Bulk Longitudinal Waves Research Articles

Evaluation of epoxy crosslinking using ultrasonic Lamb waves

The use of epoxy adhesives in structural bonding provides lightweight materials, however the assessment of the integrity and quality of the joint is of critical concern. Thus it is essential to know if the adhesive is well crosslinked. This work deals with the nondestructive acoustic characterization of epoxy networks, representative of the adhesive family, of different crosslinking density; i.e. conversion. Different curing cycles were applied and differential scanning calorimetry measurements allowed the determination of their glass transition temperature and epoxy conversion. The acoustic study was performed on epoxy plane plates, all in the glassy state and well beyond the gel point. The methods were based on the propagation of bulk longitudinal and shear waves, as well as on guided Lamb waves. Depending on the conversion of the epoxy, it was shown that the changes in thermo-mechanical properties, resulting from different degrees of cure, greatly influence the acoustic behavior of some Lamb modes if a selection of the sensitive modes has been performed upstream.

A Comparative Study on the Elastic Characteristics of an Aluminum Thin-Film Using Laser Optical Measurement Techniques

The increase of a surface area-to-volume ratio with the reduction of material dimensions significantly alters the characteristics of materials from their macroscopic status. Therefore, efforts have been made to establish evaluation techniques for nanoscale films. While contact mechanics-based techniques are conventionally available, non-contact and nondestructive methods would be preferable in case damages left on a sample after testing are not desirable, or an in situ assessment is required. In the present study, the Young’s modulus of an aluminum thin-film was evaluated using two different laser optical measurement techniques. First, microscale beam testing has been performed so that the resonant frequency change of a microfabricated cantilever beam induced by coating of a 153 nm thick aluminum layer on its top surface can be detected using a laser interferometer in order to evaluate the mechanical property through modal analysis using the finite element method. Second, picosecond ultrasonics were employed for cross-verification so that the mechanical characteristics can be evaluated through the investigation of the longitudinal bulk wave propagation behavior. Results show that the Young’s moduli from both measurements agree well with each other within 3.3% error, proving that the proposed techniques are highly effective for the study of nanoscale films.

Thickness Resonance Acoustic Microscopy for Nanomechanical Subsurface Imaging.

A nondestructive scanning near-field thickness resonance acoustic microscopy (SNTRAM) has been developed that provides high-resolution mechanical depth sensitivity and sharp phase contrast of subsurface features. In SNTRAM technology, we excited the sample at its thickness resonance, at which a sharp change in phase is observed and mapped with a scanning probe microscopy stage in near field to provide nanometer-scale nanomechanical contrast of subsurface features/defects. We reported here the remarkable subsubsurface phase contrast and sensitivity of SNTRAM by exciting the sample with a sinusoidal elastic wave at a frequency equal to the thickness resonance of the sample. This results in a large shift in phase component associated with the bulk longitudinal wave propagating through the sample thickness, thus suggesting the usefulness of this method for (a) generating better image contrast due to high S/N of the transmitted ultrasound wave to the other side of the sample and (b) sensitive detection of local variation in material properties at much better resolution due to the sharp change in phase. We demonstrated that the sample excited at the thickness resonance has a more substantial phase contrast and depth sensitivity than that excited at off-resonance and related acoustic techniques. Subsurface features down to 5-8 nm lateral resolution have been demonstrated using a standard sample.

Surface Brillouin scattering observation of higher order resonances in annealed, ion-implanted CVD diamond

The phase velocity of Surface Acoustic waves exhibits no dispersion in homogeneous materials. However, normal or anomalous dispersion takes place in layered systems. This dispersion effect has been used to determine the elastic constants of thin films. However, gradients in materials properties in the near surface region lead to dispersion effects also and therefore can be easily detected by surface acoustic waves (SAWs). We have used this technique to study changes in shear elastic constants of diamond irradiated with carbon ions in the energy range typically used in doping semiconductor materials. The range of the radiation damage extends from the surface to a depth of ≈0.3 μm. The fluence used for implantation was chosen so that the damaged diamond layer would not reform after thermal annealing at ambient pressure. In this study we generated and detected SAWs on the implanted and annealed diamond face after deposition of a very thin Pt film of thickness of ≈20nm to enhance surface reflectivity. With increasing dispersion (k∥d), the Rayleigh wave velocity falls gradually from that of crystalline diamond to that of annealed amorphous layer. At critical values of product of parallel wave vector and film thickness (k∥d), Sezawa modes split off from the bulk wave threshold of the substrate (transonic state). These are guided modes with the displacement field having an oscillating component in the layer, and falling off exponentially in the substrate. In combination with the velocity of the longitudinal bulk waves, the Poisson ratio and Young's modulus of the implanted region were calculated.

Experimental investigation of the dispersion of Scholte-Stoneley waves on a periodically corrugated surface

The dispersion of the phase velocities of the Scholte-Stoneley waves on a periodically corrugated interface is experimentally investigated and presented. The Scholte-Stoneley waves are generated through diffraction of the incident bulk longitudinal waves in water on a solid-fluid (brass-water) interface with one-dimensional grooves. The diffractions resulting from both the incident longitudinal waves and the generated Scholte-Stoneley waves are experimentally detected in a polar scan. The extracted velocity-frequency curves first confirm that the incident bulk wave is not dispersive and further show that the Scholte-Stoneley wave generated on the periodic interface is also not dispersive, although the velocity-frequency curves have oscillatory features.

레이저 초음파를 이용한 체적종파의 박막 내 전파특성 연구

본 논문에서는 나노스케일 금속박막 내에서 체적종파가 전파하는 특성을 연구하였다. 실리콘(100) 기판 위에 150 nm 두께의 크로뮴 혹은 알루미늄 박막을 적층하여 시편을 제작하였으며, 펨토초 레이저 시스템으로 구성된 시간영역 열반사율 기법(time-domain theromoreflectance technique)을 이용하여 박막 표면으로부터 여기된 탄성파가 박막과 기판의 계면에서 반향될 때 발생하는 신호를 검출하였다. 체적종파의 거동을 모사하는 열탄성 방정식을 수치해석적으로 풀어 측정값과 곡선맞춤함으로써 박막의 체적종파 속도와 탄성계수를 평가할 수 있었으며, 결과를 문헌값과 비교하여 그 타당성을 검증하였다. 본 연구로부터 확립된 레이저 계측법은 나노재료의 특성평가에 적합함을 보여주며, 이는 기존의 접촉식 파괴식 검사법의 한계를 뛰어넘을 대안을 제시한다. This paper presents the investigation of the propagation behavior of bulk longitudinal waves generated by an ultrafast laser system in thin films. A train of femtosecond laser pulses was focused onto the surface of a 150-nm thick metallic (chromium or aluminum) film on a silicon substrate to excite elastic waves, and the change in thermoreflectance at the spot was monitored to detect the arrival of echoes from the film/substrate interface. The experimental results show that the film material characteristics such as the wave velocity and Young's modulus can be evaluated through curve-fitting in numerical solutions. The material properties of nanoscale thin films are difficult to measure using conventional techniques. Therefore, this research provides an effective method for the nondestructive characterization of nanomaterials.

Directivity patterns of laser-generated sound in solids: Effects of optical and thermal parameters

In the present paper, directivity patterns of laser-generated sound in solids are investigated theoretically. Two main approaches to the calculation of directivity patterns of laser-generated sound are discussed for the most important case of thermo-optical regime of generation. The first approach, which is widely used in practice, is based on the simple modelling of the equivalent thermo-optical source as a mechanical dipole comprising two horizontal forces applied to the surface in opposite directions. The second approach is based on the rigorous theory that takes into account all acoustical, optical and thermal parameters of a solid material and all geometrical and physical parameters of a laser beam. Directivity patterns of laser-generated bulk longitudinal and shear elastic waves, as well as the amplitudes of generated Rayleigh surface waves, are calculated for different values of physical and geometrical parameters and compared with the directivity patterns calculated in case of dipole-source representation. It is demonstrated that the simple approach using a dipole-source representation of laser-generated sound is rather limited, especially for description of generated longitudinal acoustic waves. A practical criterion is established to define the conditions under which the dipole-source representation gives predictions with acceptable errors. It is shown that, for radiation in the normal direction to the surface, the amplitudes of longitudinal waves are especially sensitive to the values of thermal parameters and of the acoustic reflection coefficient from a free solid surface. A discussion is given on the possibility of using such a high sensitivity to the values of the reflection coefficient for investigation of surface properties of real solids.

Bulk longitudinal wave reflection/transmission in periodic piezoelectric structures with metallized interfaces

A theoretical study is performed of the bulk acoustic wave propagation in periodic piezoelectric structures with metallized interperiod boundaries. A crucial specific feature of such structures is that the bounded acoustic beam incident perpendicular to an interface can generate scattered (i.e. reflected and transmitted) waves over the whole area of the interface rather than only within the spot where this acoustic beam crosses the interface as it occurs in the absence of metallization. This extra generation is due to the electric potential which is induced by the incident wave on the whole metallized boundary rather than only on its part. The expressions are obtained for the reflection and transmission coefficients in the case where a longitudinal wave propagates along the 6-fold symmetry axis of a hexagonal piezoelectric. The periodicity is realized by inserting thin metallic layers (electrodes) into otherwise homogeneous material perpendicular to its 6-fold axis. The derived expressions allow the determination of the amplitude of waves arising both inside and outside the incident acoustic beam. The analysis of these expressions shows that the extra generation in question is able to significantly alter the distribution of the wave amplitudes as compared with the pattern which is obtained without taking into account the wave fields appearing outside the domain occupied by the incident acoustic beam.

Discrimination of Epoxy Curing by High Lamb Modes Order

This work is a contribution to the non destructive testing of structural adhesive bonding by ultrasonic methods. The aim of this paper is to link acoustic behaviors of epoxy bulk samples to their level of cure, quantified by a partial or a total epoxy conversion. The bulk longitudinal and shear waves velocities are measured for each sample. They are used to determine the theoretical dispersion curves of Lamb waves. Theoretical results predict a high sensitivity of some high order Lamb modes to the cure level by the variation of their wavenumber, for a given mode and for the same frequency range. In parallel, an experimental study is conducted to determine the experimental dispersion curves. The experimental results and the predicted ones are in a good agreement.

Grain Size Measurement in Steel by Laser Ultrasonics Based on Time Domain Energy

Laser ultrasonics, a technique based on the generation of ultrasonic waves by a pulsed laser and on their detection by a laser interferometer, can be used to determine grain sizes in steels. The absolute values of the average grain size can be calculated directly from the attenuation measurements of ultrasonic longitudinal bulk waves. The general methods of attenuation measurements are computed based on the amplitude of longitudinal waves. In fact, the amplitude as only one value is infected by the noise. Besides, the attenuation should be considered as the energy reduction. The method of time domain energy is proposed to compute the attenuation. The results indicate that time domain energy can improve the accuracy of the grain size prediction. The laser ultrasonic technique may be incorporated online for direct measurements of grain size during steel production. [doi:10.2320/matertrans.M2014445]

Strain solitary waves in a thin-walled waveguide

A mathematical model is proposed to describe bulk longitudinal waves in a nonlinearly elastic thin-walled cylindrical shell. The equation of motion for the longitudinal displacement is derived. In case of the homogeneous shell, this equation is reduced to the doubly dispersive equation for the linear longitudinal strain component and provides a solitary wave solution. Results of the first experimental observation of the bulk strain soliton in a duct-like shell are presented, and both the wave amplitude and velocity are estimated.

A hybrid finite element model for spiral coil electromagnetic acoustic transducer (EMAT)

This paper discusses finite element modeling of spiral coil electromagnetic acoustic transducer (EMAT) to generate bulk waves. First, a 2D electromagnetic model is developed for calculating the Lorentz force density, which is the driving force for sound wave generation within the material. Second, the calculated force at each point in the material is used as the driving force for generating sound wave modes. This model is used to predict the ultrasonic A-scan signals of bulk (longitudinal and shear) waves in isotropic homogeneous material. Spiral coil EMATs of two different coil spacings are developed for experimental studies. The model predicted results are validated by experimental results and for this, the ratio of amplitude of shear wave to longitudinal wave is used.

Latest Trends in Acoustic Sensing

Acoustics-based methods offer a powerful tool for sensing applications. Acoustic sensors can be applied in many fields ranging from materials characterization, structural health monitoring, acoustic imaging, defect characterization, etc., to name just a few. A proper selection of the acoustic wave frequency over a wide spectrum that extends from infrasound (<20 Hz) up to ultrasound (in the GHz–band), together with a number of different propagating modes, including bulk longitudinal and shear waves, surface waves, plate modes, etc., allow acoustic tools to be successfully applied to the characterization of gaseous, solid and liquid environments. The purpose of this special issue is to provide an overview of the research trends in acoustic wave sensing through some cases that are representative of specific applications in different sensing fields. [...]

Defect Detection in Thick Weld Structure Using Welding In-Process Laser Ultrasonic Testing System

A new approach of non-destructive testing for thick welded structural materials based on laser-ultrasonic technique is investigated. In this study, weld part of structural materials, which should be conventionally inspected after welding, is inspected during welding process in order to save time and cost of manufacturing. The laser-ultrasonic is a method to generate and detect ultrasonic signals by laser beams and has potential to be applied to remote inspection/monitoring of materials under welding at elevated temperature. Bulk longitudinal acoustic wave generated by a Q-switched Nd:YAG laser irradiation and detected as surface vibration by laser interferometer coupled with a long pulse detection laser is used to detect defects around the weld. To overcome the lack of sensitivity of laser-ultrasonic testing on thick welded part having a thickness of more than 100 mm at higher temperature, we have originally developed a modified synthesis aperture focus signal processing technique (m-SAFT). The in-process testing with actual piping weld having a thickness of 150 mm with high temperature more than 200 degrees C. was demonstrated. By using m-SAFT, an actual weld defect of 1.5 mm in diameter at 106 mm depth in the specimen was clearly observed. The measurement result well agreed with the result of conventional ultrasonic testing conducted after weld process and also the cross-sectional observation of the specimen.

Study on the electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices

The electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices is investigated by the transfer matrix method. Research results show the high electromechanical coupling coefficient can be obtained in these systems. The optimization design of it is also discussed fully. It is significantly influenced by electrical boundary conditions on interfaces, thickness ratios of piezoelectric and non-piezoelectric layers, and material parameters (such as velocities of pure longitudinal and transversal bulk waves in non-piezoelectric layers). In order to obtain higher electromechanical coupling coefficient, shorted interfaces, non-piezoelectric materials with large velocities of longitudinal and transversal bulk waves, and proper thickness ratios should be chosen.

Probing of crack breathing by pulsed laser-generated acoustic waves

Experimental results on all-optical monitoring of the nonlinear motion of a surface-breaking crack are reported. Crack closing is induced by quasi-continuous laser heating, while Rayleigh surface acoustic pulses and bulk longitudinal surface skimming acoustic pulses are also generated and detected by lasers. By exploiting the strong dependence of the acoustic pulses reflection and transmission efficiency on the state—open or closed—of the contacts between the crack faces, the parametric modulation of ultrasonic pulses is achieved. It is observed that bulk acoustic waves, skimming along the surface can be more sensitive to crack motion than Rayleigh surface waves. It has been found that crack closure by thermo-elastic stresses modifies the propagation paths of the acoustic rays from the point source to the point receiver. Consequently, the arrival times of the acoustic waves contain information on the state of crack closure induced by a particular intensity of laser heating. An important dependence of the detected signals on the initial width/state of the crack and on the presence of necks in the crack opening profile is revealed. It is demonstrated that the mode conversion of the skimming longitudinal bulk waves incident on the crack into the transmitted Rayleigh waves is very sensitive to imperfectness of crack closure. The proposed interpretation of the experimental observations is supported by atomic force microscopy measurements.

Probing of laser-induced crack closure by pulsed laser-generated acoustic waves

The monitoring and characterization of laser-heated crack by the laser ultrasonics technique are reported. In comparison with existing studies, where the Rayleigh and bulk skimming waves were generated by laser-induced line source, the point source is used here. Crack closure by thermoelastic stresses modifies the propagation paths of the acoustic rays from a point source to a point receiver. Thus, the arrival times of the acoustic waves contain useful information on the state of crack closure induced by a particular level of laser heating. An important dependence of the detected signals on the initial width/state of the crack and a presence of local necks/narrowings in the crack are revealed. It is demonstrated that the mode conversion of the incident skimming longitudinal bulk waves into the transmitted Rayleigh waves is very sensitive to imperfectness of cracks closure. The proposed interpretation of the laser-ultrasonics experimental observations is supported by atomic force microscopy measurements.

Employing the Waves to Measure Longitudinal Residual Stresses in Different Depths of a Stainless Steel Welded Plate

Ultrasonic stress measurement is based on the acoustoelasticity law which presents the relationship between the stress and acoustic wave velocity in engineering materials. The technique uses longitudinal critically refracted () waves that travel parallel to the material surface. The wave is a bulk longitudinal wave that propagates within an effective depth underneath the surface while the penetration depth of a wave depends on its frequency. It is possible to measure the residual stress in different depths by employing different frequencies of the waves. This paper evaluates welding residual stresses in different depths of a plate made of austenitic stainless steel (304L). The penetration depths are accurately measured for the waves produced by 1 MHz, 2 MHz, 4 MHz, and 5 MHz transducers. Residual stresses through the thickness of the plate are then evaluated by employing four different series of transducers. It has been concluded that the method is nondestructive, easy and fast, portable, readily available, and low cost and bulk measuring technique which can be accurately employed in through-thickness stress measurement of austenitic stainless steels.

Numerical modeling of thermoelastic generation of ultrasound by laser irradiation in the coupled thermoelasticity

Laser-generation of ultrasound is investigated in the coupled dynamical thermoelasticity in the presented paper. The coupled heat conduction and wave equations are solved using finite differences. It is shown that the application of staggered grids in combination with explicit integration of the wave equation facilitates the decoupling of the solution and enables the application of a combination of implicit and explicit numerical integration techniques. The presented solution is applied to model the generation of ultrasound by a laser source in isotropic and transversely isotropic materials. The influence of the coupling of the generalized thermoelasticity is investigated and it will be shown, that for ultra high frequency waves (i.e. 100GHz) generated by laser pulses with duration in the picosecond range, the thermal feedback becomes considerable leading to a strong attenuation of the longitudinal bulk wave. Moreover, the coupling leads to dispersion influencing the wave velocities at low frequencies. The numerical simulations are compared to theoretical results available in the literature. Wave fields generated by a line focused laser source are presented by the numerical model for isotropic and for transversely isotropic materials.

Relationships between the anisotropy of longitudinal wave velocity and hydroxyapatite crystallite orientation in bovine cortical bone

Quantitative ultrasound (QUS) is now widely used for evaluating bone in vivo, because obtained ultrasonic wave properties directly reflect the visco-elasticity. Bone tissue is composed of minerals like hydroxyapatite (HAp) and a collagen matrix. HAp crystallites orientation is thus one parameter of bone elasticity. In this study, we experimentally investigated the anisotropy of ultrasonic wave velocity and the HAp crystallites orientation in the axial–radial and axial–tangential planes in detail, using cylindrical specimens obtained from the cortical bone of three bovine femurs. Longitudinal bulk wave propagation was investigated by using a conventional ultrasonic pulse system. We used the one cycle of sinusoidal pulse which was emitted from wide band transmitter. The nominal frequency of the pulse was 1 MHz. First, we investigated the anisotropy of longitudinal wave velocity, measuring the anisotropy of velocity in two planes using cylindrical specimens obtained from identical bone areas. The wave velocity changed due to the rotation angle, showing the maximum value in the direction a little off the bone axis. Moreover, X-ray pole figure measurements also indicated that there were small tilts in the HAp crystallites orientation from the bone axis. The tilt angles were similar to those of the highest velocity direction. There were good correlations between velocity and HAp crystallites orientation obtained in different directions. However, a comparatively low correlation was found in posterior bone areas, which shows the stronger effects of bone microstructure. In the radial–tangential plane, where the HAp crystallites hardly ever align, weak anisotropy of velocity was found which seemed to depend on the bone microstructure.