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

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.

Residual stress distributions around indentations and scratches in polycrystalline Al2O3 and Al2O3/SiC nanocomposites measured using fluorescence probes

“…These data can be used to estimate the surface residual stresses [24]. Data were analysed by calculating the effects of biaxially compressed surface layers of varying stress level and depth on the results of the Hertzian tests.…”

Fracture of diamond coatings by high velocity sand erosion

“…Before this higher load is reached the fracture of the sand particles may occur, thereby preventing that load from being attained. Roberts et al [28,29] have investigated the effect of compressive residual stress on the fracture load in a Hertz indentation test indenting glass with a 10 mm diameter glass ball. They found that as the surface compressive stress increased from 0 (nominally "stress free") to 500 MPa the minimum fracture load increased by more than an order of magnitude.…”

Hertzian contact fatigue on alumina/alumina-zirconia laminated composites

“…For the case of a material with residual stress, the value of µ is affected by the relative value of these residual stresses with respect to peak indentation pressure. 38 If this relative value is lower than 20%, the modified value of µ by the residual stresses, labelled as µ , can be related through the value of µ without residual stresses by the approximation: µ = µb −σ r /P 1/3 (14) where b is a constant, which depends on the elastic properties of the material and the indenter. Using this relationship for µ , a similar relationship as Eq.…”