Determination of stress intensity factors for three-dimensional subsurface cracks in hypoid gears

Aim of this paper is to propose a numerical tool able to compute the stress intensity factor for the Mode I, II and III along the front of any subsurface cracks found in spiral and hypoid gear teeth, allowing to assess the criticality of the crack itself. The described approach is based on two steps: firstly the contact pressures in the un-cracked teeth are efficiently computed by an advanced contact solver; in this way the complex tooth geometry and the intricate meshing condition can be accurately considered; then, the displacements field due to those pressures is applied as boundary conditions to a finite element model of the cracked zone and the SIFs are efficiently computed. This information, together with the knowledge of the ΔK threshold value of the material, makes possible to decide whether the defect is acceptable and to evaluate the conditions of propagation.