Weakly nonlinear fracture mechanics: Experiments and theory

Material failure occurs at the small scales in the immediate vicinity of the tip of a crack. Due to its generally microscopic size and the typically high crack propagation velocity, direct observation of the dynamic behavior in this highly deformed region has been prohibitively difficult. Here we present direct measurements of the deformation surrounding the tip of dynamic mode I cracks propagating in brittle elastomers at velocities ranging from 0.2 to 0.8C _s . Both the detailed fracture dynamics and fractography of these materials are identical to that of standard brittle amorphous materials such as soda-lime glass. These measurements demonstrate how Linear Elastic Fracture Mechanics (LEFM) breaks down near the tip of a crack. This breakdown is quantitatively described by extending LEFM to the weakly nonlinear regime, by considering nonlinear elastic constitutive laws up to second order in the displacement-gradients. The theory predicts that, at scales within a dynamic lengthscale ℓ _nl from the tip of a single crack, significant logr displacements and 1/r displacement-gradient contributions arise, and provides excellent quantitative agreement with the measured near-tip deformation. As ℓ _nl is consistent with lengthscales that appear in crack tip instabilities, this "weakly nonlinear fracture mechanics" framework may serve as a springboard for the development of a comprehensive theory of fracture dynamics.