FRAGMENTATION OF THIN-FILMS BONDED TO SOLID SUBSTRATE - SIMULATIONS AND A MEAN-FIELD THEORY

We perform simulations of crack growth in a brittle-elastic two-dimens ional film bonded to a rigid substrate and subjected to an isotropic t ensile stress. We find that the resulting fracture patterns can be cla ssified according to the applied tensile stress. For a significant ran ge of stresses, the crack interactions are extremely shell range. The resulting fracture patterns are independent of stress and depend only on the initial distribution of crack nuclei. In this regime, the fract ure process is well described by a fragmentation model in which a rand om distribution of seeds nucleates pairs of oppositely directed rays w hich grow until encountering other rays. Using a mean-field approach, we obtain approximate analytical results for this model which compare well with both the simulations of the fragmentation model, and with th e fracture simulation results. Our approach is extensible to other mod els of fracture, and where numerical results exist in the literature, our mean-field solutions agree well with them.