Capturing the hardness of coating systems across the scales

Abstract

A two-dimensional multi-scale modelling approach that concurrently couples discrete dislocation plasticity and crystal plasticity finite element has been applied to study the hardness variation of coating systems across different scales, covering nano- to micro-indentation. The difference in indentation size sensitivity between film and substrate gives rise to three regimes of hardness, one typically dictated by the intrinsic coating indentation size effect, which is regulated by dislocations activity, and the other two linked to the continuum response of the coating and the substrate. We propose a new hardness formula that incorporates physics-based indentation size effects of thin films into established continuum hardness transition formulae. This formula is shown to substantially improve the hardness prediction of coating systems, particularly when relative indentation depth is at the nanometre scale.