HERTZIAN FRACTURE IN SINGLE CRYSTALS WITH THE DIAMOND STRUCTURE
BROWN UNIV PROVIDENCE RI DIV OF ENGINEERING
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Extension of an earlier theory of Hertzian fracture in brittle isotropic materials is made to include the case of brittle single crystals. A criterion is first proposed for predicting the path of a crack through an inhomogeneously stressed crystal in terms of the surface energy anisotropy of the crystal and the stresses prior to fracture occurring. This criterion is then applied to determine the geometry of cracks formed in the Hertzian stress field in crystals having the diamond structure. The computed crack geometries agree well with observation. An analysis of the fracture mechanics of crack growth into the crystal subsequently indicates that for a certain range of indenter size the Hertzian crack passes through four equilibrium stages, as it does in glass, before reaching its fully developed length. As a result Auerbachs law holds, i.e. the critical load on the indenter necessary to produce a fully developed Hertzian fracture is proportional to the radius of the indenter. This law is confirmed by Hertzian fracture tests on silicon single crystals. Finally, possible application of the Hertzian test to the study of some mechanical properties, such as fatigue, of brittle single crystals is indicated.