R. Bruce Thompson

Ultrasonic scattering from imperfect interfaces: A quasi-static model

A quasi-static model for the ultrasonic transmission and reflection at imperfect interfaces is developed. The interface is represented by a distributed spring, determined by the change in static compliance of the medium with respect to one with a perfect interface, and a distributed mass, representing excess mass at the interface. Comparison of the model predictions to exact solutions for two simple cases illustrates its accuracy at low frequencies. The spring stiffnesses can be derived from existing solutions for the elastic displacement of materials containing cracks and inclusions under static load. Results for a variety of cases are reviewed. Applications of the model to study the characteristics of partially contacting surfaces in several problem areas of current interest are discussed.

Angular dependence of ultrasonic wave propagation in a stressed, orthorhombic continuum: Theory and application to the measurement of stress and texture

A theory for ultrasonic wave propagation in a symmetry plane of a biaxially stressed, orthorhombic continuum is presented. Since many of the material parameters which appear in the analysis are unknown, in particular the third‐order elastic constants of polycrystalline metals, emphasis is placed on the angular dependence of the velocities. An expansion to first order in stress‐induced anisotropy and to second order in textural anisotropy reveals terms with twofold, fourfold, and sixfold symmetry. Scenarios are proposed for using various properties of this symmetry to deduce the difference in magnitude and directions of the principal stresses independent of textural anisotropy and the textural anisotropy independent of the stresses. Experimental results are presented for the cases of aluminum, 304 stainless steel, and copper.

A paraxial theory for the propagation of ultrasonic beams in anisotropic solids

The necessity of nondestructively inspecting cast steels, weldments, composites, and other inherently anisotropic materials has stimulated considerable interest in wave propagation in anisotropic media. Here, the problem of an ultrasonic beam traveling in an anisotropic medium is formulated in terms of an angular spectrum of plane waves. Through the use of small angle approximations, the integral representation is reduced to a summation of Gauss–Hermite eigensolutions. The anisotropic effects of beam skew and excess beam divergence enter into the solution through parameters that are simply interpreted in terms of the slowness surface. Both time harmonic and pulsed solutions are discussed. Formulas are also presented for transmission of a beam through a curved interface between two media. Examples are given illustrating how this method may be applied to predicting beam patterns during ultrasonic inspections.

Influence of anisotropy on the dispersion characteristics of guided ultrasonic plate modes

Dispersion curves are developed for elastic wave propagation in an anisotropic plate of monoclinic or higher symmetry. Emphasis is placed on analytic expressions for various features. Generalization of the isotropic Rayleigh–Lamb dispersion relations are derived for the cases of (a) propagation along a material symmetry axis and (b) propagation in a general direction. Examination of the high‐frequency limit of the lowest symmetric and antisymmetric mode dispersion curves yields expressions for the half‐space surface or Rayleigh wave velocity. It is shown that the dispersion curves for these modes can exhibit multiple crossings in approaching this limit, and an analytic solution is presented for the constant crossing interval that occurs for propagation along symmetry directions. The analytic results are illustrated by extensive numerical calculations for a variety of degrees of anisotropy with emphasis placed on the relationship between the slowness curves governing partial wave propagation and various features of the dispersion curves.

Higher harmonics of finite amplitude ultrasonic waves in solids

Absolute measurements of the amplitude of the first four harmonicof 30‐MHz finite amplitude ultrasonic waves are reported for fused silica samples of various lengths and for aluminum single crystals with different amounts of cold work. The harmonically distorted motion of the end of the sample is detected by a capacity microphone and the individual harmonics are then selected and amplified by a heterodyne receiver with flat frequency response from 30 to 250 MHz. The fused silica data are found to be in excellent agreement with a model of Fubini, originally developed for gases, which for solids depends on the second‐ and third‐order elastic constants but none of the higher constants. A discussion is presented of the reasons for the insensitivity of the measurements to the values of the fourth‐ and higher‐order elastic constants. Agreement with the model of Fubinin is not observed in single crystal aluminum. The quantitative differences are not fully consistent with existing models for dislocation contribut...

Relations between elastic constants Cij and texture parameters for hexagonal materials

Ultrasonic techniques have recently been applied to the texture characterization in polycrystalline aggregates of hexagonal crystals. The basis of this application lies in the relations between the elastic constants Cij of the aggregates, which can be inferred from ultrasonic wave velocity measurements, and the orientation distribution coefficients. This communication presents such relations for aggregates which possess orthotropic material symmetry and hexagonal crystal symmetry for Voigt, Reuss, and Hill averaging methods in a unified and concise representation.

The elastic moduli of a thick composite as measured by ultrasonic bulk wave pulse velocity

One thick filament-wound composite in the form of a large thick-walled cylinder with locally orthorhombic symmetry has been measured by ultrasonic velocity to calculate its elastic moduli. The basic assumption was that small sections of the composite could be treated as a homogeneous body analogous to a crystal for ultrasonic propagation. The experimental work and the results as best expressing homogeneous body theory are presented. Because of the high anisotropy with the normal to the layers (the three-direction) much different from the axial and hoop directions, it was necessary to calculate slowness surfaces with approximate values of c13 and c23 in order to find the directions of the Poynting vectors to use in making actual measurements on c12 and c13.

Measurement of crack opening stresses and crack closure stress profiles from heat generation in vibrating cracks

A method is described to measure crack opening stresses and closure stress profiles of a surface-breaking crack. Vibration is used to generate frictional heat by rubbing crack face asperities. Heat is generated at regions of contacting crack asperities under low, but nonzero, closure stress. Increasing force is applied to incrementally open the crack and measure the locations of crack heating as a function of applied load. Surface crack closure stresses are approximated from the heating locations as the load is varied and the crack opening stress is measured from the load required to fully open the crack and terminate heat generation.

Application of the boundary element method to elastic wave scattering by irregular defects

A time-harmonic boundary element formulation for elastic wave scattering in 3D is adapted to ultrasonic NDE. Defect classes addressed are volumetric voids and inclusions, and crack-like elliptical voids. For axisymmetric flaws, comparisons are made with method of optimal truncation (MOOT) and transition-matrix calculations. Comparison to experiment is made for more general shapes. For crack-like voids, comparisons are made with the Kirchhoff, geometric theory of diffraction (GTD), and quasistatic asymptotic approximations. The efficiency and usefulness of the boundary element method (BEM) in finding the bounds of applicability of these approximate theories are demonstrated. An example of a flaw characterization technique based on intermediate frequency scattering data simulated by BEM is given. The ability of BEM to handle nonplanar incident fields, as described by a transducer beam model, is shown. Other computational and modeling efficiencies of the BEM are noted.

Predicting ultrasonic grain noise in polycrystals: A Monte Carlo model

A Monte Carlo technique is described for predicting the ultrasonic noise backscattered from the microstructure of polycrystalline materials in a pulse/echo immersion inspection. Explicit results are presented for equiaxed, randomly oriented aggregates of either cubic or hexagonal crystallites. The model is then tested using measured noise signals. Average and peak noise levels and the distribution of the noise voltages are studied as the density of grains changes.