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.     

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.     

Measurement of Stress Intensity Factors of a Mixed-Mode Interface Crack by a Speckle Photography

The image-processing system based on a two-dimensional Fourier transform is presented for the analysis of Young’s fringes pattern created from a double-exposure speckle photograph. The fringe spacing and orientation are determined using only one Young’s fringes pattern without any other diffraction halo patterns. The stress-intensity factors of a mixed-mode interface crack were measured by speckle photography. A compact normal and shear specimen with an interface crack was employed. This specimen enables us to carry out the experiment under various kinds of mixed-mode loading. A steel and an epoxy resin were used as dissimilar materials. The displacement along the crack lines at the free surface was measured by speckle photography. The K₁ and K₁₁ values were determined by a least squares method using displacement data along the crack lines. Three-dimensional finite element analysis was carried out on the same specimen. An accuracy of stress intensity factors obtained by the speckle photography was discussed by comparison of results obtained by the finite element analysis.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.     

The governing equations of Moiré interferometry II. Gratings at ±45° to the measurement axes

The effects of tilting of the grating plane on moiré interferometric fringe patterns are studied using the method of Livnat and Post (Experimental Mechanics, 25(4) (1985) 6–360). Tilting may result either from rigid-body rotations or from out-of-plane displacement gradients. Tilting may introduce a significant error if it is assumed that the fringes represent contours of in-plane displacement, particularly if the in-plane deformation is small compared with the out-of-plane displacement gradient. Knowledge of the surface slope appears to be sufficient to correct the error. It is also shown that the fringe patterns do not capture the added displacement caused by rigid-body rotations exactly. The implications of these effects are briefly discussed for an experiment measuring the deformation at the tip of a crack in a ductile steel, in which the out-of-plane displacement gradients are relatively large.     

Estimating the sizes of surface cracks based on Hall element measurements of the leakage magnetic field and a dipole model of a crack

A method is proposed for estimating the sizes of surface cracks in magnetic materials. The method is based on applying a magnetic field, then determining the leakage magnetic field in the vicinity of a crack by moving a Hall element on the surface of the material along one or two scanning lines crossing the crack, and measuring the corresponding Hall voltage distribution. A dipole model of a crack is utilized, in which a surface crack is considered as being full of magnetic dipoles aligned parallel to the applied field, and whose density varies linearly along the depth of the crack. Analytical expressions are derived for the z-component of the intensity of the leakage magnetic field, and for the measured Hall voltage in the vicinity of a crack with an arbitrary cross-section along its long axis when it is perpendicular to the applied field. The crack sizes and the parameters of the distribution of magnetic dipoles along the crack depth are computed by crack inversion, which represents a regression for the Hall voltage distribution. A variable theoretical Hall voltage distribution is fitted to the measured Hall voltage distribution by minimizing the corresponding RMS error, which gives the unknown parameters at the end of the minimization. Hall voltage distributions are measured on ferromagnetic steel samples containing one artificial surface crack. Some crack inversions are performed for estimating the maximum crack depth and the crack width of cracks with rectangular and isosceles triangular cross-sections along the long crack axis. The accuracy of these crack inversions increases by utilizing either Hall voltage distributions measured along only one of the scanning lines, instead of along both scanning lines, or by using more precisely measured Hall voltage distributions. The fast and accurate estimation of the maximum crack depth and the crack width by such crack inversions could be important for pipeline inspection. Other crack inversions are performed for determining the cross-section along the long axis of the investigated cracks with satisfactory results. Received: 2 March 2001 / Accepted: 10 April 2001 / Published online: 25 July 2001     

Detection and evaluation of the depth of surface cracks in conductive materials by using a loop antenna

A new method is developed for detection and evaluation of the depth of surface cracks in conductive materials. The main components of the measurement equipment are a conductive wire and a loop antenna, both of which are located as close as possible to the surface of the investigated material, while the antenna loop is perpendicular to the surface and parallel to the wire. Supplying of electrical potential with microwave frequency f and amplitude |_s| to the wire results in spreading of induced current close beneath the surface of the material. The induced current redistributes in the vicinity of surface cracks, and some of the current paths flow along the crack walls. This leads to generation of a time-variable magnetic field mostly within the volume of the crack, which is detected by the loop antenna. A theoretical analysis is presented of the contributions of the different types of generated magnetic fields to the potential drop with amplitude |U_s| measured by the antenna. The distribution of the ratio R(dB)=|U|/|U_s| is measured for specimens of paramagnetic and ferromagnetic steel which contain three artificial cracks with depths of 0.5 mm, 1 mm, and 2 mm, and frequency f=300 MHz of the supplied electrical potential. It turns out that artificial cracks with a depth of d 0.5 mm, located at distances from x=3 mm to x=15 mm from the wire, can be detected. The largest sensitivity of crack detection is achieved for x4 mm when the long axis of a crack is perpendicular to the wire. The crack response of the measured ratio R is proportional to the crack depth when the loop of the antenna is located above or slightly outside an artificial crack, and at least 4 mm from the wire. This relation could be used for evaluation of the depth of real surface cracks. The notable decrement of the crack response outside the crack can indicate the location of the crack tips on the surface of the specimen. It is shown that a loop antenna with a diameter of 7 mm provides the largest crack response, as well as that the developed method can be applied to both paramagnetic and ferromagnetic materials. An example of the detection of a real crack by an antenna is reported for the first time. PACS 81.70.Ex; 84.40.Ba; 84.32.Ff     

An experimental method for eliminating effect of rigid out-of-plane motion on 2D-DIC

The out-of-plane motion is one of the most important factors that affect the precision of two-dimensional digital image correlation (2D-DIC). In this paper, a novel solution is presented to improve conventional 2D-DIC by eliminating the effect of out-of-plane motion, including translation and rotation. Firstly, an experimental technique using two projected laser strips is proposed to measure the out-of-plane motion of a planar specimen. A theoretical model is then established to predict the pseudostrains caused by out-of-plane motion based on the pin-hole imaging model. Using the measured out-of-plane displacement, the captured deformed images used in 2D-DIC are amended to eliminate the effect of out-of-plane motion by the theoretical model. Finally, two experiments were conducted to validate the effectiveness of the proposed method. Results indicate that application of the proposed method can effectively eliminate the errors caused by out-of-plane motion.     

超声散斑相移法测量技术

超声散斑相移法能满足工程建设中对水下物内层界面关键点位移进行测量的特殊要求。测量时,引入数字参考信号与物面测点上的散斑信号进行数字干涉,获得叠加信号强度。界面位移前后,应用软件逐步改变参考信号相位,可逐步改变叠加信号强度,根据这些信号强度值可计算出测点的位移量。应用此技术对水下试件内层表面的法线和切线方向上的位移进行了实测,测量结果与理论值有较好的吻合;研究表明打磨后的粗糙外层界面不影响应用相移法进行测量。在应用相移法测量时,不需声像转换,不需全场扫描,测量精度不受散斑尺寸限制。      

Application of stereo vision to the study of mixed-mode crack-tip deformations

A stereo vision is applied to evaluate crack-tip parameters for fracture specimens subjected to a mixed-mode loading (tension and shear). By using a special loading device, the applied remote loading is oriented at an angle with respect to the axis of the crack. At each loading angle, the calibrated vision system was rotated so that the axis of the crack is parallel to the horizontal or vertical axis of the image frame. At a load close to the crack initiation, the displacement field around the crack-tip region of the fracture specimen was measured relative to a specimen coordinate system located at the crack tip of the fracture specimen. During the experiment, the fracture specimen was subjected to rigid body translation and rotation. Hence, the displacement fields are affected by the rigid body translation and rotation. Using the experimentally determined displacements and the analytically determined displacements with several higher order terms being included, the stress intensity factors and the amount of rigid body translation and rotation were calculated through a least-squares fit. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. Experimental results indicate that a K_I and K_II dominant region is observed in the corrected displacement fields.     

Inspection of out-of-plane surface movements over small areas using electronic Speckle Pattern Interferometry

Electronic Speckle Pattern Interferometry (ESPI) has been used to observe and measure out-of-plane surface displacements over very small areas (1 mm². It is proposed to use this technique to measure the differential out-of-plane surface displacements which occur at a crack tip due to the formation of a plastic zone when the crack is put under an increasing incremental tensile load.     

A modified moiré interferometer for three-dimensional displacement measurement

This paper presents a new optical interferometric system, MMI-T/G, composed of a modified four-beam moire interferometer and a Twyman/Green interferometer. The MMI-T/G system can measure threedimensional displacement fringe patterns with a single loading on the specimen, and the in-plane and out-of-plane displacement fields can be measured independently and defined clearly. The optical setup has the advantages of structural novelty, flexibility, and high fringe contrast. Moreover, the in-plane displacement sensitivity is twice of that of the normal moire interferometer. The measuring techniques to obtain the fringe patterns and displacement fields using the MMI-T/G system axe described. The experimental results of thermal displacement of an electronic device are shown.     

Simultaneous quantitative evaluation of in-plane and out-of-plane deformation by use of a carrier method of large image-shearing shearography

A carrier method for separating out-of-plane displacement from in-plane components based on large imageshearing shearography is presented. A reference surface is fixed on the side of a test object. They are illuminated by two expanded symmetric illuminations respectively. The carrier is introduced by rotating the reference surface to modulate the displacement of an object. By using Fourier transform to demodulate the modulated fringe pattern, two phase maps, which include out-of-plane and in-plane displacements, can be obtained. Then the out-of-plane displacement can be easily separated from in-plane displacement by subtraction and addition of the two unwrapped phase distributions. The principle of the method is presented and proved by a typical three-point-bending experiment. Experimental results show that the method enjoys high visibility of carrier fringes. The system does not need a special beam as a reference light and has simple optical setup.     

Two-frame phase-shifting interferometry for retrieval of smooth surface and its displacements

A new two-frame interferometric method with a blind phase shift of a reference wave is proposed for the reconstruction of smooth surface relief areas. In this method, a correlation approach based on the determination of correlation coefficient between intensity distributions of two interferograms is applied for the phase shift extraction. An algorithm for this method realization is developed and its performance is verified on test surfaces. An experimental setup containing a Twiman-Green interferometer was used in the reconstruction of smooth surfaces of metal specimens using the developed algorithm. Surface displacement phase fields were generated in case of a CT-notched specimen made of an aluminum alloy by the interactive procedure of element stitching of two surface reliefs and subtracting the surface relief after cyclic loading from the initial one. The received surface displacement fields allow us to determine the studied specimen fatigue process zone (FPZ) and FPZ size.     

NON-DESTRUCTIVE EVALUATION OF HORIZONTAL CRACK DETECTION IN BEAMS USING TRANSVERSE IMPACT

Numerical and experimental studies for crack detection in beam employing transverse impact are presented. In the numerical study, a beam model of wave propagation is developed to calculate the time history of beam response before, over and after the crack region. It is expected that the resulting wave in the beam will be scattered by the crack and will carry information on the location and geometry of the crack. Experiments using a scanning laser vibrometer on specimens containing simulated crack are then conducted to verify the numerical results. Comparison study between the numerical results and experimental observations are conducted; good correlation between theory and experiment is observed. The beam model of wave propagation and adaptive multilayer perceptron networks (MLP) are then used for inverse identification of crack parameters (i.e., crack location, depth and length) in the beams. Time-domain displacement responses calculated using the present beam model containing predetermined crack parameters are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of an unknown crack in a beam using experimental displacement responses measured with a scanning laser vibrometer. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of the crack.     

电子散斑干涉位移场分离技术及其在三维测量中的应用

提供了一种可将离面位移与面内位移分离的三维位移场测量方法.在双光束电子散斑干涉中增加参考光,使这一路参考光为两光束所共用.两束光各自独立地对变形物体进行测量,结合相移技术,可分别得到包含离面和面内位移信息的二幅位相图.只需简单的位相运算就能够将面内位移场与离面位移场分离.在竖直方向上,采用两光束对称照明被测物,直接测量面内位移竖直方向分量.本文将该技术应用到柴油机油泵测量上,得到了油泵的三维位移场.该技术为三维位移场的测量提供了一种新的有效途径,也为柴油机零部件的强度和刚度分析评价提供了新的方法.     

Generation of the derivative of out-of-plane displacements in the high-sensitivity grating interferometry configuration

A simple method for determining the surface slope of a specimen under test in the high-sensitivity grating interferometry setup is proposed. The information on the derivative of out-of-plane displacement is obtained by software subtraction of two primary interferograms: a conventional one and one with diffraction orders laterally displaced in the image plane. Very good coincidence between the theoretical and experimental results has been obtained. The method can be used for studying static and transient events depending on the fringe pattern analysis method used.     

Ultrasound diffusion for crack depth determination in concrete

The determination of the depth of surface-breaking cracks in concrete specimens using an ultrasound diffusion technique is discussed. Experiments were carried out on precracked concrete specimens of varying crack depths (0%-40% of the specimen thickness). Contact transducers were placed at the specimen surface with source and receiver separated by the crack. Tone-burst excitations over a frequency range of 400-600 kHz were used. At these frequencies, ultrasound is scattered considerably by the heterogeneities in the concrete. In the limit of many scattering events, the evolution of energy may be modeled as a diffusion process. The arrival of the peak diffuse energy at the receiver is delayed due to the presence of crack. This delay is the prime indicator used for determining crack depth. Numerical and analytical analyses were also used for comparison. These results are in basic agreement with the experiments. In addition, these analyses are used to study the limits of this technique. In particular, it is shown that this technique is applicable to cracks greater than the scattering mean-free path, which is estimated at about 1 cm for these specimens. Aspects of practical implementation are also discussed.     

A novel approach to high-sensitivity grating interferometry

The authors propose a new approach for obtaining information about in-plane and out-of-plane displacements of an object tested using high-sensitivity grating interferometry. The interferences of each of the specimen grating diffraction orders with a reference beam are recorded separately. Computer addition and subtraction of the phase functions calculated from the interferograms give the in-plane and out-of-plane displacement values, respectively. The authors present their experimental work, and then compare their results with those obtained using a conventional grating interferometry approach.     

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。      

A linear least squares approach for evaluation of crack tip stress field parameters using DIC

In the present work, an experimental study is carried out to estimate the mixed-mode stress intensity factors (SIF) for different cracked specimen configurations using digital image correlation (DIC) technique. For the estimation of mixed-mode SIF׳s using DIC, a new algorithm is proposed for the extraction of crack tip location and coefficients in the multi-parameter displacement field equations. From those estimated coefficients, SIF could be extracted. The required displacement data surrounding the crack tip has been obtained using 2D-DIC technique. An open source 2D DIC software Ncorr is used for the displacement field extraction. The presented methodology has been used to extract mixed-mode SIF׳s for specimen configurations like single edge notch (SEN) specimen and centre slant crack (CSC) specimens made out of Al 2014-T6 alloy. The experimental results have been compared with the analytical values and they are found to be in good agreement, thereby confirming the accuracy of the algorithm being proposed.