Invariant Fractocohesive Length in Tough Hydrogels with Strongly Rate- and Temperature-Dependent Mechanical Properties

Tough hydrogels with dynamic physical bonds exhibit pronounced viscoelasticity, making their mechanical properties, such as modulus, fracture energy (Γ), and fracture work (Wf), strongly dependent on stretch rate and temperature. Despite this, the influence of viscoelasticity on the fracture process and the associated characteristic length scale remains elusive. Here, we investigate two representative viscoelastic hydrogels: a dual-cross-linked hydrogel combining permanent covalent cross-links with reversible metal-coordination bonds, and a supramolecular hydrogel cross-linked solely by hydrogen bonds. Both systems display significant rate- and temperature-dependence in elastic modulus, fracture energy, and fracture work. However, their fractocohesive length (Lf = Γ/Wf), which characterizes the size of the fracture process zone, exhibits only minimal variation with stretch rate and temperature. This near-constancy of Lf is corroborated experimentally by flaw-sensitivity tests, which also indicate that the flaw-sensitivity length remains largely unchanged. Furthermore, finite element simulations confirm a mostly consistent size of the fracture process zone under different loading conditions, whereas the magnitude and distribution of stress are distinct. These findings suggest that Lf is a robust and generalizable descriptor for characterizing the fracture behaviors of viscoelastic soft materials, providing a simple yet powerful basis for understanding fracture mechanisms and designing damage-tolerant soft materials under diverse conditions.