Energetic Size Effect Law at the Microscopic Scale: Application to Progressive-Load Scratch Testing

AbstractA 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, θeq. Then, we express the dependence of the nominal strength, σN, on the structural size, Λ, via a scaling relationship. The theoretical developments are later implemented in an experimental procedu...