basis of this limited usefulness of the second type of research that the first group has claimed the superiority of its own methods, although the latter have also been known to be ineffective when confronted with highly complex, but realistic design problems.

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The crack growth in the non-uniform stress field due to the contact loading of a spherical ball on an elastic half-space is described quantitatively for the case of an isotropic brittle solid. This theoretical understanding provides a basis for the Hertzian test which may be used to measure three important surface properties of strong solids and consequently their strength. These are fracture toughness, surface crack size densities and residual stress. All examples of applications of the test are described in detail for glass but the application to a wider variety of strong materials is implied and gives the test a wider significance.

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