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Elastic-wave modulation approach to crack detection: Comparison of conventional modulation and higher-order interactions

机译：弹性波调制方法用于裂纹检测：常规调制和高阶相互作用的比较

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Comparison of recent theoretical estimates with experiments has indicated that the ultimate sensitivity of the conventional modulation technique of crack detection is mainly determined by the background modulation produced by the quadratic component of the atomic nonlinearity of the matrix material. Much smaller level of masking nonlinear effects is typical of higher-order interactions due to cubic and higher-order components in the power-series expansion of the background nonlinearity of the solid. In contrast, the level of formally higher-order components originated due to nonlinearity of crack-like defects can be comparable with that of the first-order components. Such strongly increased efficiency of higher-order interactions is due to the fact that crack-like defects often demonstrate non-analytic (non power-law) nonlinearity even for moderate acoustic amplitudes. Besides the increased level, the higher-order components arisen due to non-analytic nonlinearity of cracks can demonstrate significantly different functional behavior compared to manifestations of the atomic nonlinearity. This difference can also help to discriminate the contributions of the defects and the background atomic nonlinearity. Here, we focus on the main differences between the modulation components arisen due to cubic terms in the power-series expansion of the atomic nonlinearity and similar components generated by clapping Hertzian nonlinearity of inner contacts in cracks. We also examine experimental examples of higher-order modulation interactions in damaged samples. These examples clearly indicate non-analytical character of the defects' nonlinearity and demonstrate that the use of higher-order modulation effects can significantly improve the ultimate sensitivity and reliability of the modulation approach to detection of crack-like defects.
机译：最近的理论估计与实验的比较表明，裂纹检测的常规调制技术的最终灵敏度主要取决于基体材料原子非线性的二次分量所产生的背景调制。由于实体背景非线性的幂级数展开中的立方和高阶分量，掩蔽非线性效应的水平要小得多，这是高阶相互作用的典型特征。相反，由于裂纹状缺陷的非线性而产生的形式上较高阶分量的水平可以与一阶分量的水平相当。这种高阶交互作用的效率大大提高是由于这样的事实，即即使对于中等声振幅，裂纹状缺陷也经常表现出非解析（非幂律）非线性。除了增加的水平外，由于裂纹的非解析非线性而产生的高阶分量与原子非线性的表现相比，可以表现出明显不同的功能行为。这种差异也可以帮助区分缺陷的贡献和背景原子的非线性。在这里，我们集中讨论由于原子非线性的幂级数展开中的三次项而引起的调制分量之间的主要差异，以及通过对内部接触的赫兹非线性进行拍击而生成的类似分量。我们还研究了受损样品中高阶调制相互作用的实验实例。这些例子清楚地表明了缺陷的非线性的非分析特性，并表明使用高阶调制效应可以显着提高调制方法检测裂纹状缺陷的最终灵敏度和可靠性。

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