From bending to stretching driven peeling of heterogeneous adhesives

Abstract

We study theoretically the peeling behavior of adhesives. Adopting a fracture mechanics approach, we derive the equation of motion of the adhesion front propagating at the interface between the adhesive and the substrate from which the peel strength is inferred. The originality of our approach lies in the description of the interplay during peeling between the stretching and the bending modes of deformation of the adhesive that is described as a F{\''o}ppl-Von Karman's thin film. Considering first a straight adhesion front, we retrieve the most salient feature of homogeneous adhesives, namely a peeling angle dependent peel strength driven by bending at large angles and by stretching at low angles. We also derive the shape of the adhesive that can be described using a single bending length scale derived from our model. We then investigate the impact of adhesion heterogeneities. We evidence that the deformations of the adhesion front are governed by a non-local interface elasticity the strength of which decreases with the peeling angle. This phenomenon reflects the transition between a stretching dominated peeling at low angle to a bending driven peeling at large angles that is captured in our model. This transition impacts the stability of adhesive fronts that relaxe more slowly from perturbations and gives rise to a stronger toughening effect in presence of a disorder distribution of adhesion energy at low peeling angles. Overall, this study sheds light on the central role played the elastic deformations of adhesives on their peeling behavior. The proposed framework unfolds the complex interplay between the deformation of adhesives and the peeling driving force that may be leveraged to engineer heterogeneous adhesives with enhanced properties. It also provides rich insights on the mechanisms underlying the emergence of non-local elasticity in interface problems.