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Description
Yalin Yu1 Chad Landis1 Rui Huang1

1, The University of Texas at Austin, Austin, Texas, United States

Based on a linear poroelastic formulation, we present an asymptotic solution of the crack tip fields for steady-state crack growth in polymer gels. A linear finite element method is developed for numerical analysis. A strip with a semi-infinite crack under plane-strain condition is studied in details. The crack-tip fields by the numerical analysis agree with the asymptotic solution with a crack-tip stress intensity factor, which varies slightly with the crack velocity due to the poroelastic effect and generally smaller than the stress intensity factor predicted by linear elasticity. The size of the poroelastic crack-tip field is characterized by a diffusion length scale that depends on the crack velocity. For relatively fast crack growth, the diffusion length is small compared to the strip thickness, and the crack-tip field transitions to the elastic K-field at a distance proportional to the diffusion length. In this case, the energy release rate by a modified J-integral decreases with increasing crack velocity. For relatively slow crack growth, the diffusion length is comparable to or greater than the strip thickness, and the crack-tip field is confined by the strip thickness and transitions to a one-dimensional diffusion zone ahead of the crack tip. In this case, the energy release rate increases with increasing crack velocity. These results suggest that, if the intrinsic fracture toughness of the gel is independent of the crack velocity, the apparent fracture toughness including the energy dissipation due to solvent diffusion would be generally greater than the intrinsic toughness and depends non-monotonically on the crack velocity or the strip thickness.

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