A model for crack initiation in elastic/plastic indentation fields

Abstract

A model is proposed for the initiation of microfracture beneath sharp indenters. Using a simple approximation for the tensile stress distribution in the elastic/plastic indentation field, in conjunction with the principle of geometrical similarity, fracture mechanics procedures are applied to determine critical conditions for the growth of penny-like “median cracks” from sub-surface flaws. The analysis provides a functional relationship between the size of the critical flaw and the indentation load necessary to make this flaw extend. Initiation is well defined (unstable) only if the critical flaw lies within a certain size range; outside this range, large flaws can extend stably but small flaws can not extend at all. No flaws can extend below a characteristic minimum load, values of the indentation variables at this load accordingly providing useful threshold parameters. These quantities involve the intrinsic deformation/fracture parameters, hardness and toughness, in a fundamental way, thereby establishing a basis for materials selection in fracture-sensitive applications.