Partial cone crack formation in a brittle material loaded with a sliding spherical indenter

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Abstract
In the preceding paper Frank & Lawn (1967) investigated theoretically the development of a cone crack in the strongly inhomogeneous Hertzian stress field. The analysis outlined in that paper is now extended to incorporate a sliding motion of the spherical indenter across the specimen surface, assuming a uniform coefficient of friction over the contact area. Sliding is found to have a large influence on the quasistatic stress field in the loaded specimen, and this in turn affects the ultimate geometry of the cracks. The precise shape of the partially developed cones thus formed is a function only of the Poisson ratio of the specimen material and the coefficient of friction. Criteria determining when surface fracture will occur, expressed as relationships between the critical normal load P$_c$ acting on the specimen and the indenter radius r, are calculated as before. The Auerbach law found for purely normally loaded specimens, namely that P$_c$ is proportional to r, over a certain range of r, should cease to hold when the coefficient of friction exceeds about 0.02. P$_c$ then becomes very nearly proportional to r$^2$, which corresponds to a critical stress criterion. The effect of sliding on the value of P$_c$ becomes large with larger values of the coefficient of friction; this is of particular relevance to studies of the surface damage of brittle materials.

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