CONTACT MECHANICS OF HERTZIAN CONE CRACKING

Quasi-static indentation of brittle materials with a spherical indente r produces Hertzian cone cracks. The variation of cone crack length wi th load is measured by indenting soda-lime glass blocks with a 3.17 mm diameter hardened steel ball and photographing the cracks through a s ide face of the blocks. Assuming that the contact pressure distributio n is Hertzian, axisymmetric boundary elements are used to accurately c alculate stress intensity factors along the front of the cone crack by adapting the modified crack closure integral. The boundary element re sults are verified through comparisons with finite element calculation s and prior results in the literature. The Mode I stress intensity fac tor is found to be a positive monotonically decreasing function of con e crack length, provided that the contact radius is not greater than t he cone crack radius at the surface. Calculations using the Hertzian p ressure distribution predict that the cone crack will arrest when the contact radius is greater than the cone crack length at the surface. H owever, experimental observations suggest that as the contact radius a pproaches the cone crack radius at the surface, interaction effects le ad to a non-Hertzian pressure distribution. Detailed finite element co ntact mechanics of the actual cracked body are used to show that the c ontact pressure is singular at the edge of contact once the contact ra dius becomes equal to the cone crack radius. Furthermore, cone crack g rowth continues even when contact between the indenter and the cracked body occur outside of the cracked region, which is consistent with ex perimental observations. This latter aspect of cone crack growth canno t be predicted on the basis of a Hertzian pressure distribution.