Stretching experiments with various geometries are performed using a custom-built tensile tester to reveal the intriguing features of the mechanical softening phenomena of filled elastomers in loading-unloading cycles, commonly known as the Mullins effect. The dissipated energy (D), residual strain (ε), and dissipation factor (Δ; the ratio of D to input strain energy) in the loading-unloading cycles are evaluated as a function of the maximum stretch in cyclic loading (λ) using three types of extension, i.e., uniaxial, planar, and equibiaxial extension, for silica-filled elastomers with various filler contents, and with or without a silane coupling agent. The dissipated energy D and ε increase with an increase in λ, and they depend on the type of extension when compared at the same λ: D and ε increase in the order of equibiaxial, planar, and uniaxial extension. In contrast, the values of Δ obtained for various degrees and types of extension are collapsed into a single curve when the first invariant of the deformation tensor (I) corresponding to λ is employed as a variable: Δ steeply increases with an increase in I in the small deformation regime of I < 3.2, while Δ levels off in the large deformation regime of I > 3.5. The plateau values of Δ increase with an increase in filler content. The characteristic dependence of Δ on I in each of the small and large deformation regimes is expected to reflect the destruction process of the inherent structures, including filler networks and the filler-polymer interface, and the friction between the fillers and the rubber matrix, respectively.

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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 (λi,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,m 2 – 2I 2,m)1/2 where I 1,m = λ x,m 2 + λ y,m 2 + λ z,m 2 and I 2,m = λ x,m 2λ y,m 2 + λ y,m 2λ z,m 2 + λ z,m 2λ x,m 2) 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 i λ 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.

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The incorporation of a stiff and brittle phase into a soft and flexible polymer network makes double network hydrogels remarkably tougher than the conventional one. It also induces a stress softening in cyclic loading, which is seemingly identical to that of filled rubbers. Therefore, material models proposed for double network hydrogel are mostly based on continuum damage theories of filled elastomers. However, recent experimental studies clearly distinguish double network hydrogels from filled elastomers by the damage cross-effect in multiaxial deformation. In this paper, a micromechanical model for double network hydrogels under multiaxial deformation is proposed on the basis of the analytical network-averaging concept. Accordingly, the directional fracture of the first network results from cumulative damage in all directions. Furthermore, the strong interpenetration of the two networks is taken into account. The proposed analytical model includes very few physically motivated material constants and demonstrates excellent agreement with comprehensive experimental data of double network hydrogels under multiaxial loading conditions.

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cis-1,4-Polyisoprene (IR) elastomers harden via strain-induced crystallization (SIC) when the imposed stretch (λ) exceeds the onset value of SIC (λ*). We investigate the Mode-I fast crack growth in the IR sheets as a function of λ in a pure shear geometry. The steady-state crack velocity (V) increases with increasing λ, and V exceeds the shear wave speed of sound at λ > λs. Further stretch beyond λ* (>λs) causes SIC-driven hardening, resulting in a pronounced increase in V. The characteristics of the crack-tip strain field are also significantly influenced by the SIC-driven hardening: The crack-tip opening displacement increases with increasing λ at λ < λ* but exhibits an abrupt reduction beyond λ*. The crack-tip singularity and the area of strain increment caused by the crack growth change discontinuously around λ*. The abrupt variations in these crack-tip characteristics result from the considerable differences in the mechanical properties prior to the crack growth between the entirely amorphous state at λ < λ* and the partially crystallized state at λ > λ*.