Size effects in adhesive contacts of viscoelastic media

TL;DR

This study investigates how the maximum force needed to detach a sphere from a viscoelastic surface depends on contact size, revealing size effects during transient conditions and modifying existing crack theories to account for these effects.

Contribution

The paper introduces a deterministic model combining Lennard-Jones potential and standard linear solid viscoelasticity to analyze size effects in adhesive contacts.

Findings

Pull-off force is independent of contact size under quasi-static conditions.

Size effects emerge during transient conditions with larger contacts involving more dissipation.

Modified Persson's crack theory captures the observed size-dependent behavior.

Abstract

Is the maximum force required to detach a rigid sphere from a viscoelastic substrate dependent on the initial value of the contact radius? Experimental and theoretical investigations reported in the literature have given opposite responses. Here, we try to answer the above question by exploiting a fully deterministic model in which adhesive interactions are described by Lennard-Jones potential and the viscoelastic behaviour with the standard linear solid model. When the approach and retraction phases are performed under quasi-static conditions, the substrate behaves as an elastic medium and, as expected, the pull-off force Fpo (i.e., the maximum tensile force) is found to be independent of the maximum contact radius amax reached at the end of loading. Size-dependent effects are instead observed (i.e., pull-off force Fpo changes with amax) when transient effects occur as the larger the contact area, the greater the size of the bulk volume involved in the dissipation. Results are also discussed in the light of viscoelastic crack Persson's theory, which is modified to capture size effects related to amax.