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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 ( λ 1 , λ 2 ) with corresponding intensities ( H 1 , H 2 ) . The asymptotic stress field σij is of the form σ ij = H 1 r λ 1 − 1 f ij ( λ 1 , θ ) + H 2 r λ 2 − 1 f ij ( λ 2 , θ ) , where fij describe the angular dependence θ of σij, 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 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 ( 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.
A Design Strategy for Mushroom-Shaped Microfibrils With Optimized Dry Adhesion: Experiments and Finite Element Analyses
Enhanced dry adhesion of micropatterned polymeric surfaces has been frequently demonstrated. Among the design parameters, the cap geometry plays an important role to improve their performance. In this study, we combined experiments on single polyurethane mushroom-shaped fibrils (with a stalk diameter of 80 µm and height of 125 µm) against flat glass, with numerical simulations implementing a cohesive zone. We found that the geometry of the mushroom cap strongly affects the interfacial crack behavior and the pull-off stress. The experimental and numerical results suggest that optimal adhesion was accompanied by the appearance of both edge and interior interfacial cracks during separation. Finite elemental analyses revealed the evolution of the interfacial stress distributions as a function of the cap thickness and confirmed the distinct detachment mechanisms. Furthermore, the effect of the stalk diameter and the Young's modulus on the adhesive force was established, resulting in an optimal design for mushroom-shaped fibrils.