Time-dependent fracture of mode-I cracks in poroviscoelastic media

Fluid-infiltrated porous materials such as polymeric gels are often found to behave like poroviscoelastic materials, which have time-dependent mechanical behavior resulting from flow-induced and viscoelastic deformations. The fracture phenomena of polymeric gels can be affected by the two aforementioned transient deformations. This research analyzed the concurrent deformation of the solid skeleton and the migration of pore fluid driven by the inhomogeneous stress field around the tip of a crack in a poroviscoelastic medium under constant applied tensile stresses at infinity using finite element analysis. The instantaneous fracture energy was calculated using J-integral formula and cohesive elements around the crack tip in the FEM simulations. The numerical results have been verified with the theoretical predictions at the undrained and drained limits for poroelastic cases. The required length of cohesive zone for the accuracy of the instantaneous energy release rate at the undrained limit needs to be smaller than the size of the inner K (stress intensity factor) dominated region. The cohesive zone length is particularly small for permeable cracks. For both permeable and impermeable cracks in poroviscoelastic media, the value of instantaneous energy release rate usually increases with time. However, for the poroviscoelastic materials of decreasing time-dependent Poisson's ratio, the value decreases during the time when viscoelastic relaxation occurs before drainage. The delayed time to fracture can be estimated by the intrinsic fracture energy and the time-dependent J curves obtained for permeable and impermeable cracks in poroviscoelastic media.