Surface acoustic wave attenuation in polycrystals: Numerical modeling using a statistical digital twin of an actual sample.

Grain boundary scattering-induced attenuation and phase-velocity dispersion of Rayleigh-type surface acoustic waves are studied with a time-domain finite-element method (FEM). The FEM simulation incorporates a realistic material model based on matching the spatial two-point correlation function of a Laguerre tessellation with that obtained from optical micrographs of a previously studied aluminum sample. Plane surface acoustic waves are excited in a multitude of statistically equivalent virtual polycrystals, and their surface displacement fields are averaged for subsequent extraction of the coherent-wave attenuation coefficient and phase velocity. Comparisons to previous laser-ultrasonic experiments, an analytical mean-field model, and the FEM results show good agreement in a broad frequency range from about 10 to 130MHz. Observed discrepancies between models and measurement reveal the importance of spatial averaging in the context of mean-field approaches and suggest improvement strategies for future experimental studies and advanced analytical models. A different attenuation power law for Rayleigh waves is found in the stochastic scattering regime compared to bulk acoustic waves.

Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media with statistically equiaxed grains.

The influence of a polycrystals' grain structure on elastic wave scattering is studied with analytical and numerical methods in a broad frequency range. A semi-analytical attenuation model, based on an established scattering theory, is presented. This technique accurately accounts for the grain morphology without prior assumptions on grain statistics. This is achieved by incorporating a samples' exact spatial two-point correlation function into the theory. The approach is verified by using a finite element method (FEM) to simulate P-wave propagation in 3D Voronoi crystals with equal mean grain diameter, but different grain shape uniformity. Aluminum and Inconel serve as representatives for weak and strong scattering cubic class materials for simulations and analytical calculations. It was found that the shape of the grains has a strong influence on the attenuation curve progression in the Rayleigh-stochastic transition region, which was attributed to mode conversion scattering. Comparisons between simulations and theory show excellent agreement for both materials. This demonstrates the need for accurately taking the microstructure of heterogeneous materials into account, to get precise analytical predictions for their scattering behaviour. It also demonstrates the impressive accuracy and flexibility of the scattering theory which was used.

Optical tracking of picosecond coherent phonon pulse focusing inside a sub-micron object.

By means of an ultrafast optical technique, we track focused gigahertz coherent phonon pulses in objects down to sub-micron in size. Infrared light pulses illuminating the surface of a single metal-coated silica fibre generate longitudinal-phonon wave packets. Reflection of visible probe light pulses from the fibre surface allows the vibrational modes of the fibre to be detected, and Brillouin optical scattering of partially transmitted light pulses allows the acoustic wavefronts inside the transparent fibre to be continuously monitored. We thereby probe acoustic focusing in the time domain resulting from generation at the curved fibre surface. An analytical model, supported by three-dimensional simulations, suggests that we have followed the focusing of the acoustic beam down to a ~150-nm diameter waist inside the fibre. This work significantly narrows the lateral resolution for focusing of picosecond acoustic pulses, normally limited by the diffraction limit of focused optical pulses to ~1 µm, and thereby opens up a new range of possibilities including nanoscale acoustic microscopy and nanoscale computed tomography.

Inverse characterization of plates using zero group velocity Lamb modes.

In the presented work, the characterization of plates using zero group velocity Lamb modes is discussed. First, analytical expressions are shown for the determination of the k-ω location of the zero group velocity Lamb modes as a function of the Poisson's ratio. The analytical expressions are solved numerically and an inverse problem is formulated to determine the unknown wave velocities in plates of known thickness. The analysis is applied to determine the elastic properties of tungsten and aluminum plates based on the experimentally measured frequency spectra.

Experimental and numerical study of the excitability of zero group velocity Lamb waves by laser-ultrasound.

The excitability of zero group velocity (ZGV) Lamb waves using a pulsed laser source is investigated experimentally and through numerical simulation. Experimentally, a laser based ultrasonic technique is used to find the optical spot size on the sample surface that allows an optimal coupling of the optical energy into the ZGV mode. Numerical simulations, using the time domain finite differences technique, are carried out to model the thermoelastic generation process by laser irradiation and the propagation of the generated acoustic waves. The experimental results are in good agreement with the numerical predictions. The experimentally and numerically obtained responses of the plate are investigated by a short-time Fourier transform. The responses show that the source diameter does not affect the fundamental behavior of the temporal decay of the ZGV mode.

Comparison of numerical and effective-medium modeling of porosity in layered media.

In this study, modeling approaches for porosity in layered media are presented and compared. First, an effective-medium model is used to account for the frequency-dependent attenuation of the elastic waves. The effective-medium model is based on a single-scattering approach, i.e., it neglects multiple-scattering effects. Then, the effective-medium model is compared in time-domain finite element simulations. The numerical model allows the study of the scattering of the elastic waves on randomly distributed spherical cavities and also accounts for multiple-scattering effects. The models are compared to investigate the validity of the effective-medium model approach. The calculated reflected laminate responses and transmission spectra from the two models show a good agreement.

Characterization of the spatio-temporal response of optical fiber sensors to incident spherical waves.

In this study a theoretical framework for calculating the acoustic response of optical fiber-based ultrasound sensors is presented. The acoustic response is evaluated for optical fibers with several layers of coating assuming a harmonic point source with arbitrary position and frequency. First, the fiber is acoustically modeled by a layered cylinder on which spherical waves are impinged. The scattering of the acoustic waves is calculated analytically and used to find the normal components of the strains on the fiber axis. Then, a strain-optic model is used to calculate the phase shift experienced by the guided mode in the fiber owing to the induced strains. The framework is showcased for a silica fiber with two layers of coating for frequencies in the megahertz regime, commonly used in medical imaging applications. The theoretical results are compared to experimental data obtained with a sensing element based on a pi-phase-shifted fiber Bragg grating and with photoacoustically generated ultrasonic signals.

On the crossing points of the Lamb modes and the maxima and minima of displacements observed at the surface.

This article elaborates on the crossing points of the frequency-wavenumber branches for the symmetric and anti-symmetric Lamb modes in a homogeneous plate. It is shown both theoretically as well as experimentally that at these crossing points either the normal or the longitudinal components of modal displacement attain an extreme value, i.e. a maximum or it vanishes. This behavior is assessed herein using a method due to Mindlin, who showed that the dispersion curves for a plate with mixed boundary conditions - which are associated with uncoupled shear and dilatational modes - provide bounds to the spectral lines of the free plate. Therefore, a subset of the crossing points of the symmetric and antisymmetric Lamb modes for a free plate coincide with the crossing points for a plate with mixed boundary conditions.

Golay code modulation in low-power laser-ultrasound.

The current work presents a correlation-based detection technique with application in modulated laser-ultrasonics. In standard use of coded sequences the impulse response of a system is recovered in the time domain with improved signal to noise ratio (SNR). The presented method is an extension of this technique, where the response to a chirped waveform is restored with improved SNR; hence, the response is in a well-defined frequency range. To achieve this goal the chirped waveforms are modulated by Golay codes. It will be shown that the response to this bandlimited carrier waveform can be recovered in the time domain with improved signal to noise ratio using a cross-correlation technique. Improvement in the SNR is discussed analytically and it is shown that this improvement is proportional to the square root of the length of the applied sequences. Experimental applications in laser-ultrasound are shown using modulated laser diodes as excitation sources with an output power of ∼1W. In the experiments a plate with a thickness of 50µm is investigated using Lamb waves in the MHz range to confirm the predicted improvement in the SNR. Golay codes with three different lengths were used with 7, 9 and 11 bits resulting in 2(7)=128, 2(9)=512, and 2(11)=2048 repetitions in an individual signal, respectively. The predicted improvements of 2 in the SNR between the 7 and 9 bits, and between the 9 and 11 bits waveforms, respectively, were well approximated by the experimentally obtained values of 1.83 and 2.17. As Lamb wave dispersion curves can be used for the characterization of plates or layered samples by inverse problems, it is also shown that by using multiple measurement points the recovered waveforms can be utilized in the evaluation of the dispersion relation.

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.

Characterization of broadband fiber optic line detectors for photoacoustic tomography.

The frequency response of fiber optic line detectors is investigated in the presented paper. An analytical model based on oblique scattering of elastic waves is used to calculate the frequency dependent acousto-optical transfer functions of bare glass optical and polymer optical fibers. From the transfer functions the transient response of fibers detectors to photoacoustically excited spherical sources is derived. Photoacoustic tomography is simulated by calculating the temporal response of arrays of fiber optic line detectors and subsequent image reconstruction. The results show that the choice of the fiber material is of significant importance and influences the quality of imaging.

Stability analysis of second- and fourth-order finite-difference modelling of wave propagation in orthotropic media.

The stability of the finite-difference approximation of elastic wave propagation in orthotropic homogeneous media in the three-dimensional case is discussed. The model applies second- and fourth-order finite-difference approaches with staggered grid and stress-free boundary conditions in the space domain and second-order finite-difference approach in the time domain. The numerical integration of the wave equation by central differences is conditionally stable and the corresponding stability criterion for the time domain discretisation has been deduced as a function of the material properties and the geometrical discretization. The problem is discussed by applying the method of VonNeumann. Solutions and the calculation of the critical time steps is presented for orthotropic material in both the second- and fourth-order case. The criterion is verified for the special case of isotropy and results in the well-known formula from the literature. In the case of orthotropy the method was verified by long time simulations and by calculating the total energy of the system.

Wave propagation in a wooden bar.

In this paper we will present a method to determine the material properties of a wooden bar with rectangular cross-section using guided waves in the measurement. We modelled the wood as an orthotropic material with nine independent constants. We determined the dispersion curves theoretically in the three-dimensional case using a semi-analytical finite element method. In our laboratory we excited transversal and longitudinal waves in wooden bars of 2.5-4 m length by piezoceramic transducers. We measured the displacement or the velocity of the surface of the bar by a laser-interferometer. The dispersion curves of the bar are determined from the measurement by the linear prediction method. We related the dispersion curves and the material properties. We found the material properties by parametric model fitting.