substratum. We consider the dependence on the strain of the mean fragment size and also the e nsuing pattern of cracks. We find that the mean fragment size obeys a power-law dependence on the strain; the exponent of the power law is r elated to the strength of disorder (i.e.; the behavior of the assumed PD for breakdown thresholds in the vicinity of zero). Moreover, the mo de of fragmentation also depends on the disorder's strengths: for smal l disorder (narrow PDs) the system fragments through crack propagation , for strong disorder (wide PD, starting from zero) the cracks are for med by the coalescence of initially independent point defects.