Ultrasonic attenuation and velocity in AS/3501-6 graphite fiber composite

The ultrasonic group velocity and attenuation were measured as a function of frequency for longitudinal and shear waves in the Hercules epoxy matrix (3501-6) and in the principal directions of the unidirectional Hercules graphite fiber epoxy composite (AS/3501-6). Tests were conducted in the frequency ranges 0.25–14 MHz and 0.5–3 MHz for longitudinal and shear wave modes, respectively. While the attenuation increased with frequency for all wave modes, the group velocity was independent of frequency for all wave modes. In studying the effects of transducer-specimen interface couplant and pressure, it was found that for each transducer, there exists a frequency-dependent saturation pressure corresponding to the maximum output amplitude of the signal.     

Bulk shear wave propagation in an epoxy: attenuation and phase velocity over five decades of frequency

Proportionality between the ultrasonic wave attenuation coefficient in epoxies and other polymers and frequency is a commonly observed but little understood phenomenon. How it is ultimately explained will depend on the breadth of the frequency range over which it is significant. This paper presents results of experiments to measure loss in a single epoxy material over 5 decades of frequency using 4 complementary techniques - dynamic mechanical analysis, microwave excited low-frequency resonances, a novel guidedwave technique based on a metal-epoxy-metal sandwich, and a conventional pulse mode ultrasonic spectrometer. The results are confined to bulk shear waves in the epoxy. They confirm the linear relationship between attenuation and frequency, and it is shown that the broadband behavior of the attenuation and shear wave phase velocity is consistent with the Kramers- Kronig relationships.     

Energy flux characteristics of inhomogeneous waves in anisotropic thermoviscoelastic media

This study aims to calculate the wave-field characteristics of four attenuating waves in anisotropic thermoviscoelastic medium. An energy balance equation relates the complex-valued energy flux vector to the time-averaged densities of kinetic energy, strain energy and dissipated energy of plane harmonic waves in the medium. A complex slowness vector defines the inhomogeneous propagation of an attenuating wave in the medium. This slowness vector is specified with the phase velocity and the two non-dimensional attenuation parameters of the wave. One of the attenuation parameter defines the inhomogeneity strength of the wave as a measure of its deviation from homogeneous propagation. The phase velocity, attenuation parameters, polarizations of particles, propagation direction are combined to define the group velocity, ray direction and quality factor of attenuation of an inhomogeneous wave in the medium. Numerical examples are considered to study the variations of these characteristics of energy flux with propagation direction and inhomogeneity strength for each of the four attenuating waves in the medium. The effects of anisotropic symmetries are analyzed on the velocities of waves. The decay-rate of energy densities is exhibited with offset in the propagation-attenuation plane.     

Utilization of Ultrasonic Measurements for Determining the Variations in Microstructure of Thermally Degraded 2205 Duplex Stainless Steel

The aim of this study is to investigate the changes in attenuation of longitudinal waves and velocity of shear wave modes for assessing variations in the microstructure of thermally degraded 2205 duplex stainless steel samples that were aged isothermally at 700°C and 900°C for different time intervals. The evaluation of material microstructural changes such as phase transformation and second phase precipitation which are related to material properties is of primary importance to ensure quality of components. This paper presents evidence that indicate that the attenuation coefficient of the longitudinal mode is sensitive to gradual microstructural changes produced by the aging treatments. The gradual changes in microstructure are associated with reduction of impact properties. On the other hand, for samples aged at 700°C, the velocity of the fast mode of shear wave show changes at high aging times and does not show changes at early aging times were the materials properties are already degraded.     

Modelling of attenuation of Lamb waves using Rayleigh damping: Numerical and experimental studies

In this study, the Lamb mode attenuation constants were derived in terms of the attenuation coefficient, group velocity and central frequency of excitation of the Lamb mode, using the Rayleigh damping model. Attenuation of Lamb waves, both fundamental symmetric and anti-symmetric modes, propagating through viscoelastic media (cross-ply glass/epoxy laminate) was modelled using the Finite Element Method. Numerically simulated attenuation of Lamb waves using Lamb mode attenuation constants was found to be in good agreement with the assumed attenuation. Experiments were performed on a quasi-isotropic laminate, employing air-coupled ultrasonic transducers, to measure the attenuation coefficient. Lamb mode attenuation constants, computed using the attenuation coefficient, were used to model the attenuation of the Lamb mode in quasi-isotropic laminates. Numerically simulated amplitude variation was found to be in good agreement with that computed from experiments.     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

Lamb wave excitation by Hertzian contacts with applications in NDE

Excitation of Lamb waves in solid plates by point-like Hertzian contacts for material characterization and nondestructive testing is investigated. A 2 dimensional model using normal mode theory is used to predict the relative excitation efficiency of the lowest order Lamb waves in anisotropic solid plates. Hertzian contact transducers with PZT-5H piezoelectric material and quartz buffer rods are realized to operate in the 200 to 500 kHz range for experimental verification. Single mode operation with the lowest order antisymmetric Lamb wave (A ₀) mode is achieved in various plates at in agreement with theoretical predictions. The technique is applied for material characterization on single crystal silicon samples and defect detection in composite plates. The phase velocity anisotropy of the A₀ mode is measured with signal-to-noise levels exceeding 65 dB. In (111) cut silicon plates the absolute phase velocity is measured with ±0.05% accuracy. The phase velocity anisotropy and effects of delamination in layered composite plates are calculated using the surface impedance approach. The experiments on graphite/epoxy composite plates agree with these calculations and show the potential of the method for defect detection with high resolution     

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.     

有限长叉指换能器激发表面波及体波声场的数值模拟

采用数值方法,模拟了有限长叉指换能器(IDT)在半无限大压电晶体中激发的表面波和体波声场在晶体界面上的分布情况。在数值模拟所得结果的基础上,将频率域内的位移分量做傅立叶反变换得到时间域内声波脉冲振幅随时间的分布,并对界面上三个位移分量含有的声波模式进行分析,其中场位移分量1沿波的传播方向,位移分量2为平行于IDT指条方向,位移分量3沿基片表面法线方向。分析结果表明,界面上各位移分量中除Rayleigh波外,还含有不同比例的体波成分。其中,在位移分量1和位移分量3中占主要成分的是准纵波,在位移分量2中占主要成分的是准慢切变波。它们均按照指数方式在表面上进行传播衰减,其中准慢切变波的衰减速度小于准纵波的衰减速度。IDT指条数相对较多时的体波振幅要大于指条数相对较小时的体波振幅,且在距离IDT较近的范围内IDT指条数相对较多时体波衰减更快。     

Ultrasonic Velocity and Attenuation in Epoxy Resin/Granite (Marble) Powder Composite

In this research, gamma radiation has been used to graft styrene and acrylic acid monomers onto marble (M) and granite (G) powder, with irradiation doses 30, 10 kGy, respectively. The grafted marble and granite powders were used as filler of epoxy composites. They added to an epoxy resin at 20, 60, and 100 wt% and then cured at room temperature. Ultrasonic velocities and attenuation measurements in epoxy composites at 4 MHz in the 25–300°C temperature range in addition to Fourier Transform Infrared (FTIR) analysis had been investigated. The ultrasonic compression wave velocity and the shear wave velocity measurements were performed using the pulse-echo technique, and then wecalculated elastic modulus, Young’s modulus, longitudinal and shear moduli, and Poisson’s ratio. In addition to attenuation at different temperatures of epoxy/granite composites, ultrasonic results indicated that the ultrasonic wave’s velocities V_L and V_s increased with the increase of (M, G) content and a linear relation was observed. Also, the attenuation of epoxy was stable and appeared to increase at temperature 385°C, while the addition M or G to epoxy composites increased the attenuation.     

The propagation of elastic waves through a textured granular material

When an ultrasonic wave passes through a block of metal, the wave is attenuated, i.e. its amplitude decreases with distance. The principal cause of this attenuation is believed to be scattering of the wave at the grain boundaries. Since neighbouring grains will in general have different crystallographic orientations and the velocity of sound depends on the orientation, a proportion of the wave will be lost due to reflection and mode conversion at each grain boundary. This problem was first tackled by Lifshitz and Parkhomovski [1], who considered the problem of a cast material which has equiaxed grains with no preferred orientation. They also assumed that the anisotropy within a single grain is small and they obtained expressions for the attenuation of longitudinal and shear waves. Their results have subsequently been shown to be a useful approximation even for the case of steels where the anisotropy within a grain is not small. Many metals which have been worked in some way, e.g. forging or welding, exhibit a textured structure in which the grains may on average be elongated in a particular direction or there may be a preferred crystallographic orientation, or both. In this case the bulk metal will no longer be isotropic, and the results of Lifshitz and Parkhomovski will not apply. In this paper we show how the approach used by Lifshitz and Parkhomovski may be modified to tackle such problems. General results for the attenuation are presented in terms of averages over the particular distribution of orientations. Detailed results are presented for a particular distribution which is a representation of austenitic weld metal.     

杂质吸收对一维掺杂声子晶体缺陷模的影响

为了研究杂质吸收对一维掺杂声子晶体缺陷模的影响,引入复波数,推导出一维掺杂声子晶体的转移矩阵,计算了一维掺杂声子晶体的透射系数和反射系数随衰减系数的变化特征.得出杂质的衰减系数对一维掺杂声子晶体透射波中和反射波中的缺陷模都有显著的影响.在透射波中,随着衰减系数的增加缺陷模峰高迅速降低,κ在0～0.002k范围内缺陷模比较明显.当衰减系数增加到0.005k时,缺陷模几乎消失.反射波中的缺陷模随着衰减系数的变化也有相同的特征.     

Ultrasonic wave propagation in carbon fibre-reinforced plastics

The attenuation and velocity of the longitudinal and shear waves in unidirectional carbon/epoxy composites have been measured as a function of the fibre volume fraction over the frequency range, 1.84 to 11.9 MHz, using the pulse-echo technique. The decrease of attenuation with fibre volume fraction suggested that the high attenuation in the composites was caused by viscoelastic losses in the epoxy matrix rather than scattering losses by the fibre. The attenuation increased with frequency, while the velocity was found to be independent of frequency.     

A single-lap shear specimen for determining the effect of strain rate on the interlaminar shear strength of carbon fibre-reinforced laminates

A new design of single-lap shear specimen for determining the effect of loading rate on the interlaminar shear strength of laminated composites is described. Finite element analyses are used to optimize the specimen geometry and minimize the variation in the shear stress and the magnitude of the normal stress along the interlaminar failure plane. Experimental results are obtained at a quasi-static and an impact rate of loading for the interlaminar shear strength parallel to the fibres in both unidirectional carbon/epoxy and unidirectional carbon/polyetheretherketone (peek) laminates and at interfaces across which the fibre orientation is 0°/90° and ±45°. Results for carbon/epoxy laminates are compared with those from an earlier investigation using a double-lap specimen geometry and show a similar small dependence on loading rate. No significant effect of loading rate was observed for the carbon/peek laminates.     

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.     

Time-resolved line focus acoustic microscopy of layered anisotropic media: application to composites

This paper presents theoretical and experimental studies of the time-domain response of line focus acoustic microscopy from a layered anisotropic medium. A method for elastic constant reconstruction from acoustic microscopy signatures also is presented. The microscopy response is complicated by multiple reflections in the layers and by the anisotropic nature of the material. The model is based on a new, stable recursive stiffness matrix algorithm developed for a multilayered anisotropic medium, which is applied to the interpretation of the time-resolved acoustic microscopy signature. Specific examples are given for unidirectional and multidirectional graphite epoxy composites. It is shown that the fluid load has a significant effect on the leaky surface waves in these composites, increasing surface wave speed above that for the slow transverse wave. This results in its absence from the microscopy signature of the surface wave. The theoretical results are compared with experiments carried out using a line focus PVDF transducer developed at National Institute of Standards and Technology (NIST). Time-resolved acoustic microscopy has been applied to the determination of elastic constants of a unidirectional composite or of one lamina in a cross-ply composite. The lateral waves and multiple reflections of bulk waves appearing in the microscopy signatures are used for the elastic properties reconstruction. The reconstruction results are compared to data obtained by the self-reference double-through-transmission ultrasonic bulk wave method.     

Monitoring of delamination onset and growth during Mode I and Mode II interlaminar fracture tests using guided waves

A delamination monitoring method was proposed to characterize Mode I and Mode II delamination onset in carbon fiber/epoxy (CF/EP) composite laminates through interrogation of guided waves activated and captured using piezoelectric actuators and sensors in a pitch–catch configuration. Mode I and Mode II interlaminar fracture tests were conducted using double cantilever beam (DCB) and end notch flexure (ENF) specimens to evaluate the proposed method. The changes in wave propagation velocity and wave magnitude (or attenuation), and the degree of waveform similarity between excitation and response signals, were calculated as delamination-sensitive wave parameters and plotted versus displacement recorded using a materials testing system. The kink points determined from wave parameter–displacement curves agreed well with the deviation from linearity (NL), visual observation (VIS) and maximum load (Max) points, which are often used in conventional methods for determining interlaminar fracture toughness. The propagation characteristics of the A₀ wave mode in a low frequency range were demonstrated to have high sensitivity to Mode I and in particular Mode II delamination onset in CF/EP composite laminates. It was concluded that the guided waves propagating in the DCB and ENF specimens were capable of determining Mode I and Mode II interlaminar fracture toughness, complementing current practices based on visual inspection or trivial interrogation using load–displacement curve alone.     

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.     

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.     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.