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

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 (phi(f) and c(x), respectively), and temperature (7) 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 delta from the parabolic one expected by the linear elastic fracture mechanics (LEFM), the parabolic curvature a, and the non-dimensional quantity a delta. The dependence of these parameters on the input tearing energy Gamma is successfully explained by the weakly nonlinear theory of dynamic fracture (WNLT), which considers the contribution of the second-order shear modulus mu((2)) to the strain field in addition to that of the first-order shear modulus mu((1)), independently of phi(f), c(x) and T, unless delta exceeds a limit value (delta(c)). SBR/SI shows an appreciably larger value of delta(c) than the carbon-black filled acrylonitrile butadiene (NBR/CB) elastomers. The smaller value of delta(c) for NBR/CB is attributed to that the contribution of the third-order nonlinear modulus mu((3))/mu((1)), which is not considered in WNLT, is appreciably higher than that in SBR/SI. The magnitude of the threshold tearing energy Gamma(c) for the onset of the velocity transition shows a good correlation with the fracture toughness W-C normalized by the nonlinear elastic constant mu(3)((1))/mu((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. (C) 2016 Elsevier Ltd. All rights reserved.