Scratch test model for the determination of fracture toughness

We revisit the scratch test within the framework of linear elastic fracture mechanics. In the analysis, we employ an Airy stress function approach to determine stresses and displacement in the vicinity of the scratch-blade–material interface, which serve as input for the evaluation of the energy release rate by means of the J  -Integral. In contrast to previous models, the energy release rate thus found scales with the sum of the applied forces squared. This entails a linear relation between the applied forces and wd, where w is the scratch width and d the scratch depth. This analytical scaling is validated using experimental scratch data on cement paste and sandstone, which shows that the proposed approach provides a convenient way to determine the fracture toughness from scratch tests carried out with different scratch widths and depths.