Crack-tip shape in the crack-growth rate transition of filled elastomers

- Filled elastomers show a discontinuous-like transition of the crack-growth rate in a narrow range of the tearing energy.
- Crack-tip shapes deviate from the expectation of the linear elastic fracture mechanics in a high-rate regime.
- Weakly nonlinear elasticity theory, which considers the second-order elasticity, successfully explains the crack-tip shapes.
- Threshold tearing energy for the transition is governed by the effect of nonlinear elasticity and fracture toughness.

The velocity transition in crack-growth dynamics and the accompanying changes in crack tip shapes are investigated for the elastomers composed of styrene-butadiene rubber and silica filler (SBR/SI). The concentrations of filler and cross-link (ϕf and cx, respectively), and temperature (T) are extensively varied in order to change the degree of nonlinearity in elasticity of the elastomers. The shapes of the crack tip are characterized by three parameters, i.e., the deviation δ from the parabolic one expected by the linear elastic fracture mechanics (LEFM), the parabolic curvature a, and the non-dimensional quantity aδ. The dependence of these parameters on the input tearing energy Γ is successfully explained by the weakly nonlinear theory of dynamic fracture (WNLT), which considers the contribution of the second-order shear modulus μ(2) to the strain field in addition to that of the first-order shear modulus μ(1), independently of ϕf, cx and T, unless δ exceeds a limit value (δC). SBR/SI shows an appreciably larger value of δC than the carbon-black filled acrylonitrile butadiene (NBR/CB) elastomers. The smaller value of δC for NBR/CB is attributed to that the contribution of the third-order nonlinear modulus μ(3)/μ(1), which is not considered in WNLT, is appreciably higher than that in SBR/SI. The magnitude of the threshold tearing energy Γc for the onset of the velocity transition shows a good correlation with the fracture toughness Wc normalized by the nonlinear elastic constant μ(1)3/μ(2)2 in WNLT. This result indicates that the magnitude is governed by the combined effect of the degree of nonlinearity in elasticity and the fracture toughness.

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