Determination of Surface Residual Stresses in Brittle Materials by Hertzian Indentation: Theory and Experiment

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Abstract
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‐breaking crack in the neighborhood of the contact will propagate. There is a threshold 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 to produce Hertzian fracture are predicted for alumina and glass, assuming that the variation of the residual stress over the length of the crack is small. Two methods of analysis (one approximate, one more general) are presented that enable the residual stress to be calculated from the shift in threshold load; the only further information required is a knowledge of the radius of the sphere, the elastic constants of the sphere and substrate, and also the fracture toughness of the substrate (or use of a stress‐free specimen as a reference). No measurement of any crack length is necessary. Experimental results are presented for the residual stress levels determined in glass strengthened by ion exchange. Indenting balls of a variety of materials with a range of elastic mismatch to the glass substrate were used, so as to evaluate the effects of elastic mismatch and interfacial frictional tractions on the results obtained. The results obtained by Hertzian indentation are consistent with residual stress levels determined by differential surface refractometry. We also present results on alumina specimens with induced surface stresses.

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