Fracture mechanics model for subthreshold indentation flaws

Abstract

A fracture mechanics model for subthreshold indentation flaws is. described. The model describes the initiation and extension of a microcrack from a discrete deformation-induced shear “fault” (shear crack) within the contact zone. A stress-intensity factor analysis for the microcrack extension in residual-contact and applied-stress fields is used in conjunction with appropriate fracture conditions, equilibrium in Part I and non-equilibrium in Part II, to determine critical instability configurations.

In Part I, the K-field relations are used in conjunction with the Griffith requirements for crack equilibrium in essentially inert environments to determine: (i) the critical indentation size (or load) for spontaneous radial crack pop-in from a critical shear fault under the action of residual stresses alone; (ii) the inert strengths of surfaces with subthreshold or postthreshold flaws. The theory is fitted to literature data for silicate glasses. These fits are used to “calibrate” dimensionless parameters in the fracture mechanics expressions, for later use in Part II. The universality of the analysis in its facility to predict the main features of crack initiation and propagation in residual and applied fields will be demonstrated. Special emphasis is placed on the capacity to account for the significant increase in strength (and associated scatter) observed on passing from the postthreshold to the subthreshold domain.