2D axisymmetric X-FEM modeling of the Hertzian cone crack system

Abstract

Hertzian cone cracks are nowadays a scholarly case making it possible to understand fracture of materials. However, the simulation of this physical phenomenon is not trivial and most theoretical models lead to the prediction of cone crack angles different from those observed experimentally. In the past, finite-element models have been developed based on a re-meshing procedure to explain this difference successfully, but with some limitations due the algorithms used. In this paper, we propose to use the X-FEM method to model Hertzian cone crack propagation with a 2D axisymmetric approach. The effect of various numerical parameters, such as mesh size or time step, is investigated and it is shown that they do not have a great impact on the crack angle result. The analysis of the stress field induced leads us to understand the difference in terms of cone crack angle based on the pre-existing stress field and those experimentally observed. As a conclusion, X-FEM is very efficient to reproduce faithfully several characteristics of the Hertzian cone crack phenomenon in a very simple manner.