Analysis of Hertzian indentation fracture using a phase field approach

The formation and further evolution of cracks caused by the compression of a stiff indenter onto the surface of an initially defect-free brittle solid is a fascinating problem of fracture mechanics. Its prediction, however, is still a challenging task since crack nucleation is caused by a rather weak stress concentration in the contact near-field. The present contribution focuses on phase field simulation of indentation fracture, including crack formation at some a priori unknown location outside of the contact region and the subsequent formation of a cone crack. While the phase field method, at first glance, appears to be a promising tool to simulate the current problem we elaborate critical issues and discuss essential modifications. Finally, the indentation fracture process is simulated showing the effect of varying indenter radii on crack initiation and the influence of Poisson's ratio on the angle of cone crack propagation in good agreement with experimental findings and other theoretical studies.