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

A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale l(nl), 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 retarded time t - tau(d), where the delay time tau(d) scales with the ratio of l(nl) and the typical wave speed c(nl) within the nonlinear zone. The resulting equation is shown to agree with known results in the quasistatic 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(nl). This prediction is corroborated by experimental results, demonstrating the emergence of crack tip inertialike effects.