CONTINUOUS BEHAVIOR IN A SIMPLE-MODEL OF THE ADHESIVE FAILURE OF A LAYER

A fine-scale model of the removal of an adhesive layer by a uniform st ress is described. The initial motivation of this modeling project was a description of the removal of a layer of filter cake from cylindric al filters by back-pulse pressure cleaning. The model includes the bon ding forces of adhesion between the layer and a substrate, as well as the forces of cohesion between imaginary ''gridblocks'' within the lay er. For applied stresses (pressures) greater than a threshold value, s ome of the layer is removed, with the amount of this failure depending upon the pressure as well as the average adhesive and cohesive forces . The cohesive forces reduce and sharpen the threshold because they in crease the stress near broken adhesive bonds. We have performed simula tions on a variety of sizes, with the largest being 64 000 gridblocks. Our analysis indicates that the regions of failure are compact with a rough boundary whose perimeter fractal dimension is D-p = 1.30 +/- 0. 05. In this model, the threshold exhibits the gradual decrease as the system size increases, which is well understood for the general materi al failure problem in disordered media. Appealing depinning schemes wi th universal power-law fits of the pressure dependence of the failure rate or the extent of failure are rendered meaningless by the size dep endence of the threshold. However, an ad hoc fitting scheme provides a reasonably successful collapse of the failure data to a universal cur ve.