Probability of cone crack initiation due to spherical contact loading

The probability of the extension of surface cracks due to spherical indentation is analyzed. Contact loading problems typically result in multi-axle and strongly inhomogeneous stress fields near the contact surface. This property which strongly affects the stress intensity factors is taken into account in the failure analysis. Edge cracks were selected to model the actually occurring surface flaws. The stress intensity factors were integrated with the weight function method, and propagation of pre-existing cracks was assessed by using an energy release rate failure criterion. For the statistical analysis the Weibull theory was extended in some points. By applying the method to the cone crack formation during a spherical indentation, it was found that the probability for cone crack formation increases abruptly, when a certain yield load is exceeded. Therefore, the loading range can be divided into a critical and a less critical section, which were found to correlate to separated spatial regions of an occurring local risk of fracture. Because of the effects discovered, it seems to be inevitable to consider the strongly inhomogeneous stress fields in a failure analysis of a contact loading problem.