Transition from continuous to discontinuous material failure in a simple model of an adhesive layer

摘要

A fine-scale, quasistatic model was used to study the removal of a disordered adhesive layer by a uniform force applied perpendicular to the layer. The model includes randomly chosen bonding forces of adhesion between imaginary "gridblocks" within the layer and a substrate, as well as cooperative forces of cohesion between adjacent gridblocks. For small cooperative forces, the amount of failure varies continuously with the applied force F. From infinitesimal failure at a minimum threshold value of the force, the fraction of the layer removed, f(m)(F), increases to encompass the total layer, as the applied force increases. This layer-removal function sharpens as the cooperative forces are increased; i.e., the slope of the layer-removal function, Delta f(m)/Delta F, increases, so that the amount of failure is more and more sensitive to changes in the applied force. Indeed, this slope diverges with an exponent gamma approximate to 0.85 when the cooperative forces are approximately 2.1 as large as the adhesive forces. At small values of the cooperative forces, the layer-removal initiates at many locations and spreads to nearby blocks. The perimeter enclosing the area removed is fractal with a dimension D-p approximate to 1.3. Increasing the cooperative forces causes the failure to initiate at fewer locations in the array, but to spread farther because of the larger cooperative forces. At the critical value of 2.1 for the ratio of cohesive to adhesive forces, the number density of these initiation sites goes to zero, and the ''correlation'' length (average range of the spread of failure) diverges with exponent v approximate to 0.5. The characteristic time required for failure also diverges at the same critical value of cohesive/adhesive ratio; with an exponent, Delta approximate to 0.9. Therefore, increasing the cooperative forces of cohesion effects a transition from the continuous response reminiscent of systems with depinning transitions to the discontinuous response characteristic of standard material fracture. Indeed, the divergent correlation length signals a transition to the long-range elastic forces that have enabled mean-field (fiber-bundle) models to be used in the study of standard material fracture. [S1063-651X(98)07012-3]. [References: 41]