# On the application of fracture mechanics mixed-mode models of sliding with friction and adhesion

## TL;DR

This paper critically examines the application of fracture mechanics mixed-mode models to sliding adhesive contacts, highlighting discrepancies with experimental observations and suggesting semi-empirical models as more practical alternatives.

## Contribution

The paper analyzes the limitations of the Menga, Carbone & Dini theory in modeling sliding adhesive contacts and advocates for semi-empirical approaches for better experimental agreement.

## Key findings

- MCD theory predicts contact area increase not observed experimentally.
- MCD theory suggests size effects and JKR curve distortion not seen in practice.
- Pure mode I contact in MCD leads to unbounded contact area, challenging interpretation.

## Abstract

As recently suggested in an interestring and stimulating paper by Menga, Carbone & Dini (MCD), applying fracture mechanics energy concepts for the case of a sliding adhesive contact, imposing also the shear stress is constant at the interface and equal to a material constant (as it seems in experiments), leads to a increase of contact area which instead is never observed. We add that the rigorous MCD theory also predict a size effect and hence a distortion of the JKR curve during sliding which is also not observed in experiments. Finally, a simpler example with the pure mode I contact case, leads in the MCD theory to an unbounded contact area, which is difficult to interpret, rather than a perhaps more correct limit of the Maugis-Dugdale solution for the adhesive sphere when Tabor parameter is zero, that is DMT's solution. We discuss therefore the implications of the MCD theory, although they may be rather academic: recent semi-empirical models, with an appropriate choice of the empirical parameters, seem more promising and robust in modelling actual experiments.