Fracture scaling relations for scratch tests of axisymmetric shape

Scratch testing and scratch test analysis continues to gain momentum in Applied Mechanics, due to the possibility offered by this method to assess fracture properties at very fine scales. In this paper, we derive general scratch force scaling relations for axisymmetric scratch probes defined by single variable monomial functions. These relations are used to define fracture criteria with and without consideration of the development of shear stresses at the probematerial interface. The approach is illustrated for common scratch probe geometries: conical probe, flat punch, and hemi-spherical probe. Application of the proposed method to micro-scratch tests on two materials (an aluminum alloy and a thermoplastic polymer) using a Rockwell probe (a conical probe ending in a hemi-spherical shape) illustrates the versatility of the approach: First, the scratch force-depth scaling relations provide a means to determine the degree of the homogeneous function characterizing the scratch probe. Second, the fracture criteria enable an experimental assessment of the fracture toughness. The good agreement between the fracture toughness determined by scratching and values reported in the open literature show the potential of the proposed method for determining fracture properties of materials at even smaller scales.