Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

Wavelet analysis of plate wave propagation in composite laminates

A new approach is presented for the analysis of transient waves propagating in composite laminates. The wavelet transform (WT) using the Gabor wavelet is applied to the time–frequency analysis of dispersive plate waves. It is shown that the peaks of the magnitude of WT in the time–frequency domain are related to the arrival times of group velocity. Experiments are performed using a lead break as the simulated acoustic emission source on the surface of quasi-isotropic and unidirectional graphite/epoxy laminates. For predictions of the dispersion of the flexural mode, Mindlin plate theory is shown to give good agreement with the experimental results. The planar source location based on the flexural wave is performed using a triangulation method. The use of frequency-dependent arrival time of output signal and angular dependence of group velocity provides accurate results of source location for anisotropic laminates.     

不同预制体结构炭/炭复合材料烧蚀性能

采用电弧驻点烧蚀实验方法, 测试了分别以细编穿刺毡和针刺无纬布整体毡为增强体的2种C/C复合材料的烧蚀率, 并用电子扫描显微镜观察了烧蚀表面形貌。结果表明: C/C复合材料的烧蚀由化学烧蚀和机械剥蚀共同控制, 以机械剥蚀为主; 细编穿刺毡结构C/C复合材料由于Z向纤维束的存在, 加速了材料烧蚀表面粗糙度的变化, 烧蚀率略高于针刺无纬布整体毡结构C/C复合材料; 针刺无纬布整体毡结构C/C复合材料中无纬布层与烧蚀气流垂直, 具有良好的烧蚀性能。      

A method of determining acoustical physical constants for piezoelectric materials by line-focus-beam acoustic microscopy

We developed a new method of determining acoustical physical constants (elastic constant, piezoelectric constant, dielectric constant, and density) of piezoelectric materials with high accuracy. This method acquires velocities of leaky surface acoustic waves (LSAWs) excited on the water-loaded specimen surface, measured by line-focus-beam (LFB) acoustic microscopy, and bulk velocities of longitudinal and shear waves, measured with planewave transducers replacing the LFB device in the same system, together with the dielectric constants and density measured independently, for a small number of specimens. For LiNbO₃ and LiTaO₃ crystals, we demonstrated that we could accurately determine the constants by choosing proper propagation directions of LSAWs and bulk waves for three principal X-, Y-, and Z-cut specimens and one rotated Y-cut specimen [(104) plate for LiNbO₃ and (012) plate for LiTaO₃]. The accuracy is nearly the same as that for the constants determined only from the bulk wave velocities     

Surface Wave Utility in Composite Material Characterization

Abstract

A surface wave velocity measurement technique is used to supply supporting measurements in the computation of elastic constants for practical nondestructive evaluation of composite materials. Theoretical modeling work is carried out to illustrate the surface wave velocity changes as a function of angle with respect to the axes along the fibers of a unidirectional graphite epoxy composite material for a variety of different problems, including porosity (PC) changes, fiber volume fraction (FF) changes, and delamination. Experiments are conducted on two unidirectional reinforced composites and a (0–90)_s cross ply graphite epoxy laminate to illustrate the surface wave velocity measurements and the inverse computation procedure for evaluation of the stiffness coefficients. Variations of the feature values in the stiffness matrix are also discussed for inhomogeneities, delaminations through cracking, and large defects.     

Effective behavior of inelastic fiber-reinforced composites

The average behavior of unidirectional fiber-reinforced composites, whose constituents are anisotropic in the elastic region and isotropic viscoplastic in the inelastic region, is determined. In the special case of perfectly elastic phases, effective moduli of the composite are obtained. Extensive comparisons between the effective behavior of the composite, as predicted by the present theory and by other theoretical, numerical and experimental approaches, are given.     

Compensation of shear waves in photoacoustic tomography with layered acoustic media

An image reconstruction formula is presented for photoacoustic computed tomography that accounts for conversion between longitudinal and shear waves in a planar-layered acoustic medium. We assume the optical absorber that produces the photoacoustic wave field is embedded in a single fluid layer and any elastic solid layers present are separated by one or more fluid layers. The measurement aperture is assumed to be planar. Computer simulation studies are conducted to demonstrate and investigate the proposed reconstruction formula.     

Feasibility on fiber orientation detection of unidirectional CFRP composite laminates using one-sided pitch–catch ultrasonic technique

It is important to assess fiber orientation, material properties and part defect because strength and stiffness of composites depend on fiber orientation of CFRP (carbon fiber reinforced plastics). A one-sided pitch–catch setup was used in the detection and evaluation of ultrasonic wave behavior and fiber orientation in the unidirectional CFRP composite laminates. Two Rayleigh wave transducers were joined head-to-head and used in the pitch–catch mode on the surface of the composites. The pitch–catch signal was found to be more sensitive than normal incidence backwall echo of longitudinal wave to subtle flaw conditions in the composite. Especially, one-sided ultrasonic measurement was made with using a Rayleigh wave transducers and the Rayleigh ultrasonic waves were extensively characterized in the CFRP composite laminates. Also, a conventional scanner was used in an immersion tank for extracting fiber orientation information in the unidirectional laminate. Therefore, it is thought that the proposed method is useful to evaluate integrity of CFRP laminates.     

Line-focus acoustic microscopy measurements ofNb2O5/MgO and BaTiO3/LaAlO3thin-film/substrate configurations

Line-focus acoustic microscopy has been used to measure the phase velocities of surface acoustic waves on bare MgO and bare LaAlO₃ , and on Nb₂O₅/MgO and BaTiO₃/LaAlO₃ thin-film/substrate configurations. The thin films are polycrystalline materials. The substrates are anisotropic single-crystals. The measured angular variation of the surface acoustic wave velocities has been used to determine the elastic constants of MgO substrate and Nb₂O₅ thin-film. It has been assumed that the Nb₂O₅ films may be considered as essentially isotropic. The measurements for LaAlO₃ and BaTiO₃/LaAlO₃ show anomalies which are attributed to twinning in the LaAlO₃ substrate     

Existence of longitudinal and transverse waves in anisotropic thermoelastic media

Four waves propagate in an anisotropic thermoelastic medium. The fastest among them is a quasi-longitudinal wave. The slowest of them is a thermal wave. The remaining two are called quasi-transverse waves. The prefix ‘quasi’ refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these four waves are not mutually orthogonal. Hence, unlike anisotropic elastic media, the existence of a longitudinal wave may not imply the existence of a transverse wave, by default. The existence of a purely longitudinal wave in an anisotropic thermoelastic medium is ensured by the stationary characters of three expressions. These expressions involve components of phase direction with elastic (stiffness and coupling) and thermal coefficients of the thermoelastic medium. The existence of a purely transverse wave is ensured by the two equations restricting the choice of thermoelastic (stiffness and coupling) coefficients. The existence of longitudinal and transverse waves along the coordinate axes and in the coordinate planes are discussed for general anisotropy. The discussion is extended to orthotropic materials, and the existence of pure phases is explored along few specific phase directions.     

Characterization of heterogeneous matrix composites using scanning acoustic microscopy

Acoustic microscopy was used to examine the morphology of multi-phase matrices and composites. The acoustic microscopy imaging could easily resolve the rubber domains dispersed within a thermosetting or thermoplastic continuous phase. However, because the thermoplastic and thermosetting phase domains had comparable elastic moduli, the resolution between them was not always clear. Rayleigh wave distortion of imaging remained as one of the serious limitations that needed to be overcome in order for this technique to be widely utilized in heterogeneous/anisotropic media. In its present form, the acoustic imaging technique can be used to augment other existing analytical tools in order to generate more detailed morphological information that is useful in understanding structure-property relationships for multi-phase toughened matrices used in advanced composites.     

Thermal stress-focusing effect in a spherical Zirconia inclusion with dynamically transforming strains

Some composite materials, such as Zirconia-toughened ceramics, are remarkable materials which have high strength, a high elastic modulus, and an improved toughness, etc. These good qualities are made possible through the stress-induced phase transformation of composite particles, which is accompanied by an impact cooling. When a spherical inclusion in an infinite elastic domain is suddenly subjected to an instantaneous phase transformation, stress waves occur at the surface of a spherical inclusion at the moment thermal impact is applied. The wave may accumulate at the center and show stress-focusing effects, even though the initial stress may be relatively small. This paper analyzes the thermal stress-focusing effect caused by the instantaneous anisotropic phase transformations in the spherical Zirconia inclusion. By use of ray theory, the numerical results give a clear indication of the mechanism of stress-focusing in an inclusion embedded in an infinite elastic medium.     

Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.     

Non-reflecting boundary conditions for plane waves in anisotropic elasticity and poroelasticity

The paper presents exact non-reflecting boundary conditions for transient plane waves in an anisotropic elastic solid for oblique incidence. The boundary conditions are expressed through the eigenvectors of the acoustic tensor and are written in impedance form as a relation between the velocity vector and the traction vector. The approach is extended to anisotropic fluid-saturated porous solids. Exact plane-wave non-reflecting boundary conditions are derived for transient non-dissipative waves in a medium with infinite or zero permeability, and for steady-state dissipative waves.     

Scattering of Thermal Waves and Non-steady Effective Thermal Conductivity of Unidirectional Fibrous Composites with Functionally Graded Interface

In this paper, a thermal wave method is applied to investigate the non-steady effective thermal conductivity of unidirectional fibrous composites with a functionally graded interface, and the analytical solution of the problem is obtained. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the fibrous composite. The scattering and refraction of thermal waves by a cylindrical fiber with an inhomogeneous interface layer in the matrix are analyzed, and the results of the single scattering problem are applied to the composite medium. The wave fields in different material layers are expressed by using the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The theory of Waterman and Truell is employed to obtain the effective propagating wave number and the non-steady effective thermal conductivity of composites. As an example, the effects of a graded interface on the effective thermal conductivity of composites are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. In the region of intermediate and high frequencies, the effect of the properties of the interface on the effective thermal conductivity is greater. Comparisons with the steady thermal conductivity obtained from other methods are also presented.     

Surface wave utility in composite material characterization

A surface wave velocity measurement technique is used to supply supporting measurements in the computation of elastic constants for practical nondestructive evaluation of composite materials. Theoretical modeling work is carried out to illustrate the surface wave velocity changes as a function of angle with respect to the axes along the fibers of a unidirectional graphite epoxy composite material for a variety of different problems, including porosity (PC) changes, fiber volume fraction (FF) changes, and delamination. Experiments are conducted on two unidirectional reinforced composites and a (0–90)_s cross ply graphite epoxy laminate to illustrate the surface wave velocity measurements and the inverse computation procedure for evaluation of the stiffness coefficients. Variations of the feature values in the stiffness matrix are also discussed for inhomogeneities, delaminations through cracking, and large defects.This paper was presented at the Symposium of Wave Propagation in Structural Composites at Berkeley, American Soceity of Mechanical Engineering AMD Volume 9D, June 20–22, 1988.     

A self-consistent approach to dynamic effective properties of a composite reinforced by distributed spherical particles

Summary A self-consistent approach to dynamic effective properties of a composite reinforced by randomly distributed spherical inclusions is studied. The coherent plane waves propagating through the particle-reinforced composite are of attenuation nature. It implies that there is an analogy between the particle-reinforced composite and the effective medium with complex-valued elastic constants from the viewpoints of wave propagation. A composite sphere consisting of the inclusion, the matrix and the interphase between them is assumed embedded in the effective medium. The effective wavenumbers of the coherent plane waves propagating through the particle-reinforced composite are obtained by the dynamic self-consistent conditions which require that the forward scattering amplitudes of such a composite sphere embedded in the effective medium are equal to zero. The dynamic effective properties (effective phase velocity, effective attenuation and effective elastic constants) obtained by the present dynamic self-consistent approach for SiC-Al composites are compared numerically with that obtained by the effective field approach at various volume concentrations. It is found that there is a good agreement between the two approaches at a relatively low frequency and low volume concentration but the numerical results deviate from each other at a relatively high frequency and high volume concentration.     

A method for calibrating the line-focus-beam acoustic microscopy system

Absolute accuracy of the line-focus-beam (LFB) acoustic microscopy system is investigated for measurements of the leaky surface acoustic wave (LSAW) velocity and attenuation, and a method of system calibration is proposed. In order to discuss the accuracy, it is necessary to introduce a standard specimen whose bulk acoustic properties, (e.g., the independent elastic constants and density) are measured with high accuracy. Single crystal substrates of gadolinium gallium garnet (GGG) are taken as standard specimens. The LSAW propagation characteristics are measured and compared with the calculated results using the measured bulk acoustic properties. Calibration is demonstrated for the system using two LFB acoustic lens devices with a cylindrical concave surface of 1-mm radius in the frequency range 100 to 300 MHz.