Model of Strength Degradation from Hertzian Contact Damage in Tough Ceramics

Abstract

A model of strength degradation for ceramics subject to damage from contact with hard spheres is developed. Primary attention is focused on tough ceramics with heterogeneous microstructures which deform in a quasi‐plastic mode. Brief consideration is also given to ideally brittle ceramics which form classical ring cracks, as a comparative baseline. Strength vs indentation load data from two microstructurally controlled ceramics, silicon nitride and a micaceous glass‐ceramic, illustrate distinctive strength degradation responses: in fine‐grain (F) form, ideally brittle failure from ring cracks, with abrupt strength loss at the critical load for crack initiation followed by a slow falloff at increasing load; in coarse‐grain (C) form, failure from within the quasi‐plastic zone, with continuous strength loss beyond a load well above that for the onset of yield, and with even slower falloff. Failure in the latter materials occurs from contact‐induced microdamage flaws with two essential elements: an inner closed shear crack with frictional sliding faces (“shear fault”), which forms within the confining compression–shear contact field; an outer annular, kinked crack that initiates at the fault edges (“wing crack”), and that extends in tensile local mode. The critical fault–crack is modeled as a virtual crack, with the residual field from the inner fault stabilizing the net driving force on the outer wing crack during ensuing tensile loading. Finite element modeling is used to evaluate the nonlinear elastic–plastic contact fields, and to provide a relationship between residual shear fault stress and contact load. The model accounts for the essential qualitative and quantitative features of the strength–load data, with provision for catastrophic degradation at high fault densities and extreme loads by microcrack coalescence. The model also contains the ingredients for analysis of contact fatigue, via attrition of the frictional tractions on the residual fault.