Shear-induced contact area anisotropy explained by a fracture mechanics model
This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces on an adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanics model where two phenomenological mode-mixity functions are introduced to describe the weak coupling between modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixity functions have been interpolated using the data of a single experiment and then used to predict the behavior of the whole set of experimental observations. The model extends an idea by Johnson and Greenwood, to solve purely mode I problems of adhesion in the presence of a nonaxisymmetric Hertzian geometry, to the case of elliptical contacts sheared along their major or minor axis. Equality between the stress intensity factors and their critical values is imposed solely at the major and minor axes. We successfully validate our model against experimental data. The model predicts that the punch geometry will affect both the shape and the overall decay of the sheared contact area.