Velocity transition in the crack growth dynamics of filled elastomers: Contributions of nonlinear viscoelasticity.

The crack growth dynamics of the carbon-black (CB) filled elastomers is studied experimentally and analyzed while focusing on both kinetics and crack tip profiles. The CB amounts are varied to change the mechanical properties of the elastomers. Static crack growth measurements simultaneously reveal the discontinuous-like transition of the crack growth rate v between the "slow mode" (v≈10^{-5}-10^{-3} m/s) and "fast mode" (v≈10^{-1}-10^{2} m/s) in a narrow range of the input tearing energy Γ and the accompanying changes in the crack tip profiles from blunt to sharp shapes. The crack tip profiles are characterized by two specific parameters, i.e., the deviation δ from the parabolic profile and the opening displacement a in the loading direction. The analysis based on the linear and weakly nonlinear elasticity theories of fracture dynamics demonstrates that the Γ dependence of δ and a is simply classified into three groups depending on the mode (slow or fast) and the magnitudes of δ, independent of CB volume fractions. The theories well explain the results in the slow and fast modes with small magnitudes of δ, while they fail to describe the data in the fast mode with large magnitudes of δ, where the contributions of the strong nonlinearity and/or energy dissipation become significant. The correlation between a power-law relationship Γ∼v^{α} observed in the fast mode and the linear viscoelasticity spectrum is also discussed. The correlation in elastomers with low CB volume fractions is quantitatively explained by the theory of Persson and Brener [Phys. Rev. E 71, 036123 (2005)PLEEE81539-375510.1103/PhysRevE.71.036123], whereas the deviation from the theory becomes appreciable for elastomers with higher CB volume fractions which exhibit strong nonlinear viscoelasticity.