Investigating Multiaxial Mullins Effect of Carbon-Black-Reinforced Elastomers Using Electrical Resistivity Measurements

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 carbon-black (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 (ρS), representing the degree of residual destruction of the CB network, increases with the biaxial strain for small imposed deformation. However, ρS 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 ρS 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.