Weakly nonlinear fracture mechanics: experiments

and theory

Eran Bouchbinder · Ariel Livne · Jay Fineberg

 

Received: 26 February 2009 / Accepted: 2 November 2009

© Springer Science+Business Media B.V. 2009

 

Abstract 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 modeI cracks propagating in brittle elastomers at velocities ranging from 0.2 to 0.8Cs .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 lnl from the tip of a single crack, significant log r displacements and 1/r displacement-gradient contributions arise, and provides excellent quantitative agreement with the measured near-tip deformation. As lnl 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.