Universal relation between crack-growth dynamics and viscoelasticity in glass-rubber transition for filled elastomers

The characteristic power-law relationship between crack-growth speed (v) and tearing energy (Gamma), Gamma similar to v(alpha) in high speed regime (typically, v/c(s) > 10(-3) where c(s) is the shear wave speed), is investigated for the filled elastomers with varying systematically the material parameters. The types of rubber, the concentration of filler and cross-linker concentration are widely varied in order to change the viscoelastic spectra of the elastomers. The power-law relationship is correlated with linear viscoelastic spectra, since Gamma and the relaxation modulus are similarly dependent on temperature. An universal relation is found between the exponents alpha and kappa of the relaxation modulus G(t) similar to t(-kappa) in the glass-rubber transition regime, independently of the material parameters. The expectations of the existing theories fail to account for the observed relation, in particular for the elastomers with high filler contents or low cross-linker concentrations. The universal alpha-kappa relation found here will contribute to predict the crack speed in high speed regime from the linear viscoelastic spectra of the elastomers, and will give a definite basis for the theoretical development in the crack-growth dynamics of elastomers.