The Mullins effect is commonly observed in the mechanical properties of elastomer/filler composites: The stress during unloading or second loading is considerably lower than the first loading stress. We measured the mechanical stresses and electrical conduction to investigate the Mullins effect in carbonblack (CB)-reinforced elastomers under various biaxial stretching. Imposing the small equibiaxial strain of 30% increases the electrical surface resistivity in the deformed state by more than 3 orders of magnitude, indicating the breakdown of the initial conductive percolated CB network. The resistivity of the relaxed unloaded states (ρ S ), representing the degree of residual destruction of the CB network, increases with the biaxial strain for small imposed deformation. However, ρ S saturates at large deformations, indicating that the residual CB-network destruction does not increase further. The mechanical dissipation factor (Δ; the ratio of energy dissipation to input work) and ρ S obtained at various degrees and types of deformation can be described by a single variable, i.e., the first invariant of deformation tensor. This indicates that the orthogonal strains cause the residual damage of the CB network and the internal mechanical damage.

Anisotropy of the internal damage caused by imposed deformation, which is called stress-softening or Mullins effect, was investigated for a carbon-black (CB) filled styrene butadiene rubber (SBR/CB) by a sequence of two tensile measurements. A wide-width pristine sheet specimen satisfying pure shear (planar) stretching geometry was first subjected to a single loading-unloading cycle with a maximum stretch (λ m ). The rectangular subsamples were cut out from the unloaded and relaxed sheet specimen such that the long axis had an angle of θ = 0° or 90° relative to the pre-stretching axis. Subsequently, uniaxial stretching of the subsamples was conducted, and the internal damage (D 0 or D 90 ) at each angle was evaluated as a function of λ m from the difference in the uniaxial stress-strain data between the subsamples and the pristine samples. Almost no anisotropy ( f = D 0 /D 90 ≈ 1) was observed for the internal damage in the moderate λ m regime of λ m < 3. This is in contrast to a large damage anisotropy ( f ≈ 3) in the corresponding λ m regime previously reported for a silica filled SBR with silane coupling agent (SBR/Silica). The f values for SBR/CB in the high λ m regime of λ m > 3 increased with λ m and became comparable to those in SBR/Silica. The significantly large difference in the internal damage anisotropy between SBR/CB and SBR/Silica reflects the differences in the types of destructed molecular bonding for the filler networks and filler/rubber interfaces between the two elastomers.

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