Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels

Abstract

Hydrogels are used in a variety of applications ranging from tissue engineering to soft robotics. They often undergo large deformation coupled with solvent diffusion, and structural integrity is important when they are used as structural components. This paper presents a thermodynamically consistent method for calculating the transient energy release rate for crack growth in hydrogels based on a modified path-independent J-integral. The transient energy release rate takes into account the effect of solvent diffusion, separating the energy lost in diffusion from the energy available to drive crack growth. Numerical simulations are performed using a nonlinear transient finite element method for center-cracked hydrogel specimens, subject to remote tension under generalized plane strain conditions. The hydrogel specimen is assumed to be either immersed in a solvent or not immersed by imposing different chemical boundary conditions. Sharp crack and rounded notch models are used for small and large far-field strains, respectively. Comparisons to linear elastic fracture mechanics (LEFM) are presented for the crack-tip fields and crack opening profiles in the instantaneous and equilibrium limits. It is found that the stress singularity at the crack tip depends on both the far-field strain and the local solvent diffusion, and the latter evolves with time and depends on the chemical boundary conditions. The transient energy release rate is predicted as a function of time for the two types of boundary conditions with distinct behaviors due to solvent diffusion. Possible scenarios of delayed fracture are discussed based on evolution of the transient energy release rate.

Poroelastic toughening in polymer gels: A theoretical and numerical study

“…where we have defined the energy release rate G. This expression is consistent with that obtained in Bouklas et al (2015) following a different derivation and in the finite deformation context. Notice that Φ is pathindependent since the choice of the path C enclosing R is arbitrary.…”

“…In this spirit, here we study the propagation of a semi-infinite, parent crack in an infinite polymer gel that is loaded in Mode I conditions and immersed in a solvent. Previous theoretical works on related problems have considered stationary (Wang and Hong, 2012;Hui et al, 2013;Bouklas et al, 2015) or steadily-growing (Atkinson and Craster, 1991;Radi et al, 2002) cracks, without discussing either fracture propagation criteria, or the effect of poroelastic processes in the near-tip region on the toughness of the system. Moreover, previous experimental data (Tanaka et al, 2000;Lefranc and Bouchaud, 2014;Zhang et al, 2015) on fracture of gels have been interpreted by invoking several dissipation sources, such as viscoelasticity, which have been quantified through phenomenological models.…”

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

“…Each ring provides a calculation of the contour integral. The J‐integral was calculated using a domain integral method, and the J value is the average of the values calculated for each element of the rings, excluding the innermost one surrounding the crack tip, which is considered inaccurate. The total number of elements of the model is 49 490.…”

Poroelastic Effects on the Time- and Rate-Dependent Fracture of Polymer Gels

“…By assuming a specific size distribution of microcracks, they proposed a statistical theory on the lifetime prediction of a swollen gel. Bouklas et al [20] studied the effects of solvent diffusion on the crack-tip fields and the energy release rate for stationary cracks in polymer gels using a nonlinear, transient finite element method. They proposed a modified J-integral for calculating the time-dependent crack-tip energy release rate for quasi-static crack growth in gels, with which delayed fracture was discussed as a possible scenario under certain chemo-mechanical conditions.…”

“…Based on the previous studies [20,24,26,27], we present in this paper the primary results concerning the poroelastic effects on the time-and rate-dependent fracture of polymer gels, including both delayed fracture and steady-state crack growth. In particular, the modified J-integral method is emphasized (Sec.…”