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The mechanics of detachment is analysed for 2 D flat-bottomed planar pillars and 3 D 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 (λ 1 ,λ 2 ) with corresponding intensities (H 1 ,H 2 ). The asymptotic stress field σ ij is of the form σ ij = H 1 r λ1-1 f ij (λ 1 , θ)+H 2 r λ2−1 f ij (λ 2 , θ) , where f ij describe the angular dependence θ of σ ij , and r is the radial distance from the corner. The stress intensities (H 1 ,H 2 ) 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 3 D) or pillar width (in 2 D). 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 (H 1 ,H 2 ). 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.
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 Hc 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.
