Theoretical analysis of Hertzian contact fracture: Ring crack

The axisymmetric fracture behavior of brittle materials under an applied indentation force is investigated by considering the pile-up of Somigliana ring dislocations. For such a mixed-mode crack problem, the stress intensity factors (SIFs) and strain energy release rate are obtained by solving a system of Cauchy singular integral equations. The Auerbach range is extensively studied during the formation of a shallow ring crack. The Auerbach constant is also determined from the exact solutions, enabling the prediction of surface energy from Hertzian indentation tests. The obtained results can be used to extract the fracture parameters of brittle materials by using the indentation technique.