大型复杂装备的微弱疲劳损伤在逐渐累积后会导致突发性失效，如何及时对这类早期微弱损伤进行识别和评估是亟待解决的问题。现存普遍使用的多种传统超声无损检测方法能够识别宏观结构不连续，而基于高阶弹性模量分析的非线性超声无损检测方法则由于能够对疲劳导致的微观结构改变进行观测和评价而在近年来引起关注，然而针对这种物理效应的机理和谐振波的传播规律等基础性问题有待进一步研究。本文对波束混叠法这一非线性超声无损检测方法和在评价材料早期疲劳损伤中的应用开展了理论和实验研究，通过对谐振波成分的传播特性的分析，进一步为将其作为一种衡量材料早期疲劳损伤的指标提供方法和依据。 首先，运用高分辨率的半离散中心差分方法，分别对材料非线性作用下点源和线源激励情况下的响应进行了分析，为后续波束混叠方法中的响应的研究提供了对比和参照。其次，对材料非线性影响下反向共线两列纵波、反向共线的纵波与剪切波、同向共线的纵波与剪切波等三种激励情形下的共线波束混叠过程进行研究，探讨了谐振波的产生和沿扩展路径的变化趋势。通过正反相两次响应叠加的方式，直接获取和观察到和频与差频两种谐振波的生成与扩展情况。在两列相向纵波混叠情形中，通过对具有不同激励频率比的响应进行观察，发现谐振波的产生并不严格受限于谐振条件和极化条件。在两列相向纵波与剪切波混叠的情形中，发现正反相响应叠加法得到的谐振波成分是单组激励下得到的相同频率成分中的一部分，且是唯一随非线性系数变化而改变的信号段，从而对以往惯用的单组激励下以响应中谐振频率成分直接表征材料性能退化的做法予以纠正。再次，利用相控阵的激励方式，对材料非线性作用下两列非共线超声波在弹性半平面内的相互作用和谐振波的生成和扩展情况进行了研究。结果表明，在非共线波束混叠过程中，和频与差频成分可在其扩展路径的切向方向观测到；在多束观测点射线中，距离观测点越远的射线上出现谐振波幅值最大值的位置距离射线起点越近。在相控阵的参数设计中发现，阵列的宽度和阵列元素的密度对于响应中谐振波的幅值最大值产生影响。通过波束夹角的敏感度分析获知，波束夹角的微弱改变并不会起到明显的干预和抑制作用，但是响应幅值的峰值位置及其大小对于不同波束夹角会呈现出不同的特征。最后，应用非共线波束混叠方法，对6061铝合金材料发生微小形变时的结构件进行检测，分别对产生0.8%应变控制下10次与50次循环载荷和初始完整结构三种情况下的响应信号进行分析和评价，可以看到对于发生微小形变的材料，在响应中能够观测到差频谐振波成分的存在。对于一些形变较小的情形，即使在实验信号稳定性较差的情况下，依然可以通过信号延拓的方法，使谐振波成分得以突显出来。而对于未经形变的完整结构，在同样的激励条件下则无法观测到谐振波的存在。研究表明，非共线波束法可以用来对早期疲劳阶段发生的微观结构改变进行有效评价，可以将响应中的谐振波幅值作为衡量材料性能退化程度的重要指标。 通过以上对共线与非共线情形下由两列超声波束在具有材料非线性的固体内发生混叠后的响应及在此过程中谐振波的生成与扩展情况的理论分析，和波束混叠方法在评价材料微弱疲劳损伤中的实验研究，不仅揭示了非线性波束混叠这一物理过程的内在规律，也为评价材料早期微弱损伤提供了理论指导和有效方法。 关键词:非线性超声波检测，共线与非共线波束混叠法，高阶弹性模量，微弱疲劳损伤检测

 Weak material fatigue damage of large complex equipment will lead to sudden failure after gradual accumulation, and it is an urgent problem to be solved that how this kind of early weak damage can be identified and evaluated. Most of the existing ultrasonic nondestructive evaluation techniques are able to detect macrostructure discontinuities in fatigue, while nonlinear ultrasonic techniques based on the higher-order elastic modulus have the advantage of assessing the microstructure changes prior to crack formation, which have aroused much attention in recent years. In this thesis, numerical and experimental studies on wave mixing and its application in evaluating material fatigue at the early stage have been implemented. The study of the propagation features of the resonant wave component in the response offers the potential of the newly developed technique to detect early damage in structural materials. The main work of this thesis includes the following aspects. In the first part, a high-resolution semi-discrete central scheme is applied to solve the nonlinear wave propagation problem in the cases of point source and line source respectively, providing a benchmark and comparison for the cases of wave mixing. In the second part, three cases of collinear wave mixing and generation and propagation of resonant waves are studied, including the L-L wave mixing in the opposite direction, the L-S one in opposite directions, and the L-S one in the same direction as well. Pulse-inversion technique is applied here to superpose reponses of two antiphase input signals, and resonant waves and higher harmonic waves can be obtained and observed directly and independently. In the case of L-L wave mixing in opposite directions, different ratios of driving frequencies are applied, and results show that the generation of resonant waves is not strictly limited to resonance and polarization conditions. In the case of L-S wave mixing in opposite directions, it is found that the resonant component obtained from pulse-inversion technique is one part of that from the related single pair of stimulation, and is also the only part of the response that changes with material nonliearity. This rectifies the common understanding that the whole part of resonant component from a single pair of stimulation can be used to characterize the degradation of materials. In the third part, the case of non-collinear wave mixing in an elastic half space with material nonlinearity is investigated and the generation and propagation of resonant components in the process are also examined. The phased array technique is applied here to implement the oblique incidence on the boundary. The results show that under certain appropriate conditions both components of sum and difference frequencies can be clearly observed especially in the tangential direction. For several rays of observation points around the interaction zone, the further it is away from the excitation sources, generally the earlier the maximum of amplitude arises. From the parametric analysis of the phased array, it is found that both the length of array and the density of element have impact on the maximum of amplitude of the resonant waves. Through the sensitivity analysis of the angle between beams, it can be seen that a minor deviation of the angle will not suppress or intervene the generation of the resonant wave, but the location and the specific value of the maximum of responses will chage with the angle. In the last part, aluminum alloy 6061 specimens with low cycle fatigue are detected with the method of non-collinear wave mixing. Specimens under three different conditions are evaluated, including 10 and 50 cyclic loadings under 0.8% strain control, and perfect condition as well. The resonant component of difference frequency is observed from the output signal in the two cases of low cycle fatigue mentioned above. It can be drawn that even though the experimental signals fluctuate quite a bit, these tiny deformations can still be measured by amplitudes of resonant components by means of pulse-inversion technique, when fundamental frequency components can be largely removed. For the specimen in perfect condition, no such resonant components can be obtained under the same excitation. To sum up, non-collinear wave mixing can be used to effectively evaluate low cycle fatigue, and the amplitude of resonant component can be taken as a measure of performance degradation of materials. In conclusion, after the investigation of collinear and non-collinear wave mixing in solids with material nonlinearity and generation and propagation of related resonant components, and also the implementation of experiments evaluating material degradation with low cycle fatigue, not only a more insight and better understanding of the physical phenomenon is gained, but also the research process provides with certain reference significance and practical experience for engineering application of evaluating weak damage of materials at an early stage using the method of ultrasonic wave mixing. Keywords: nonlinear ultrasonic wave method, collinear and non-collinear wave mixing technique, third-order elastic constants, detection of weak damage in fatigue