Fracture scaling relations for scratch tests of axisymmetric shape Ange-Therese Akono, Franz-Josef Ulm n Massachusetts Institute of Technology, Cambridge MA 02139, United States article info Article history: Received 22 March 2011 Received in revised form 8 December 2011 Accepted 14 December 2011 Available online 22 December 2011 Keywords: Scratch test analysis Axisymmetrical probe Fracture mechanics Scaling Fracture toughness abstract 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 probe–material 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. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Scratching a weaker material with a tougher one is no doubt the most elemental conceptualization of a mechanics-of- materials test ever conceived by mankind. In use as a tool to compare the relative hardness of two materials since ancient time, the first abstraction of scratch resistance into a quantitative metric of material classification is due to Carl Friedrich Christian Mohs (1773–1839), who in 1824 put the ability of one mineral sample to scratch another on an ordinal (rank- ordering) scale, the Mohs scale of mineral hardness (Bowden and Tabor, 1964). Scratch force criteria as a basis for comparison of scratch resistance of materials emerged throughout the 20th century, and namely the scratch hardness, H T , that links the horizontal scratch force, F T , required to move the scratch probe, to the contact area between the probe and the scratched material projected in the scratch direction, A LB : F T ¼ def H T A LB ð1Þ All this led to the development of instrumented scratch tests in the early 1970s, in which the applied forces and acoustic emissions generated by microcracks are measured simultaneously (Wilshaw and Rothwell, 1971). In turn, these advances in instrument development were the stepping stone to link a measurable mechanical event, i.e. force or hardness, to material behavior, i.e. plastic or fracture behavior. They enabled theoretical works in scratch test analysis that ultimately Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmps Journal of the Mechanics and Physics of Solids 0022-5096/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2011.12.009 n Corresponding author. E-mail address: ulm@mit.edu (F.-J. Ulm). Journal of the Mechanics and Physics of Solids 60 (2012) 379–390