Ultrasonic backscattering in polycrystals with elongated single phase and duplex microstructures

An analytical solution for a three dimensional integral representation of the backscattering (BS) coefficient in polycrystals with elongated (generally ellipsoidal) grains is obtained; it is a natural generalization of the known explicit result for the BS coefficient in polycrystals with spherical grains. New insights into the dependence of the BS signal on frequency and averaged ellipsoidal grain radii are obtained. In particular it has been shown that the dominant factor for the backscattering is the averaged interaction length of the ellipsoidal grain in the direction of wave propagation, instead of the ellipsoidal cross-section. The theory was applied to a simplified model of Ti alloy duplex microstructure and was compared with experiment. For the experimental data analysis directional backscattering ratios are introduced and shown to be advantageous for characterization of duplex elongated microstructures/microtextures. In addition to the geometrical parameters of the elongated microtextures, the BS directional ratios depend on the newly introduced nondimensional material parameter q. The parameter q exhibits the relative contribution of the second phase (crystallites) to the backscattering signal, the effect of which is measurable and important. Comparison of the model with experiment shows there is a significant advantage in using the directional ratios of backscattering coefficients for data analysis.     

Explicit model for ultrasonic attenuation in equiaxial hexagonal polycrystalline materials

Attenuation coefficients for longitudinal and transverse ultrasonic waves are obtained in explicit form for untextured hexagonal polycrystalline materials. The equations obtained are easy to use for interpretation and evaluation of experimental results for ultrasonic characterization of microstructures. The attenuation coefficients are separated into two terms, corresponding to incident wave scattering into longitudinal and transverse waves. It is shown that the general expressions for attenuation coefficients in the long wavelength (Rayleigh) and short wavelength (stochastic) regimes transit to the known classical asymptotics. Simple equations to estimate the frequency range of the transition from the Rayleigh to stochastic regimes are also given. An example of experimental measurements in Ti alloy is provided to illustrate application of the model; the results show reasonable agreement between the experiment and the model with no adjustable parameters.     

Nonexponential dissipation in a lossy elastodynamic billiard: comparison with Porter-Thomas and random matrix predictions

We study the dissipation of diffuse ultrasonic energy in a reverberant body coupled to a waveguide, an analog for a mesoscopic electron in a quantum dot. A simple model predicts a Porter-Thomas distribution of level widths and corresponding nonexponential dissipation, a behavior largely confirmed by measurements. For the case of fully open channels, however, measurements deviate from this model to a statistically significant degree. A random matrix supersymmetric calculation is found to accurately model the observed behaviors at all coupling strengths.     

Mode counts in an aluminum foam.

Measurements of the ultrasonic modal density of a disordered elastic frame, a 20 pore-per-inch open-celled aluminum foam, are reported. While the material is dissipative, with a Q only around 700, sufficiently careful signal processing has allowed reliable counts of the modes up through a few hundred, corresponding to wavelengths comparable to the strut lengths. The modal density is found to be essentially constant over this range, and to bear no resemblance to theoretical estimates based on long-wavelength effective moduli.     

Fluctuations in diffuse field-field correlations and the emergence of the Green's function in open systems

Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.     

3-D voltage model for detection of sound radiated from anisotropic materials

The elastic behavior of composite materials has been characterized experimentally by employing a 3-D voltage calculation to model transmission or reflection experiments. With sound propagation along material symmetry directions, integration over the incident-plane angle alone is generally sufficient to model the transducer voltage accurately. In general material directions this integration must be extended to account for asymmetrical variations in the reflection or transmission coefficient out of the incident plane. Theoretical and experimental results illustrate this effect and the relationship between 2-D and 3-D calculations. Experimental measurements are used to in the reconstruction of viscoelastic properties in composite plates. The influence of the phi-dependent integration on the voltage, in the 3-D calculation, is particularly strong when the incident angles are small and the wave paths are large, as typically experienced in air-coupled measurements.     

Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies

Noise generated in an ultrasonic receiver circuit consisting of transducer and amplifier is usually ignored, or treated as a nuisance. Here it is argued that acoustic thermal fluctuations, with displacement amplitudes of 3 fm, contain substantial ultrasonic information. It is shown that the noise autocorrelation function is the waveform that would be obtained in a direct pulse/echo measurement. That thesis is demonstrated in experiments in which direct measurements are compared to correlation functions. The thermal nature of the elastodynamic noise that generates these correlations is confirmed by an absolute measurement of their strength, essentially a measurement of the sample temperature.     

In-plane elastic property characterization in composite plates

This article presents a method to deduce the in-plane elastic properties of multilayered composite plates. Drawing on a synthetic-aperture technique developed for the elucidation of materials properties in air-coupled ultrasonics, this new method exploits the high elastic anisotropy of composite materials to permit an accurate measurement of directional in-plane stiffness. It is found that comparisons of experimental measurements with plate stiffnesses calculated on the basis of lamination theory agree to within several percent for uniaxial and biaxial laminates and to within 10 percent for quasi-isotropic laminates. It is further shown that the method is largely insensitive to transducer deployment angle within a range related to the transducer beamwidth.