Behavior of a fluid filled subsurface crack under moving hertzian loading

Cracking of a fluid filled subsurface crack is studied by the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The induced hydrostatic fluid pressure inside the crack is calculated through an iterative scheme with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume (COV). The stress intensity factors at the tips of the fluid filled crack are analyzed and the effective quadrature formulae are given for the evaluation of the COV. A hypothesis is introduced that the crack propagation is initiated when the elastic strain energy release rate reaches the critical fracture toughness and is arrested when the energy release rate is below the arrest toughness. Based on the energy criterion, predictions will be attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed for various loading conditions.