A probabilistic method for the detection of obstructed cracks of beam-type structures using spatial wavelet transform

This paper reports both the theoretical development and the numerical verification of a practical wavelet-based crack detection method, which identifies first the number of cracks and then the corresponding crack locations and extents. The value of the proposed method lies in its ability to detect obstructed cracks when measurement at or close to the cracked region is not possible. In such situations, most nonmodel-based methods, which rely on the abnormal change of certain indicators (e.g., curvature and strain mode shapes) at or close to the cracks, cannot be used. Most model-based methods follow the model updating approach. That is, they treat the crack location and extent as model parameters and identify them by minimizing the discrepancy between the modelled and measured dynamic responses. Most model-based methods in the literature can only be used in single- or multi-crack cases with a given number of cracks. One of the objectives of this paper is to develop a model-based crack detection method that is applicable in a general situation when the number of cracks is not known in advance.

To explicitly handle the uncertainties associated with measurement noise and modelling error, the proposed method uses the Bayesian probabilistic approach. In particular, the method aims to calculate the posterior (updated) probability density function (PDF) of the crack locations and the corresponding extents.

The proposed wavelet-based crack detection method is verified and demonstrated through a comprehensive series of numerical case studies, in which noisy data were generated by a Bernoulli–Euler beam with semi-rigid connections. The results show that the method can correctly identify the number of cracks even when the crack extent is small. The effects of the number of cracks and the crack extents on the results of crack detection are also studied and discussed in this paper.     

Laser Multi-mode Scanning Thermography Method for Fast Inspection of Micro-cracks in TBCs Surface

Conventional non-destructive testing methods are difficult to be applied in defect detection of thermal barrier coating (TBCs) because of some of its characteristics, such as porosity and thin thickness, etc. For detecting surface cracks in TBCs, a laser multi-modes scanning thermography (SMLT) method has been developed in this paper, combining fast scan mode using linear laser with fine scan mode using point laser on the tested specimen surface. Linear scanning has a large detection range and detection speed, and point scanning has a higher sensitivity. Through the theoretical analysis, numerical simulation and experimental verification, five unique thermal response features of the cracks stimulated by two scanning modes were discovered and summarized. These features in the thermal images include temperature sharply rising in local region, distinct increase of the area of high temperature zone, obvious ‘tailing’, ‘dislocation’ and thermal obstruction phenomenon, respectively. Therefore, with the corresponding post-processing algorithm developed here, the location and shape of surface cracks in TBCs can be efficiently detected by analyzing the information of these thermal response features. Validation tests showed that the surface cracks with the width of more than \(20\,\upmu \hbox {m}\) can be quickly detected in line-scan stage, while in point-scan stage, the \(9.5\,\upmu \hbox {m}\) wide surface cracks can be accurately detected.     

基于弱磁技术的火车轮踏面裂纹检测

针对火车轮踏面易萌生细小裂纹的问题,提出一种无需励磁,利用地磁场磁化的无损检测方法.根据火车轮踏面结构设计探头工装,利用弱磁检测仪器采集车轮踏面磁感应强度信号,分析预制裂纹缺陷的磁异常信号特征,对比不同深度裂纹的磁异常信号幅值,通过傅里叶最小二乘拟合得到缺陷深度的定量算法,根据极值差法与拉依达准则对火车轮踏面进行智能识...     

Structural damage identification using transfer matrix with lumped crack properties

A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measured and predicted displacements. The method is verified using several numerical models as well as experiments with cracked beams. The TM is shown to be suitable for local identification and also fast and accurate compare to other methods.     

Small crack growth rates from simple sequences containing underloads in AA7050-T7451

Fatigue crack growth in materials that display confined slip show crack path changes that are dependant on the loading history. In these materials certain variable amplitude loading patterns can produce strong slip bands ahead of the crack tip. One of these patterns of loadings involving bands of high R cycles followed by one or two underloads also produce distinct features or progression marks on the fracture surface that have been used to delimit small blocks of constant amplitude cycles. The same loading pattern also produces strong slip bands ahead of the fatigue crack both in the plane of the crack and out of plane. These slip bands affect the direction and possibly the rate of propagation of the fatigue crack. Thus these loading patterns make an ideal marker to look at small crack growth rates in the presence of slip bands.This paper reports on the crack growth rates for a series of fatigue cracks grown in AA7050-T7451 coupons, from near initiation to near failure. The aim of this work was to generate constant amplitude crack growth data for use in predictions that is more useful for predicting crack growth lives than that obtained from long crack constant amplitude tests. Three simple sequences which applied small bands of constant amplitude loading were used in the fatigue tests preceded by a loading sequence to produce a progression mark to delimit the bands. The fatigue cracks in the coupon initiated from etch pits on the surface of the coupons. The width of the bands of constant amplitude growth in these sequences were measured under a microscope. The growth in these sequences was found to be faster than for long cracks under constant amplitude loading.     

Interaction of a penny-shaped crack with an elliptic crack under shear loading

The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter _i up to the order _i⁵,(i=1,2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289–313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.     

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, S_max/₀. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from complete slip before opening to opening in mode I before mode II shear offset. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.     

电子束焊接K418高温合金裂纹的影响及组织与性能研究

目的探究工艺参数对K418高温合金焊接裂纹的影响,减少焊接过程中裂纹的产生。方法采用真空电子束对2mm的薄板K418高温合金进行焊接试验,通过改变工艺参数来调控焊接裂纹,使用光学显微镜对焊缝显微组织进行观察,使用显微硬度计对试样进行硬度测量,万能拉伸计对接头进行拉伸试验,使用扫描电镜对断口进行观察。结果在焊接束流为24 mA,焊接速度为600 mm/min时,扫描波形为O形,频率为500 Hz时,焊接接头表面未发现裂纹。通过拉伸试验发现断裂位置为母材,其断口为典型脆性解离断裂。结论采用合适的工艺参数可以减少或消除焊接接头表面裂纹的形成。     

Fast Characterization of the Width of Vertical Cracks Using Pulsed Laser Spot Infrared Thermography

In-service non-destructive detection of cracks is a challenging task for industries to prevent failures. In the last decades several methods based on infrared thermography have been proposed to detect vertical cracks. In a recent paper, the authors used a lock-in thermography setup with focused laser excitation to characterize the width of infinite vertical cracks accurately. As this method is very time consuming, we propose in this work to measure the width of an infinite vertical crack using pulsed laser spot infrared thermography. A semi-analytical solution for the surface temperature of a sample containing such a crack when the surface is illuminated by a pulsed Gaussian laser spot close to the crack is obtained. Measurements of the surface temperature on samples containing calibrated cracks have been performed using an infrared camera. A least square fit of the surface temperature is used to retrieve the thickness of the crack. Very good agreement between the nominal and retrieved thickness of fissure is found, even for widths down to 1 \(\upmu \)m, confirming the validity of the model.     

A surface acoustic wave technique for monitoring the growth behavior of small surface fatigue cracks

The theory of Kino and Auld which relates the reflection coefficient of acoustic waves from a crack to its size is summarized. A scattering model is evaluated from this theory concerning the reflection of surface acoustic waves (SAW) from a small surface fatigue crack at a frequency such that the crack depth is much smaller than the acoustic wavelength. Acoustic predictions of crack depth are compared to postfracture measurements of depth for small surface cracks in Pyrex glass, 7075-T651 aluminum, and 4340 steel. Additionally, the minimum detectable crack depth as limited by the acoustic noise level is determined for several typical aluminum and steel alloys. The utility of SAW reflection coefficient measurements for inferring crack depth, crack growth, and crack opening behaviorin situ during fatigue cycling is discussed.     

圆柱类金属构件表面裂纹的激光超声识别方法研究

为了利用激光超声技术有效地识别圆柱表面裂纹,提出利用圆柱表面波信号增强和小波包-奇异值分解(WPT-SVD)方法识别圆柱类金属构件表面裂纹的位置和深度。建立了圆柱的激光超声显式有限元模型,分析了圆柱表面裂纹对表面波的模式转化作用。利用圆柱表面裂纹在激发源位置附近时激光超声扫描信号增强的现象,识别圆柱表面裂纹的位置。在已识别圆柱表面裂纹位置的基础上,通过分析圆柱表面裂纹检测信号的时频特点,利用WPT-SVD提取圆柱表面信号的时频特征,定义参数k r表征裂纹深度的变化,识别圆柱表面裂纹深度。搭建了激光超声圆柱表面裂纹检测实验系统,开展了实验研究,实验结果表明所提出的圆柱表面信号增强和WPT-SVD方法可以识别出圆柱表面裂纹的位置和深度。     

Coefficients of the crack tip asymptotic field for a standard compact tension specimen

The coefficients of the crack tip asymptotic field of a standard compact tension (CT) specimen are computed using a hybrid crack element (HCE). It allows the direct calculation (without post-processing) of not only the stress intensity factor (SIF) but also the coefficients of higher order terms of the crack tip asymptotic field. Approximate closed-form expressions for the first five terms for the CT specimen that are accurate for shallow to very deep cracks are obtained by fitting the computed data. The SIF formula proposed by Brown and Srawley (1966) is shown to be accurate when the crack length to depth ratio () ranges from 0.35 to 0.75. The formula proposed by Newman (1974) and Srawley (1976) is accurate for 0.15. However, the accuracy of available formulas for the second T-term in the literature is quite disappointing. Numerical results also show that, unlike the notched three-point bend beam and the wedge splitting specimen, the second T-term of the CT specimen is always positive.     

自然环境下路面裂缝的识别

论文提出了一种基于分数阶微分和图像形态学的路面裂缝检测算法。分数阶微分能有效增强信号中、高频部分,非线性保留信号的低频部分,通过构建分数阶微分掩模算子,增强裂缝信息特别是平滑区域中弱信号信息。利用图像形态学算子提取裂缝,通过组合中值滤波去除孤立噪声点。实验结果表明,该算法比传统算法能更有效地检测出细小裂缝信息,是一种具有较强鲁棒性且高效实用算法。     

Tensile strength and crack nucleation in boron fibres

Boron fibres of about 100m diameter have been tested to fracture in a micro-tensile testing machine. The fracture surfaces have been investigated using a scanning electron microscope and classified according to the fracture nucleation type. Comparison with the measured fracture stresses proved a significant correlation with the type of crack nucleation. Transverse cracks, nucleated at the edge of radial cracks along the fibre axis direction, are the most critical weakening feature. Also crack nucleation at the external fibre surface implies a low tensile strength, and is discussed in terms of a notch effect of the well-known nodular surface topography.     

Detection of the Subsurface Cracks in a Stainless Steel Plate Using Pulsed Eddy Current

The nondestructive method to detect subsurface defects is limited because conventional eddy current are concentrated near to the surfaces adjacent to the excitation coil. The PEC technique enables detection of cracks buried deeper under the surface with relatively small current density. In the present study, an attempt has been made to investigate detection of subsurface cracks using a specially designed double-D differential probe. The tested sample is a SS304 with a thickness of 5 mm; small EDM notches were machined in the test sample at different depths from the surface to simulate the sub surface cracks in a pipe. The designed PEC probe has two excitation coils and two detecting Hall-sensors. The difference between two sensors is the resultant PEC signal. The cracks under the surface were detected using peak amplitude of the detected pulse; in addition, for a clear understanding of the crack depth, the Fourier transform is applied. In time domain, the peak amplitude of the detected pulse is decreased, and in the frequency domain, the magnitude of the lower frequency component has been increased with an increase in the crack depth. The experimental results have indicated that the proposed differential probe has the potential to detect the sub surface cracks in a stainless steel structure.     

硫化锌热冲击试验与裂纹间距预报

重点研究了硫化锌热冲击开裂机理和热冲击裂纹间距、深度的预报。10mm厚硫化锌试块的燃气急热试验表明:裂纹间距随热冲击能量的增大而减小,热冲击过程中加热面最先出现非贯穿裂纹,停止加热后,裂纹贯穿试件。结合传热和热强度仿真分析,获得了热冲击过程中试件的瞬态温度场和应力场。基于材料性能的损伤演化理论,以裂纹间距和深度为变量,利用最小能量原理,获得了热冲击裂纹间距的理论预报方法,预测结果与试验吻合较好,进而分析了断裂韧性、热胀系数、材料初始模量对裂纹间距、裂纹深度的影响。该文的研究对深入理解硫化锌的热冲击失效机制,对其改性和研制具有重要意义。     

Path prediction of I + III mixed mode fatigue crack propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the propagation rate expression and the path prediction. It is found that during the mode transformation process, the crack propagation rate is still controlled by the mode I stress intensity factor; and Paris equation also holds for the relationship between and ΔK_I . Crack propagation path can be predicted only when both the crack mode transformation rate and propagation rate are available.     

Fatigue Propagation of Fibre-Bridged Cracks in Unidirectional Polymer-Matrix Composites

In order to improve the fatigue resistance of polymer-matrix composites by materials design, or to conceive micromechanics based models for life predictions, the underlying micromechanisms must be understood. Experimental investigations have revealed fibre-bridged cracking as a toughening micromechanism that retards further fatigue crack growth in a unidirectional 0° carbon-fibre-reinforced epoxy. The bridging fibres exert a closing traction on the crack surfaces, thereby reducing the driving force for crack growth. In this study, the growth of bridged cracks has been quantified by a surface replication technique. The da/dN–K curve defined in terms of nominal stress-intensity factors shows a crack retarding behaviour. The crack growth curve can be replotted in terms of the effective stress-intensity factor where the contribution of the cohesive crack surface forces from the bridging fibres are taken into account. This curve falls somewhat closer to that of the neat matrix material, but the difference is still considerable, and it shows a decelerating propagation. Therefore, there must be other active toughening mechanisms besides fibre bridging, that slow the crack propagation down, and account for the fatigue resistant behaviour of the tested material. Ways by microstructural design to promote the fatigue resistant mechanisms are discussed.     

Ultrasonic Measurement of the Crack Depth and the Crack Opening Stress Intensity Factor Under a No Load Condition

This paper describes a new methodology for evaluating the crack depth and the crack opening stress intensity factor of small closed cracks using an ultrasonic technique. Surface connected back-wall cracks of depth ranging from 0.4 to 4.0 mm in steel specimens are considered. The crack corner echo amplitude of an ultrasonic shear wave, SW, beam of 50° incidence in material is used. First, the ultrasonic echo response of an open crack is determined as a function of crack depth. Next, based on changing the crack closure stress, an empirical relation between the crack closure stress and the crack-echo response is formulated. The crack depth and the crack closure stress of an unknown closed crack based on these relations are determined by inverse analysis of the ultrasonic response of the crack. From the evaluated crack depth and crack closure stress, the crack opening stress intensity factor is determined. The accuracy and reliability of this new nondestructive evaluation (NDE) method is verified by comparing the evaluated crack depth with the actual one. The latter is measured on the fractured surface obtained after carrying out ultrasonic testing. The ultrasonic method developed is proved to be a powerful tool for quantitative and nondestructive evaluation of the crack depth as well as the crack closure stress.