On the scaling of strength of flat and mushroom-shaped ends of microstructured adhesives

Abstract Considerable research has been conducted on shape of pillar ends for optimal adhesion. In experiments with elastomers, it has been found that mushrooms-ended ones are superior to flat-ended ones, but early experiments have suggested an extremely strong scaling in strength with pillar radius (del Campo et al. Langmuir 23:10235–10243, 2007). We discuss various theories and experimental results on scaling of strength, and in particular, we elaborate recent experiments on single pillars with mushroom ends finding that the scaling on strength is much less surprising. When the ratio of tip to shaft radii increases toward an optimal value, the mode of failure changes from edge to center defects, and the scaling of strength changes from that associated with the presence of the classical linear elastic fracture mechanics stress singularity at the corner of the flat-ended punches caused by large friction at the interface, with that caused by the population of defects immersed on a nearly uniform stress field in the mushroom center. Strong scaling of strength therefore is also accompanied with large scatter of strength.