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 (Delta; the ratio of D to input strain energy), and the ultimate elongation of network strands (lambda(i,m)*) in each loading-unloading cycle are evaluated as a function of the imposed maximum elongation in the i-direction (lambda(i,m), i = x, y) in each cycle. The modulus reduction and Delta depend on the stretching mode when compared at the same lambda(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,m(2) - 2I(2,m))(1/2) where I-1,I-m = lambda(2)(x,m) + lambda(2)(y,m) + lambda(2)(z,m) and I-2,I-m = lambda(2)(x,m)lambda(2)(y,m) + lambda(2)(y,m)lambda(2)(z,m) + lambda(2)(z,m)lambda(2)(x,m)) is used as a variable. This is in contrast to that Delta of the filler-reinforced elastomers, which undergo apparently similar mechanical hysteresis, which shows the corresponding universal relation using I-1,I-m as a variable. The difference in governing variable indicates that the influence of the cross-effect of strains (lambda(i)lambda(j); i,j = x,y,z and i not equal j) on Delta is pronounced in the DN gels whereas it is minimal in the filled elastomers. Characteristically, lambda(i,m)* is close to lambda(i,m) in every type of deformation, indicating that in the end of the loading most of the chains with lower extensibility than lambda(i,m) undergo fracture whereas most of the long chains with higher extensibility than lambda(i,m) remain intact. The elongation lambda(i,m)* has no appreciable cross-effect of strains in contrast to the modulus reduction as well as Delta.