Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

Signal enhancement in Rayleigh wave interactions using a laser-ultrasound/EMAT imaging system

Enhancement of signal amplitudes from Rayleigh wave interaction at solid surface features has been investigated when signals were detected by an in-plane electromagnetic acoustic transducer (EMAT). A laser-ultrasound system was used to inspect surface-breaking slots, serving as artificial defects. Nd:YAG laser pulses were delivered onto a metal surface via an optical fiber and focused to a line source by a cylindrical lens. An in-plane EMAT receiver detected transient surface acoustic waves. A-scan signals and B-scan images from surface defects revealed increased signal amplitude up to 2.8+/-0.3 depending on the distance of the transducer from a slot. An explanation is based on the interaction of the EMAT sensor with the Rayleigh wave. A supporting computer model was derived to show that experimental signal enhancements were consistent with numerical predictions.     

Nondestructive evaluation of cylindrical parts using laser ultrasonics

We applied the laser ultrasonic technique for detecting surface breaking slots in steel cylinders (25 mm in diameter). The observation of the detected signal over a long time (500 micros), shows that the interaction of the two contra-propagating incident Rayleigh waves reinforce the echoes coming from the defect. These echoes are slowly growing with time whereas the main signals decrease. This energy transfer occurring at each revolution of the waves around the cylinder allows the detection of cracks having a depth (h approximately 80 microm), very small compared to the Rayleigh wavelength (lambda approximately 2 mm). The evaluation of the material was performed by processing the detected signal in a sliding time window. A cross-correlation is made either between a reference signal and the signal from the tested sample or between two signals probed for two different positions of the sample. In both cases, the slope of the cross-correlation coefficient versus the number of turns is proportional to the depth of the slot.     

激光激发声表面波在缺陷板材中散射过程的有限元分析

利用有限元法模拟了金属板材中激光激发的声表面波经过缺陷位置时发生散射的瞬态过程,采用线状激光源作为超声导波的激发源.针对三种不同深度的表面缺陷以及三种亚表面缺陷的模型进行了对比计算,结果显示缺陷的深度及位置对声表面波的时域特征存在显著的影响.表面缺陷深度越深将产生较大幅度的表面反射回波,亚表面缺陷的影响将取决于缺陷上顶面距离板材上表面的距离.因此,数值模拟结果表明通过分析激光产生的表面波形可以判定近表面缺陷的尺寸和所处的位置.     

激光超声检测带过渡圆角平板表面缺陷的数值研究

为了研究激光激发出的超声波在带过渡圆角的金属平板上的传播规律和检测表面缺陷的方法,采用有限元法模拟了该类平板中的激光超声现象,分析了表面波在圆角区域的传播规律和与表面缺陷的作用过程。数值结果表明:激光激发出纵波、横波和Rayleigh波等,其中Rayleigh波主要存在于表面mm量级,并且在过渡圆角处发生模式转换生成了直达波R′和模式转换波R_R等多种表面波;经过过渡区域后的声波在表面缺陷处发生了反射和透射现象,通过B扫图可以检测缺陷的位置。随着缺陷深度的增加,表面波的透射系数不断减小,且透射波R_t和R_st存在0.5 μs左右的到达时间差,该时间差与缺陷深度近似成线性正相关。数值结果为激光超声检测带过渡圆角的平板表面缺陷提供了有价值的参考。     

Ultrasonic sizing of short surface cracks

This paper presents a method for ultrasonic sizing of surface cracks based on time domain and frequency domain Rayleigh wave near-field analysis. The procedure allows for the entire range of ratio of crack depth to Rayleigh wavelength a/λ to be covered with one single measurement. In the time domain the time-of-flight method was extended to cracks smaller than the wavelength by correlation of the time delay of the transmitted Rayleigh wave with the crack depth. In the frequency domain, the inverse scattering problem was solved by comparison of the measured scattering coefficients and central frequencies of the reflected and transmitted Rayleigh waves with theoretical curves. The sizing procedure was demonstrated experimentally with narrow slots and real fatigue cracks. The out-of-plane displacement component was measured pointwise in the scattered near field by means of laser interferometry. The determination of the scattering parameters in the near field was enabled by a procedure that allows for the Rayleigh wave to be separated from the other modes scattered at the defect. The experimental results showed good accuracy and repeatability down to the smallest available ratio of crack depth to Rayleigh wavelength a/λ = 0.15.     

Conventional electromagnetic acoustic transducer development for optimum Lamb wave modes

Lamb waves are normally utilized for inspecting thin metal sheets. Wheel type probes using piezoelectric oscillators have generally been used as the sensors for Lamb waves. Recently, the electromagnetic acoustic transducer (EMAT) has been developed and is beginning to be used as a Lamb wave detector. We have developed a useful type of transducer for Lamb waves. The new EMAT consists of a meander coil with a narrow distance of 2.5 mm and has a symmetrical structure in the vertical direction for both surface sides. The new EMAT can generate Lamb waves with variable wavelengths corresponding to the frequency range from approximately 300 kHz to 2.5 MHz and multiple modes, and can also generate selected symmetrical and anti-symmetrical mode Lamb waves. It is demonstrated that the optimum Lamb wave mode could be produced by the appropriate positioning of the EMATs and controlling the phase (same or inversed) of the electrical signal driving the device. The described EMAT can be used to examine steel (or other material) sheets of different thickness. It is also shown that the S0 (0.3 MHz) mode Lamb wave is the most effective for the deepest (up to 6 mm) penetration.     

Modal expansion analyses of ultrasonic Lamb waves generated by electromagnetic ultrasonic transducers

A modal expansion approach has been proposed for investigating generation of ultrasonic Lamb waves by electromagnetic acoustic transducers（EMATs）.Based on the current distribution of the EMAT＇s meandering coil,the formal solution for the Lorentz surface stress applied on the plate surface has been derived.Then the function of the wave-number spectral density of the Lorentz surface stress for generating ultrasonic Lamb waves has been obtained using the spatial Fourier transform.On this basis,with the modal expansion approach for waveguide excitation,the mathematical expression of the Lamb wave＇s mode expansion coefficient has been deduced,which is closely related with the geometrical parameters of the EMAT＇s meandering coil.The mathematical relationship between the Lamb wave＇s mode expansion coefficient and the EMAT＇s geometrical parameters,obtained in this paper,lays a theoretical foundation for exactly analyzing generation of Lamb waves by EMATs.Further,the numerical analyses performed indicate that the Lamb wave＇s mode expansion coefficient can be appropriately adjusted by changing the geometrical parameters of the EMAT＇s coil,and thus the unwanted Lamb wave modes can be effectively restrained.This result provides a theoretical basis for generating a single and pure Lamb wave mode by the meandering coil EMAT.     

Shear Wave Field Radiated by an Electromagnetic Acoustic Transducer

The horizontally polarized ultrasonic shear wave field emitted by an electromagnetic acoustic transducer （EMAT） is studied by the surface force distribution on the EMAT approximately described as an inhomogeneous horizontal shear force. The shear wave directivity pattern is plotted by numerical calculations based on our strictly analytic solutions of the wave field we presented previously. An experimental system of EMAT generation and piezoelectric transducer reception is set up to check the predictions of the theoretical wave field by measuring the ultrasonic signals through aluminium block. The directivity pattern of the wave field obtained from the experimental results conforms the theoretical prediction, which lays a foundation for engineering applications of EMATs.     

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。     

Analysis of multiple wavelengths of Lamb waves generated by meander-line coil EMATs

The electromagnetic acoustic transducers (EMATs) with a meander-line coil possess the capability of generating Lamb waves carrying multiple wavelengths, and the characteristics of multiple wavelengths is analyzed by developing a spatial transversal filter model for the EMAT. It is shown that the characteristics is due to the wavelength spectrum of the EMATs, which is a wavelength-domain representation of information about the wavelength components, and the magnitude of each components is modulated by an envelope which depends on the geometric pattern of the meander-line coil. The characteristics of multiple wavelengths might cause the multi-modes phenomenon, therefore a method for removing the effect of multiple wavelengths is proposed. It is shown that the effect can be removed by designing an EMAT which can produce a special envelop to suppress the harmonic wavelengths. Experiments are set up to study the characteristics of multiple wavelengths and verify the validity of the proposed method.     

多通道超声兰姆波检测板状结构中的裂纹

超声兰姆(Lamb)波在结构缺陷检测方面愈来愈受到重视,但目前Lamb波的应用局限于单信号源激励,单通道接收的方法,容易受到噪声干扰,其后续的信号分析处理也比较复杂。本文旨在采用多通道Lamb波对板状结构中的裂纹进行定量分析与诊断。在铝板的表面凿刻出不同深度的凹槽作为裂纹,通过线阵换能器采集在一定传播距离内的多通道Lamb波信号,并采用二维傅里叶变换分析在不同深度的裂纹下,Lamb波模式能量的变化规律。结果表明,相对于完好铝板中的Lamb波信号,裂纹的存在会使Lamb波发生模式转换现象,并且转换模式能量百分比随裂纹深度的增加而线性增加。其结果为Lamb波评价板状结构中的裂纹状况提供了一种可能的方法。     

Selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers

In this paper, we describe a modal expansion approach for the analysis of the selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers(EMATs). With the modal expansion approach for waveguide excitation, an analytical expression of the Lamb wave's mode expansion coefficient is deduced, which is related to the driving frequency and the geometrical parameters of the EMAT's meander coil, and lays a theoretical foundation for exactly analyzing the selective generation of Lamb waves with EMATs. The influences of the driving frequency on the mode expansion coefficient of ultrasonic Lamb waves are analyzed when the EMAT's geometrical parameters are given. The numerical simulations and experimental examinations show that the ultrasonic Lamb wave modes can be effectively regulated(strengthened or restrained) by choosing an appropriate driving frequency of EMAT, with the geometrical parameters given. This result provides a theoretical and experimental basis for selectively generating a single and pure Lamb wave mode with EMATs.     

Coupling mechanism of an EMAT

Electro-magnetic acoustic transducers (EMATs) generate ultrasonic waves in metals through an electromagnetic coupling mechanism. A concept for EMAT generation, using a coil alone without a permanent magnet, but with a pulse generator and a sample, is introduced. A simplified equivalent coil circuit is given, and has been validated by experimental measurements. Such an equivalent circuit is useful for excitation current calculations, which have often been neglected in previous publications in this area but have proved to be of great importance in considering the efficiency and frequency characteristics of ultrasonic generation. Due to the coil sample coupling, the equivalent coil inductance is dependent on the electrical conductivity and magnetic permeability of the metal sample, the lift-off, the coil orientation relative to the metal sample and the coil configuration. The use of a coil alone to generate ultrasound has limited applications as a suitable ultrasonic detector must also be used, but where appropriate this type of generation source provides a robust, non-contact and inexpensive means of ultrasonic generation without worrying the permanent magnet attracting ferromagnetic particles that can prevent from practical on-line application of EMATs.     

Finite element analysis of Rayleigh wave interaction with finite-size,surface-breaking cracks

The interaction of surface acoustic waves with finite-size, surface-breaking, semi-circular cracks is studied numerically, and experimentally. We focus on the behavior of the reflection coefficient of the Rayleigh wave from such cracks in the far field of the crack, when the depth of the crack is comparable to the wavelength of the interrogating surface wave. The cases in which the depth of the crack is much smaller or much larger compared to the wavelength have been extensively investigated by many authors and are not considered here except for validating the numerical and experimental results in these regimes. The theoretical, finite element, and experimental results presented are in very good agreement over the range were the crack depth is much smaller or much larger compared to the wavelength of the incident Rayleigh wave. In the transition regime, between these two limiting cases, only the finite element and experimental data show good agreement since the theoretical predictions are no longer applicable. In the high crack depth to wavelength ratio (a/lambda(R)) regime, the finite element and experimental results close to the crack approach the limiting value of the reflection coefficient from a 90 degrees corner.     

Numerical simulation of evaluation of surface breaking cracks by array-lasers generated narrow-band SAW

Most of the factors limiting the extensive application of laser-based ultrasonic for nondestructive evaluation of surface breaking crack are its poor sensitivity, low efficiency relative to conventional contact ultrasonic methods and limit on the dimension of the cracks. For this reason, a new technique that multiplepulse narrow-band ultrasound generated by laser arrays has been proposed. It is found that crack detection dependent on spectrum of narrow-band ultrasound generated by laser arrays can be operated with low amplitude requirements. In this paper, the narrow-band ultrasound generated by pulse laser arrays interacting with surface breaking cracks has been simulated in detail by the finite element method (FEM) according to the thermoelastic theory. The pulsed array lasers were assumed to be transient heat source, and the surface acoustic wave (SAW) which propagating on the top of the plate was computed based on thermoelastic theory. Then the frequency spectrums of both reflected waves by crack and transmission ones through crack were compared with the direct waves. Results demonstrate that multiple-frequency components of the narrow-band ultrasound were varied with change of the depth of surface breaking cracks significantly, which provides the possibility for precise evaluation of surface breaking cracks.     

The analysis of adhesive bonds using electromagnetic acoustic transducers

The paper presented here outlines a technique for examining aerospace adhesive bonds using electromagnetic acoustic transducers (EMAT). The main restriction on the use of bonded structures is the lack of a reliable, applicable non-destructive test. Simple acoustic theory shows that a shear wave at normal incidence to an interface should be a more sensitive probe of interfacing coupling than a longitudinal wave. Conventional piezoelectric shear transducers require a very viscous couplant which makes scanning problematic. The EMAT described here consists of a pancake coil, and a permanent magnet behind the coil provides a static magnetic field normal to the surface of the sample and the plane of the coil. The EMATs used have the advantage of generating broadband radially polarized shear waves, while requiring no acoustic couplant. They are also comparable in size to typical piezoelectric transducers. The broadband nature of the transducer gives it a high spatial resolution in the direction of wave propagation. Experiments performed on plate-like samples have successfully detected deliberately constructed defects, while monitoring the adhesive thickness. Defects have been identified using a C-scan technique using a single EMAT in send-receive mode from either side of the bond.     

Lift-off compensation for improved accuracy in ultrasonic lamb wave velocity measurements using electromagnetic acoustic transducers (EMATs)

The crystalline texture of a sheet metal strongly affects its formability, so having knowledge of this texture is of great industrial relevance. The texture of rolled sheet metals, such as aluminium and steel, may be determined by ultrasonic measurement of the velocity of the zero order symmetric (S(0)) Lamb wave as a function of angle to the rolling direction. Electromagnetic acoustic transducers (EMATs) may perform this measurement without contacting the sample, therefore reducing perturbation to the plate wave system, as they are electromagnetically coupled to the sheet. The EMAT system measurements are non-destructive and may be made in real time, therefore offering advantages over the conventional techniques such as X-ray and neutron diffraction. It has been noticed that in the two EMAT pitch-catch system, the apparent arrival times of the ultrasonic waves change with variation in lift-off (distance between sample and transducer) due to impedance and aperture effects. For precise and accurate texture parameters to be obtained, accurate absolute ultrasonic velocity measurement is required and hence lift-off must be compensated for. This is of particular importance to online inspection systems where constant lift-off may be difficult to maintain. The impedance behaviour of various coil geometries has been investigated as a function of lift-off and frequency and compared to the received ultrasonic signal and the drive current pulse profile. Theoretical models have been used to explain the observed behaviour, and hence a scheme has been proposed for the compensation of lift-off effects in real time.     

Circuit-field coupled finite element analysis method for an electromagnetic acoustic transducer under pulsed voltage excitation

This paper presents an analytical method for electromagnetic acoustic transducers (EMATs) under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation (FFT). In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting’s theorem. Then the currents under different frequencies are calculated according to Ohm’s law and the pulsed current excitation is obtained by inverse fast Fourier transformation (IFFT). Lastly, the sequentially coupled finite element method (FEM) is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board (PCB) coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Further- more, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied.     

表面垂直裂痕诱发瑞利波散射的数值分析

激光激发的声表面波为材料表面缺陷的检测提供了有力的工具.针对含缺陷材料在模型边界上的复杂性,建立了基于平面应变的有限元模型并选取了相同厚度但含有不同深度的表面裂痕的单层铝板进行了对比计算,得到了声表面波经过不同深度的表面裂痕时产生的反射及透射信号波形的时域特征.进而引入了基于Wigner-Ville分布理论的时-频分析方法计算裂痕前、后散射的瞬态表面波的能量在时间-频率平面内分布的情形.结果显示：声表面波接近中心频率的某一频率成分在经过深度小于其中心波长的表面缺陷时,随着裂痕深度的增加,对应于该频率的反射系数呈现单调递增的趋势;而透射系数呈现递减的特征,这一结果可以为激光超声检测表面缺陷提供一种定量的表征手段.