Universal scaling and nonlinearity in surface layer fragmentation

We analyze disordered one-dimensional bond-network models and investigate the influence of nonlinear force-elongation relations F proportional to/x/(m) on the fragmentation of coatings under tension. We aim to elucidate the interplay between the nonlinear forces and the random failure thresholds of the bonds. After an initial stage, the mean fragment length [L] scales with the applied strain epsilon, [L] proportional to epsilon(-alpha), where alpha=m/(m+1) for weakly disordered and alpha=m/(m+2) for strongly disordered coatings.