Size effects in abrasion of brittle materials

Small indentations and scratches can be made in highly brittle materials such as glass or silicon without any associated fracture. It is proposed that this effect, which is usually explained in terms of flaw statistics, is in fact governed by a strain energy criterion which can be defined quantitatively if the tensile field which initiates fracture is known. Using a model of the field of residual stress around an indentation proposed by Swain and Hagan (1976), it is shown that the critical size of indentation for fracture to occur should be about 12(ET/Y²), where E is Young's modulus, Gamma fracture surface energy, and Y the yield stress for plastic flow in uniaxial compression. The critical size parameter is evaluated for silicon.