T. A. Gray

A model relating ultrasonic scattering measurements through liquid–solid interfaces to unbounded medium scattering amplitudes

The relationship between scattering data obtained from ultrasonic experiments, in which the waves are excited and detected in a finite measurement geometry, and unbounded medium, farfield scattering amplitudes is considered. For a scatterer in a single fluid medium, a Green’s function approach is used to develop an approximate, but absolute, relationship between these experimental and theoretical cases. Electromechanical reciprocity relationships are then employed to generalize to a two medium case in which the scatterer is located in an elastic solid which, along with the ultrasonic transducer, is immersed in a fluid medium. The case explicitly considered is one in which the incident waves are quasiplanar over the volume of the flaw and the scattering amplitudes are slowly varying over the range of angles subtended by the receiving transducer. Analytic approximations are developed for the absolute relationship of the received transducer signal to the unbounded medium scattering amplitudes, and formal exp...

Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints

The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (φ′=φ), and those having nonparallel water rays (φ′ ≠ φ). The φ′ = φ categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two φ = φ′ geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical φ′ ≠ φ geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.

The interaction of ultrasound with imperfect interfaces: Experimental studies of model structures

Model specimens are prepared, each of which may be viewed as two sections of similar material joined imperfectly at a planar interface. Measurements of the ultrasonic reflection from, mode conversion at, and/or transmission through these imperfect interfaces, are reported. The interface structures include distributions of pores, contacts, and inclusions. Included are both near-periodic and random cases. As the frequency is increased, the measured reflection coefficients generally show an initially linear increase from zero, followed by a maximum which may exhibit multiple peaks, and a subsequent decay. These results are interpreted in terms of a quasi-static model and an independent scattering model for ultrasonic interactions with imperfect interfaces.

The radiation of elliptical and bicylindrically focused piston transducers

Expressions for the radiation of elliptical and bicylindrically focused piston transducers are derived within the Fresnel approximation. For the axial fields, the result takes the form of either a simple analytical expression (small perturbations from the circular piston case), a single quadrature in a real variable (unfocused and some focused cases), or a single quadrature in a complex variable (near focal points). The full fields are represented by a series of localized, Gauss–Hermite eigenfunctions. Numerical examples are used to illustrate the agreement of the two solutions for on‐axis fields and to shed light on questions of the convergence and the selection of initial scaling parameters of the Gauss–Hermite expansion.

A Technique for Quantitatively Measuring Microstructurally Induced Ultrasonic Noise

In ultrasonic inspections of aircraft engine components, the detectability of critical defects can be limited by grain noise. This is likely to be the case for subtle defects, such as hard-alpha-phase inclusions in titanium alloys, where the difference between the acoustic impedances of the defect and host is small. A sound quantitative description of grain noise in such alloys is essential for accurate estimates of flaw detection reliability. In this work we present a method for quantifying backscattered grain noise by using positional averaging to determine the root-mean-squared (rms) noise level. The measured noise level will depend on details of the measurement system, as well as on inherent material properties of the alloy. We present a preliminary model of the noise measurement process which accounts for system effects, and we compare its predictions with experiment. We then indicate how the rms noise data can be processed to extract a factor which parameterizes the inherent noise severity independent of the measurement process.

Model‐Assisted Probability of Detection Validation for Immersion Ultrasonic Application

Model assisted probability of detection (MAPOD) is a method of calculating probability of detection versus flaws size curves which utilize physics‐based models to reduce the time, cost, and complexity of POD studies with respect to those conducted by purely empirical approaches. An approach to utilizing models combined with empirical data in calculating POD curves based on immersion ultrasonics as the example case is described. Before MAPOD calculations can be performed, the applicable physics‐based model must be validated to accuracy consistent with the desired accuracy of the resulting POD curve. In this case, the Thompson‐Gray ultrasonic measurement model was used. For the purposes of validating the MAPOD approach, a specimen was configured that would allow empirical data to be collected that would serve the dual purpose of providing input to the MAPOD calculation as well as providing input to empirical POD calculations (MIL‐HDBK‐1823). Validation of the MAPOD approach consisted of directly comparing t...

Reflection of ultrasonic waves from imperfect interfaces: a combined boundary element method and independent scattering model approach

A numerical technique for obtaining interface reflection coefficients for imperfect bonds between similar materials for a wide range of distributed defects is developed. A numerical boundary element method is utilized to find the far-field scattering amplitudes of a single defect for a normally incident plane wave. Then, the normal incidence reflection coefficient for a planar distribution of such defects is obtained from the independent scattering model. As a validation, the reflection coefficients are compared to the quasi-static model results where the latter are available. This establishes the basis for one application of the new model, the determination of spring constants which are not available. Other applications of the model, including studies of the response at frequencies beyond the quasi-static limit, the ratio of longitudinal to transverse wave reflectivities, and the effects of selected multiple scattering are discussed.

Ultrasonic NDE Techniques for Integrally Fabricated Rotors

Solid-state bonding methods, e.g., diffusion bonding and pressure welding, are becoming common manufacture and repair techniques for gas turbine engine components. Effective NDE inspection techniques are crucial to the utilization of this approach due to the high stresses on the bond plane associated with jet engine operation. Recently we have examined ultrasonic techniques for assessing bond quality including leaky Rayleigh waves and critical angle longitudinal waves[1], for which the illuminating waves are nearly normal to the bond plane, and longitudinal waves at near grazing incidence to the bond[1]. Based upon preliminary theoretical analyses[1,2] of ultrasonic reflectivity from imperfect interfaces, it was found that the reflection coefficient for both longitudinal and shear waves increases to unity as the incident angle approaches grazing[1]. In contrast, the bond reflection coefficients for near normal incidence can be quite small, depending upon the degree of imperfection of the bond. A second drawback to the first two approaches mentioned is that surface roughness of the blade can cause scattering noise which dominates the signals reflected from the bond. The grazing incidence technique suffers less from these problems since the probe is oriented nearly normal to the surface of the blade and the interaction of the beam with the surface is minimized.

A Model for Ultrasound Transmission Through Graphite Composite Plates Containing Delaminations

The propagation of elastic waves through materials and their interactions with flaws are fundamental phenomena underlying many nondestructive evaluation techniques. Over the past decade, considerable research has led to a good understanding of these phenomena for isotropic materials. For example, it is now possible to predict the absolute signals that will be observed when flaws of simple shapes, e.g., circular cracks or spherical pores, are examined in an immersion test through planar or cylindrically curved surfaces [1]. These models have now been used to successfully predict the probability of detection (POD) [2], an important figure of merit of a practical inspection, and it has been suggested that this capability will find important applications in a) the validation of existing NDE techniques, b) the design of new NDE techniques, or c) the consideration of inspectablility in part design [3,4].

Evaluation of Ultrasonic Beam Models for the Case of a Piston Transducer Radiating Through A Liquid-Solid Interface

In order to accurately predict the performance of immersion ultrasonic inspection techniques, it is necessary to have a model for the transducer radiation process. This model should include the case of propagation of the ultrasonic beam at oblique incidence through liquid-solid interfaces of complex geometries. Included should be the effects of diffraction, refraction, focussing and aberrations upon the beam shape.