The effect of the effective polymer network on the extremely large deformation and fracture behaviors of polyacrylamide hydrogels

Current constitutive theories and fracture models face difficulties in capturing the extremely large deformation and fracture behaviors of hydrogels, because the structural and mechanical properties of the effective polymer network dominated in hydrogels are still unknown. In this study, we propose a periodic random network (PRN) method to construct the effective polymer network model of polyacrylamide (PAAm) hydrogel from the bottom up and reveal the effect of the effective polymer network on the extremely large deformation and fracture behaviors of PAAm hydrogels. It is surprising that the PRN models determined by only three parameters capture the extremely large deformation and fracture behaviors of PAAm hydrogel in uniaxial tension experiments very well. The PRN models measure that only about 20 % of monomers and crosslinkers form the effective network in the PAAm hydrogel samples in this work, and the mean monomer number of the effective chains in PAAm hydrogels deviates a lot from that estimated by the ideal network assumption. An anisotropic damage accumulation process of PAAm hydrogel under extremely large deformation before bulk fracture is predicted by PRN models, which has been observed in previous experiments but not explained. This is the fundamental cause that the Lake-Thomas model underestimates the intrinsic fracture toughness of PAAm hydrogels very much. This work provides an insightful method to measure the structural and mechanical properties of hydrogels.