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首页> 外文会议>IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity Jul 16-20, 2000 Manchester, United Kingdom >THEORY OF CRACK FRONT WAVES
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THEORY OF CRACK FRONT WAVES

机译：裂纹前波理论

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A crack front wave is a disturbance of the edge of a propagating crack, which remains localised about the edge as it propagates. Because it is confined to the vicinity of the edge, a crack front wave propagates without attenuation, unless some local mechanism for dissipation is present. This article presents the theory underlying crack front waves. It is more general than any presented previously. First, the presence of a non-singular term in the stress field near the unperturbed crack edge is shown to introduce dispersion, which becomes negligible as frequency tends to infinity; the previously-published work that neglected this term and predicted that the crack front wave is non-dispersive thus has only asymptotic validity, in the limit of high frequency. In addition, the present analysis is conducted for a crack which propagates through a medium that is viscoelastic rather than elastic; again, the previous elastic result is recovered as frequency tends to infinity. Explicit results are presented in the case that the frequency of the disturbance is high: the leading-order term is the one previously found for elasticity, while the first correction term yields both dispersion and attenuation, proportional to (frequency)~(-1). The virtue of the asymptotic analysis is that it is applicable to any isotropic viscoelastic medium: the properties of the medium enter only through two-term expansions (for high frequency) of the (complex) phase speeds of longitudinal and shear waves. The analysis reproduces but generalises results recently published elsewhere by the authors, for the case of crack propagation through a Maxwell fluid, with frequency-independent Poisson's ratio.
机译：裂纹前波是对正在传播的裂纹边缘的干扰，随着裂纹的传播，裂纹在边缘处始终处于局部状态。由于裂纹前波被限制在边缘附近，因此除非存在某种局部耗散机制，否则裂纹前波将无衰减地传播。本文介绍了裂纹前波的理论基础。它比以前介绍的任何内容都要笼统。首先，表明在未受扰动的裂纹边缘附近的应力场中存在非奇异项会引入色散，随着频率趋于无穷大，色散可以忽略不计。先前发表的忽略该术语并预测裂纹前波是非弥散性的工作因此仅在高频率范围内具有渐近有效性。另外，本分析是针对通过粘弹性而不是弹性的介质传播的裂纹进行的。同样，随着频率趋于无穷大，先前的弹性结果得以恢复。在扰动频率很高的情况下给出了明确的结果：前导项是先前发现的弹性项，而第一个校正项会产生色散和衰减，与（频率）〜（-1）成比例。渐近分析的优点在于，它适用于任何各向同性的粘弹性介质：介质的属性仅通过纵向波和剪切波的（复）相速度的二阶展开（对于高频）进入。该分析再现但概括了作者最近在其他地方发表的结果，涉及裂纹通过麦克斯韦流体传播的情况，具有与频率无关的泊松比。

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