On mixed-mode fracture mechanics models for contact area reduction under shear load in soft materials

TL;DR

This paper compares different mixed-mode fracture mechanics models for soft materials under shear, highlighting their impact on contact area reduction and the sensitivity of transition behaviors to model assumptions.

Contribution

It introduces a new mixed-mode model and demonstrates how model choice affects predictions of contact area and transition points in soft material friction.

Findings

Transition to sliding is highly sensitive to the mixed-mode model form.

Different models predict varying behaviors like inflexion points or jumps in contact area.

Unstable points differ under load and displacement control.

Abstract

The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have been proposed where the mixed mode toughness is interpreted with phenomenological fitting coefficients introducing weaker coupling between modes than expected by the "purely brittle" model. We compare here two such previously proposed models and introduce a third one to show that the transition to sliding is very sensitive to the form of the mixed-mode model. In particular, after a quadratic decay of the contact area with load for modest tangential loads, there could be an inflexion point and an asymptotic limit, or a jump to the Hertzian contact area. We find also that the unstable points are different under load or displacement control. The idea that the mixed mode function and parameter should be an interface property may be erroneous.