SUMMARYIn this paper we develop analytical solutions for scratch hardness-strength relations for 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. 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.

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