Contact mechanics of hertzian cone cracking

Quasi-static indentation of brittle materials with a spherical indenter produces Hertzian cone cracks. The variation of cone crack length with load is measured by indenting soda-lime glass blocks with a 3.17 mm diameter hardened steel ball and photographing the cracks through a side face of the blocks. Assuming that the contact pressure distribution is Hertzian, axisymmetric boundary elements are used to accurately calculate stress intensity factors along the front of the cone crack by adapting the modified crack closure integral. The boundary element results are verified through comparisons with finite element calculations and prior results in the literature. The Mode I stress intensity factor is found to be a positive monotonically decreasing function of cone crack length, provided that the contact radius is not greater than the cone crack radius at the surface. Calculations using the Hertzian pressure distribution predict that the cone crack will arrest when the contact radius is greater than the cone crack length at the surface. However, experimental observations suggest that as the contact radius approaches the cone crack radius at the surface, interaction effects lead to a non-Hertzian pressure distribution. Detailed finite element contact mechanics of the actual cracked body are used to show that the contact pressure is singular at the edge of contact once the contact radius becomes equal to the cone crack radius. Furthermore, cone crack growth continues even when contact between the indenter and the cracked body occur outside of the cracked region, which is consistent with experimental observations. This latter aspect of cone crack growth cannot be predicted on the basis of a Hertzian pressure distribution.