Steady-state crack growth in polymer gels: A linear poroelastic analysis

Abstract

Based on a linear poroelastic formulation, we present an asymptotic analysis of the crack tip fields for steady-state crack growth in polymer gels. A finite element method is then developed for numerical analysis. A semi-infinite crack in a long strip specimen subject to plane-strain loading is studied in detail. The crack-tip fields from the numerical analysis agree with the asymptotic analysis with a poroelastic stress intensity factor, which is generally smaller than the stress intensity factor predicted by linear elasticity due to poroelastic shielding. Similarly, the crack-tip energy release rate calculated by a modified J-integral method is smaller than the applied energy release rate. The size of the poroelastic crack-tip field (or K-field) is characterized by a diffusion length scale that is inversely proportional to the crack speed. For relatively fast crack growth, the diffusion length is small compared to the strip thickness (small-scale diffusion), and the poroelastic K-field transitions to an elastic K-field at a distance proportional to the diffusion length. In this case, the crack-tip energy release rate decreases with increasing crack speed under the same loading condition. For relatively slow crack growth, the diffusion length is greater than the strip thickness (large-scale diffusion), and the poroelastic crack-tip field is confined and transitions to a one-dimensional diffusion zone ahead of the crack tip. In this case, the energy release rate increases with increasing crack speed. Both immersed and not-immersed crack face conditions are considered. Under the same loading conditions, the poroelastic stress intensity factor and the modified J-integral are higher for the immersed case than not-immersed, but they approach the same values at the fast and slow crack limits. In general, if the crack-tip energy release rate is taken to be the intrinsic fracture toughness of the gel, the applied energy release rate as the apparent fracture toughness is greater due to energy dissipation associated with solvent diffusion, which is referred to as poroelastic toughening. It is proposed that the modified J-integral can be used to determine the intrinsic fracture toughness of the gel in experiments, which may or may not depend on crack speed. Moreover, the present results are found to be qualitatively consistent with previous experiments on the effects of solvent viscosity and crack-tip soaking.