Angle of Hertzian Cone Cracks

This paper discusses the difference between the experimentally observed angle of Hertzian cone cracks and the angle defined by the trajectories of the preexisting stress fields. It is argued that there is no reason why these angles should be the same, as has usually been assumed. A finite element method has been used to model the growth of cracks in the Hertzian stress fields. In this model, the crack is incrementally advanced along the direction of maximum strain energy release, as calculated by the evolving, rather than the preexisting, stress fields. For the modeled Hertzian indentation system, a cone crack is observed to grow, but at an angle which is significantly different from that defined by the normal to the maximum preexisting tensile stress. The angle of the cone crack, as grown in the model, is in excellent agreement with observations on experimentally grown cone cracks in glass, with the same Poisson's ration. It is proposed that, in general, cracks will grow along paths that result in the maximum release of strain energy. For asymmetric, nonuniform preexisting stress fields, such paths do not necessarily coincide with the normal to the maximum preexisting tensile stress.