Analytical models of scratch hardness

The ability of one material to abrade or scratch another has a long history as the basis of a scale of hardness and is clearly related to the now more common measure of hardness as the resistance of a material to indentation. However, there is no simple relation between the values of hardness from these two tests. Producing an abraded groove in the surface of a specimen involves large plastic strains, and a number of analytical models have been proposed for this process based on such techniques as slip line field theory and the theorems of plastic load bounding. While there is reasonable agreement between the predicted and measured values of the loads, these methods are much less satisfactory in providing estimates of the patterns of deformation or strain around the groove and these limitations may be associated with some of the idealizations relatively simple models make about material behaviour — such as isotropy and a neglect of elastic effects. The scratch testing of brittle solids can also involve plastic behaviour facilitated by the high local hydrostatic compressive stresses generated close to the tip of a sharp indenter. Scratch hardness is also finding applications as a test for the integrity of coated substrates, although the modes of failure here may be more complex than those observed in homogeneous materials.