Cohesive detachment of an elastic pillar from a dissimilar substrate

Abstract

The adhesion of micron-scale surfaces due to intermolecular interactions is a subject of intense interest spanning electronics, biomechanics and the application of soft materials to engineering devices. The degree of adhesion is sensitive to the diameter of micro-pillars in addition to the degree of elastic mismatch between pillar and substrate. Adhesion-strength-controlled detachment of an elastic circular cylinder from a dissimilar substrate is predicted using a Dugdale-type of analysis, with a cohesive zone of uniform tensile strength emanating from the interface corner. Detachment initiates when the opening of the cohesive zone attains a critical value, giving way to crack formation. When the cohesive zone size at crack initiation is small compared to the pillar diameter, the initiation of detachment can be expressed in terms of a critical value H c of the corner stress intensity. The estimated pull-off force is somewhat sensitive to the choice of stick/slip boundary condition used on the cohesive zone, especially when the substrate material is much stiffer than the pillar material. The analysis can be used to predict the sensitivity of detachment force to the size of pillar and to the degree of elastic mismatch between pillar and substrate.NAF is grateful for financial support in the form of an ERC MULTILAT Grant 669764, and to the US ONR (N62909-14-1-N232, project manager, Dr. Dave Shifler). NAF and RMcM acknowledge support from the Alexander von Humboldt Foundation in the form of their Forschungspreise, which enabled them to undertake research at INM-Leibniz Institute for New Materials, Saarbrücken. EA acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant agreement no. 340929