Ultrasonic Imaging and the Long Wavelength Phase

Elastodynamic and acoustic wave scattering play an essential role in various inspection methods such as sonar and ultrasonic tomography. Recently there has been considerable interest in the implications of long wavelength elastodynamic scattering for the characterization of flaws in elastic solids [1-6]. If the scattering amplitude is expanded as a power series in the frequency, the leading term is real and varies as the frequency squared. The next term varies as the frequency cubed and is purely imaginary. The evaluation of the phase variation in the long wavelength limit requires the ratio of these terms. Most effort to date has been invested in understanding the dependence of the coefficient of the frequency squared term on the size, shape, orientation and material properties of the scatterer. Richardson [3] and Kohn and Rice [4] have shown that, for an anisotropic elastic inclusion in an otherwise isotropic and homogeneous elastic space, the coefficient depends on at most 22 parameters. In addition, efficient numerical programs have been constructed to evaluate this coefficient for ellipsoidal inclusions. Other work has related it to the stress intensity factor for flaws which are crack-like [5]

Scattering of Elastic Waves by Small Surface-Breaking or Subsurface Cracks in Three Dimensions

The long-wavelength limit of elastic wave scattering by surface cracks in 3d is considered. It is shown that, if the crack is normal to the surface, the scattering can be described by two real parameters, one of which may be taken to be the crack size. The other therefore depends on shape, orientation, and burial depth. Many computed illustrations are given. It is concluded that the amount of information about cracks obtainable by low frequency elastic wave scattering is very limited

Elastic Wave Scattering Methods: Assessments and Suggestions

I was asked by the meeting organizers to review and assess the developments over the past ten or so years in elastic wave scattering methods and to suggest areas of future research opportunities. I will highlight the developments, focusing on what I feel were distinct steps forward in our theoretical understanding of how elastic waves interact with flaws. For references and illustrative figures, I decided to use as my principal source the proceedings of the various annual Reviews of Progress in Quantitative Nondestructive Evaluation (NDE). These meetings have been the main forum not only for presenting results of theoretical research but also for demonstrating the relevance of the theoretical research for the design and interpretation of experiment. In my opinion a quantitative NDE is possible only if this relevance exists, and my major objective is to discuss and illustrate the degree to which relevance has developed. I apologize if any one feels slighted by my not mentioning a particular work To keep the size of “review” manageable, I had to be brief and to the point

The Automation of the Born Inversion for Ultrasonic Flaw Sizing

The Born approximation has been widely employed as a basis for determining flaw sizes using individual pulse-echo waveforms together with the assumption of an ellipsoidal flaw geometry. A major difficulty in implementing such algorithms has been the determination of the time delay corresponding to the flaw centroid. However, both the time delay calculation and the flaw size determination itself can be performed in an optimal fashion using statistical estimation techniques with an appropriate error model. We will discuss the application of these techniques to an automated flaw-sizing algorithm requiring a minimum of operator input, and will compare the results obtained by this method with those obtained by previous operator-intensive methods

Ultrasonic Characterization of Porosity in Composite Materials by Time Delay Spectrometry

The presence of porosity in a wide range of materials, whether ceramics, steel or fiber reinforced composites, has a dramatic effect on the strength and mechanical properties of that material. Therefore, the presence of any porosity in a composite laminate during the manufacture of aerospace components is a basis for component rejection

Elastic Wave Scattering from Multiple Voids (Porosity)

The purpose of the work described in this paper is the development of an ultrasonic measurement technique which provides a convenient way to detect dilute porosity conditions in materials and to extract certain properties of the flaw distribution which are important in failure prediction. Use has been made entirely of ultrasonic backscatter measurements; thus, the technique differs considerably from other investigations which lead to porosity determinations in that no reliance is placed upon either attenuation measurements or precise ultrasonic velocity measurements [1,2]. The technique thus possesses a distinct advantage for practical implementation, i.e., it is a “one-sided” measurement which does not require ultrasonic echo returns from an opposite face of the sample in order to be useful. At present, the work is limited to dilute porosity concentrations. Reasons for this limitation will become clear in the paper. With additional effort it is expected that this limitation can be removed and the work extended to larger concentrations

Ultrasonic Characterization of Microspherical Inclusions in Zirconia and Crystallized Glass

In high performance ceramic materials the critical flaw size is ≃ 10 µm. Not all inclusions are equally detrimental to the structural properties. Therefore it is necessary to determine their size and composition.</p

Technique for Generation of Unipolar Ultrasonic Pulses

Substantial progress has been made in recent years in the development of inverse elastic wave scattering theories for use in ultrasonic nondestructive evaluation (NDE). These include theories that are applicable in different ultrasonic frequency ranges and include formulations in various approximations [1–15]. It is by application of these inverse scattering solutions to ultrasonic inspection results that quantitative measures of the size, shape, and orientation of a flaw can be determined

Low Frequency Scattering by a Planar Crack

The detection of cracks with the aid of ultrasonics is an important nondestructive evaluation technique. The corresponding theoretical problem of the scattering of elastic waves by cracks has attracted considerable attention. Scattering of time harmonic plane wave by an isolated two dimensional Griffith, or an penny-shaped crack in an unbounded elastic medium has been studied extensively. However, studies of the scattering problem by a three dimensional crack other than circular shape have been rather limited. Few studies of scattering from an elliptical crack in an elastic body of infinite extent can be found in the literature. Datta[1] studied the problem using the method of matched asymptotic expansion. Gubernatis et al. [2] and Budiansky and O’Connell [3] have used the elastostatic approximation to determine the scattered field. The backscattered field from an elliptical crack has been obtained by Kino [4] in the low frequency limit by a formula derived from elastodynamic reciprocity theorem. An integro-differential equation technique was employed by Roy [5]–[6] to study the same problem.</p

Modeling of Ultrasonic Signals from Weak Inclusions

Recent research efforts aimed at improving the detection of hard-alpha inclusions have emphasized the need for accurately modeling the responses from such weakly-reflecting inclusions. The need arises because of the rare natural occurrence of hard-alpha inclusions, and consequently, the lacks of suitable experimental samples. These difficulties lend impetus to the application of signal modeling to augment and extend the experimental data in assessing detectability. Currently, a new approach is being developed for the purpose of predicting time-domain echoes from inclusions of specified morphology. This work is the continuation of our previous study of flat-bottomed holes [1–2] in constructing a methodology for estimating the probability of detection of flaws in titanium alloys based on a combination of physical and statistical models