Rate effects in detachment of a spherical probe from fibrillar adhesive surfaces

Abstract

Rate effects in fibrillar adhesive surfaces have received increasing attention recently. However, the requirement for taking into account the viscoelastic behavior of the material, combined with the backing layer coupling, complicates the theoretical treatment. As a result, the role of rate effects, particularly on the array level, remains unclear. This work focuses on a general problem: a rigid spherical probe is detached from a viscoelastic fibrillar adhesive surface at a certain velocity. A theoretical framework is proposed based on the Lee & Radok corresponding principle and the Schapery approximation for crack initiation in viscoelastic solids. The fibril force across the array is explicitly determined during the dynamic detaching process. Simulation results reveal the influence of rate effects on the adhesion response, the preload dependence, and the effective work of adhesion of the fibrillar surface. As expected, the adhesion force monotonically increases with the retraction velocity. An interesting phenomenon is observed at intermediate velocities that modest preload is favorable to the pull-off force while an overlarge one would have an adverse effect. The pull-off force would finally approach a lower steady-state constant at a sufficiently high preload value. Most significantly, it is found that the dependence of the effective work of adhesion on the crack velocity is almost independent of the basic properties of the fibrillar surface when traversing typical parameter space. This indicates that the contribution of the viscoelastic-induced adhesion enhancement can be approximately decoupled as a multiplicative term in the overall effective work of adhesion. For a sufficiently large probe radius, this rate-dependent characteristic can be well captured by the continuum theory of viscoelastic crack propagation.