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.     

Rayleigh-Lamb Waves in Transversely Isotropic Thermoelastic Diffusive Layer

Propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, thin elastic layer of finite width is studied, in the context of the theory of coupled thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves, namely, quasi-elastodiffusive (QED) mode, quasi-mass diffusion (QMD) mode, and quasi-thermodiffusive (QTD) mode can propagate in addition to quasi-transverse waves (QSV) mode and the purely quasi-transverse motion (QSH) mode, which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the layer are derived. The amplitudes of displacements, temperature change, and concentration for symmetric and skew symmetric modes of vibration of the layer are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient, and amplitudes of displacements, temperature change, and concentration are presented graphically in order to illustrate and compare the results analytically. Some special cases of the frequency equation are also deduced and compared with the existing results.     

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。     

Thickness Measurement for Thin Films and Coatings Using Millimeter Waves

An accurate technique for measuring the thickness of dielectric thin films and coatings is presented in this paper. Millimeter-wave sensors operated at 80 GHz are placed near the sample surface. A better than m sensitivity of the phase of the received signal with respect to sample thickness can be achieved. A theoretical model consisting of a vertical electric dipole over a two-layer structure is used to generate calibration information and to guide the optimization of sensor placement. To facilitate the theoretical study, we devise an efficient and reliable numerical algorithm for evaluating Sommerfeld integrals. This algorithm surpasses the performance of conventional numerical methods and renders fast convergence even in the worst-case scenario, when the transmitter and the receiver have the same elevation and the materials are lossless.     

Generalized Rayleigh-Lamb equation

The dynamics of the vapor-liquid interface when a solid particle heated to a high temperature comes into contact with a cold liquid is analyzed. The generalized Rayleigh-Lamb equation taking into account temperature changes in the liquid and the vapor, the saturation vapor pressure change associated with it, and the emergence of the mass flux due to liquid evaporation at the interface is deduced. At medium parameters far from the critical point, the generalized Rayleigh-Lamb equation reduces to its well-known form. Around the critical point, the difference between the obtained equation and arising modes of changes of the vapor-liquid interface can be rather considerable. Unlike the well-known Stefan problem, far from the critical liquid temperature, the phase transition temperature and, respectively, the saturation vapor pressure change with the vapor-liquid interface movement, which yields various modes of dynamics of the vapor cavity. In the special case of small variations from the stationary mode, an analytical solution for the problem on a small change in the vapor cavity radius with time was developed.     

复合材料弹性模量的激光超声测量方法研究

本文利用激光超声方法来测量碳纤维/环氧树脂复合材料的弹性模量,详细介绍了测量原理和测量系统.利用Q值可调的Nd∶YAG脉冲激光器在复合材料试件中激发超声波,超声波由激光超声接收仪接收,经过解调器后在数字示波器上显示,获取超声声速.根据超声声速与材料弹性模量之间的固有关系,可以反演材料的弹性模量.实验表明,利用激光超声方法获得的测量结果与采用动态法得到的理论参考值相吻合,偏差在3%以内,并且操作简单可行.     

Plane Waves in Generalized Thermo-microstretch Elastic Solid with Thermal Relaxation Using Finite Element Method

The propagation of plane waves in a thermo-microstretch elastic solid half-space as proposed by Lord?CShulman as well as the classical dynamical coupled theory are discussed. The problem has been solved numerically using a finite element method. Numerical results for the displacement components, force stresses, temperature, couple stresses, and microstress distribution are obtained. The variations of the considered variables through the horizontal distance are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity for different values of the relaxation time.     

Reaction Driven Elastic Waves in Solid Media

Chemical reactions and phase transformations couple in solid systems with the stress fields. When reaction rates become of the same order as the rate of relaxation of mechanical perturbations, the reactions can stabilize elastic waves in the system. Density varies with temperature and conversion and since the elastic waves are driven by the gradients in temperature and conversion, these source terms travel with the same speed as the reaction front. A model is presented for elastic waves in solid media, driven by a moving source term that is well approximated by a delta function. The propagation velocity of this source is constant, but it can propagate either subsonically or supersonically. The effects of precompressing the sample, applying a force at one boundary, and varying the strength of the source term with time are included in the discussion. The model is useful to study transformation reactions under shock-compression, ultrafast deflagrations, and detonations in the solid phase.     

Measurement of Interfacial Fracture Toughness of Surface Coatings Using Pulsed-Laser-Induced Ultrasonic Waves

This research develops a new technique for the measurement of interfacial fracture toughness of films/surface coatings using laser-induced ultrasonic waves. Using pulsed laser ablation on the bottom substrate surface, strong stress waves are generated leading to interfacial fractures and coating delamination. Simultaneously, a laser ultrasonic interferometer is used to measure the normal (out-of-plane) displacement of the top surface coating in order to detect coating delamination in a non-destructive manner. We can thus determine the critical laser energy for delamination, yielding the critical stress (that is, the interfacial strength). Subsequently, to examine the interfacial fracture toughness, additional pulsed laser irradiation is applied to a pre-delaminated specimen to show that the delamination area expands. This type of interfacial crack growth can be visualized using laser ultrasonic scanning. Furthermore, the calculation of elastic wave propagation was carried out using a finite-difference time-domain method) in order to accurately estimate the interfacial stress field. In this calculation, the stress distribution around the initial delamination is calculated to obtain the stress intensity factor. Based on the experimental and computational results, interfacial fracture toughness can be quantitatively evaluated. Since this technique relies on a two-laser system in a non-contact approach, it may be useful for a quantitative evaluation of adhesion/bonding quality (including both interfacial fracture strength and toughness) in various environments.     

应用数字图像相关方法测试航空复合材料的弹性常数EI北大核心CSCD

通过数字图像相关方法对三种航空复合材料的弹性常数进行了测试。通过对DICM理论分析,依据ASTM标准提出合理的测试方案使得DICM的应变测试精度达到25με,满足航空复合材料测试要求。同时应用DICM和电测法对比测试了三种不同航空复合材料的弹性常数,实验结果表明这两种方法得到的实验结果相对误差较小,应力-应变曲线基本重合,DICM能够很好地反映航空复合材料的应变响应和精确测试其弹性常数。     

弹性模量在用柔度法测量疲劳裂纹长度中的影响

用不同整体刀口设计的三点弯曲SE(B)试样做了两组疲劳裂纹扩展速率 (FCGR)试验 ,分析了弹性模量在柔度法测量疲劳裂纹长度中的影响。结果表明 ,用柔度法测量的弹性模量值偏大或偏小 ,都将影响到lg(da dN) lgΔK曲线的准确性 ,为在FCGR试验中采用SE(B)试样时整体刀口设计类型的选择提供了试验依据。     

Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.     

低弹钛合金弹性模量的无损评价

以掠入射纵波法研究了超声波在Ti6Al4V合金和Ti27Nb8Zr时效样品中的传播速度,推算其弹性模量,并与拉伸法获得的弹性模量进行比较.结果发现:两种方法测得的数值较为接近,相差仅为3.6%,表明掠入射纵波法实现低弹钛合金弹性模量的无损评价是可行的,这为小尺寸稀有合金样品弹性指标的评价提供了极有价值的测试方法.应用该方法进一步考察了时效温度对Ti18Nb7Zr弹性模量的影响,结果表明:随着时效温度的升高,弹性模量E,切变模量G,体弹模量K分别增加11%,10%和6%,泊松比σ仅下降了1.2%.分析认为:弹性模量的变化与合金的组织由层片状的β+α向弥散分布的α相和β相的转变密切相关.     

The Diffraction of Elastic Waves on the Tip of Slots

The diffraction of elastic waves on the tip of cracks has been widely used in detecting defects. It is always difficult to fabricate a real crack in the laboratory. In this investigation, a slot of width 0.3 mm is used as an alternative to simulate the fatigue crack. The slot of 0.3 mm width is embedded in a cylindrical block. The diffractions of elastic waves on the tip of the artificial slot are measured for three test blocks made of steel, aluminum, and brass, respectively. In the experiment, the amplitudes of diffracted waves at various receiving angles are recorded and compared with the theoretical predictions of diffraction on a fatigue crack tip. The influences of incident angle and frequency and material of the test block are presented. By examining the discrepancies of diffractions on the slots and cracks, one is able to evaluate the feasibility of replacing a real crack by an artificial slot, once the real crack is not available.     

Two-Temperature Effects on Plane Waves in Generalized Thermo-Microstretch Elastic Solid

In this article, the effect of two temperatures on plane waves propagating through a generalized-thermo-microstretch elastic half-space solid has been investigated. The surface of the medium is subjected to a mode-I crack, and the $z$ axis is pointing vertically into the medium. Two fascinating theories of generalized thermo-elasticity presented by Green and Naghdi and named as without energy dissipation (GN-II) and with energy dissipation (GN-III) have been used. Governing equations for each particular case are also derived, and a solution is obtained. An analytical technique of normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, the temperature, and the couple stresses distribution. The variations of the considered variables against the vertical distance are illustrated graphically. Comparisons are made with the results between type II and III in generalized-thermo-microstretch and in a particular case (without microstretch constants). Numerical work is also performed for a suitable material with the aim of illustrating the results. It is found that the maximum amplitude is obtained for the maximum value of the two temperature parametric constant.     

Digital Impedance Measurement by Generating Two Waves

A digital measurement system is described which measures the voltages across a voltage divider consisting of a reference resistor and the unknown impedance. The voltages across reference and unknown are converted so that their magnitude and phase are digitally determined.     

Residual Stress Measurement in Steel Plates and Welds Using Critically Refracted Longitudinal (LCR) Waves

Abstract

The application of acoustoelasticity using critically refracted longitudinal (L_CR) waves is described for measuring residual stress in welded steel plates. Residual stresses are self-equilibrating and may exist in a material that has been deformed in a nonhomogeneous manner. When unknown residual stress is present in a structure, the true stress may become significantly greater than the working stress. In a corrosive environment, highly stressed areas that have not been properly stress relieved are prone to stress corrosion cracking. Areas near welds are particularly susceptible to stress corrosion cracking.

Two welded plates were investigated for the present work: one hot-rolled and the other cold-rolled. Residual stresses are usually greatest after welding. Further, longitudinal stress (i.e., stress parallel to the weld bead) is typically greater than the component transverse to the weld bead. Since the acoustoelastic behavior of the L_CR wave is largest when propagated parallel to a uniaxial stress, the L_CR wave traveling parallel to the weld bead was used to investigate the stress changes after stress relieving of the welded plates. Both 1 MHz and 2.25 MHz probe frequencies were used in this study. The stress changes in the welds and in the cold-rolled plate were clearly indicated by the L_CR data.

Two verification methods were used: hole drilling (HD) and neutron diffraction (ND). The stress relief was verified by the hole-drilling technique. While the HD technique showed about the same stress magnitude as found by the L_CR results, the orientation was reversed. The stress orientation was probably caused by the grinding process used to flatten the weld bead. Texture was also investigated using a neutron diffraction (ND) technique on the (001)[110] texture. The through-the-thickness technique yields an average of the orientation distribution of the (110) planes. At locations in the parent metal and in the weld, the distribution was found to be very similar, indicating uniform texture throughout the weld and parent metal zones.     

两种介质中爆轰波和冲击波连续测量技术研究

通过自制的有机玻璃压导探针,对炸药、有机玻璃和水中的爆轰波和冲击波进行连续测量,得到了爆轰波和冲击波的时间历程演化曲线。由此计算出炸药爆速、有机玻璃和水中冲击波速度随时间的变化曲线;再由有机玻璃和水的冲击雨果尼奥关系式和动量定理,计算得到了炸药爆压、有机玻璃和水近场冲击波速度、压力变化曲线。结果表明:理论计算结果与有机玻璃和水的冲击波和炸药爆压试验结果基本吻合,能够准确反映冲击波在有机玻璃和水中的衰减规律。     

Numerical Analysis on Laser-Generated Guided Elastic Waves in a Hollow Cylinder

Numerical analyses are presented for laser-generated guided elastic waves in a hollow cylinder. Time-dependent displacement at the outer surface of a hollow cylinder is expressed by summation of longitudinal and flexural type modes by employing the normal mode expansion (NME) method, then the transient waveforms excited by a single beam of laser pulse and four beams of laser pulse with an axisymmetric spatial distribution are calculated numerically. The influence of the spatial distribution of laser pulses on the waveforms are discussed in detail, and the features of major modes are explained based on dispersion curves. Finally, the total waveform of longitudinal modes obtained by the NME method is compared to that predicted by the finite element method (FEM), and a good agreement is obtained.