Distinctive Characteristics of Internal Fracture in Tough Double Network Hydrogels Revealed by Various Modes of Stretching

The cyclic stretching measurements in various geometries including uniaxial, planar, unequal, and equal biaxial extension reveal the distinctive features of the internal fracture in the double network (DN) hydrogels with high toughness, which are composed of the rigid and brittle first network and the soft and ductile second network. The initial modulus, residual strain after unloading, dissipated energy (D), dissipation factor (Δ; the ratio of D to input strain energy), and the ultimate elongation of network strands (λ_i,m*) in each loading–unloading cycle are evaluated as a function of the imposed maximum elongation in the i-direction (λ_i,m, i = x, y) in each cycle. The modulus reduction and Δ depend on the stretching mode when compared at the same λ_i,m, but each of them exhibits a universal relation independently of the stretching mode when the corresponding magnitude of the deformation tensor (m_m; m_m = (I_1,m² – 2I_2,m)^1/2 where I_1,m = λ_x,m² + λ_y,m² + λ_z,m² and I_2,m = λ_x,m²λ_y,m² + λ_y,m²λ_z,m² + λ_z,m²λ_x,m²) is used as a variable. This is in contrast to that Δ of the filler-reinforced elastomers, which undergo apparently similar mechanical hysteresis, which shows the corresponding universal relation using I_1,m as a variable. The difference in governing variable indicates that the influence of the cross-effect of strains (λ_iλ_j; i,j = x,y,z and i ≠ j) on Δ is pronounced in the DN gels whereas it is minimal in the filled elastomers. Characteristically, λ_i,m* is close to λ_i,m in every type of deformation, indicating that in the end of the loading most of the chains with lower extensibility than λ_i,m undergo fracture whereas most of the long chains with higher extensibility than λ_i,m remain intact. The elongation λ_i,m* has no appreciable cross-effect of strains in contrast to the modulus reduction as well as Δ.