Spherical indentation fatigue cracking

The maximum principle stress in spherical indentation occurs at the periphery of the contact area. In a purely elastic material, the radial stress component σr is tensile whilst the hoop component σθ is compressive. The positions of σr and σθ are reversed in an elastic-plastic material under fully plastic indentation, where σr is tensile and σθ is compressive. It follows that the relative positions of σr and σθ vary as the load increases from yield towards the fully plastic deformation. This was demonstrated using a finite element (FE) model, where σr, initially positive, was found to increase to a maximum and then decline with increasing load. In contrast, σθ was negative at the yield load, but increased monotonically with increasing load to become the maximum principle stress component. The FE analysis is in line with experimental observations of fatigue induced by cyclic indentation. Ring cracks were generated with lower peak loads but fatigue fracture was dominated by radial cracks when cycling was done with higher peak loads. However, shallow ring cracks were observed to form under all loads. It is believed that the shallow ring cracks result from short-range asperity interactions, which are not modelled in the FE analysis.