Lamb波在含孔隙功能梯度材料中传播特性的研究

研究了含有孔隙的功能梯度材料(Functionally Gradient Materials,FGMs)中Lamb波的传播特性。利用本征函数展开法和孔隙率与弹性常数之间的关系,讨论了不同孔隙率情况下有限厚度铁基氧化铝功能梯度材料中Lamb波的相速度色散曲线,分析了孔隙率对铁基氧化铝功能梯度材料中Lamb波相速度的影响。研究结果表明Lamb波的相速度色散曲线能够同时反映功能梯度材料的弹性模量、泊松比、密度和孔隙率四个方面的信息,为含有孔隙的功能梯度材料弹性性质的反演提供了理论依据。     

应用兰姆波测定材料弹性参数的反演方法

提出基于兰姆波基础阶对称模式的反演方法来估计材料的弹性常数。兰姆波在存在复杂边界的结构中传播时,时域上边界回波相互混叠,各波包成分难以识别。根据兰姆波的频散特性,选取群速度最快对称模式的低频,用于反演计算。利用相位展开法获取基础阶对称模式的相速度实验值;建立以相速度实验值、弹性常数估计值、频率为变量的误差函数,当误差函数最小时,相速度实验值与基于弹性常数估计值的频散曲线吻合度最好。结合薄铝板、发电机大功率电机的线棒绝缘层、转向架的弹性常数反演过程,并进行误差分析,验证基础阶对称模式反演方法的可行性、通用性。     

Analysis of elastic wave propagation in a functionally graded thick hollow cylinder using a hybrid mesh-free method

In this paper, a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference (NFD) methods is presented to calculate the velocity of elastic wave propagation in functionally graded materials (FGMs). The physical domain to be considered is a thick hollow cylinder made of functionally graded material in which mechanical properties are graded in the radial direction only. A power-law variation of the volume fractions of the two constituents is assumed for mechanical property variation. The cylinder is excited by shock loading to obtain the time history of the radial displacement. The velocity of elastic wave propagation in functionally graded cylinder is calculated from periodic behavior of the radial displacement in time domain. The effects of various grading patterns and various constitutive mechanical properties on the velocity of elastic wave propagation in functionally graded cylinders are studied in detail. Numerical results demonstrate the efficiency of the proposed method in simulating the wave propagation in FGMs.     

Elastic property measurement using Rayleigh-Lamb waves

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Elastic Property Measurement Using Rayleigh-Lamb Waves

Abstract

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/μs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Determination of the Elastic Symmetry of a Monolithic Ceramic using Bulk Acoustic Waves

A nondestructive optimal determination of elastic properties from ultrasonic bulk wave velocity measurements on a monolithic ceramic plate immersed in water is presented. This procedure, that is applicable to flat plates with unknown material properties, is based on already established methods and includes discussions, using experimental data, on the reliability of the elastic property identification, such as the stiffness tensor and the material symmetry. By solving inverse propagation problems deduced from the Christoffel equation and depending on wave speed measurements, we show that the studied sample can be described by twenty-one dependent stiffness constants and that its intrinsic elastic material symmetry was hexagonal (or transversely isotropic).     

Wave propagation through engineering materials; assessment and monitoring of structures through non-destructive techniques

Elastic wave propagation has been used for decades for assessment of the structural integrity of engineering materials. The advantage it offers is the direct connection to elastic properties, the relatively easy application through commercial equipment as well as numerous empirical correlations between pulse velocity and material strength or quality in general. Advanced features like frequency dependence of wave parameters may further improve the characterization capacity. Concrete materials due to their inherent microstructure, which is enhanced by the existence of damage-induced cracking, exhibit a complicated behavior concerning the propagation of pulses of different frequencies. The different wave lengths interact with inhomogeneities according to their size and therefore, leave their signature on the phase velocity and attenuation versus frequency curves. Although experimental measurements are troublesome in concrete structures, mainly due to attenuation of high frequencies, it is suggested that, whenever possible, application of different frequencies can provide a more detailed insight on the internal condition of the structure. Apart from classical elastic wave studies, the scattering microstructure of concrete exercises strong influence on the elastic signals emitted after cracking events, distorting therefore crucial acoustic emission parameters used for the characterization of the structural integrity. In the present paper experimental evidence of dispersion and examples on how it can be utilized in concrete non destructive inspection are presented and discussed.     

Investigation of fracture characterizations of functionally graded materials

In this paper, the mode I crack problem of functionally gradient materials (FGMs) with the gradient direction parallel to the crack is discussed, and the differences of stress distribution between the gradient materials and the homogeneous materials are analyzed. It is shown that a mode I crack problem of FGMs with the gradient direction parallel to the crack direction can become a mixed‐mode crack problem. In FGMs, the crack initiation angles are determined by the fracture toughness gradient, elastic modulus and crack mode. If the gradient coefficients are small, the crack initiation angles in FGMs are the same as those in homogeneous materials. If the elastic modulus gradient is large, the principal stress terms without the gradient coefficients can be ignored in obtaining the crack initiation angle. In this study, all the above results are generalized to the mixed‐mode crack problems with arbitrary angle between the gradient direction and the crack direction.     

Optimization design of a Lamb wave device for density sensing of nonviscous liquid

A Lamb wave device composed of a piezoelectric plate loaded with a nonviscous liquid layer is presented. The relation between the Lamb wave phase velocity and the liquid density can be used for liquid density sensing. In this paper, utilizing the partial wave theory, the concept of effective permittivity is introduced to analyze the Lamb wave's excitation and the phase velocity calculation under a certain liquid density. The interface between the Lamb wave device and the liquid layer is metallized to eliminate the influence of liquid electrical properties when sensing liquid density. Based on the theory model, the phase difference measurement method is adopted to study the device's sensitivity to liquid density. In order to achieve high sensitivity to liquid density with sufficient excitation efficiency of Lamb wave, the optimal parameters of the Lamb wave device including plate thickness and cut orientation are obtained by numerical calculation. The experimental results are found to be in agreement with the theoretical simulations, verifying the validity of the theory model and the practicability of the optimization design.     

基于三维弹性理论的碳纤维板中Lamb波建模

基于主动Lamb波的结构健康监测是目前复合材料结构损伤监测技术研究的热点之一,了解Lamb波的传播特性对进行可靠的损伤监测非常重要.本文结合经典三维弹性理论与Lamb波的运动位移方程,对碳纤维复合材料板中传播的Lamb波传播特性进行了建模研究,在此基础上推导了碳纤维板的相速度频散曲线,并讨论了Lamb波传播方向与坐标轴之间的夹角及碳纤维铺层方向对频散曲线的影响,建模结果证明了这种建模方法的正确性.     

Identification of interfacial parameters in a particle reinforced metal matrix composite Al6061–10%Al2O3 by hybrid method and genetic algorithm

The mechanical behavior of interfaces between matrix and inclusions in composite materials has a strong influence on their mechanical properties such as the strength and the toughness of these materials. To effectively predict the mechanical behavior and investigate the effects of interface properties on the composites, a novel hybrid/inverse numerical method is proposed in conjunction with experimental measurements of real microstructure. This method is based on a combination of hybrid/inverse analysis, finite element method and an improved genetic algorithm (GA). A non-continuum four-node interface element is adopted to simulate the interface behavior of a metal matrix composite whose displacement field has been measured by experiment. By way of the observed failure occurring on the interface in the experiment, a hybrid/inverse analysis for estimating the four unknown mechanical parameters of the interface is carried out by using an improved GA and the interface element model mentioned. Approximate interfacial parameters obtained from the proposed method can reasonably simulate interfacial failure which is in agreement with that observed experimentally. It is found that the proposed hybrid/inverse method is simple and robust for solving complex interfacial problems in composites.     

The fracture analysis of a graded coating/substrate system of finite thickness with arbitrary spatial variations of coating properties: Plane deformation

A new multi-layered model for functionally graded materials (FGMs) with continuously varying elastic properties is developed. The model divides the FGM into multiple layers. In each layer the material properties vary linearly and are continuous on the sub-interfaces. With this new multi-layered model, we solve the crack problems of an FGM coated strip under the in-plane deformation. The method employs the Fourier integral transform technique and singular integral equation theory. The stress intensity factors are calculated. Comparisons between the present model and other existing models show some advantages of the new model: (i) it involves no discontinuities of the material properties at the sub-interfaces; and (ii) it can be used to analyze the crack problems of FGMs with properties of arbitrary variations.     

Thermo-mechanical behavior of a viscoelastic FGMs coating containing an interface crack

In this paper the plane thermo-mechanical behavior of a crack in a viscoelastic functionally graded materials (FGMs) coating with arbitrary material properties bonded to a homogeneous substrate is studied. In order to avoid the complex forms that describe the viscoelastic properties of FGMs, a multi-layered model for the FGMs coating is developed. The compliance and thermal conductivity in the multi-layered model linearly vary in each layer. In this mixed boundary value problem, the system is reduced to singular integral equations and solved numerically with the Lobatto-Chebyshev collocation technique. Using the correspondence principle and Laplace transform, the problem of an interface crack between a homogeneous substrate and a viscoelastic FGMs is solved. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the multi-layered model. The numerical results confirm that the fracture toughness of materials can be greatly improved by the graded variation of material parameters. It is also confirmed that the specific variation of material parameters greatly influences the fracture behavior of viscoelastic FGMs coating.     

Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads

Considering rotary, in-plane inertias, and fluid velocity potential, the dynamic characteristics of fluid-conveying functionally graded materials (FGMs) cylindrical shells subjected to dynamic mechanical and thermal loads are investigated, where material properties of FGM shells are considered as graded distribution across the shell thickness according to a power-law, and dynamic thermal loads applied on the shell is considered as non-linear distribution across the thickness of the shell. The linear response characteristics of fluid-conveying FGM cylindrical shells are obtained by using modal superposition and Newmark’s direct time integration method.     

An analytical approach for fracture and fatigue in functionally graded materials

The problem of brittle crack propagation and fatigue crack growth in functionally graded materials (FGMs) is addressed. The proposed analytical approach can be used to estimate the variation of the stress-intensity factor as a function of the crack length in FGMs. Furthermore, according to the Paris’ law, the fatigue life and the crack-tip velocity of crack propagation can be predicted in the case of fatigue crack growth. A comparison with numerical results obtained according to the Finite Element method will show the effectiveness of the proposed approach. Detailed examples are provided in the case of three-point bending beam problems with either a FGM interlayer, or a FGM external coating. A comparison is presented between two types of grading in the elastic modulus: a continuous linear variation in the FGM layer and a discrete approximation with a multi-layered beam and a constant Young’s modulus in each layer.     

磁电弹功能梯度材料板中的波动特性

假设材料常数和电、 磁常数沿板厚方向呈梯度变化, 将电磁功能梯度材料板沿厚度方向划分为层单元, 建立单元的控制方程, 然后根据单元之间的连续条件将单元控制方程装配成系统的控制方程, 求解控制方程, 得到不同模态波的弥散曲线, 分析了电磁参数对波的弥散特性的影响, 同时研究了材料梯度对弹性位移、 静电势和静磁势分布的影响, 并对磁电功能梯度材料中波的六个特征波面进行了分析。计算结果表明材料梯度引起弹性位移、 静电势、 静磁势的分布集中于材料参数梯度减少的方向, 材料为正交各向异性弹性材料。      

Finite element modelling of lamb waves propagation in 2D plates and thin sheets for damage detection

Structural health monitoring is an evolving technology applied to identify, locate and quantify severity of damages in structures before failure. Lamb waves have become a keen interest for inspection since they can be used to monitor a large area from one single location. The objective of this research is to simulate lamb wave response using finite element method and its application to crack detection and identification in thin metallic engineering structures. Two types of specimen i. e. two‐dimensional aluminium plate and thin aluminium sheets are simulated using commercially available finite element package ABAQUS. Initially phase velocity and group velocity dispersion curve are plotted for aluminium material. Thereafter simulation of individual specimens with cracks and without cracks is performed. Simulation results were compared and validated with actual results and were found to be in reasonably good agreement. This is certainly done by employing group velocity and time of flight for the distance travelled between the monitoring point and crack position. Assessment of lamb waves sensitivity to various sizes and shapes of cracks like rectangular and circular are also investigated and its effect on the structure is discussed in detail.     

Lamb waves in a thin isotropic layer between two anisotropic layers

Attenuative Lamb wave propagation in adhesively bonded anisotropic composite plates is introduced. The isotropic adhesive exhibits viscous behavior to stimulate the poor curing of the middle layer. Viscosity is assumed to vary linearly with frequency, implying that attenuation per wavelength is constant. Attenuation can be implemented in the analysis through modification of elastic properties of isotropic adhesive. The new properties become complex, but cause no further complications in the analysis. The characteristic equation is the same as that used for the elastic plate case, except that both real and imaginary parts of the wave number (i.e., the attenuation) must be computed. Based on the Lowe's solution in finding the complex roots of characteristic equation, the effect of longitudinal and shear attenuation coefficients of the middle adhesive layer on phase velocity dispersion curves and attenuation dispersion curves of Lamb waves propagating in bonded anisotropic composites is visualized numerically.