Quantify the failure zone and elastic release zone: A new insight into intrinsic fracture of polymer networks

The intrinsic fracture energy of polymer networks describes the minimum energy required for crack propagation, excluding any inelastic dissipation within the bulk. Recent studies have demonstrated that the intrinsic fracture energy arises from two distinct contributions. The first contribution ${\Gamma }_f$ is the energy dissipated by the rupture of polymer chains along the crack path, where these chains constitute the failure zone. The second contribution ${\Gamma }_e$ is the elastic energy released from the relaxation of polymer chains adjacent to the broken chains, where these chains constitute the elastic release zone. While existing models could predict the intrinsic fracture energy of polymer networks successfully, a quantification of the two intrinsic fracture energy contributions remains elusive. Here, utilizing polyacrylamide hydrogel, we conduct a series of pure shear tests to measure the fracture energy. The size of real elastic release zone is precisely controlled in this study by varying the heights of pure shear samples. Then, for the first time, ${\Gamma }_f$ and ${\Gamma }_e$ of the polyacrylamide hydrogel are quantitatively identified based on the relationship between the apparent fracture energy and the height of sample. Moreover, our development of a modified loop-opening model represents a significant advancement in the field. This model accounts for polymer network imperfections and incorporates parameters with clear physical meanings, aligning remarkably well with our experimental findings. Based on our model, we propose a novel method for determining the size of failure zone. Furthermore, our findings offer insights into the discrepancies observed in fracture energy measurements obtained through various testing methods. This study enhances the understanding of intrinsic fracture mechanisms within polymer networks and lays the groundwork for the design of tougher polymer materials.