Mixed mode stress intensity factors for a crack parallel to the free surface of a half-plane under uniform loading

The Griffith crack, a central crack in an infinite plane under uniform loading, is converted to a subsurface one by moving close to a loaded edge of the plane. Subsurface cracks initiate under rolling contact fatigue conditions. In this paper, first, finite element model of the Griffith crack has been developed and validated by calculating stress intensity factors (SIFs) under uniform tension and shear loadings. Then, by moving the crack close to a parallel edge of the plane, mixed mode SIFs of the subsurface crack have been determined for a wide range of the cracks depths. Non-symmetrical geometry with respect to the crack edge causes coupling between fracture modes and so, considerable shear and tension fracture modes under tension and shear loadings, respectively. The ratio of SIF for the coupling mode to the direct mode is creased up to 69% for the length to depth ratio of 20. Also, by fitting third-degree polynomials to the mixed mode SIFs, four geometry correction factors have been obtained for SIFs of subsurface cracks under uniform loadings. These approximate equations can be used easily and efficiently by engineers. Also, the relations can be utilized as a primary estimation for non-uniform loadings, especially when the crack length as well as the load variation along it is small.