Inspection of cracks using laser-induced ultrasound with shadow method: Modeling and validation

A numerical model based on the finite element method (FEM) is developed for crack inspection using laser-induced ultrasonic waves with the shadow method. Before the simulation, the numerical code is verified by comparing the directivity patterns of ultrasonic waves with the experiment. The use of thermo-elastically generated ultrasonic waves for crack detection and evaluation with the shadow method is investigated by simulation. The simulation is validated by comparing with the experiment.     

铝合金板疲劳微裂纹超声红外成像检测的数值及实验研究

超声红外成像检测技术是一种发展迅速的新型无损检测技术,可用于检测材料表面或近表面的缺陷,由于对缺陷具有选择性加热的特点,近年来备受检测行业的关注。该文在铝合金板中制作疲劳微裂纹,在板中激励声波,裂纹表面因振动摩擦生热,用红外摄像仪记录板表面温度分布。拍摄的红外图像序列经傅里叶变换后得到的幅值和相位图能清晰显示裂纹的特征,测量到的裂纹长度误差达到4.3%。用有限元模拟超声在板中裂纹处的生热过程,研究板中超声在裂纹处的励热机制。超声激励时间、裂纹表面间摩擦系数和裂纹开口宽度直接影响裂纹处的励热效果,最高温度通常位于裂纹尖端附近。模拟和实验结果均表明超声红外成像检测技术能对板中疲劳微裂纹实现快速检测,提供有效、可信的检测结果。     

基于等效弹性模量的微裂纹-超声波非线性作用多阶段模型

提出了一种基于等效弹性模量的微裂纹-超声波非线性作用多阶段模型.该模型将微裂纹微观层面的界面几何特征和宏观层面的界面相对运动统一为介观单元弹性模量的变化,利用等效弹性模量表征损伤区域的"应力-应变",然后利用分段函数来描述微裂纹-超声波非线性相互作用,最后通过有限元仿真对波动方程进行求解,验证了模型的有效性,获得了超声波在经过微裂纹后传播的非线性波动规律.仿真结果表明本文提出的模型相比于双线性刚度模型、接触面模型,能更好地体现一个谐波周期内超声波经过微裂纹损伤区域时波形会发生畸变.同时,仿真实验还分析了裂纹倾角、裂纹长度和超声波激励幅值对超声波经过微裂纹后产生的二次和三次谐波的幅值的影响.最后,对比分析了该模型的仿真计算结果与实验测试结果,表明本文提出的多阶段模型与实验测试均能较好地体现微裂纹-超声波非线性作用产生的二次谐波信号,且结果基本一致,验证了模型的有效性.该模型为开展超声波非线性效应定量检测微裂纹提供了一种新的仿真手段.     

振动声调制技术下微裂纹的非线性响应分析

采用非线性弹簧模型对振动声调制技术下微裂纹产生的非线性调制效应进行解释。从理论上分析了振动声调制技术下微裂纹产生非线性调制现象的原理,将微裂纹的开合状态等效为非线性弹簧。利用有限元软件构建并仿真微裂纹非线性弹簧模型,分别观察不同激励下裂纹界面的开合状态及混合声波的传播特性。结果表明,微裂纹界面随低频声波呈周期性开合,使得通过裂纹界面的高频声波与低频声波相互调制而产生非线性现象。在以上研究基础上,开展振动声调制实验研究。对比仿真结果,非线性调制系数R在实验条件下和仿真随低频激励幅值的变化趋势相同,证明了该模型的正确性。该模型为振动声调制技术应用于微裂纹的超声非线性检测提供了理论依据。      

Simulation of ultrasonic lamb wave generation, propagation and detection for a reconfigurable air coupled scanner

A computer simulator, to facilitate the design and assessment of a reconfigurable, air-coupled ultrasonic scanner is described and evaluated. The specific scanning system comprises a team of remote sensing agents, in the form of miniature robotic platforms that can reposition non-contact Lamb wave transducers over a plate type of structure, for the purpose of non-destructive evaluation (NDE). The overall objective is to implement reconfigurable array scanning, where transmission and reception are facilitated by different sensing agents which can be organised in a variety of pulse-echo and pitch-catch configurations, with guided waves used to generate data in the form of 2-D and 3-D images. The ability to reconfigure the scanner adaptively requires an understanding of the ultrasonic wave generation, its propagation and interaction with potential defects and boundaries. Transducer behaviour has been simulated using a linear systems approximation, with wave propagation in the structure modelled using the local interaction simulation approach (LISA). Integration of the linear systems and LISA approaches are validated for use in Lamb wave scanning by comparison with both analytic techniques and more computationally intensive commercial finite element/difference codes. Starting with fundamental dispersion data, the paper goes on to describe the simulation of wave propagation and the subsequent interaction with artificial defects and plate boundaries, before presenting a theoretical image obtained from a team of sensing agents based on the current generation of sensors and instrumentation.     

Simulation and experimental study of the influence of a front face layer on the response of ultrasonic transmitters

Using a theoretical model, we simulate the ultrasonic pressure generated by a piezoelectric transmitter whose active element has its front face perfectly connected to a layer with parallel faces. This simulation takes into consideration the characteristic parameters of the piezoelectric ceramic, the layer and the propagation medium.Verification of the validity of the model is carried out by assessing, qualitatively and quantitatively, theoretical and experimental responses obtained with different values of layer thickness. Having correctly verified the model solely by simulation, we examine the influence of the nature of the layer on the transmitter response and give an energetics interpretation of the results. We conclude that by using a simple theoretical model, we may forecast the experimental response of a transducer which has a front face layer.     

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.     

An efficient approach to optimize the vibration mode of bar-type ultrasonic motors

The electromechanical coupled dynamic model of the stator of the bar-type ultrasonic motor is derived based on the finite element method. The dynamical behavior of the stator is analyzed via this model and the theoretical result agrees with the experimental result of the stator of the prototype motor very well. Both the structural design principles and the approaches to meet the requirements for the mode of the stator are discussed. Based on the pattern search algorithm, an optimal model to meet the design requirements is established. The numerical simulation results show that this optimal model is effective for the structural design of the stator.     

轨道板中超声兰姆波传播的有限元计算和实验*

该文针对我国高速铁路轨道板缺陷的非接触动态检测问题,研究了空气耦合超声兰姆波在轨道板中的传播规律。首先,给出了轨道板中超声兰姆波的相速度和群速度频散曲线,结果表明:随着频厚积的增加,频散现象越明显,并且A0相速度收敛于Rayleigh波的波速。然后,建立轨道板中波传播的有限元模型,计算得到兰姆波传播的群速度为2220 m/s,且二维傅里叶变换系数的较大值沿Rayleigh波的频散曲线分布。最后,在沪杭高铁嘉兴南站进行了现场测试,以8.8°倾斜角向轨道板激励产生超声兰姆波,激发产生的兰姆波模态群速度为2325 m/s,且二维傅里叶变换分析其系数的较大值沿Rayleigh波的频散曲线分布。有限元计算结果和实验结果均与理论计算结果一致。该研究为后续轨道板缺陷的非接触动态检测提供了理论依据和实验方法。     

Acoustic wave transmission through piezoelectric structured materials

This paper deals with the transmission of acoustic waves through multilayered piezoelectric materials. It is modeled in an octet formalism via the hybrid matrix of the structure. The theoretical evolution with the angle and frequency of the transmission coefficients of ultrasonic plane waves propagating through a partially depoled PZT plate is compared to finite element calculations showing that both methods are in very good agreement. The model is then used to study a periodic stack of 0.65PMN-0.35PT/0.90PMN-0.10PT layers. The transmission spectra are interpreted in terms of a dispersive behavior of the critical angles of longitudinal and transverse waves, and band gap structures are analysed. Transmission measurements confirm the theoretical calculations and deliver an experimental validation of the model.     

损伤度函数模型用于3种钢层裂的二维数值模拟

 把损伤度函数模型嵌入到二维有限元程序DEFEL中,并对3种钢（HR-2钢、2169钢及45钢）的平板撞击层裂实验进行了数值模拟,在模拟中计及材料的屈服硬化效应和Bauschinger效应的影响,较好地再现了实测自由面的速度历史,同时给出了样品中的损伤分布及其发展。在数值模拟中发现,断裂面附近所受最大拉应力介于由声学近似解析计算的层裂强度和从三项式固体状态方程出发得出的断裂理论值之间,并对三者之间的差异作了分析,表明数值模拟结果是合理的。     

The interaction of the S0 Lamb mode with vertical cracks in an aluminium plate

This article presents the interaction of the first symmetric Lamb mode S0 with vertical cracks in an aluminium plate placed in vacuum. The cracks are symmetrical regarding to the median plane of the plate and their heights are increasing from 0% to 100% of the plate thickness, by steps of 25%. The frequency-thickness product is chosen to be lower than the S1 frequency cut-off. A modal decomposition method is used to solve the diffraction problem. The variation with the height of the crack of the reflection and transmission coefficients of modes propagating in the far field is predicted. The displacement fields at both sides of the cracks are also calculated, so that it is possible to quantify the crack-opening displacement. These results are compared to numerical predictions obtained using a finite element software. Measurements are also conducted and compared to the predictions.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

A quantum field theory of lattice dynamics at finite temperature

A quantum field theoretical treatment of three-dimensional cubic crystals at finite temperature is presented from the view-point of the spontaneous breakdown of the spatial translational invariance using thermo field theory. The effective interaction Hamiltonian is constructed by taking into account the dynamical map of the molecular density operator which is obtained from the Ward-Takahashi relations. The acoustic phonons are expected to be the excitation of particle-hole pairs. The conventional secular equation for the lattice vibrations is obtained by neglecting some quantum effects in the Bethe-Salpeter equation for the molecular density fluctuations. The phonon spectra, the phonon propagators and the dynamical map of the molecular density operator are calculated at finite temperature.     

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional(3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S_0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e.,nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.     

Nonlinear constitutive behavior of ferroelectric materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results. Supported by the National Natural Science Foundation of China (Grant No. 10572138)     

Theoretical and experimental research on a disk-type non-contact ultrasonic motor

We developed a disk-type non-contact ultrasonic motor based on B22 vibration mode. The rotors of SU-8 photoresist are fabricated by the UV-LIGA process to control their shapes and thicknesses. So the structures of them are optimized by the experiments. It is found that the revolution speed of disk-type non-contact ultrasonic motor not only depends on the vibration amplitude of the stator, but also the weight and construction of the rotors. The maximum revolution speed of the optimal rotor is 3569 rpm at the input voltage of 20 V and the driving frequency of 45.6 kHz. The exciting principle of traveling wave is presented with theoretical equations. The electric signals applied to the piezoelectric ceramic are designed by the principle. The natural frequency and corresponding vibration mode are calculated and analyzed using finite element method. It is shown that experimental results are in good agreement with simulation, which verifies the effectiveness of the finite element model. Moreover, the levitation distance between the stator and rotor is measured by a CCD laser displacement transducer.     

超声无线输能的声电转换通道设计

通过对超声无线输能系统的声电转换通道进行理论分析,利用电声传输线类比法构建了声电转换通道的一维仿真模型,并利用有限元仿真软件进一步构建了声电转换通道的有限元仿真模型,提高了模型的精确度和适用范围。进行了超声无线输能的实验,并将仿真结果与实验测量结果进行对比,仿真模型的有效性得到验证。利用所建仿真模型分析了负载阻抗对系统能量传输效率的影响规律,对声电转换通道进行了优化,确定了系统的共振频率和最佳负载阻抗。在以上研究基础上建立的超声无线输能实验系统,能够成功透过8 mm厚的铜板点亮20 W灯泡,能量传输效率达到57%,实验证明了利用超声透过金属板进行能量无线传输是切实可行的。      

基于有限元的空耦超声相控阵Lamb波激发与检测

基于非接触式空气耦合超声换能器的无损检测技术在常规板材、纤维复合材料、层状结构材料、粘接界面等的检测中有了长足的发展。但是因为空气耦合超声本身的限制,对于如何提高空气声换能器的发射效率和接收灵敏度、提高检测中接收的信噪比成为这一领域的重要课题。因此有必要结合最新的信号处理技术探索新的无损检测形式。本文通过提出了基于电容式的空气声换能器阵列的构建和制作方法,应用有限元数值方法对一维线阵的空气声换能器阵列的动态偏转特性进行了模拟,并使用构建流固耦合模型对二维的空气声场及板材中的位移场进行计算。通过一维空气耦合相控阵的声束动态偏转激励了各向同性板中的Lamb波A₀ 和S₀模式,并进行了分析,验证了此模型可以进一步用于基于空气耦合相控阵激励的Lamb波的无损检测中。