Lateral cracking at linear sharp contacts

A fracture mechanics analysis is developed for lateral cracking at linear sharp contacts. Such contacts are commonly encountered as surface scratches formed by loaded wedges, rolled particles, or dragged asperities. The most visible features of a scratch are the lateral cracks extending parallel to the surface from the linear contact. The analysis here takes an energy-based approach to predict lateral crack length as functions of contact load and geometry and material modulus, hardness, and toughness, independent of the scratch origin. The basis of the analysis is the relaxation of residual elastic energy associated with contact deformation and conversion into surface energy associated with lateral cracking. The analysis is supported by experimental measurements of cracks from dragged and rolled contacts. The analysis is applied in derivation of the mineralogical Mohs scale, providing a fundamental basis for the scale in terms of material properties and a clear definition of scratch resistance supported by experiment. The need for more measurements in this field is highlighted