Energetic size effect law at the microscopic scale: Application to progressive-load scratch testing

A scratch test consists in pulling a diamond stylus across the surface of a weaker material; it is widely applied in several fields of science and engineering, including polymer damage, metal wear, thin-film quality control, and strength of rocks. Recently, there has been an upsurge of interest in the fracture analysis of materials via scratch testing. In this study, the energetic size effect law (SEL) is applied at the microscopic scale for progressive-load scratch tests using a Rockwell C diamond probe. First, we employ dimensional analysis to connect the scratch force to the projected load-bearing area and to the perimeter for an axisymmetric scratch probe. In a second step, based on geometrical considerations, we approximate the real scratch probe geometry with a cone of equivalent half-apex angle, θ_eq. Then, we express the dependence of the nominal strength, σ_N, on the structural size, Λ, via a scaling relationship. The theoretical developments are later implemented in an experimental procedure so as to assess the solid fracture toughness and characteristic length directly from micro-scratch test measurements. The microscopic SEL is first tested on homogeneous materials, such as paraffin wax, polycarbonate, polyacetal, and aluminum. An excellent agreement is found between the theoretical predictions and measurements from conventional fracture testing methods, such as three-point bending tests on single-edge notched specimens. The theoretico-experimental framework is then extended to an extensive characterization campaign including conventional portland cement paste, natural shale, and organic-rich shale. For more than 10 different materials, the nominal strength exhibits a distinct scaling in 1/√1 + Λ/Λ₀, as predicted by the SEL.