Detection and localization of multiple cracks in a stepped shaft

The presence of a crack in a shaft causes a slope discontinuity in the elastic line of the shaft. There are crack detection techniques, available in the literature, exploiting the slope discontinuity arising because of the crack in the shaft. Steps present in a shaft are expected to interfere with the results obtained through these identification techniques based upon slope discontinuity. It would be even more difficult to identify a crack if it is near a step as both the step and the crack will cause slope discontinuities. A multi‐crack identification technique has been developed (Singh S. K. and Tiwari R. (2010). Mech. Machine Theory 45, 1813–1827; Singh S. K., Tiwari R. and Talukdar S. (2009). IUTAM Proc. in Recent Trends in Rotor Dynamics, March 23–26, IIT Delhi, India) which uses shaft‐forced responses at several frequencies to identify the number of cracks and their locations over the shaft. The algorithm uses normalization of quadratic coefficients obtained from measured responses of a cracked shaft and from simulated responses of the intact shaft for detecting the slope discontinuity. In the present work, the effect of steps in the shaft on crack identification has been analysed. Cracks are assumed to be both near the step and far from the step. The identification algorithm works well for both the simulation cases.     

Elasto-plastic element-free Galerkin method

In this paper the element free Galerkin method (EFGM) has been extended to be used in the elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the literature. In doing so the power law work hardening behavior has been employed and the value of J-integral has been used as a base for comparison of the results.First and second authors wish to express their gratitude to the Office of Research Affairs of Sharif University of Technology for financial support to conduct this research. The second author wishes to appreciate Professor Tom Hyde head of the School of 4 M in the University of Nottingham for his guidance and providing some research facilities.     

Stress-intensity factor and crack opening for a linearly viscoelastic strip with a slowly propagating central crack

The stress-intensity factor and the size of the crack opening have been calculated for a linearly viscoelastic strip with a slowly propagating central crack. The edges of the infinitely long strip are displaced normal to the crack and both clamped and shear-free strip edges have been investigated. The results are based on the solution to the problem of a suddenly loaded strip with a stationary crack. The resulting integral equation has been solved numerically for arbitrary crack length and analytical solutions in form of asymptotic series are given for crack length up to about half the strip width. The response to a propagating crack is found by superposition.This work represents part of a Ph.D. Thesis submitted to the California Institute of Technology. The author gratefully acknowledges the support of this work by the National Aeronautics and Space Administration under Research Grant NGL-05-002-005, GALCIT 120.     

基于裂纹诱导弦挠度的Timoshenko梁裂纹无损检测

研究了基于Timoshenko梁静态挠度识别梁中裂纹位置及损伤程度的计算方法。首先,将梁开闭裂纹等效为单向旋转弹簧,利用Delta函数和Heaviside函数,得到了具有任意开闭裂纹数目梁的等效抗弯刚度,求得了开闭裂纹Timoshenko梁弯曲变形的显式闭合通解,给出了闭合通解待定常数的迭代求解方法。其次,建立了裂纹诱导弦挠度函数,证明了在裂纹处裂纹诱导弦挠度曲线斜率存在突变,为裂纹位置识别提供了理论依据。在此基础上,给出了裂纹等效旋转弹簧刚度的近似计算公式。最后,通过数值试验,将所建立的方法分别应用于裂纹位置及损伤程度已知的简支和固支Timosheoko梁裂纹位置识别和损伤程度计算,结果表明该文建立的裂纹损伤识别方法不仅具有一般的适用性,而且具有较高的精度和可靠性。     

ON CRACK PHASES OF PARTICULATE-REINFORCED METAL MATRIX COMPOSITES

Abstract Crack growth mechanisms have been investigated in 6061 aluminum alloy reinforced with alumina particles (Al₂O₃/6061 Al composites). This has led to the identification of six crack phases: unstable growth; long crack growth; near-threshold long crack growth; short crack growth; pre-cease short crack growth, and non-growth phases. A crack phase diagram for particulate-reinforced composites is presented here which displays the range of applied stress and crack length for each phase. Each phase boundary corresponds or relates to an overall material property. The inability of particles to resist long crack growth has been rationalized by the variation of crack tip-cyclic plasticity and fracture energy due to the presence of particles.     

Computation analysis of interlaminar fracture of laminated composites

The interlaminar fracture behavior of laminated composites has been investigated. Contact and friction along the crack surfaces is taken into account in the finite element modeling of the delamination crack growth. Mode I, mode II and mixed mode loading conditions at the crack tip have been analyzed. For the cracks with contact and friction along the crack surfaces the virtual crack closure integral method is used in order to calculate separated energy release rates. Computational modeling and analysis of cross-ply laminates in three-point bending has been performed. Contact elements were used in order to prevent the material interpenetration along the crack surfaces. Comparison of the results obtained with and without using contact elements has been carried out and significant differences between the correlated values of the energy release rates have been found. The influence of the coefficient of friction on the energy release rates was found to be significant for short delamination crack lengths but insignificant for long cracks. Numerical analyses of experimental data obtained for unidirectionally reinforced glass fiber composites by double cantilever beam tests and by notched flexure tests have been carried out. For the double cantilever beam test geometric linear and nonlinear finite element analyses have been performed and critical energy release rates were calculated. For the end notched flexure test the contact problem has been solved taking into account that adjacent to the support contact and friction will occur. For the double cantilever beam test the critical energy release rates obtained by linear and nonlinear finite element solution has been compared with those from four different analytical data reduction methods (the area method, the Berry method, the modified beam analysis, the compliance method). For the end notched flexure test the critical energy release rates, calculated by the finite element analysis and taking into account contact and friction along the crack surfaces, have been compared with those obtained by conventional beam analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

简支梁裂纹位置识别的一种简单方法

由等效线弹簧来模拟裂纹引起的软化效应,基于铁摩辛柯梁理论得到含裂纹简支梁横向振动的频率计算式,由此获得识别裂纹位置的一种近似方法。文中利用梁的二维有限元模态分析数据进行裂纹位置的识别,结果表明该法在较宽的高跨比范围内,有好的效果;裂纹的深度对识别精度影响不大。     

海洋平台油气管道疲劳裂纹AE信号特征提取及识别研究

为了将声发射(AE)技术实际应用到监测海洋平台油气管道疲劳裂纹中,需要解决管道振动干扰以及疲劳裂纹AE信号有效特征提取的问题,而问题的关键在于对管道结构疲劳裂纹AE信号特征提取及识别算法的研究。在已有研究的基础上,提出了一种基于经验模态分解(EMD)为特征提取的疲劳裂纹识别方法,将管道振动干扰问题和疲劳裂纹AE信号有效特征提取问题联系在一起,对特征元素进行优化并剔除无效噪声干扰信息,通过概率神经网络(PNN)对疲劳裂纹信号进行识别。试验结果表明,PNN结合基于EMD为特征提取的疲劳裂纹识别法能够取得良好的效果,为声发射技术监测海洋平台油气管道疲劳裂纹提供了试验和理论依据。     

Fracture Analysis of Concrete Structural Components Accounting for Tension Softening Effect

This paper presents methodologies for fracture analysis of concrete structural components with and without considering tension softening effect. Stress intensity factor (SIF) is computed by using analytical approach and finite element analysis. In the analytical approach, SIF accounting for tension softening effect has been obtained as the difference of SIF obtained using linear elastic fracture mechanics (LEFM) principles and SIF due to closing pressure. Superposition principle has been used by accounting for non-linearity in incremental form. SIF due to crack closing force applied on the effective crack face inside the process zone has been computed using Green's function approach. In finite element analysis, the domain integral method has been used for computation of SIF. The domain integral method is used to calculate the strain energy release rate and SIF when a crack grows. Numerical studies have been conducted on notched 3-point bending concrete specimen with and without considering the cohesive stresses. It is observed from the studies that SIF obtained from the finite element analysis with and without considering the cohesive stresses is in good agreement with the corresponding analytical value. The effect of cohesive stress on SIF decreases with increase of crack length. Further, studies have been conducted on geometrically similar structures and observed that (i) the effect of cohesive stress on SIF is significant with increase of load for a particular crack length and (iii) SIF values decreases with increase of tensile strength for a particular crack length and load.     

Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method

In this paper, Voronoi cell finite element method (VCFEM), introduced by Ghosh and coworkers (1993), is applied to describe the matrix-inclusion interfacial debonding for particulate reinforced composites. In proposed VCFEM, the damage initiation is simulated by partly debonding of the interface under the assumption of the critical normal stress law, and gradual matrix-inclusion separations are simulated with an interface remeshing method that a critical interfacial node at the crack tip is replaced by a node pairs along the debonded matrix-inclusion interface and a more pair of nodes are needed to be added on the crack interface near the crack tip in order to better facilitate the free-traction boundary condition and the jumps of solution. The comparison of the results of proposed VCFEM and commercial finite element packages MARC and ABAQUS. Examples have been given for a single inclusion of gradually interfacial debonding and for a complex structure with 20 inclusions to describe the interfacial damage under plane stress conditions. Good agreements are obtained between the VCFEM and the general finite element method. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials. The financial support by the Special Funds for the National Major Fundamental Research Projects G19990650 and the National Natural Science Foundation of China No. 59871022 are gratefully acknowledged.     

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning,J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago. The work presented in this paper is supported by sponsored research projects of the Aeronautics R & D Board, Government of India and their support is acknowledged.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Computation of stress intensity factors (KI, KII) and T-stress for cracks reinforced by composite patching

To increase the operational life of defected structures, a repairing method using composite patches has been used to reinforce cracked components. Due to various advantages of composite materials, this method has received much attention from researchers and engineers. Considerable investigations have been performed to highlight the effect of bonded composite patches on the fracture parameters such as stress intensity factors (SIF) and J-integral. However the effect of composite patches on the T-stress, the constant stress term acting parallel to the crack, has not been investigated in the past. In this paper, the finite element method is carried out to analyze the effect of bonded composite patches for repairing cracks in pure mode I and also mixed mode I/II conditions, by computing the stress intensity factors and the T-stress, as functions of the crack length, the crack inclination angle and the type of composite material. In pure mode I condition, the finite element analysis is carried out for three different specimens: centre crack, double edge crack and single edge crack specimens. For mixed mode I/II condition the analysis is conducted on an inclined central crack of various slant angles. For both pure mode I and mixed mode I/II, the numerical results show that composite patching has considerable effect on the T-stress.     

基于小波分析的Timoshenko梁裂缝识别研究

采用等效转动弹簧代替梁内的不扩展横向裂缝,研究Timoshenko裂缝梁的横向振动特性,建立了一种与有限元分析相结合的、基于模态参数的小波分析识别Timoshenko梁内裂缝的方法。以一简支梁为例,通过建立含横向不扩展裂缝的Timoshenko梁的有限元模型,用Lanczos法对结构的模态进行了计算分析,求出了基本振型和转角模态。分别应用mexh小波和db小波为母小波对二者做小波变换,进行多尺度分析,通过小波系数模极大值位置识别出梁内的裂缝。并对识别结果进行对比,发现识别Timoshenko梁裂缝时,基于转角模态小波变换的方法对小波基、尺度的要求较低,变换后的小波系数线更为平滑,奇异性特征更为明显,故运用转角模态小波变换来识别Timoshenko梁裂缝,较之运用基本振型小波变换的方法更为方便、有效。该方法对Timoshenko梁裂缝识别的工程应用具有参考价值。     

Application of 3D wavelet transforms for crack detection in rotor systems

The dynamics and diagnostics of a cracked rotor have been gaining importance in recent years. The early detection of faults like fatigue cracks in rotor shafts are very important to prevent catastrophic failure of the rotor system. Vibration monitoring during start up or shut-down is as important as during steady state operation to detect cracks especially for machines such as aircraft engines which start and stop quite frequently and run at high speeds. So, the transient data of the cracked rotor has been transformed using the wavelet transforms for crack detection. Most of the works quoted in the literature used 1D wavelets or 2D wavelets (Continuous Wavelet Transform-CWT) for crack detection. The crack detectors in the signals are both time as well as frequency dependent. So, the use of 2D wavelets is also not enough to detect the crack. In the present work a 3D wavelet (CWT) has been utilized which clearly indicates both the time and frequency features of the crack. The presence of sub-criticals in the CWT may be a best crack indicator but it is not always reliable. The addition of noise to the signal may sometimes lead to inaccurate results. So, there is a need to identify a parameter in addition to the sub-criticals. The phase angle between the two signals (cracked and un-cracked) or two transverse vibrations can be a better crack indicator because it is very less sensitive to noise disturbance. So, to extract the above phase angle a new transform has been applied called Cross Wavelet Transform (XWT). The XWT is exploited for the first time to a rotor fault detection system in the present work. Some interesting results have been obtained using the same. The advantage of the XWT is that both, the phase angles between the transverse signals and also the amplitudes of sub-criticals are viewed in a single plot. Parametric analysis is also carried out by varying crack depth and crack position for diagnostic purposes. The inverse problem of crack identification (i.e. determining the crack parameters through known vibration data) has also been carried out using Artificial Neural Network (ANN).     

The Interaction between a Crack and a Particle Cluster

A numerical method has been developed to study the interaction between a crack and second phase particles in a discontinuously reinforced composite material. The simulation is achieved using a ‘dual’ boundary integral method, coupled with a maximum energy release rate criterion for determining the direction of crack propagation. The method has been applied to a composite material composed of components having the elastic properties of Aluminium (matrix) and Silicon Carbide (reinforcement). In particular, the method is used to investigate the crack trajectory and energetics as it interacts with a single particle and with clusters consisting of two particles or a random distribution of ten particles. It is found that although the energy release rate is affected by the particle(s) at relatively large distances, the crack trajectory is not substantially altered until the crack is very close to the particle(s). A pre-existing interface flaw is observed to attract the crack and substantially increase the energy release rate. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

An approach for analysis of poled/depolarized piezoelectric materials with a crack

In this paper, the influence of dielectric medium inside a crack on crack growth, in an infinite poled or depolarized ceramic, has been studied by employing an electric boundary condition derived from the exact boundary conditions proposed by Sosa (1996). The effect of remanent polarization has also been examined. The results obtained show that electric displacement on crack surfaces is not always zero. Hence, for studying fracture problems of piezoelectric ceramics with cracks accurately, the exact boundary conditions should be implemented. In addition, the results indicate that the effect of remanent polarization is equivalent to that of a positive electric field and it cannot be neglected. It is also found that a positive electric field always has a tendency to open a crack, and a negative electric field tends to close a crack.     

On saturation-strip model of a permeable crack in a piezoelectric ceramic

Summary. The saturation-strip model for piezoelectric crack is re-examined in a permeable environment to analyze fracture toughness of a piezoelectric ceramic. In this study, a permeable crack is modeled as a vanishing thin but finite rectangular slit with surface charge deposited along crack surfaces. This permeable saturation crack model reveals that there exists a possible leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a first-order approximated solution is obtained with respect to slit height, h ₀, in the analysis of electrical and mechanical fields in the vicinity of a permeable crack tip. The permeable saturation crack model presented here also considers the effect of charge distribution on crack surfaces, which may be caused by any possible charge-discharge process in the dielectric medium inside the crack. A closed form solution is obtained for the permeable crack perpendicular to the poling direction under both mechanical as well electrical loads. Both local and global energy release rates are calculated. Remarkably, the global energy release rate for a permeable crack has an expression, where M is elastic modulus, a is the half crack length, is permittivity constant, and e is piezoelectric constant. This result is in a broad agreement with some experimental observations and may be served as the fracture criterion for piezoelectric materials. This contribution elucidates how an applied electric field affects crack growth in piezoelectric ceramic through its interaction with permeable environment surrounding a crack. The author would like to acknowledge the support from the Academic Senate Committee on Research at University of California (Berkeley) through the fund of BURNL-07427-11503-EGSLI.