Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability

Eran Bouchbinder

doi:10.1103/PhysRevLett.103.164301

paper

Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability

arXiv:0908.1178 · doi:10.1103/PhysRevLett.103.164301

Abstract

A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $ℓ_{n l}$ , symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields at time $t$ are determined by the crack path at a {\bf retarded time} $t - τ_{d}$ , where the delay time $τ_{d}$ scales with the ratio of $ℓ_{n l}$ and the typical wave speed $c_{n l}$ within the nonlinear zone. The resulting equation is shown to agree with known results in the quasi-static regime. As a first application in the fully dynamic regime, an approximate analysis predicts a high-speed oscillatory instability whose characteristic scale is determined by $ℓ_{n l}$ . This prediction is corroborated by experimental results, demonstrating the emergence of crack tip inertia-like effects.

4 pages, 2 figures; minor changes

Dynamic Crack Tip Equation of Motion: High-speed Oscillatory Instability

Abstract

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