A semi-analytical approach to mode-I stress intensity factor and fracture energy of a circular crack in a poroviscoelastic medium

This paper presents a semi-analytical method to evaluate the mode-I stress intensity factor and fracture energy for a circular crack in a poroviscoelastic medium under axisymmetric strain conditions. The analysis employs the Laplace-Hankel transform technique and displacement functions to address the coupling of viscoelasticity and fluid drainage. A closed-form expression for the stress intensity factor is derived in the Laplace domain and numerically inverted to the time domain. The method is applied to both impermeable and permeable cracks under constant remote stress, and the instantaneous fracture energy is determined from the stress intensity factor. To validate the semi-analytical findings, a finite element model incorporating cohesive zone elements is developed, and the J-integral is used to compute the instantaneous fracture energy. Results indicate that fluid drainage leads to time-dependent increases in the stress intensity factor and fracture energy, influenced by changes in the effective Poisson's ratio and medium thickness. For materials with viscoelastic relaxation times much longer than drainage times, the stress intensity factor stabilizes after drainage, while fracture energy continues to evolve. This framework provides significant insights into the time-dependent fracture behavior of circular cracks in poroviscoelastic media, incorporating the effects of finite thickness.