Flat punch adhesion: transition from fracture-based to strength-limited pull-off

The adhesion of a cylindrical flat punch to a surface due to interatomic forces is a well-known problem that is important in many applications, including indentation experiments and the adhesion of fibrillar structures. Traditionally, the pull-off force has been related to the work of adhesion and punch geometry via the Kendall solution that uses a Griffith energy balance to assess crack propagation and pull-off. More recently, it has been shown that under certain conditions, notably at small punch diameters, the contact can behave in a 'strength-limited' fashion in which the interface separates uniformly rather than via crack propagation. Here, a Maugis-Dugdale-type analysis of power-law-shaped bodies in contact is used to examine the change in behaviour from the fracture-based Kendall solution to strength-limited pull-off for cylindrical flat punches. The transition from fracture-based to strength-limited behaviour is described in terms of a non-dimensional parameter that is similar to previous quantities used to describe the transition and is a function of the punch size, the elasticity of the contact, and the adhesion properties. The results of this relatively simple analysis compare favourably with results from more complex computational simulations. In addition, the results are used to develop a function that quantifies the transition between the Kendall solution and the strength-limited solution in order to facilitate interpretation of adhesion measurements in the transition regime between the two limits. Finally, the power-law analysis is used to assess the sensitivity of the transition to the exact shape of the punch.