Roughness of tensile crack fronts in heterogenous materials

Abstract

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent $\zeta =1/2$, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for $\zeta$.

7 pages

Cited by in corpus (9)

• Crack propagation through phase separated glasses: effect of the characteristic size of disorder
• Roughness of moving elastic lines - crack and wetting fronts
• The ideas behind the Self Consistent Expansion
• Energy dissipation statistics in the random fuse model
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• On the Self-Affine Roughness of a Crack Front in Heterogeneous Media
• Asymptotic Matching the Self-Consistent Expansion to Approximate the Modified Bessel Functions of the Second Kind