Determination of surface residual stresses in brittle materials by Hertzian indentation: Theory and experiment

Hertzian indentation has been used to determine the surface residual stress levels in brittle materials. In this method, a hard sphere is pressed into the surface of the material: at a critical load a preexisting surface-brea king crack in the neighborhood of the contact will propagate. There is a th reshold load below which no such crack, of whatever size, can be propagated . The presence of a residual stress in the surface will lead to a shift in this threshold load. The effects of residual stresses on the minimum load t o produce Hertzian fracture are predicted for alumina and glass, assuming t hat the variation of the residual stress over the length of the crack is sm all. Two methods of analysis tone approximate, one more general) are presen ted that enable the residual stress to be calculated from the shift in thre shold load; the only further information required is a knowledge of the rad ius of the sphere, the elastic constants of the sphere and substrate, and a lso the fracture toughness of the substrate (or use of a stress-free specim en as a reference). No measurement of any crack length is necessary. Experi mental results are presented for the residual stress levels determined in g lass strengthened by ion exchange. Indenting balls of a variety of material s with a range of elastic mismatch to the glass substrate were used, so as to evaluate the effects of elastic mismatch and interfacial frictional trac tions on the results obtained. The results obtained by Hertzian indentation are consistent with residual stress levels determined by differential surf ace refractometry. We also present results on alumina specimens with induce d surface stresses.