Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev Lett. 2009 Oct 16;103(16):164301. doi: 10.1103/PhysRevLett.103.164301.
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.
基于近场非线性区的自治性、对称性原理、因果关系和尺度分析，提出了一个动态裂纹尖端运动方程。因果关系意味着在时间 t 的渐近线性弹性场由在延迟时间 t-tau(d)的裂纹路径决定，其中延迟时间 tau(d)与非线性区内的 l(nl)和典型波速 c(nl)的比值有关。结果表明，所得到的方程与准静态范围内的已知结果一致。作为在完全动态范围内的首次应用，近似分析预测了高速振荡不稳定性，其特征尺度由 l(nl)决定。实验结果证实了这一预测，表明了裂纹尖端惯性效应的出现。
