Timothy A. Gray

Analytic Diffraction Corrections to Ultrasonic Scattering Measurements

Ultrasonic theories generally predict a scattering amplitude which relates a spherically spreading, far-field scattered wave to an incident plane wave. In ultrasonic immersion measurements, the frequency and angular dependences of the scattering amplitude are convolved with those of the transmitting and receiving transducers and the propagation through the liquid-solid and solid-liquid interfaces. This paper presents a set of approximate corrections for these effects for the cases of angle beam inspection through planar, spherically curved or cylindrically curved surfaces. The primary parameters in the correction are the function D, which corrects for the diffraction effects occurring during a transducer calibration experiment, and the function C, which describes the on-axis pressure variation of the beam. Values of C and D are available in the literature for the case of a piston transducer radiating into an infinite fluid medium. The major portion of this paper is concerned with the extension of those results to the aforementioned two media problems in which mode conversion, refraction, diffraction, and focussing all play interrelated roles. Results of preliminary experiments to test the corrections are also included.

Probability of Detection Modeling for Ultrasonic Testing

Ultrasonic (UT) inspection can be used to detect a wide variety of subsurface discontinuities, such as inclusions, cracks and voids, as well as associated reactive or diffusion zones. In comparison with Eddy-Current inspection, much less work has been done on the determination of the Probability of Detection POD of UT inspections. This is because, unlike Eddy-Current inspection, it is very difficult to produce synthetic sub-surface flaws that adequately represent the acoustic properties of the naturally-occurring flaws (see Burkel et al., 1996). Here traditional methods for POD determination are difficult to apply.

Kirchhoff Approximation Revisited—Some New Results for Scattering in Isotropic and Anisotropic Elastic Solids

Through a series of numerical studies that compare the Kirchhoff approximation to more exact scattering theories, it is demonstrated that the Kirchhoff approximation can accurately predict the pulse–echo peak-to-peak responses of spherical pores and circular cracks in isotropic media over a very wide range of cases that extend well beyond the limits normally associated with this approximation. The reason for this good agreement is shown to lie in the ability of the Kirchhoff approximation to model accurately the very early time response of the flaw. It is also shown that in the Kirchhoff approximation the pulse–echo response of an arbitrary traction-free scatterer in an isotropic elastic solid is identical to the same response obtained using a scalar (fluid) scattering model. This leads to simple analytical expressions for the pulse–echo far-field scattering amplitude of some canonical geometries (circular cracks, spherical voids, cylindrical holes) and to simplified numerical expressions for more general scatterers. For general anisotropic volumetric flaws in a anisotropic elastic solid, it is shown that a high-frequency asymptotic evaluation of the Kirchhoff approximation yields an explicit analytical expression for the pulse–echo leading-edge response of the flaw. Explicit expressions are also given for the pitch–catch response of an elliptical-shaped flat crack in a general anisotropic solid.

Progress on Ultrasonic Flaw Sizing in Turbine Engine Rotor Components: Bore and Web Geometries

The application of generic flaw sizing techniques to specific components generally involves difficulties associated with geometrical complexity and simplifications arising from a knowledge of the expected flaw distribution. This paper is concerned with the case of ultrasonic flaw sizing in turbine engine rotor components. The sizing of flat penny shaped cracks in the web geometry will be discussed and new crack sizing algorithms based on the Born and Kirchhoff approximations will be introduced. Additionally we propose a simple method for finding the size of a flat, penny shaped crack given only the magnitude of the scattering amplitude. The bore geometry is discussed with primary emphasis on the cylindrical focussing of the incident beam. Important questions which are addressed include the effects of diffraction and the position of the flaw with respect to the focal line. The appropriate deconvolution procedures to account for these effects will be introduced. Generic features of the theory will be compared with experiment. Finally, the effects of focused transducers on the Born inversion algorithm are discussed.

Indirect evaluation of system parameters for pulsatile flow in flexible tubes

A finite-element model for predicting pulsatile flow and pressure waveforms along a flexible tube is developed. The model is used in conjunction with a parameter estimation scheme to investigate the feasibility of estimating the vessel radius and compliance and peripheral resistance from measurements of flow and pressure waveforms. Model predictions are compared with experimental measurements to assess the accuracy of the method. The computer simulation satisfactorily predicts both pressure and flow waveforms for a variety of boundary conditions. Results show that the sensitivity of the waveforms to parameters generally depends on the type of boundary conditions and on the variable used in the estimation scheme. Vessel radius could not be determined reliably due to lack of sensitivity of the waveforms to this parameter. However, both the vessel compliance and peripheral resistance could be estimated satisfactorily for certain boundary conditions.

Use of Physics‐Based Models to Guide the Extrapolation of Aircraft Engine Ultrasonic POD Data to Small Flaw Sizes

In the determination of POD by techniques such as A‐hat versus A, the slope of a plot of log (flaw response) versus log (flaw size) is determined empirically by a regression analysis. This often works quite well. However, in the analysis of ultrasonic data obtained in the detection of naturally‐occurring, hard‐alpha inclusions in titanium alloys, a very low slope has been obtained. Physically, this is presumably the result of the complex morphology of the flaws, which leads to a very weak dependence of flaw response of flaw area. In the context of the POD analysis, this low slope of the regression line implies that very small flaws would produce a significant response, and hence a POD curve that retains a relatively large value at these small flaw sizes, in conflict with field experience. In this paper, the causes of this apparent inconsistency are identified and a procedure to correct for it is presented. The essential idea is that there is a change in slope of the regression line when flaw sizes become ...

Application of Ultrasonic Pod Models

The ability to quantify the reliability of nondestructive evaluation (NDE) inspection techniques is required to integrate inspectability into the component design process. Inspectability is typically evaluated on the basis of the design engineer’s experience and knowledge of NDE. While this approach can yield adequate designs with regard to inspection reliability, the potential for uninspectability remains. There is also the possibility that the designer’s knowledge of the reliability of NDE techniques may be limited to “standard” approaches which may be be inadequate for new component geometries or materials. This could lead the design engineer to imagine that a given component is inadequately inspectable and to redesign the part when the correct solution is either to modify the inspection protocol or to select a different technique. Alternatively, models which predict inspection reliability could be used to weigh the trade-offs and risks associated with selection among candidate NDE techniques to be applied to inspection of a given component design and to identify NDE system configurations for optimal reliability. This approach is, in fact, a key feature of the Unified Life Cycle Engineering concept currently being developed by the Air Force[l].

Ultrasonic POD Model Validation and Development for Focused Probes

The growing need to quantify the ability to inspect a component at the design stage requires accurate and computationally efficient analytical models of the inspection process. In ultrasonics, a computer model has been developed which can simulate signals obtained from both crack-like and volumetric defects [1,2], and can estimate their probability of detection (POD) [3,4]. This model can be used to predict and optimize the inspection reliability with respect to the inspection system, the component design, and the critical defects.

Model-Based Characterization of Planar and Focused Immersion Ultrasonic Transducers

Advanced ultrasonic nondestructive evaluation techniques require well characterized transducers. This need may arise, for example, because modern, cost-efficient fabrication procedures necessitate high reliability inspection through non-planar surfaces and for which careful control of the beam pattern in needed. An example of this is the developing procedure for inspection of titanium billet material for subtle flaws, such as hard-alpha inclusions [1]. Large aperture, bicylindrical focusing transducers are being developed, and characterization procedures are also being formulated for that activity. Methods are required to relate design parameters, such as crystal and lens shape, to the ultrasonic fields that will be generated in the billet. Advanced signal processing methods, such as characterization of noise due to ultrasonic scattering from grains, require precise knowledge of probe characteristics, as well. For example, model-based approaches to calculating a grain scattering “figure of merit” [2] require the ability to deconvolve transducer effects from measured noise signals. Knowledge of transducer characteristics is also essential for the application of ultrasonic measurement models [3,4] to the prediction of flaw signal amplitudes as measured through curved component surfaces and in a variety of materials. This geometry and material transferrability issue is of great importance in new methods applied to designing for inspectability.

A Comparison of the Axial Fields of Gaussian and Piston Transducer Radiation After Passage Through Cylindrical Surfaces at Oblique Incidence

An integral describing the a piston transducer through a axial radiation of cylindrical liquidsolid interface at oblique incidence is reviewed. Numerical difficulties associated with an essential singularity of the integrand near a focal point are overcome by transformation to the complex plane and deformation of the contour of integration. Expressions for the radiation of a Gaussian transducer in the same geometry are obtained by extending techniques used in the analysis of coherent optical systems. Numerical comparisons of the two solutions are presented for selected cases.