Detachment of an adhered micropillar from a dissimilar substrate

Abstract

The mechanics of detachment is analysed for 2D flat-bottomed planar pillars and 3D cylindrical pillars from a dissimilar elastic substrate. Application of an axial stress to the free end of the pillar results in a singularity in stress at the corner with the substrate. An eigenvalue analysis reveals that the stress field near the corner is dominated by two singular eigenfields having eigenvalues (λ1,λ2) with corresponding intensities (H1,H2). The asymptotic stress field σij is of the form σij=H1rλ1−1fij(λ1,θ)+H2rλ2−1fij(λ2,θ), where fij describe the angular dependence θ of σij, and r is the radial distance from the corner. The stress intensities (H1,H2) are calculated numerically, using a domain integral approach, as a function of the elastic mismatch between the pillar and substrate. The singular zone extends across approximately 10% of the pillar diameter (in 3D) or pillar width (in 2D).Interfacial failure is predicted for an assumed crack emanating from the corner of pillar and substrate. For the case of an interfacial crack that resides within the domain of corner singularity, a boundary layer analysis is performed to calculate the dependence of the interfacial stress intensity factor K upon (H1,H2). When the crack extends beyond the domain of corner singularity, it is necessary to consider the full geometry in order to obtain K. A case study explores the sensitivity of the pull-off stress to the flaw size and to the degree of material mismatch. The study has implications for the optimum design of adhesive surface micropatterns, for bonding to either stiffer or more compliant substrates.