Research into ultrasonic NDE techniques for the inspection of multilayered structures relies strongly on the use of modeling tools which calculate dispersion curves and reflection and transmission spectra. These predictions are essential to enable the best inspection strategies to be identified and their sensitivities to be evaluated. General purpose multilayer modeling tools may be developed from a number of matrix formulations which have evolved in the latter half of this century and there is now a formidable number of publications on the subject. This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications. >

Matrix techniques for modeling ultrasonic waves in multilayered media

Ultrasonic guided wave inspection is expanding rapidly to many different areas of manufacturing and in-service inspection. The purpose of this paper is to provide a vision of ultrasonic guided wave inspection potential aswe move forward into the new millennium. An increased understanding of the basic physics and wave mechanics associated with guided wave inspection has led to an increase in practical nondestructive evaluation and inspection problems. Some fundamental concepts and a number of different applications that are currently being considered will be presented in the paper along with a brief description of the sensor and software technology that will make ultrasonic guided wave inspection commonplace in the next century.

A Baseline and Vision of Ultrasonic Guided Wave Inspection Potential

T he diffusivity of ultrasound in an untextured aggregate of cubic crystallites is studied theoretically with a view towards nondestructive characterization of microstructures. Multiple scattering formalisms for the mean Green's dyadic and for the covariance of the Green's dyadic (and therefore for the energy density) based upon the method of smoothing are presented. The first-order smoothing approximation used is accurate to leading order in the anisotropy of the constituent crystallites. A further, Born, approximation is invoked which limits the validity of the calculation to frequencies below the geometrical optics regime. Known result for the mean field attenuations are recovered. The covariance is found to obey an equation of radiative transfer for which a diffusion limit is taken. The resulting diffusivity is found to vary inversely with the fourth power of frequency in the Rayleigh, long wavelength, regime and inversely with the logarithm of frequency on the short wavelength, stochastic, asymptote. The results are found to fit the experimental data.

Diffusivity of ultrasound in polycrystals

Review of air-coupled ultrasonic materials characterization.

SUMMARY
We perform a theoretical study of the effect of fine layering on the compressional-wave velocities and attenuation coefficients in fluid-saturated rocks. This effect in a permeable rock differs from that in a purely elastic solid because of the local flow of the pore fluid across the interfaces, which is caused by the passing wave. For analytical calculations. Biot theory is applied to non-homogeneous (randomly and periodically layered) porous media leading to Biot's equations with variable coefficients. By analysing these equations with the help of a statistical perturbation technique we obtain the velocity and normalized attenuation 1/Q of the fast compressional wave as a function of frequency f. Both attenuation and velocity dispersion are found to obtain their maximum values near some frequency f0, at which the Biot slow-wave attenuation length equals the mean inhomogeneity size (mean layer thickness or characteristic length). In the low-frequency limit, 1/Q is proportional to f1/2 for random and to f for periodic layering. At frequencies higher than f0, attenuation decreases with increasing frequency as f−1/2, regardless of the particular type of layering. The results for periodic layering are in a good agreement with recently published exact results. The results for the more realistic case of random layering with exponential correlation reveal more gradual changes of velocity and attenuation versus frequency than those for a periodically layered medium.

Velocity and attenuation of elastic waves in finely layered porous rocks

We have developed a unified approach to solve for the attenuation and phase velocity variations of elastic waves in single‐phase, polycrystalline media due to scattering. Our approach is a perturbation method applicable for any material whose single‐crystal anisotropy is not large, regardless of texture, grain elongation, or multiple scattering. It accurately accounts for the anisotropy of the individual grains. It is valid for time‐harmonic waves with all ratios of grain size to wavelength. It uses an autocorrelation function to characterize the geometry of the grains, and thereby avoids coherent artifacts that occur if the grains are assumed to have symmetrical shapes and suggests new methods for characterizing distributions of grains that are irregularly shaped. We have carried out numerical calculations for materials that are untextured and equiaxed, and have cubic‐symmetry grains and an inverse exponential spatial autocorrelation function. These calculations agree with the previous calculations which are valid in the Rayleigh, stochastic, and geometric regions, and show the transitions between these regions. The complex transition between the Rayleigh and stochastic regions for longitudinal waves, and the severe limitations of the stochastic region for grains with fairly large anisotropy are of particular interest.

A unified theory for elastic wave propagation in polycrystalline materials

Spatial autocorrelation functions effect the scattering processes and the effective propagation constants of elastodynamic waves in single‐phase, polycrystalline media. The spatial autocorrelation function W(r1,r2) is the probability that the two points r1 and r2 are in the same grain. A ‘‘grain’’ is a discrete, homogeneous domain within an inhomogeneous medium which is composed completely of such domains. One way to calculate W(r1,r2) is empirically. It employs cord lengths measured on a micrograph, and thus provides a means of determining the autocorrelation function for real materials. A second way to calculate W(r1,r2) is analytically, and employs expressions for the probability density of the cord lengths. Analytical calculation allows the use of assumptions about the geometrical nature of the grains in a material to be incorporated into theoretical expressions for effective propagation constants, and gives measures of effective ‘‘grain size.’’ Two specific assumptions have been important for such ca...

Spatial autocorrelation functions for calculations of effective propagation constants in polycrystalline materials

A complex-transducer-point model for finite emitting and receiving ultrasonic transducers

An efficient numerical model is described for predicting the pulse‐echo response of an ultrasonic transducer insonifying a cylindrically layered medium from the inside. A rigorous 3‐D formulation of the problem is first developed. Reduction to an approximate but computationally much more efficient form is accomplished based on several general assumptions regarding the geometrical properties of the transducer and the cylindrically symmetric layered medium. Within these constraints, the model accurately accounts for diffraction, attenuation, and dispersion in the interior immersing fluid and for reflection from the multilayered annular region that may contain strong internal resonances. Calibration of the temporal response of the transducer and associated measurement electronics is an integral part of the model, which is formulated using reciprocity relations for cylindrical coordinates. The principal application for the model is the ultrasonic internal inspection of pipes.

Mathematical model for internal ultrasonic inspection of cylindrically layered structures

The interaction of transducer‐excited ultrasonic pulsed beams with fluid‐loaded elastic plates is treated with a computationally efficient analytical model. The model synthesizes the frequency‐domain voltage, due to a single transducer operated in reflection (pulse‐echo) mode and a pair of tranducers in transmission mode, utilizing an approach that is based on (1) expansion of transducer fields in terms of quasi‐Gaussian beams modeled via the complex‐source‐point technique and its recent extension to finite receivers, and on (2) complex wave‐number spectral decomposition and synthesis to solve the beam–structure interaction problem. First, a reference solution for the frequency‐domain reflected and transmitted fields is expressed in terms of spectral integrals over two‐dimensional infinite spectra of plane waves weighted by the plate reflection or transmission coefficient. Subsequent expansion in terms of a finite sum of integrals representing multiply reflected beams propagating within the plate, combined with high‐frequency asymptotics and inverse Fourier transformation of the frequency‐domain data, yields the time‐domain voltage as a finite sum of purely compressional (P), purely shear (S), and P–S coupled arrivals. Of particular interest is the new higher‐order asymptotic expansion developed to account for shear waves excited in the plate by the finite angular spectrum of beams at normal incidence. Both reference and asymptotic solutions have been implemented in numerical codes and validated against experimentally generated data. This is shown in a follow‐up paper. The methodology presented here can be applied under more general conditions of transducer orientation and focusing, and also for elastic media with more than one layer.

Ultrasonic pulsed beam interaction with a fluid‐loaded elastic plate: Theory

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