Analysis of the scratch test for cohesive-frictional materials

Abstract

In this thesis we develop analytical solutions for the relations between scratch hardness and strength properties of cohesive-frictional materials of the Mohr-Coulomb and Drucker-Prager type. Based on the lower-bound yield design approach, closed form solutions are derived for frictionless scratch devices, and validated against computational upper bound and elastoplastic Finite Element solutions. The influence of friction at the blade{material interface is also investigated, for which a simple computational optimization is proposed. The model is extended to porous cohesive-frictional materials through the use of a homogenized strength criterion based on the Linear Comparison Composite theory. Relations between scratch hardness, porosity and strength properties are proposed in the form of fitted functions. Illustrated for scratch tests on cement paste, we show that the proposed solutions provide a convenient way to determine estimates of cohesion and friction parameters from scratch data, and may serve as a benchmark to identify the relevance of strength models for scratch test analysis.