12 research outputs found
Generalized ultrasonic scattering model for arbitrary transducer configurations
Ultrasonic scattering in polycrystalline media is directly tied to microstructural features. As a result, modeling efforts of scattering from microstructure have been abundant. The inclusion of beam modeling for the ultrasonic transducers greatly simplified the ability to perform quantitative, fully calibrated experiments. In this article, a theoretical scattering model is generalized to allow for arbitrary source and receiver configurations, while accounting for beam behavior through the total propagation path. This extension elucidates the importance and potential of out-of-plane scattering modes in the context of microstructure characterization. The scattering coefficient is explicitly written for the case of statistical isotropy and ellipsoidal grain elongation, with a direct path toward expansion for increased microstructural complexity. Materials with crystallites of any symmetry can be studied with the present model; the numerical results focus on aluminum, titanium, and iron. The amplitude of the scattering response is seen to vary across materials, and to have varying sensitivity to grain elongation and orientation depending on the transducer configuration selected. The model provides a pathway to experimental characterization of microstructure with optimized sensitivity to parameters of interest
Simplified approach to the application of the geometric collective model
The predictions of the geometric collective model (GCM) for different sets of
Hamiltonian parameter values are related by analytic scaling relations. For the
quartic truncated form of the GCM -- which describes harmonic oscillator,
rotor, deformed gamma-soft, and intermediate transitional structures -- these
relations are applied to reduce the effective number of model parameters from
four to two. Analytic estimates of the dependence of the model predictions upon
these parameters are derived. Numerical predictions over the entire parameter
space are compactly summarized in two-dimensional contour plots. The results
considerably simplify the application of the GCM, allowing the parameters
relevant to a given nucleus to be deduced essentially by inspection. A
precomputed mesh of calculations covering this parameter space and an
associated computer code for extracting observable values are made available
through the Electronic Physics Auxiliary Publication Service. For illustration,
the nucleus 102Pd is considered.Comment: RevTeX 4, 15 pages, to be published in Phys. Rev.
Wigner Distribution of a Transducer Beam Pattern Within a Multiple Scattering Formalism for Heterogeneous Solids
Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids