Review of Progress in Quantitative Nondestructive Evaluation

This work is part of a continuing effort to develop a capability for quantifying the scattering of ultrasonic waves by arbitrarily shaped flaws. The general problem of elastodynamic behavior of a homogeneous, isotropic defect in an otherwise homogeneous, isotropic fullspace is cast as a Boundary Integral Equation (BIE). A general scattering model is needed to provide information for probability of detection (POD) models and inversion schemes for cases when low or high frequency approximations are not appropriate. Previously the Boundary Element Method (BEM), a method for solving the BIE, was adapted to NDE and the void problem was investigated [1]. Here we focus on the inclusion problem, experimental verification, and to overall extensions of the capability.

Due to more intensive use of civil and military aircraft there are growing demands for accurate and reliable methods in non-destructive testing. One of the areas receiving specific attention is the detection and characterisation of corrosion [1]. The study presented here is concerned with the scattering of ultrasound waves from an isolated corrosion pit on the remote side of a thick aluminium plate. The corrosion pit is represented by a three-dimensional hemispherical surface indentation of radius a in an elastic half-space, and the wave field generated by an ultrasonic transducer is assumed to be a time harmonic plane wave incident on to the surface feature at an arbitrary angle, see Fig. 1. The scattering problem is solved by means of a boundary method, and the surface displacements in the vicinity of the scatterer and the scattered far-field components are represented for compressional waves incident at 60 degrees and shear waves normally incident on to the surface obstacle. The diameter of the surface indentation can vary between the fraction of a wavelength and two wavelengths. The results shown here were calculated for 2a/λ = 0.5 and 1.0.

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.

Scattering characteristics have been calculated for a spherical inclusion with partially debonded interphase conditions. Three scattering characteristics of the scattered field have been selected for investigation: 1) the frequency response at a fixed point, 2) the scattered field at a fixed frequency along an observation line, and 3) the radiation pattern. The compliant interphase between the inclusion and the surrounding elastic matrix has been modeled by a layer of distributed springs which offers resistance to relative displacements in the two tangent and the normal directions. Two basic assumptions are made for the spring model of the interphase: 1) The springs are linear, and 2) The interphase is very thin so that the effect of inertia of the interphase can be neglected. These assumptions are acceptable in the low frequency range. The partial debonding of the interphase is modeled by setting the spring constants (defined per unit area) equal to zero along part of the interphase.

In non-destructive testing, it has been suggested that wavelength or frequency dependent Rayleigh wave scattering coefficients could provide a means of characterising surface defects. Only a few Rayleigh wave scattering problems have analytic solutions and most workers have resorted to numerical techniques [1]. In this paper we present details of a new model that can deal with general surface defect geometries. The scheme is used to model Rayleigh wave scattering from curved corners, steps and slots. The implications of the results for a Rayleigh wave based defect characterisation method are discussed briefly.

The scattering of time-harmonic acoustic waves from an elastic solid immersed in a fluid with the transmission of elastic waves into the solid is a generic problem of interest to various disciplines. A solution strategy for this class of problems is of direct significance to the NDE community, where such knowledge can contribute to a simulation scheme for an ultrasonic immersion scanning system with randomly distributed, subsurface flaws. Use of the boundary element method (BEM) is known to be an effective tool in handling such scattering problems, especially in the mid range frequencies where asymptotic approximations fail. The strength of the method lies in exact modelling of the interaction; the drawback being its loss of efficiency in the the high frequency regime.

Scattering by inhomogeneities in homogeneous media can be analyzed in an elegant manner by reducing the problem statement to the solution of a system of singular integral equations over the surface of the scatterer [1]. This system can be solved in a relatively straight forward manner by the use of the boundary element method [2]. An inhomogeneity in an interface between two solids of different mechanical properties presents some additional complications to the numerical analyst. These complications are discussed in this paper. In deriving the system of singular integral equations, it was decided to use the Green’s functions for the unbounded regions of the two materials, rather than the single Green’s function for the space of the joined half spaces. This approach introduces a considerable simplification in the integrands, but at the expense of the addition of a set of boundary integral equations over the interface between the two solids, outside of the inhomogeneity. In the boundary element approach the domain of these equations has to be truncated. Specific results are presented for backscattering by a spherical cavity in the interface of solids of different elastic moduli and mass densities.

Nonlinear inversion is the process of estimating material property values from a set of measured data. The map between the parameters and the measured data is a mathematical model. The specific mathematical model to be used in this study is the acoustic wave equation. This equation is linear in the field variable; however, it is nonlinear in the model parameter.

Analysis and prediction of the response of composite laminates to external loads are essential for the design of composite structures. This in turn requires a precise knowledge of their mechanical properties including their constitutive behavior. It is reasonable to assume that, in the bulk, the overall behavior of unidirectional graphite/epoxy composites is the same as that of a homogeneous, transversely isotropic material with its symmetry axis along the fiber direction. Then the linear elastic response of the material can be described by means of five elastic constants. If the values of these constants can be determined, then the stress analysis of a laminate with a given number and stacking order of the laminae can, in principle, be carried out. However, the measurement of the elastic constants by conventional, destructive techniques is difficult and often, inaccurate. Thus, the availability of alternative, preferably nondestructive methods, for the determination of the elastic costants of the material would be extremely helpful.

The problem of flaw characterization can be viewed as a multi-step process (Fig. 1) where decisions are made as to flaw type (a classification process) and geometry (a sizing process). Previously, we have described our work on the use of the expert system FLEX for determining if an unknown flaw is a volumetric flaw or a crack [1] and the use of equivalent flaw sizing algorithms whereby the flaw is sized in terms of a best fit ellipsoid (for volumetric flaws) or ellipse (for cracks) [2]. Here, we will describe some of our work on how classification information can be used to improve sizing estimates and on the use of new, more efficient sizing algorithms.

Within the last ten years there has been a renewed interest in simulation of stress wave propagation because of the availability of fast supercomputers with large memory capabilities [1,2,3]. Only recently have a few investigators [4,5] applied these simulations to problems where elastic anisotropy was included as a major factor. The massive output of results from these simulations, together with the added complexity of coupled phenomena that uniquely exist for a given anisotropy, defies intuition. To grasp the significance of these simulations requires scientific visualization [6] of these complex physical phenomena. Such visualizations often require a movie format to better understand the physics of particular problems [7]. In this study we simulated the experimental measurement of a shift in the quasi-transverse bulk wave propagation in an off-axis unidirectional graphite/epoxy composite in plane strain [8]. The purpose of the simulation was to aid the nondestructive evaluation engineer in designing an acoustic array to improve the measurement of the shift in the QT wave propagation direction [9]. Previously a finite element model [5] was used to simulate this measurement. In this study we demonstrate the advantages of using a finite difference model to simulate this experiment and, with special visual aids, observe the physics.

For most of the complicated geometries encountered in ultrasonic nondestructive evaluation (NDE) applications, finite element (FE) solutions [1–4] of the elastic wave equation are usually limited because of the spatial discretization required for accuracy. Artificial boundaries introduced to limit the spatial dimensions of a given problem can cause unwanted reflections which corrupt the desired response. The simplest approach to this problem is to ensure that the model is large enough for the unwanted reflections to be separated from the desired signal in the time domain. But this becomes very expensive for most applications, especially for full 3-D geometries. Models for infinite media, therefore, are very important for numerical modeling in 3-D and even in many 2-D practical applications.

The architecture of conventional (von Neumann) computers, with a single processor and millions of memory units, is inherently inefficient for most applications. In fact, while the processor is extremely busy all the time, only a very small portion of the memory is active. Larger computers are even less efficient, since the ratio of processing power to memory is even smaller and the length of computation is dominated by the ever increasing time required to move data between processor and memory. To overcome this so-called “von Neumann bottleneck,” a new kind of computer, called the “Connection Machine” (CM) has been designed, with a larger number (thousands) of processors, connected in a programmable way, in the framework of a fixed physical wiring scheme [1]. This parallelism allows an opportunity to efficiently reformulate the problem to be studied and modify the approach [2-4]. Currently, the memory available is limited and requires some care in programming. This limitation should decrease with new CM-type machines.

A common approach to study the acoustic field in an isotropic elastic half-space has been to use the equations of linear, isotropic elasticity together with Fourier or Hankel transforms [1,2]. The result is a definiteintegral representation of the field at an arbitrary point in the half-space owing to a prescribed stress applied to the free surface. The complicated integral can be evaluated asymptotically to give the far field radiation. Furthermore, the theoretical expressions for the directivity patterns from a variety of acoustic sources, radiating into an isotropic elastic half-space have been presented by several authors [1–4]. A similar theoretical analysis applied to an anisotropic solid medium fails because the potential theory method is not applicable to the anisotropic problem.

In a recent paper Nayfeh et al. [1] presented theoretical and experimental results for the propagation of longitudinal waves in a composite whose microstructure was large enough to cause observable velocity dispersion. Only wave propagation along the fiber axis of a uniaxial laminate was considered. A reflection coefficient was also derived for the case of normal incidence and parallel to the fibers. For ultrasonic inspection applications, what is required is the ability to analyze situations in which the wave is incident at arbitrary angles. Analysis of such general situations are, however, difficult to treat. A relatively simpler two-dimensional composite, which has been analyzed for an off-normal incident angle [2], consists of a bilaminated model with layers bonded and stacked normal to the x₃-direction. The structure occupies the half-space x₂ ≥ 0 as illustrated in Fig. 1. The composite is immersed in water such that the x₂-direction is normal to the fluid-composite interface and the wave is incident from the fluid in the x₁-x₂ plane. For this model the reflection coefficient and the characteristic equation for the propagation of fluid-composite interfacial waves was calculated. The results reported in [2] are also restricted such that the individual composite components are isotropic.

In immersion ultrasonic testing, a beam of sound must pass through a liquid-solid interface before it can interact with subsurface defects. In modern quantitative NDE studies, it is essential to know the beam properties in the solid so that flaw scattering variations, transducer diffraction corrections, etc. can be estimated. Using high frequency asymptotics and the method of stationary phase, we show here that analytical expressions can be derived for the wavefield radiated by a piston transducer, where the transducer is oriented normal to a plane liquid-solid interface (Fig. 1). In the main beam of the transducer these expressions will be shown to be equivalent to the solutions Schoch obtained for a single fluid medium [1].

In our previous work [1,2,3,], we have studied in detail the radial-axial modes in an infinitely clad isotropic rod. We have shown that in metal matrix composites, where the fibers are stiffer than the matrix, many of these modes are leaky, transmitting energy into the surrounding medium. The existence of this leakage energy offers a potential means for monitoring and imaging the characteristics of the interface zone [2,3,4,]. Detailed numerical methods have been developed for analyzing radial-axial leaky modes in composite systems [1]. The present paper shows an example of these methods applied to determining the sensitivity of the maximum phase velocity to the matrix density changes for leaky modes.

A mathematical model for the propagation of elastic disturbances through a cylindrically wound thick composite specimen is presented. The primary purpose of the modelling effort is to provide a means by which the elastic constant tensor corresponding to the specimen can be determined by in-situ measurements, in which case the effect of the curved fibre geometry must be addressed in the theoretical model. Hence the material is modelled as a cylindrically anisotropic medium, which is of orthotropic symmetry. Ray theory techniques give rise to the identification of curved ray paths along which a disturbance propagates in any one of three normal modes with a constant velocity of propagation. Thus the determination of the elastic constants from in-situ time-of-flight measurements has been reduced to the level of simplicity involved in ascertaining elastic constants from measurements made on a media possessing the usual cartesian symmetry. Finally, it will be shown that the eikonal equations for the cylindrically orthotropic media give rise to the following simple description of the ray geometry: The rays propagate so as to maintain a constant angle of attack with respect to the surfaces which describe the symmetry of the medium.

An elastic layer, or plate, immersed in a fluid possesses plane-wave reflection and transmission properties which are related to the propagation characteristics of guided waves in the layer. If the fluid density is much less than that of the plate, this relationship amounts to a correspondence and has been used to deduce the velocity dispersion of Lamb waves in numerous studies of ultrasonic reflection [1–3]. Under conditions of heavy fluid loading (ie, when the ratio of fluid to solid density approaches or exceeds unity), the fluid begins to play a decisive role in controlling both the propagation and reflection characteristics of waves in the immersed plate. A vivid illustration of this behavior is seen in the locus of curves determined by the transmission maxima (reflection coefficient zeroes) for a graphite-epoxy composite plate immersed in water. It has been shown through both measurement and calculation [4,5] that for certain values of incident angle and frequency, the total transmission loci in this case correspond neither to the Lamb waves in vacuum nor to the leaky guided waves in the fluid-coupled plate.

Obliquely incident (predominantly P-wave) beam inputs from an ultrasonic transducer into a layered bounded composite elastic plate are suitable for detection of weak debonds because they generate on the bond lines the tangential shear to which this kind of flaw responds. In previous studies, the beam-flaw interaction and scattering mechanisms were explored by expressing the fields in both the unflawed and flawed environments in terms of the set of P-SV coupled modes capable of propagating in the plate [1–5]. As may be anticipated, the reference data generated in this manner exhibited beam-like features of the fields in observational domains characterized by only a few P-SV coupled beam reflections between the outer boundaries of the perfectly bonded plate, thereby indicating that the normal modes do not parametrize the process in terms of the “observables” in the data. The problem is therefore re-parametrized here by direct beam tracking. As before [1,2], our model is two-dimensional and comprises a two-layer aluminum plate in vacuum, with a weak debond region modeled by a quasi-Gaussian pliability profile.

One of the technique that is often used in the measurement of phase velocities of guided elastic modes is the zero-crossing shift technique. Using this technique, one measures time delays (usually through a counter) of a specific zero-crossing for a number of different separation distances of two transducers. The phase velocity V_p is computed as the slope of the distance-delay plot. For non-dispersive waves, this produces no problem as the pulse retains its shape as it propagates.

The theory of elastic wave propagation in fluid-saturated porous solids was established by Biot in 1956 [1,2]. Biot predicted the existence of three bulk modes: fast compressional wave, slow compressional wave, and shear wave. However, experimental confirmation of Biot’s theory at ultrasonic frequencies was not achieved until 1980 when Plona [3] observed slow compressional waves on fluid-saturated synthetic porous solids by using mode conversion technique. Since that time, Plona’s method has been adopted as a major approach to measure slow compressional wave in fluid-saturated porous media.

Today the use of adhesive bonds is more developed in many industries and more specifically in Space Industries. Its development is limited by the possibility to make a non-destructive evaluation of the quality of the bond. Up to now, the inspection of the cohesion and the thickness of the glue are well controlled. With regard to the adhesion, the problem is not yet solved.

A topic of ongoing interest to the manufacturing community is the development of models to simulate ultrasonic (UT) inspections of manufactured parts. In previous work [1] we presented a model approach for predicting the effects of internal flaws upon throughtransmitted UT signals. This approach, which combines Auld’s reciprocity formula and a Kirchhoff approximation, proved very successful in simulating normal-incidence inspections of graphite/composite plates containing seeded delaminations. A key ingredient of our approach is the Gauss-Hermite (GH) model for the propagation of bulk ultrasonic waves in homogeneous media [2,3]. This beam model, in which one expands a time-harmonic displacement field in terms of a truncated set of Gauss-Hermite basis functions, has a number of desirable features. The ultrasonic transducer generating the waves may be planar, focussed, or of unusual design. The expansion coefficients which multiply the basis functions are obtained by numerical integrations over the face of the transducer. Once these transducer-dependent constants have been calculated, displacement fields can be rapidly computed. Paraxial approximations are available which describe how a given expansion function is modified by passage through a planar or curved interface. The use of these approximations makes the model especially well suited for problems in which a beam is being propagated through successive layers of material: computation times are nearly identical for single-layer and multi-layer problems. The layers can be either isotropic or anisotropic in nature, although in the current formulation of the model there are some restrictions on the direction of propagation for anisotropic materials [3]. Because the model employs paraxial approximations it is not appropriate for highly divergent beams, or for beams striking interfaces near the critical angle of incidence.

A calculation of diffraction loss versus normalized (dimensionless) distance is needed to correct ultrasonic attenuation measurements for beam spreading and arrive at the intrinsic material attenuation as a function of frequency.

In this paper we report on the experimental results demonstrating the potential of using cylindrical guided waves (CGW) for inspection of steam generator tubing (SGT). The CGW ultrasonic technique is intended to complement the present eddy current (EC) practice for in-service inspection as well as to provide an alternative tool for pre-service inspection. Below, we review the current NDE practice for SGT and the motivation of this study.

The propagation of a longitudinal wave in an isotropic cylinder has been used in the inspections of pumps and shafts of a nuclear power plant [1]. An ultrasonic technique called the “cylindrically guided wave technique” (CGWT) has been developed that can detect simulated circumferential defects through long metal paths in metallic materials being used for bolts and studs [1]. In the recent development of the sizing process for the cylindrically guided wave technique, the wave scattering at the circumferential crack can be formulated in terms of the guided cylindrical waves which mathematically result from the cylinder frequency equation. Therefore, a detailed investigation of the cylinder frequency equation is in order in the sizing process for bolt and pump-shaft inspections.

In the design of an eddy current inspection device, it is useful to have available a means of visualizing the eddy current distribution produced in the material to be tested. This is evidenced by the widespread use of the early models of Dodd and Deeds [1], who provided analytic solutions for the field in a number of axisymmetric probe geometries. The analytic approach was later extended [2–4] to include a more general class of coils, and was applied to the case of a circular, air-core horizontal coil [4].

Early NDE research primarily focused on the ability to develop techniques which could detect flaws in structures. Eddy currents, induced by exciting coil probes placed over a structure, were found to be a valuable tool in detecting flaws in conducting materials. In recent years, efforts have been expanded from the detection of defects to a more quantitative characterization of flaws. In metallic structures, the important flaw characteristics consist of the flaw’s depth, position, size, shape, and material properties (flaw electrical conductivity, magnetic permeability etc.). This paper continues our efforts of the past two years to recover flaw characteristics from eddy current data.

A problem fundamental to all electromagnetic methods of NDT is that of modeling accurately the changes in an applied field that are produced by a flaw. The structure of such fields depends significantly on two dimensionless numbers. The first of these is the ratio of the skin-depth δ to the global length scale of the perturbed field, which is given by the crack dimension l Many studies relate specifically to thin-skin fields where δ/l « 1 and the present study is also in this context. Within the classification of thin-skin fields, widely different surface distributions can arise depending on the value of the second parameter m=l/µ_rδ where µ_r is the relative magnetic permeability of the metal specimen [1]. Values of m vary from very small to very large depending on the material properties and the operating frequency. In the Wolfson Unit at University College London a great deal of work has been done at frequencies around 103 Hz on cracks in ferromagnetic steels where µ_r is large enough to make m small. The limiting form of surface field obtained as m- 0 is then the surface unfolded field [1,2]. On the other hand, many other investigations have been carried out on non-magnetic materials whereµ_r=1 so that m is large in thin-skin situations (e.g. Auld et al. [3]). In this case the algorithm for constructing the surface field around a flaw is based on a Born approximation which considers the surface field outside a surface-breaking crack to be unchanged by the presence of the flaw.

A general three-dimensional eddy-current probe model, developed by Sabbagh Associates and reported in [1], [2] and [3], has been adapted for the calculation of probe-flaw interactions. The theoretical model, [4] and [5], uses integral equations with dyadic Green’s function kernels, and is applicable to both probe and flaw calculations at arbitrary skin depths and frequencies. Discrete approximations of the integral equations are solved using a highly efficient algorithm based on recent developments in numerical techniques and their application to the solution of large problems in electromagnetic field-theory.

In eddy-current nondestructive evaluation, the electromagnetic field is usually excited by a probe carrying a time-harmonic current and flaw information inferred from the amplitude and phase of the probe signal. In principle, transient excitation of eddy-currents would seem to offer great advantages since the probe response contains the equivalent information of a spectrum of frequencies. This paper explores a number of basic transient solutions due to normal air-cored coils and shows how the induced emf in a coil is related to its coupling coefficient.

The electrically small loop is of great practical importance in finding direction and probing magnetic fields. In [1], it was proposed for communication from above ground to observation points within coal mines. In this paper, the interactions of electromagnetic field, produced by a current-excited small loop, with lossy and lossless materials are investigated. The use of a small loop for the NDE of composite materials is also presented. To achieve these goals, solutions of interface problems become necessary. Since the exciting current is not restricted to be time-harmonic, we will solve the problems in the time domain. Also, to obtain economic requirements for computer resources, both storage and running time, a potential approach instead of vector field codes is developed.

Finite element (FE) studies of energy/material interactions associated with the nondestructive evaluation (NDE) of materials have not only yielded useful information concerning the physics of new NDE phenomena [1] but also provided “test-beds” for the simulation of NDE situations too difficult to replicate in a laboratory environment [2]. FE code has been developed for the analysis of those NDE processes governed by elliptic [3], parabolic [4] and hyperbolic [5] partial differential equation (PDE) types taking advantage of axisymmetry wherever possible in order to conserve computer capacity. In those situations requiring fine spatial and/or temporal discretization, it has been found that the FE code makes excessive demands on even the best computer resources. Examples of this situation include the finite element modeling of the remote field effect in large diameter pipelines [6] and the simulation of ultrasonic wave propagation through large structures [7].

This paper continues the authors effort in numerical modeling of electromagnetic forward scattering for high frequency nondestructive testing (NDT) applications. Started in [1], a two-dimensional problem in the time domain was solved by finite difference method in conjunction with a local absorbing boundary condition located some distance away from the scatterer. In the present work, more complicated, three-dimensional models in the frequency domain are considered. A typical electromagnetic NDT situation involves interaction of a given incident wave field with a material sample. Numerical modeling of such an NDT situation usually involves a large solution domain or inverting a very large matrix, as a direct consequence of the following two features. One is the unboundedness of the problem, because it is assumed that the incident wave field is emitted from and the measurement is performed in an infinite background medium. In finite difference or finite element modeling, an artificial boundary condition (more or less, frequency dependent) is located far away from the scatterer in order to simulate the nonreflecting nature of the scattered wave field. Another feature is the vector nature of the electromagnetic wave. Thus, the field variable at each nodc in the solution domain has three components. To get rid of the interface condition, finite element modeling usually reformulates the problem by introducing scalar and vector potentials, which means more unknowns per node and even larger matrices. The purpose here is to review and propose a class of edge-based methods with minimal solution domains, fewer independent unknowns and higher accuracy. These methods use a new class of elements having unknowns on the edges (tangential component of field along the edge) instead of the nodes. By using vector basis functions, each edge has only one degree of freedom (first order model)[2].

Differences between conventional single frequency eddy current (EC) nondestructive testing (NDT) and remote field eddy current (RFEC) NDT are summarized schematically in Fig. 1. In the testing of steam generator tubing, a differential probe (Fig. la) is used to produce impedance plane trajectories (Fig. lc) which are indicative of the tubes condition. From a numerical simulation or modeling point of view, the finite element (FE) prediction of such impedance plane trajectories [1-3] requires a geometry of the dimensions shown in Fig. le. The relatively small mesh sizes associated with the FE simulation of EC probe behavior are a distinct advantage in that only modest computer resources are required. Indeed, for axisymmetric geometries, such code can run on a personal computer.

There are many approaches to 3D eddy current analysis. Typical methods for the eddy current analysis are the A-ø method and the T-ω method. Both methods require variables in space as well as in a conductor. We have already proposed the T method [1, 2, 3], where a magnetic scalar potential ω is not included and we do not need variables in space. But the method has a disadvantage that a large core memory is needed due to a dense matrix.

The numerical modeling of single frequency eddy-current phenomena based on the magnetic vector potential has been successfully applied to many NDT applications [1–3]. Despite the considerable wealth of sinusoidal eddy-current literature, the numerical modeling of pulsed eddy-currents has received little attention. Most of the recent finite element transient eddy-current NDT modeling [4,5] employs a variational time-domain formulation for 2D and axisymmetric geometries. Since this model was tested against experimental measurements, it lacks rigorous quantitative verification required to be a useful NDT design tool.

Inverse scattering models, of the type that are often used to invert eddy-current data, are inherently nonlinear, because they involve the product of two unknowns, the flaw conductivity, and the true electric field within the flaw. Computational inverse models, therefore, often linearize the problem by assuming that the electric field within the flaw is known a priori. In this paper we describe how conjugate gradients might be applied to solve the nonlinear problem. The model is developed for an anisotropic material such as graphite epoxy, and is based on a method-of-moment discretization of two coupled integral equations.

The eddy current method of nondestructive testing of metals has been under extensive investigation for some time now [1]. In spite of significant advances in this technique, the eddy current quantitative measurements of cracks usually require complicated calibration procedure and often involve the use of calibration standards [1–4].

In a companion paper, [1], we developed a rigorous, nonlinear model for inverting eddy-current data by means of the conjugate gradient algorithm. In this paper we will present some results obtained from the linearized version of the rigorous model. In this version we assume that the electric field within the flaw is simply the incident field that exists in the absence of the flaw.

Surface-breaking cracks in metal sheets may be detected by injecting alternating current into the sheet and observing the resulting nonuniformity in the surface electromagnetic field.

X-ray digital tomographic methods may be classified according to the number of projections and the angular coverage required to obtain the density distribution of the object under study. At one extremity stands computerized tomography which employs multiple projections and wide angular coverage (± π). At the other extremity stand reconstruction methods employing a single projection. As the number of projections decreases, the information provided for the reconstruction becomes more incomplete. The decrease in the information content may sometimes be compensated by the use of a priori knowledge about the product and thus alleviate to some extent the ill-posedness of the problem [l–4].

The use of radioscopy (real-time radiography in which film is replaced by an electronic imaging system) is limited by the availability of appropriate image quality indicators (IQIs). Available indicators (plaque and wire type [1,21) were designed for radiographic imaging where the source, imaging system (film), and specimen are stationary and the IQI plane is oriented normal to the flux of radiation. The improvement in productivity made possible by rotating the object during inspection in real-time is inhibited by the lack of an indicator that evaluates image quality as the specimen (and the associated IQI’s) are rotated.

Quantitative nondestructive evaluation, which aims at recovering information regarding certain parameters of the materials from the nondestructive evaluation (NDE) measurements, has attracted attention of the researchers in an increasing manner over the last decade. The work presented here represents the ongoing effort in quantitative nondestructive evaluation in the form of a computer simulation of the image formation process (1,2) and represents the x-ray component of broad effort to model all of the major inspection methods (3). To date one of the major limitation of this process modeling effort is the inability to handle complex part geometries. The developed code targets simulating x-ray inspection of parts designed through computer aided design (CAD) packages. For such a simulation tool to have practical applications, the physics of initial x-ray beam generation, x-ray and target interactions, x-ray and detector interactions should be modelled with sufficient accuracy and flexibility that the effects of the adjustable parameters found on the x-ray inspection systems can be simulated. While the physics in the undertaken work is modelled after well established principles, the information regarding the geometrical representation of the target object is provided by a CAD package through the developed interface.

The resolution of a film or film — screen combination is essential for characterizing the radiographic system. The conventional methods for measuring the resolution in radiography, based on the Image Quality Indicators (IQI) and Penetrameters, are not applicable for high energy radiation (in the MV range) due to the high penetration. In addition, the IQI and Penetrameters do not measure only the spatial resolution but rather an undefined combination of the spatial and thickness resolution. Another approach used for analyzing the film resolution is based on the measurement of the radiographic response to a step function input.

The technique of tomography has long been used in radiography and in nuclear medicine to sharpen images of objects on the tomographic plane and to blur images of objects on the off-planes. The method is illustrated in Figure 1. Suppose one is interested in examining the plane T in the object. The x-ray source and the film are moved parallel to each other in the opposite directions with the plane of interest as the fulcrum. This is achieved by choosing the velocity v₁ of the x-ray source and the velocity v₂ of the film such that the ratio v₁/v₂ is equal to d₁/d₂, where d_l is the source-to-plane distance, and d ₂ is the plane-to-film distance. The objects on the plane of interest are in focus, whereas the objects on the other planes are out of focus and blurred. However, the blurrings could become quite serious in some cases and interfere with the objects of interest.

In computerized tomography, the cross-sectioned image of an object can be reconstructed from a set of projection data. It provides the ability to image internal structure which can not be inspected effectively with alternate techniques. Based on the Fourier slice theorem[l], projections in a full angular range and with sufficiently fine angular spacing are required to reconstruct a unique image. In some situations, however, complete projections are not available due to physical limitations in the data acquisition process. Image quality is degraded by the absence of complete data. Because most manufactured parts were built from a designer’s blueprint or solid modeling electronic database, a great deal is known about the physical structure of the part. Incorporating a priori information extracted from the CAD model has the potential to enhance incomplete projection CT image quality. In this paper, a model-based CT reconstruction method is presented. The a priori information used to enhance incomplete projection CT image quality is extracted from a 3-D solid modeling electronic database. Engineering database matching is conducted to extract the proper 2D cross-sectioned model image corresponding to the CT projection plane. A moment-based registration method is applied to ensure proper use of a priori information for model-based CT reconstruction. Furthermore, a projection substitution scheme, including projection alignment and automatic scaling method, is developed so that the projection data in the missing angular range calculated from a model image can be automatically rescaled to match the projection data in the available angular range. Experimental results of applying the model-based CT reconstruction method to an industrial part in both the limited-angle and the penetration-limited incomplete projection situations are presented and described. It is shown that the use of a priori information from solid models is a powerful technique for enhancing the quality of incomplete data CT images.

With an understanding of the x-ray physics of a computed tomography (CT) [1–4] scanner with discrete detectors, and with knowledge of the scanner’s geometry (the spatial relationship among the x-ray source, the detectors, and the object being scanned), it is possible to predict the achievable spatial resolution in images of objects of a certain size and density. However, if the size of the x-ray focal spot must be changed or if an object larger or smaller than the one for which the scanner is optimized is to be scanned, the spatial resolution may change. To maximize spatial resolution for a range of objects and x-ray sources, a scanner can be designed with a variable geometry, so that the spatial relationship of the scanner components can be changed to best fit each application.

In recent years ultrasonic imaging procedures have been developed to quantify defects [1,2,3,4] for application in QNDE or medical imaging. The demands for these purposes are high resolution images, true recovering of the scattering geometry and fast computer processing. But most of the published algorithms require certain assumptions as: plane wave excitation, measurements in the farfield of the scatterer or, which is a very serious restriction, scalar wave propagation.

In ultrasonic nondestructive evaluation (NDE) studies, impulse response is often used to evaluate internal defects. Under the far-field Born approximation [1], the impulse response can be written as the product of the second derivative of the area function with respect to the coordinate along the line-of-sight and a scattering constant which depends on the material properties as well as scattering directions [2]. The line-of-sight is a straight line along the illumination direction for pulse-echo tests, and the area function is an artificial time domain waveform equal to the target cross-sectional area intersected by an imaginary transverse plane travelling along the line-of-sight. Hence the double integration of the impulse response yields the product of the area function and the scattering constant. This product is also known as the ramp function response or the ramp response. Dividing the ramp response by its integral results the area function per volume of the target (normalized area function) [2] thus eliminating the unknown scattering constant. Since the area function (or its normalized form) contains the geometric information about the target, it has been employed in studies of both radar [3–5] and ultrasonic signal imaging [6]. In this paper, an ultrasonic CT algorithm is develped, using the area function from the Born approximation previously suggested by Tam [7]. A similar imaging technique for radar signals can be found in an earlier work done by Das and Boerner [5].

Finite element analysis methods have been successfully applied to the study of ultrasonic wave propagation in elastic solids [1–4]. As a natural part of such numerical solutions. displacements are predicted for every node of the spatial discretization describing the solids geometry and at every instant of time in the temporal discretization used to define the pulse propagation through the material. All of the data constitute a solution to the forward problem and can be used to visualize wavefront propagation and interactions with defects, thus predicting displacement signals at any point in or on the solid.

Electric Current Computed Tomography (ECCT) is a technique for producing images of the electrical resistivity profile within a body from measurements made on the body’s exterior. To make these measurements, an array of electrodes is attached to the surface of the body. Sets of current patterns are applied through these electrodes and the voltages needed to maintain these specified currents are measured and recorded. These applied currents and measured voltages are then used in a reconstruction algorithm to produce images that represent approximations to the electrical resistivity distribution in the interior of the body.

The generation and detection of ultrasound with laser beams has become a viable technique in nondestructive testing of materials [1,2]. The main advantage of the technique is its intrinsic non-contact nature. Its main limitation seems to be its fairly low efficiency as compared with that of other standard NDE techniques. An interesting recent development [3–5] consists in using optical fibers to guide the laser light and illuminate the sample under investigation in virtually any desired source configuration. Another inherent advantage of the use of optical fibers is that the optical bench is completely decoupled from the sample under investigation, thus rendering the technique practical for in-situ measurements. The objective of the present study is (1) to present some preliminary experimental results complementary of those of Vogel [4] on the generation of ultrasound with an array of optical fibers; (2) to discuss the possibility of generating directional surface waves in a very narrow frequency band, thus increasing the signal-to-noise ratio; and (3), to discuss the feasibility of the directional detection of ultrasound by using an array of optical fibers as a receiver, also with the goal of increasing the signal-to-noise ratio.

Thermal imaging for the nondestructive evaluation (NDE) of materials appears to be of ever increasing importance for industrial applications. The development of new materials. both metallic and ceramic. as thermal and oxide barrier coatings present new challenges to inspection techniques. Thermal imaging methods seem ideally suited for such applications. being particularly sensitive to surface and near surface material thermal inhomogeneities that may be defect-related. However, these same sophisticated materials can pose rather sever requirements upon the efficacy of any particular type of thermal imaging. Typical problems encountered include rough. optically scattering surfaces. surfaces ranging from highly reflective to absorptive, complex surface geometry and microscopic to very macroscopic (practical components) imaging requirements.

The use of non-contact ultrasonic techniques for the inspection of wings, tail sections and fuselages of aircraft in the field environment is an attractive alternative to current contact or squirter approaches. This paper reports on the use of laser generation and detection of ultrasound for flaw detection in Gr/Epoxy composite panels. Laser-based ultrasonics is a well documented technique which has been demonstrated by many researchers [1–8] and is being applied in several industrial areas [9–11].

Laser based methods for generation and detection of ultrasound are well established laboratory tools[1]. Since only beams of light interact with the surface of an object, laser ultrasonic methods are potentially non-contacting and remote and may be used in applications involving hazardous environments or unusual component geometries. However, for use in the field as a nondestructive testing tool, or in the factory as a sensor for process control, laser ultrasonic methods suffer by comparison with more conventional contact transducer techniques with regard to their generation efficiency and sensitivity. In an effort to improve the overall sensitivity of laser ultrasonic systems, schemes for temporally and spatially modulating the laser generation source have been investigated.

Lasers offer a non-contact method for generating ultrasound. The main advantages are that specimen can be scanned more easily and the complications of a coupling layer or liquid are eliminated. Also, more accurate velocity measurements can be obtained using lasers and for holographic generation, higher frequency coherent waves can be obtained. Lasers have been used to generate ultrasonic waves in many configurations, including the generation of bulk longitudinal and shear waves, Rayleigh waves along solid surfaces, and Lamb modes in solid layers. General reviews of laser generation techniques can be found in [1] and [2].

The generation of acoustic pulses (in solids) by laser pulses has received considerable attention recently (an extensive review has been given by Hutchins[l]). Current applications are to nondestructive evaluation and materials characterization, where it is convenient to have a highly reproducible source requiring no contact with the sample [2–5]. The need to make these applications quantitative requires a theoretical model which:1) is based on fundamental principles; 2) allows the use of realistic sample and source properties; and 3) is readily usable by the research community without a major computational development effort. Doyle[6] and Schliechert et al.[7] have described approaches which meet the first two criteria, but which are very computation-intensive. We will describe and illustrate a new formulation[8] which meets all three criteria. Numerical calculations will be presented to illustrate the efficacy of this approach, with emphasis on the effects of finite source dimensions and sample surface modification. Comparison with previous point-source results will indicate when the latter may he used. Finally, we show that the small initial displacement “spike” observed in experiments with metal samples, is due to “mode conversion”(thermal-to-longitudinal) at the boundary, rather than to the finite size of the thermal source resulting from thermal diffusion. For the present we limit the discussion to the thermoelastic regime.

As an extension of the work of Kuo et al[1], we have developed a “Flying-Spot” lasersource/IR-detector camera in which the focal point of an unmodulated heating laser is moved at constant velocity across the sample while the image point of an IR detector is scanned at the same speed at a point just behind the laser beam. The detector is thus looking at the “thermal wake” of the heated spot. The time delay between heating and detection is determined by the speed of the laser spot and the distance between it and the detector image. Since this distance can be made arbitrarily small (Actually it can be made negative; the detector can lead the heated spot.), the camera is capable of making thermal wave images of phenomena which occur on a very short time scale. In addition, because the heat source is a very small spot, the heat flow is fully three-dimensional. This makes the camera system sensitive to features like tightly closed vertical cracks which are invisible to imaging systems which employ full-field heating.

Thermal wave inspection techniques utilise controlled heat diffusion to probe the surface and subsurface structure of a component [1–3]. Various techniques have been developed which use localised intensity or spatially modulated laser heating for thermal wave generation [2] and a variety sensors, acoustic, optical, and thermal, for their detection [3,4]. The quantitative application of these techniques rely on the computation of the surface temperature and its relation to the internal or surface thermal structure. Analytical solutions for the surface temperature are available for the inspection of layered structures, for example, a coating on a substrate. For samples containing defects of a finite geometry (spherical, lens, cylindrical, disc void/inclusion etc) analytical solutions are difficult to obtain. In these cases numerical methods are employed to solve the heat diffusion equation for the surface temperature. In this paper we discuss the application and limitations of finite difference method for periodic and transient heat diffusion.

Different methods of NDT of carbon-epoxy laminates have been used up till now, including ultrasonics, X-ray photography and vibrothermography. Thermal methods are now appearing, because they can be contactless and single ended [1–3]. Among these methods, pulsed back emission photothermal radiometry seems attractive because it is a simple method, where elasticity is uncoupled. So the possibility of quantitatively characterizing delaminations is offered, as the model describing the phenomenon is simple. Results recently obtained at the Office National d’Etudes et de Recherches Aérospatiales (ONERA) are presented here to demonstrate that the method is well suited to the detection, in-depth localization and characterization of delaminations in carbon-epoxy composites.

Photoinductive imaging is a unique dual-mode NDE technique that combines eddy current and thermal wave methods. The photoinductive effect, upon which this method is based, is the thermally induced change in the impedance of an eddy current probe in proximity to a conducting surface that is illuminated with a modulated light source. The change in probe impedance is caused by the temperature-induced change in the conductivity of the specimen. Typical changes in probe impedance are small, on the order of a few ppm, but because they are synchronous with the light-beam modulation, lock-in techniques can be used to detect the signals, which can then be used to image surface or near-surface defects, voids, inclusions, or other thermal or structural inhomogeneities.

Photoinductive imaging is a newly devised technique for photothermal imaging based on eddy-current detection of thermal waves [1]. Thermal waves produce a localized modulation in the specimen’s electrical conductivity, which can be detected by its effect on the impedance of a nearby eddy-current coil. This photoinductive effect can be used to image surface or near-surface cracks, voids, or inclusions. The method is limited in practice to conducting specimens, but it can be used to inspect thin, nonconducting coatings on metallic substrates, as we demonstrate here. One promising feature of photoinductive imaging is its potential for high resolution, especially when compared with the resolution possible with eddy-current probes alone. The objective of the present study was to exploit the high resolution capability inherent in this technique by adapting a photoinductive sensor developed for a fiber optic probe [2] to an existing photoacoustic microscope. In this paper we explore using this technique for typical applications in nondestructive evaluation.

Scanning acoustic microscopy (SAM) employs mechanical scanning in both x and y directions. There is one great advantage in this configuration which is that imaging is done on axis, resulting in diffraction limited resolution. However a mechanical system is inherently slow and cumbersome, even though recent advances have brought the scanning time for an image at high frequencies down to the order of a second. For the inspection of inexpensive items such as integrated circuit chips, which is done at frequencies below 100 MHz, it is imperative to have a cheap and ideally real time system. The present work describes recent developments in our laboratory in this direction.

Measurement of surface displacements resulting from acoustic wave propagation in solids has been used extensively in determining elastic properties of materials [1],[2]. Additionally, examination of acoustic wave propagation in materials has been used as a nondestructive tool in testing the integrity of structures, evaluating the size and position of bulk material defects, determining material dimensions, and in general, characterizing a number of material or structural parameters [3].

Holographic interferometry (HI) is a powerful tool for mapping of surface defects. In conjunction with various stressing techniques [l–4], it offers an NDT tool for the detection of flaws within the volume of materials. The method is advantageous for integrity characterization of components to serve under mechanical stress, where the detailed shape, size and depth of the flaw within the material are of no interest. For most applications, where integrity is tested, the moment of inertia may be used as a measure for classification of the product and for the estimation of its reliability. The presence of volumetric flaws, when the sample is under loading, is expressed in the holographic interferogram. The exterma of the fringe pattern are used for determination of the displacement distribution. The second derivative of the displacement distribution is related to the bending moment and the moment of inertia. The moment of inertia may be further processed to obtain a function free from degrading influence of the specific measuring system employed [5].

Electronic Laser Shearography is a relatively new Nondestructive Evaluation (NDE) technique that is used with excitation methods to measure differential displacements and subsequent strains at the surface of a material. Laser shearography was evaluated as an NDE technique for the inspection of adhesive bonds on fixed foam insulation for Atlas-Centaur cryogenic fuel tanks. A test program was conducted which evaluated the capability of electronic laser shearography to detect disbonds under field conditions on a full scale development test article. The test program validated laser shearography as a viable technique for the inspection of adhesive bonds in the test article configuration.

Problems of adherence of thermal protective coatings to aerospace structures have become important with their use on vehicles such as the space shuttle and for jet engine turbine blades. In these structures a dielectric coating which acts as a thermal barrier, is bonded to a conductive substrate. Failure of these coatings to adhere to the substrate can result in catastrophic failure of the vehicle. Thermal diffusivity is a parameter that can be used to assess the degree of adherence of coatings to a substrate.

This paper describes a new technique to detect cracks or flaws in conducting or ferromagnetic materials using a magnetic field visualization system. In this system there are two sources for magnetic field generation, i.e. electrical current and magnetization. And the magnetic field generated by the source could give us useful information on cracks or flaws included in the material. Thus, visualization of magnetic field would enable us to identify the shape and size of cracks. We developed a preliminary system to verify the validity of the speculation and applied it to both ferromagnetic and conducting materials with flaws. The applicability of magnetic visualization has been confirmed to be an effective method in NDE and diagnosis of magnetic equipments in the present experiment. Furthermore, combination of this method with numerical prediction could demonstrate more potential capability in the field of NDE

The new technique, introduced in this paper, has originated in the course of development of an inducing mechanism for use with the ac field measurement instrument used in detection and sizing of cracks in metals[t]. It had been known for some time that the application of an inducing mechanism capable of producing the required uniform field over the surface of the metal would add to the advantages of the ac field measurement (ACFM) technique[1,2]. This led to some activities in identifying current carrying structures which can fulfil this requirement. One structure proposed consists of two parallel wires forming a U shape which can be readily integrated with the ACFM probe, Fig.l. In practice, in order to maintain the original characteristic of the induced surface field produced by this inducing arrangement, the feeding terminals and the related wiring should be located adequately far from the metal surface.

Inspection systems are used in many areas of manufacturing to detect defects in machinery or components which might result in malfunction. Such defects often can be detected definitively by methods that establish “the truth” about whether defects are present, but these definitive methods suffer their own drawbacks: they generally are more complicated, more expensive, more time consuming and, most important of all, more destructive to the manufacturing system or components being evaluated.

Nuclear magnetic resonance (NMR) imaging [1] usually exploits the dependence of the resonance frequency (generally in the rf band) on the magnetic field strength to map spatial position onto a frequency spectrum. The magnetic field strength is given a known spatial dependence and the spins are uniformly excited with an rf field. The uniform rf field is generally produced inside a cylindrical rf coil.

Quantitative nondestructive evaluation (NDE) generally has two goals; the first is to obtain quantitative information about the mechanical and chemical properties of the sample, and the second is to obtain an image of the sample to reveal defects or anomalies. Neither approach independently gives sufficient information about the acceptability of the part, but if combined, the disposition of parts and processes can be determined.

In ultrasonic nondestructive evaluation, experimental measurements of the scattered wave field resulting from sonification of a flaw are corrupted with acoustic noise. Acoustic noise results from non-flaw related scattering or reflection of the incident waves. In many probabilistic approaches to flaw detection, classification, and characterization, a stochastic model for a noise-corrupted flaw signal is utilized where acoustic noise is assumed to be an uncorrelated, Gaussian random variable with zero mean. In addition, it is assumed that an estimate of the average power spectra of the noise is available [1–3]. The goal of the work presented here was to measure and analyze acoustic noise as a random variable. Emphasis was placed on evaluating these assumptions and on estimating the average power spectra of the noise.

The use of prior information is an important component in the ultrasonic detection, classification, and characterization of flaws. In order to take full advantage of advanced digitally based approaches to flaw detection, classification, and characterization, use of prior information will be critical. Some advanced techniques involve probabilistic approaches which start with a stochastic model for a flaw signal in which the flaw’s scattering amplitude is assumed to be an uncorrelated, Gaussian random variable with zero mean and known variance [1–4]. The goal of the work presented here was to analyze scattering amplitude as a random variable with emphasis on evaluation of these assumptions.

The increased use of composite materials and adhesive bonding technology in the aerospace industry has increased the demand for techniques and instrumentation capable of detecting the characteristic flaws in these materials. An important class of flaws includes delaminations in composite materials and disbonds in adhesively bonded joints. These flaws may be detected using ultrasonic inspection techniques, however, in many instances the component to be inspected may only be accessed from one side, thereby requiring the use of pulse-echo ultrasonics. Using conventional techniques, delaminations are usually detected by selecting a known reflection, for instance the back surface echo, to produce a C-scan image. In order to adequately determine the criticality of a delamination, however, the depth of the flaw within the laminate must also be accurately determined.[1] This may be accomplished by sequentially acquiring and processing amplitude data that contain the front and back surface echoes.

Probably the most persistent general problem in acoustic emission (AE) applications is signal source identification. Past applications of pattern recognition techniques to AE have been successful, but require measurement of a parameter such as source location, load, etc., which is well-correlated with specific source types, in addition to AE signal characteristics used as the basis of the feature [1,2]. A training set comprised of a subset of the test data has also been required since good classification features and the distribution of their values are only appropriate when applied to the specific test from which they were obtained. The solution to these problems is to find robust features, or a way to predict features and feature values. Some empirical work along these lines has been done by Pacific Northwest Laboratory (PNL), operated by Battelle Memorial Institute [1,3,4]. In this paper, a transfer function between power spectral density (PSD) feature sets is established to relate the responses of two detection channels to a given source. The method may aid in identifying robust features and in predicting feature value distributions from calibration and a priori information.

The detection of a flaw embedded in large-grained material using high-resolution broadband ultrasonic pulses is hindered by high amplitude interfering echoes (speckle) due to the unresolvable grain boundaries. The application of an optimal linear processor in this case is complicated by the fact that statistical parameters of the grain noise are not known a priori.

Advances in aerospace materials and the need to apply these materials to perform near their structural limits requires new approaches to accurately determine material composition and state, and most importantly, reliably predict service life. Unfortunately most Nondestructive Evaluation (NDE) procedures are manual in nature (even though the sensors employed may be sophisticated), particularly during the data interpretation phase. For large structures like rocket motors or aircraft fuselage elements, the amount of NDE data which must be examined to assure safety is enormous. Even with tools such as x-ray tomography, an inspector must intently study the reconstruction imagery using full concentration over long periods of time. Often problems or flaws must be identified which lie at the limits of geometrical resolution, density resolution or both. Attempts to automate this process have been frustrated by both the critical nature of the task (no machine-based approach has come close to earning confidence) and the difficulty in formulating sufficiently robust detection algorithms which account for the wide variety of manufacturing tolerances, yet maintain the specificity of a human observer without a large false alarm rate.

The inverse problem in nondestructiye evaluation involves the characterization of flaw parameters given a transducer response signal. In general the governing equations and boundary conditions describing the underlying physical phenomena are complex. Consequently analytical closed form solutions can be obtained only under. strong simplifying assumptions with regard to geometry and linearity of the problem. This precludes their use as direct inverse models for solving realistic NDT problems necessitating the need for using indirect inverse models based on pattern recognition algorithms. These inverse models classify the NDT signal as belonging to one of the classes of defects stored in a data bank as shown in Fig. 1.

A resurgence of research in artificial neural networks has sparked interest in applying these networks to difficult computational tasks such as inversion. Artificial neural networks are composed of simple processing elements, richly interconnected. These networks can be trained to perform arbitrary mappings between sets of input-output pairs by adjusting the weights of interconnections. They require no a priori information or built-in rules; rather, they acquire knowledge through the presentation of examples. This characteristic allows neural networks to approximate mappings for functions which do not appear to have a clearly defined algorithm or theory. Neural network performance has proven robust when faced with incomplete, fuzzy, or novel data.

In these years, a lot of numerical analyses based on elastic wave propagation theory have been carried out in the field of non-destructive evaluation, and responses under various conditions have been accumulated as analytical solutions. By using these results of analysis as a knowledge base, accurate informations about cracks, such as types, sizes, shapes, locations and directions, is expected to be obtained.

For PWR power plants, the steam generator (SG) provides a dynamic link between the reactor and the turbine generator. A steam generator typically consists of Inconel tubes anchored at intervals with stainless steel support plates. The primary coolant from the nuclear reactor circulates through these tubes. Heat, transferred to the secondary coolant by conduction through the tube wall, generating steam which is used for running the turbine.

During the last 10 years, TASC has undertaken several digital image enhancement projects based on nondestructive evaluation (NDE) applications. Most of these projects involved analyzing NDE imagery to determine why a critical part failed to operate as expected, or trying to recover from a failure which degraded NDE imagery or made it difficult to obtain. Examples include our studies of the Inertial Upper Stage nozzle nosecap following the unsuccessful launch of a Tracking Data Relay Satellite in the summer of 1983 [1] and our development of a video data image processing system to enhance, in real time, unevenly lit, poor-contrast signals from within the contaminated Number 2 reactor vessel at Three Mile Island [2].

As many image restoration techniques are continuing to be developed, it is increasingly difficult to compare the performance of various methods. Although some image-quality measures have been presented in the literature [1], it is inappropriate to choose a particular measure as a benchmark of performance evaluation for a wide range of applications. More importantly, none of these quality measures can be used as a performance bound which usually indicates how much potential performance can be improved for a specific restoration scheme. Therefore, it is extremely important to develop theoretical performance bounds under a variety of image and noise models for general image restoration schemes.

Morphology is the study of form and structure. In image processing, morphology refers to the analysis of structure or texture within an image. The basic principle in mathematical morphology is to probe the microstructure of the image with various geometric structures to extract features of interest from the image. These geometric structures are known as structuring elements.

Image reconstruction using limited data is a necessity in a variety of applications. These applications include CT and NMR imaging in medical and industrial applications, and synthesis imaging in radio astronomy. In X-ray CT, the incompleteness of the data can be interpreted as a lack of sampling in the spatial Fourier domain. We will show that the distortion in a limited view-angle x-ray CT imaging can be formulated as a linear distortion. An estimation procedure to restore the distorted image will be presented. Finally, we will present the results of this estimation process to X-ray CT.

In CT imaging with limited view-angle data, the image of the object’s slice is usually distorted such that it is difficult to interpret the image. Usually in industrial applications. one deals with quality testing of products which are built from on an original blueprint or model. The objective of this paper is to use the knowledge about the model and try to establish whether there is any significant difference between the object under test and the model object. We will first formulate the problem as a deconvolution problem. Then we will use the CLEAN deconvolution algorithm to restore the image.

This paper presents an approach to the reconstruction and parameter estimation of flaw models in NDE radiography. The reconstruction of flaw models rather than the flaw distribution itself reduces the required number of projections as well as the complexity of the measurement system [1,2]. In this approach, crack-like flaws are modeled as piecewise linear curves, and volumetric flaws are modeled as ellipsoids. Our emphasis here is on a method for estimating the model parameters for crack-like flaws using a linear model with more than the minimal number of required projections. Extra projections reduce the effects of measurement errors and film noise. We also present the development of the volumetric flaw model and outline a method for its inversion.

The ability to quantitatively image material anomalies with ultrasonic methods is severely restricted by the axial and lateral resolution of the interrogating transducer. Axial resolution is controlled by the pulse duration of the transducer with shorter pulse durations yielding better axial resolution. Lateral resolution is controlled by the width of the interrogating beam with narrower beams providing better lateral resolution.

Ultrasonic signal analysis and image processing play important roles in the field of NDE. Many methods of ultrasonic imaging such as A-scan, B-scan and C-scan are available. Using such images, NDE tests and analysis can be performed. However, the images are limited by the resolution limits of the imaging system which are established by many factors such as the bandwidth of the transducer, frequency of interrogation, diffraction effects, etc. One of the results of such resolution limits is the blurring of the images.

Retaining rings are assembled onto each end of electric generator rotors to support the rotor end-turn windings against rotational forces. They are attached to the ends of the slotted portion of the rotor body with an interference fit. Many of the rings presently in service are susceptible to intergranular stress corrosion cracking (IGSCC) in the presence of moisture. IGSCC seems to occur first, and tends to be more severe, at stress concentrations in the rings and adjacent to geometric discontinuities in the mating rotor surface, such as, the edges of the rotor teeth. These same geometric features also tend to cause ultrasonic reflections that are difficult to discriminate from real damage. The capability of SAFT processing of TOFD data to discriminate IGSCC from geometric reflectors was investigated using several retired retaining rings assembled to mandrels simulating the generator rotor.

Estimation of crack length and depth is of considerable interest to the eddy current testing community, due to their importance in determining the relative severity of the flaw. A paper presented at the INTERMAG-MMM conference in July, 1988 proposes an automated method for estimation using eddy current image data where the material being tested is magnetic [1]. These estimates are within two to one of the correct results over a wide range of EDM slot sizes and aspect ratios, provided the slot length is at least half the mean coil radius. A second motivation for the present work is to provide a benchmark against which other techniques, or variations such as lower sampling density or different flying heights (fixed lift-off), may be measured. Since there is no obvious reason why the same methodology should not work for non-magnetic material tests, seven different sets of data on the twelve EDM slots in a calibration block were run thru a similar algorithm. A brief description of the algorithm will be given, then the data sets will be described, and the results (including some processing variations) discussed.

In any ultrasonic NDE experiment, the distributed field properties of the transducer involved represent an important aspect of the overall measurement process. The normal velocity profile across the active face of the transducer is typically used to characterize these properties. In quantitative NDE applications, a simple parametric form is usually assumed for this profile, such as a rigid piston with either the nominal or so-called active probe diameter taken as the parameter value. It has been shown in related studies that such an approach does not characterize all UT transducers accurately in all measurement situations (particularly nearfield versus farfield locations). Thus a new method for individual transducer characterization is presented herein that is based on reconstructions of the unknown probe velocity profile from measurements of the radiated field.

The piezoelectric transducer plays a paramount role in the ultrasonic non-destructive testing systems which are increasingly employed in industry. The active element in these transducers is the piezoelectric disc and its vibration characteristics govern the performance of the transducer. One dimensional theory (1D) [1], which assumes that the piezoelectric disc vibrates in the thickness direction only as shown in Fig 1, has been used for many years. However, the 1D theory cannot predict other vibration modes, which may affect the transducer behaviour in the frequency range of interest, especially for those transducers with a small diameter to thickness (D/T) ratio.

Ultrasonic transducers operating in air in the frequency range of 1–10MHz have major applications in robotics and nondestructive evaluation. For robotics applications, high-frequency air transducers make possible range measurements with a resolution in the 30–100 μm range. For nondestructive evaluation, it is possible to make transmission C-scan systems operating in air for the inspection of composites, green ceramics, and even metals at elevated temperatures. In this work, we report on the use of ligneous materials as a matching layer for PZT-based transducers.

A novel technique has been developed for generating ultrasonic beams with spatial profiles of amplitude governed by a truncated Bessel function or Gaussian function [1,2]. Bessel beams have very unique properties; in optics Bessel beams have been shown to be diffractionless (J. Durnin et al, 1987 [3,4]). In a related work, R. W. Ziolkowski et al [5] reported experimental measurements of “acoustic directed energy pulse trains” generated by synthetic line array of ultrasonic transmitters in water. However, a Bessel function ultrasonic transducer has never been reported before. Gaussian beams also have desirable properties; they are very easy to model analytically, and a circular Gaussian function ultrasonic transducer is free of near-field nulls and far-field sidelobes associated with conventional “piston source” transducers [6]. At least three designs of Gaussian transducers have been reported in the literature in the past 30 years [7–9]. We report a method in which piezoelectric ceramic elements are poled with nonuniform electric fields shaped like Bessel or Gaussian functions such that the resulting polarization (and hence the ultrasonic amplitude) follows that of the applied poling field. Like conventional piston source transducers, such Bessel or Gaussian transducers also possess the simple “parallel plate capacitor” configuration and can be packaged likewise. Beam profiles and propagation behavior of these Bessel and Gaussian transducers have been measured experimentally in an immersion tank and the results compared well with model predictions

For a majority of ultrasonic nondestructive testing applications, the ultrasonic transducer used for transmission is also used for reception. When separate transducers are used, the receiving element is usually a duplicate of the transmitting element. In this situation, the directivity pattern of the transducer(s) is the same for transmission and reception.

In the ultrasonic testing practice of today SV- and longitudinal waves are exclusively used because these wave types can be excited by piezoelectric ultrasonic transducers introduced a long time ago.

Ultrasonic testing is a promising NDE technique for ceramic structural components. The lifetime of such components is controlled by defects and flaws. The critical flaw sizes for high performance ceramics are 25 µm and to detect such small flaws, the frequency of the transducers has to be >30 MHz [1–4]. Such transducers are usually made from ZnO, LiNbO₃, LMN composites [5], and PVDF piezoelectric materials However there are no reports of aluminium nitride (AIN) films being used for such applications In this paper the piezoelectric and dielectric properties of A1N films and their application to high frequency devices are discussed and compared with the conventional materials.

Differential eddy-current probes are attractive because of their insensitivity to lift-off effects. By using two similar coils wound in opposition we have a sensor that detects variations in the magnetic field along a line joining their centers. The impedance plane response of a differential probe to a flaw is rather more complicated than the signal from a single winding probe, but this is a price one must be prepared to pay for nullifying the lift-off signal.

The accuracy of an eddy current inspection depends in large part on the performance of the eddy current probe. Consistent performance requires identification of the eddy current probe parameters which characterize performance. These parameters could then serve as a basis for probe procurement specification. Their measurement would also provide a basis for the evaluation of probes which are currently used at inspection facilities and which may have deteriorated[1].

Eddy-current imaging has been described in detail in previous publications [1,2,3]. As with other imaging systems, the image of an object represents blurring of the structures of the object by the system point spread function (PSF). Differing from other imaging systems, the PSF is very large and causes great spatial blurring of the object. This is because the eddy-current probe is a coil; its active area is much greater than the size of a beam of light, sound, or x-rays.

In nondestructive eddy current testing (ET), wire coils are excited to induce electric currents in conducting test specimens. The distribution of these eddy currents is altered by the presence of flaws in the material or by changes in material properties. The distribution changes are then sensed by one or more detector coils.

Nuclear magnetic resonance imaging (NMRI) holds the potential for the non-destructive evaluation of ceramics and for the improvement of ceramic processing in general. It can provide valuable diagnostic information about the spatial variations of binders, plasticizers, sintering aids, deflocculants, and other organics in injection-molded and slip-cast green ceramics. Poor distribution of these organics, after subsequent processing steps such as sintering, hot isostatic pressing, and machining, can lead to final parts that are defective and/or with poor mechanical properties.

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.

The push for higher reliability of structures requires that components be adequately inspected for critical flaws. In this computer age, however, it is becoming ever easier to design and develop high performance components with little regard for their inspectability. Time worn inspection “rules of thumb” often are just not good enough to assure the inspectability of a structure which embodies a combination of new geometries and new materials. What is needed is an on-line, analytical tool for the designer which provides quantitative assessment of inspectability levels and predicts the sensitivity of inspectability measures to NDE (nondestructive evaluation) system and component design parameters.

The objective of this work was to demonstrate the application of eddy current modeling to the determination of the probability of crack detection. The method of calculation, derived from previously reported work on the boundary element method (BEM) [1], used concepts discussed in other works on probability of detection (POD) calculations [2,3]. In contrast to the earlier POD investigations, which were concerned with crack-like flaws in flat plates with a simple circular coil as the probe, the present modeling deals with a realistic part geometry and a split-D probe configuration with ferrite cores and shield. Figures 1 and 2 show the part and probe geometries, respectively; the specifics of the inspection problem are described in the first section of this paper.

Among current NDE investigations, one of the important topics is the development of so-called probability-of-detection (POD) models. This activity is important because, given a POD model, one can examine inspection systems quantitatively in terms of flaw detectability. In the area of the eddy-current (EC) testing, there are a few applicable POD models in the literature [1,2]. In this paper, we will report on a generalization of the model constructed by one of the present authors [2]. After the generalization is done, the model becomes applicable to a wider variety of flaws than before.

The purpose of ultrasonic inservice inspection (UT/ISI) of nuclear reactor piping and pressure vessels is the reliable detection and sizing of material defects. Before defects can be sized, they must first be detected. This is typically done by analyzing ultrasonic echo waveforms with an amplitude greater than a certain percentage of that of a calibration reflector such as a 10% notch [1]. Studies performed at Pacific Northwest Laboratory (PNL) [2] and elsewhere [3–5] have shown that changing the components of an ultrasonic inspection system can greatly affect echo amplitude from a defect even when conventional calibration procedures are used, thus reducing the reliability of defect detection. To address this problem, ASME code [6] has provided tolerance levels for equipment parameters (e.g., center frequency and bandwidth) when inspection components are changed. However, some of the code requirements are based on engineering judgement and lack a strong analytical foundation. In this paper, the results of sensitivity studies performed to determine the effects of equipment parameter changes to provide an analytical basis for ASME code are presented.

The aerospace industry is increasing its use of composite materials because of their high: strength and stiffness to weight ratios. These attributes not only provide a direct incentive but have a “multiplier ” effect that operates to reduce fuel consumption and engine weight. In addition these materials possess other desirable properties such as: low thermal expansion, resistance to fatigue and corrosion. In the next generation of aircraft advanced composite materials could constitute a substantial portion of an airframe structure.

The value of having a sensor capable of monitoring the progress of carbon-carbon fabrication has been previously discussed and continues to be an attractive objective [1, 2]. Acoustic emission, when correlated with gas evolution and temperature profile, has been shown to give a strong indication of the internal stresses produced during pyrolysis and the path taken to achieve stress relief under varying process conditions. A challenging aspect of the process is the high temperature at which in situ sensors must function. Distributed physical proximity to the part under fabrication is critical to insure that the data reflects the material condition in real-time.

The aerospace industry is increasing its use of composite materials because of their: high strength and stiffness to weight ratio, low thermal expansion and resistance to fatigue and corrosion. Furthermore, their elastic and thermal properties can be tailored to suit anticipated service loads. Unfortunately, the very nature of these fibre reinforced polymers makes them prone to several types of damage. Among these damage modes, interlamina disbonding, or delamination, has been found to be the most serious. This form of damage can be induced by relatively low energy impacts such as a carelessly dropped tool, runway stones, hail and once started the region of damage can grow with the load cycling incurred in normal operation.

Smart Structure Technology involving structurally integrated fiber optic reticulate sensor (SIFORS) systems could make obsolete the catastropic failures that have plagued aircraft, trains, cars......to date, [1]. The introduction of structurally integrated fiber optic damage assessment systems would permit structural integrity of a component to be monitored throughout its life. During manufacture and installation these built-in sensors would check for flaws or mishandling and therefore provide quality control. Internal damage generated by: impacts, manufacturing flaws, excessive loading or fatigue could be detected and assessed and growth of these damage zones also monitored.

Much effort has been invested in developing control methodologies that modify the joint torque profiles in a lightweight, high speed robot manipulator in order to suppress vibration in the flexible links and improve end-point positional accuracy [1-7]. Similar concerns arise regarding the interaction between structures and control methodologies for large space structures [8]. These techniques rely on a model of the flexural behavior of the link(s). Some of them operate in real-time [1,2], while others are computed prior to motion and may depend on inverse dynamics [3–6]. The principal drawback to all of these is that while the vibration modes are properties of the flexible links, the attempted solutions rely on actuation at the joint motors. This condition of non-collocation of the vibrational coordinates and the actuators’ degrees-of-freedom has hampered the satisfactory identification of a real-time controller. Furthermore, techniques for sensing have also relied on location of sensors remote from the actual vibrational coordinates [1–6,8].

New materials and structures for advanced aerospace, marine and transportation applications demand the development of sensing and control systems which are capable of optimizing structural properties in response to particular external disturbances. Optical fiber sensors embedded in such structures may be used as life cycle sensors to monitor the way in which the composites and metal structures are fabricated, the in-service lifetime performance conditions of the material, and the onset of material degradation due to a variety of causes including fatigue and impact damage.

The mechanical properties of adhesive joints depend on: 1) the bulk (cohesive) properties of the adhesive such as type of adhesive, degree of cure, porosity, et cetera and 2) the interphasial properties of the bond between the adhesive and the adherends. While several techniques have been developed for nondestructive evaluation of cohesive properties of the adhesive, the assessment of interphase properties is more complicated. It has been previously proposed [1] that an ultrasonic wave that produces shear stresses on the interphase is sensitive to its properties. This may be achieved by utilization of interface waves [1,2] or guided waves in the bonded plates [3,4,5]. Another possibility is the use of obliquely incident ultrasonic waves for interphase evaluation, analyzing signals in time or frequency domains [6,7,8].

Using reflection coefficients to obtain bond strengths and other bondline characteristics has been proposed by previous researchers(1,2). For configurations where the bondline of interest is well separated from the specimen surface and adjacent boundaries, measuring the reflection coefficient using broadband, pulse-echo, ultrasound can be done by processing the bondline echo taken directly from the A-scan. For configurations where the bondline is close to a parallel surface however, reverberations in the layer between the bondline and surface will cause successive bondline echoes to overlap in the A-scan, so that individual echoes can not be processed to determine the reflection coefficient directly. This paper presents a technique for processing the A-scan to obtain the desired reflection coefficient for the case when the bondline is near a surface.

There are two types of guided modes we can speak of in connection with adhesive bonds. First, there are the guided modes of the adhesive joint as a sandwich-like, multi-layered structure which are basically Lamb-type plate modes, and second, there are the guided modes of the adhesive layer which are interface modes between two apparently semi-infinite adherend half-spaces (see Fig. 1). Guided modes of the first type have been used for ultrasonic inspection of adhesive bonds for almost fifteen years [1–5], but it became more and more clear that the sensitivity of this technique left much to be desired. It was recently established by the authors that guided modes of the second type offer superior sensitivity to both cohesive and adhesive properties of the adhesive bond [6]. This is not surprising at all since, although the adhesive layer is only a small percentage of the total joint thickness, all defects are expected in this crucial region or on its boundaries. Consequently, an acoustic wave which is effectively confined to this very region should be more sensitive than other modes trapped in the joint as a whole. The main purpose of this paper is to develop the analytical tools needed to study the dispersive properties of guided interface waves in adhesive layers and to compare the corresponding theoretical and experimental dispersion curves.

Adhesively bonded structures are increasingly being used for marine applications. One such application involves the use of adhesively bonded cylinders of polyethylene—rubber—steel. Steel forms the inner-most cylindrical lamina and polyethylene forms the outermost layer of this component. The adhesively sandwiched lamina, rubber, is subjected to axial shear loads—tangential to the curved surfaces. For this component to perform well under load it is necessary that the adhesive bonds at the polyethylene-rubber and steel-rubber interfaces be strong and free of any deleterious delaminations. Any surface areas which are devoid of adhesive, have trapped gas, are not chemically bonded by the adhesive or are simply in mechanical contact, form areas of delaminations detrimental to the performance of these components.

A quantitative assessment of a structure’s material characteristics contributes to the safety, reliability, and useful lifetime of a structure. Thermographic nondestructive evaluation has advantages over other methods in that it is a noncontacting, quantitative measurement of the material integrity which can inspect large areas in a short period of time. A disbond between layers of a laminated structure will prevent heat from penetrating from the surface layer to the subsurface layers and will result in an increase in temperature over the disbond. The limits of this technique for detection of disbonds in solid rocket motors was investigated by computational simulation of the thermographic technique. This has an advantage over an experimental investigation, since many sample configurations and flaw sizes can be investigated at a fraction of the cost and time required for sample fabrication, data acquisition and analysis. This paper presents a series of simulations varying parameters that affect the thermal contrast such as heating time, disbond size, and thickness of the surface layer. Experimental results are presented for comparison.

The performance of adhesive bonds in primary structures strongly depends on the quality of adhesion. Many NDE methods are presently used to detect unbonded areas; however, these methods cannot be used to determine bond properties. In standard ultrasonic techniques, the velocity of bulk wave propagation through the specimen is measured by time-offlight. Unfortunately, the waves reflected from the bonded region cannot be easily identified or analyzed to determine the properties of the adhesive layer.

This paper describes an approach to prior knowledge analysis of component interfaces in data measured using X-ray computed tomography (CT). In this approach, geometric details, including the presence or absence of component separations, are estimated more precisely than is normally permitted by the CT reconstruction interval. In the following section, the problem of interface analysis in CT data is presented. The next section discusses prior knowledge analysis and lists the assumptions necessary to make this approach possible. The final two sections discuss limitations inherent in prior knowledge analysis, and results obtained using both simulated and measured CT data.

The use of adhesively-bonded structures is prevalent throughout the Navy since watertight rubber-to-metal bonds are required on many undersea systems including sonar transducers and electrical cables. In addition, adhesive bonds are used to transfer loads between rubber and metal adherends for limited structural applications. However, in each case the principal function of the adhesive bond is to provide watertight integrity for the bonded components in the hostile ocean environment where corrosion is of major concern.

The objective of this work was to provide a means of assessing the integrity of the bond between an elastomer and a metal when access is restricted to the metal side. Since the acoustic impedance of the metal was high, the acoustic reflectivity of the bond interface was nearly unity and varied but slightly between a good bond and a complete disbond. Consequently any acoustic inspection technique must accurately measure small changes in the acoustic signal. In addition extraneous variables such as transducer coupling and incidence angle must be either distinguished or eliminated. When an echo train from multiple backwall reflections was observed, the logarithmic decrement decreased but slightly when a disbond was encountered. Use of this signature for routine inspections would be very tedious and a more definitive indication is required.

Multilayered composite structures and devices have become more popular and are now routinely introduced in advanced systems to reduce size and weight and to improve performance. However, because of the combined complexity of the materials and designs used in these systems, it is a significant challenge to determine the structural integrity and reliability of a specific structure or device using nondestructive evaluation (NDE).

Adhesively joined structures are increasingly used in industry. Effective nondestructive test techniques are therefore necessary for quality control and in service inspection of bonding conditions. Commonly encountered bonding problems can be classified into three types: debonding, cohesive weakness and adhesive weakness. The former two types can be detected by such traditional ultrasonic techniques as pulse echo, through transmission, C-scan, resonance etc. The last type is the most difficult due to physically ‘perfect ’ contact between adhesive and adherent. Several ultrasonic techniques using longitudinal, shear, plate and interface waves etc. have been considered for finding the most sensitive wave type and corresponding experimental parameters [1–8]. High sensitivity was obtained in several cases. To understand the characteristics of wave reflection and refraction on the bond line for evaluating the bonding quality, various boundary conditions and different physical models have been created [9–18]: 1.ideal rigid boundary conditions (or welded bond), considered as perfect bonding,2.ideal smooth boundary conditions (or kissing bond), considered as a weak bond,3.weak boundary conditions, the bond between the rigid and smooth limits,4.intermediate layer between two solid media, to account for weak bonding.

The quality of diffusion bonds can, to some degree, be characterized using ultrasonic probes. Consequently, considerable effort has gone into the development of theories that predict the ultrasonic scattering from defective bonds. There are three major lines of development. First Baik and Thompson [1] and Angel and Achenbach [2] have examined the low frequency limit; they have described the elastic scattering by an “effective” spring-model in this regime. Second Sotiropolous and Achenbach [3,4] have developed a rigorous approach that is valid at all frequencies for the case of microcracks at the bondplane; the crucial theoretical tool in this case is the crack opening displacement. Their work is, however, restricted to the case of normally incident plane waves. Rose [5] presented an approximate method, the single scattering approximation, for computing the reflection coefficients at normal incidence; it is based on using the scattering amplitudes for the various defects at the bondplane.

The problem of deducing the integrity of a diffusion bond using reflected ultrasound is a difficult one, since many defect structures can be imagined which reflect sound in essentially similar fashions but have different failure consequences When an imperfect bond consists of a near-planar distribution of small defects, and the wavelength (λ) of the interrogating sound is large compared to the characteristic defect size, the quasi-static distributed-spring (DS) model applies [1]. This model can serve as a useful tool for interpreting signals reflected from imperfect bonds, and for choosing inspection parameters to optimize the inspection of a given bonded structure [2]. The DS model predicts that the low-frequency specular reflection properties of an imperfect bond are solely determined by a small number of inertia and stiffness constants which characterize the defect layer. Since many defect distributions can give rise to the same mass and stiffness constants, low-frequency specular reflection measurements can provide only incomplete knowledge of the distribution, even when the defect type is known. For example, if the bond plane contains a sparse distribution of identical flat circular cracks, such reflectivity measurements can determine only the product of the crack area fraction and the crack diameter [2,3]. Recent theoretical work employing an independent scattering (IS) model [4,5] predicts that resonance peaks in reflectivity-vs-frequency (R-vs-f) curves, which occur when A. and the average defect diameter are similar, can be used to size the defects. Resonance information could then be used to complement the low-frequency specular reflection data, thus permitting the determination of both average defect diameter and total defect area fraction. In the present work we report on several experiments carried out to examine the feasibility of this procedure. Specifically, we report on measurements of R-vs-f for longitudinal sound waves at normal incidence carried out in three model systems containing near-planar distributions of defects: cylindrical inclusions in water; cylindrical voids in iron; and spherical inclusions in plastic. The measurements are compared with the predictions of the DS and IS models. It is found that the IS model accurately predicts the frequency of the first peak in the R-vs-f curve, which is directly releated to the size of the defects.

During the last several years we have been investigating ultrasonic techniques for evaluating the quality of solid state weld interfaces [1,2]. Promising results have been obtained on a variety of different solid state welds by extracting features from the ultrasonic waveforms and applying pattern recognition algorithms to separate acceptable from unacceptable welds. In general, the primary difficulty in evaluating solid state interfaces is separating the influence of microstructural variations (volumetric) from the effects of interface defects (planar). To better understand the influence of microstructure on our assessment of solid state welds, we have ultrasonically and destructively analyzed steel-to-aluminum friction welds of varying weld quality and microstructure. A matrix of samples was prepared to produce microstructural variations in the aluminum. Since the steel’s microstructure was unaffected by our friction weld process, acoustic energy sent from the steel side was primarily influenced by the bondline. Thus, we could monitor the influence of the microstructure and bond quality from the aluminum side and the bondline alone from the steel side. First, ultrasonic data from the steel side of our friction welds were processed with feature extraction and pattern recognition techniques as in our previous studies to determine solid state bond quality. Then data from the aluminum side were processed the same way and the classification results were compared to the results obtained from the steel side. The discrepancies in the classification results were caused the microstructure variation in the aluminum.

In the joining of metals there is a growing use of the family of advanced methods for solid state bonding, which includes friction welding and diffusion bonding. With these joining techniques a new range of quality and inspection problems are encountered. These problems, in particular for diffusion bonds, have become well known and there are the requirements for inspection techniques which can be used to give data to correlate with the bond’s mechanical strength. Various studies [1,2,3] have considered the destructive examination of bonds and categorised these in terms of characteristics seen in an examination of micrographic sections. A range of ultrasonic studies have also been undertaken [4,5,6], however conventional C-scan techniques have yet to be shown to provide the required reliable bond characterisation.

The need for quantitative nondestructive characterization of solid-solid bonds has grown in response to the increasing industrial demand for production. The work to be reported here is restricted to diffusion bonds in metallic systems and is devoted to a correlation of the bond strength with ultrasonic results. Bond strength is defined as the ultimate stress in a uniaxial tensile test at slow strain rate. Reductions in strength are assumed to occur due to a lack of bonding over a fraction of the surfaces due to non-optimum bonding conditions. The voids produced in the unbonded areas are considered to be crack-like, containing a vacuum or at most a low-pressure gas. Diffusion of the species from the two sides to be bonded is the only process considered, thus neglecting for the moment such effects as precipitate reactions, phase transformations and grain growth. The initial work was performed using identical materials on either side, thus considering only the ultrasonic response of the voids produced at the bonded interface. This paper reports on initial studies using dissimilar materials, necessitating inclusion of the effect of the acoustic impedance mismatch. During the work on dissimilar materials, production of a brittle layer at the bond interface was examined. This brittle layer was caused by a thin layer of carbon present at the bond interface. The challenge of detection of this brittle layer is posed for the nondestructive evaluation community.

Three beryllium cylinders containing a step weld were received for ultrasonic inspection. Radiographic inspection of the welds indicated the presence of a crack in one of the welds.

Single frequency phase analysis eddy current techniques have limited potential for inspections for surface cracking in inhomogeneous ferromagnetic welded surfaces [1). Signals from these cracks are masked in noise produced by lift-off, probe wobble and local changes of the permeability of the weld, the most troublesome noise source. Surface cracks and changes in magnetic permeability create signals with phase angles that are too close to be discriminated from each other. Another method, in addition to phase discrimination, must be used to distinguish crack signals from signals created by changes in magnetic permeability. This paper explores the use of the comparison of phase and amplitude data from two probe frequencies to distinguish cracks from changes in local magnetic permeability.

Since the 1940’s, the U.S. Navy has used radiography (RT) as the inspection method for structural welds. The major advantage of radiography compared to other inspection techniques is the availability of objective quality evidence, the radiograph, as a permanent record of the inspection. Radiography has gained precedence as the inspection method to prescribe for critical welds because this permanent record is perceived to evince all discontinuities and the disposition of discontinuities is perceived to be highly accurate. This technique and the criteria used to accept or reject discontinuities have generally proved adequate, although technical limitations have been identified [1].

The propagation of ultrasound in fiber-reinforced composites is controlled by the relative magnitudes of characteristic length variables. These length variables are the wavelength (Λ), the fiber diameter (a), the thicknesses of plies (h), and the overall thickness of the component (H). It may generally be assumed that Λ is much larger than the fiber diameter (a ~ 8 µm). On the other hand wavelengths of the order of thicknesses of plies (h ~ 100 µm), but smaller than the overall thickness of the component may well occur. In that range of wavelengths the propagation of ultrasonic waves gives rise to interesting multiple reflection phenomena which are the topic of this paper.

Thick composites are in use in critical applications and are proposed for still others. It is important to measure the elastic moduli of thick composites for two reasons: (1) for design data on stiffness, and (2) for prediction of feasible wave paths for ultrasonic waves for NDE. Previously only relatively thin composites of relatively simple symmetries have been measured for their elastic moduli. Now, it is becoming necessary to measure thick composites of feasible engineering lay-ups. These generally provide the complexity of orthorhombic symmetry locally in a specimen combined with curvature in the gross structure. In this work, specimens cut from thick structures will be treated in the same way as crystals to measure the elastic moduli by means of ultrasonic wave velocities. Results on one structure will be presented. Difficulties will be analyzed.

The mechanical properties of metal matrix composites (MMCs) reinforced by discontinuous silicon carbides are governed by the properties of the reinforcing phase, as well as their morphology (whisker vs. particulate), orientation and volume fraction. The morphology of SiC particles and their orientation are major variables affecting the anisotropic properties of these composites. SiC whisker (SiC_W) reinforced aluminum MMCs tend to have higher strengths and moduli in the extrusion direction due to the high degree of whisker alignment in that direction, and these values are higher than those for SiC particulate (SiC_p) reinforced composites at a given reinforcement level [1]. SiC_p reinforced MMCs are known to be more isotropic in the extrusion plane. In situations requiring multidirectional reinforcement, particulate reinforced composites can outperform whisker reinforced composites. Thus, it is important to characterize the mechanical properties of these composites in order to develop the criteria for selecting microstructural design variables.

Recently there have been intensive studies [1,2,3] of the coefficient of reflection of ultrasonic waves from fluid-loaded composite plates. Attention has been given mainly to the loci of the reflection coefficient (RC) zeroes as functions of frequency and angle of ultrasonic wave incidence. Interest in the RC zeroes (maxima of the transmission coefficient) arose originally from their association with the leaky Lamb waves in the plate which is valid only for low fluid densities [4]. Independently of the physical meaning of the RC zeroes the spectrum carries important information on the properties of the composite and may be used for reconstruction of the elastic constants from the experimental data [5,6].

One of the important requirements for advanced composite materials is satisfaction of structure stiffness to the levels preset by the design. Such a requirement underlines the importance of nondestructive evaluation as a quality control tool to establish equivalence of the elastic properties of a manufactured composite to that of the designed composite. Several recent papers have been devoted to development of such nondestructive techniques, mainly based on application of bulk ultrasonic waves [1–5] and Lamb waves [6–8].

Considerable efforts have been made in recent years to develop quantitative nondestructive evaluation (NDE) techniques for composite materials, which are being used increasingly in primary structures. The leaky Lamb wave phenomenon has shown considerable potential as an NDE method [1]. Most results reported in this area to date have been concerned with unidirectional laminates [2–4]. This is attributed to the complexity involved in theoretically predicting the response of these materials, as well as to certain difficulties associated with the experimental research. In practice, structural composites are made up of layers in various orientations. Their stacking order is dependent upon the requirements of the particular application. Therefore, the capability of analyzing the behavior of Lamb waves in multiorientation laminates is crucial for the application of LLW to composites.

Ceramic matrix composites presently being developed are potentially well suited for high temperature structural applications. The character of the fiber-matrix bond plays a significant role in determining the fracture toughness of the material and thus its performance. Increased toughness is achieved by phenomena such as interface debonding and fiber slip or pull-out, which improve material toughness by increasing the energy required to propagate a crack [1]. In a bond that is too weak, the toughening mechanisms are not significant. However, a bond that is too strong permits a crack to propagate directly through a fiber-matrix interface without being significantly affected, resulting in brittle fracture. As a result, care is required in the manufacture of these materials to achieve optimum fiber-matrix bonding [2]. The objective of this work is to develop and evaluate techniques to nondestructively characterize the fiber-matrix interface bonds. The techniques being investigated include ultrasonic velocity and attenuation, acousto-ultrasonic response, and internal dynamic mechanical damping.

Composite materials are playing an increasingly important role as structural components. Familiar motivations for their use include the ability to achieve high ratios of strength to weight, tailored elastic stiffnesses, damage tolerance, etc. A new class of these materials which has recently received considerable attention for structural applications is the heavily deformed metal-metal composites1,2. Through extensive deformation processing of two ductile components, e.g. Nb dendrites in a Cu matrix, a fine, highly aligned, reinforced structure is produced. These heavily deformed metal-metal composites have been found to exhibit large mechanical strength in combination with high thermal and electrical conductivities at elevated temperatures3,4. In attempting to understand the mechanisms leading to these superior properties, an experimental determination of the microstructure developed during the deformation processing was undertaken. One aspect is the texture, or preferred grain orientation, developed during the deformation.

Metal matrix composites hold high promises as engineering materials. In order to take full advantage of their promising properties, the complex nature of the composites must be understood. Some questions thus arising; how do different manufacturing processes influence the microstructure and how can the mechanical properties of the composites be explained and predicted from knowledge of their microstructure.

Graphite-reinforced plastic (GRP) is being used increasingly in aircraft applications. This lightweight material, however, is difficult to inspect for impact damage. Generally, the damaged region occurs on the back side of the GRP, where it is least accessible. It has been noted that the damaged regions absorb more water from a humid atmosphere than the undamaged regions. We propose that nuclear magnetic resonance (NMR) detection of the absorbed water may be a feasible method of detecting and locating impact damage in GRP structures.

There is much need for investigating the use of eddy-current inspection with advanced composite materials, including graphite-epoxy and carbon-carbon. One of the problems in evaluating the performance of eddy-current inspection is that it is often difficult to characterize the conductivity of the fiber composite material. For example, when the material is composed of conducting fibers and a nonconducting matrix, as is the case with graphite-epoxy, the overall conductivity is a complicated quantity that depends on fiber conductivity, fiber density, fiber layup order (sample geometry), and the frequency at which the eddy-currents are being excited. Dependency on frequency and layup order, in particular, give the investigator much difficulty in interpreting any eddy-current data from experiments. If these two factors cause a weak effect, there may be a suitable range of frequencies for inspecting the material via application of somewhat standard techniques.

Advanced materials for use in the aerospace industry are presently being developed and applied at an astonishing rate. This pace is driven by the need for materials that can withstand higher operating temperatures and loads, yet remain cost competitive. As the performance demands of aerospace materials push nearer and nearer the theoretical limit for strength, the allowed flaw size in traditional materials is driven smaller, making quality control more stringent. This demand for improved performance characteristics is also generating strong interest in other materials such as: exotic alloys, ceramics and reinforced composites. A need exists for characterizing these advanced materials for composition variations, flaw content, inclusions and porosity using nondestructive techniques at all stages of the materials life cycle. These stages include initial characterization of a new material, process control during the manufacturing of the material, quality control of incoming material, and the in service inspection of the final part.

Traditional pulse-echo ultrasonic NDE techniques are useful in the evaluation for structural flaws in components manufactured from homogeneous materials (i.e. most metals). However, composite materials are often neither homogeneous nor isotropic which decreases the sensitivity of traditional techniques by making the resultant data difficult to interpret. Composite materials also tend to attenuate the ultrasonic energy to a greater degree than metals decreasing the signal-to-noise ratio needed for confident flaw detection. The attenuation is attributed to the absorption of energy by the matrix and the scattering of energy due to the inherent scatterers in the system such as fibers and small voids or porosity. For very thick composites these difficulties are amplified. In addition, a component of the attenuation due to ultrasonic beam spreading increases with thickness. As the beam spreads, spatial resolution is lost as well.

In today’s application of composites, thick composites are beginning to be used for load bearing structural members. The nondestructive evaluation of composites relies heavily on ultrasound as the probing field, but the ultrasonic NDE of thick composites poses new challenges. First, to penetrate a large thickness of composite one must use ultrasound of low frequencies, but the long wavelengths at low frequencies afford only poor resolution. Secondly, with increasing thickness, the anisotropy of the material assumes a greater importance and certain simplifying assumptions acceptable in thin composites are no longer valid. Moreover, in pulsed ultrasonic measurement of thick composites, the high total attenuation associated with the large thickness and its frequency dependence often changes the spectral content of the pulses considerably [1].

The fabrication and use of composites in thick sections create special needs for flaw detection and characterization which cannot be met by conventional nondestructive evaluation (NDE). Thick composite sections are susceptible to a variety of fabrication defects and in-service damage. Typical fabrication defects include matrix cracking, porosity, delaminations, fiber misalignment and waviness, fiber fractures, and nonuniform matrix distribution (fiber volume ratio). A consequence of fabrication defects is the variation of mechanical properties through the thickness and the buildup of residual stresses. In-service defects result from environmental factors, such as thermal gradients, and mechanical loading, such as impact.

Conventional ultrasonic C-scan imaging normally employs focussed transducers excited by high-voltage impulsive signals. The reflected wave train, containing information about the internal features of the test piece, is translated, either through analog or digital means, to an intensity (or color) and plotted as a function of transducer position on the sample. While this method is certainly effective for many inspections, it is not the only way, or perhaps even the best way, to obtain this kind of information. The purpose of this paper will be to describe an alternate means to acquire ultrasonic C-scan data using a swept-frequency tone-burst imaging technique which presents several important advantages over more conventional means.

The emergence of plate waves as a functional approach to the evaluation of thin structures, especially composite plates, has been gradual and steady. This statement may be supported by the increasing attention, in the recent publications[1,2], focussed on leaky Lamb waves in composites. The generation and the characteristics of plate wave modes, although using a quasi-local technique, has already been established and the dispersion relationships are being studied in detail, especially for isotropic cases. In practice, the critical drawbacks which have been detrimental in the widespread deployment of these methods are the complicated mode behavior and a lack of complete understanding of the mechanics involved. Thus, to fully exploit the plate waves, it is imperative that the physics of wave propagation within the thin composite structures be fully explored using experimental methods and be backed by a very strong theoretical basis in order to obtain NDE guidelines for fiber reinforced composite materials.

Conventional ultrasonic C-scanning for detection and characterization of material defects has limitations because it provides only an overall planar view of the damage without accurate definition of the size and location of flaws. Hence, a three-dimensional reconstruction from the digitized ultrasonic pulse-echo waveform database was developed for full volume evaluation of damage [1].

Materials. The materials used in this research were T300/5208 unidirectional graphite/epoxy composite panels supplied by the Army Materials Technology Laboratory. The panels were in square form of 12 in. by 12. in. with nominal thicknesses of 0.042 in. (7-ply) and 0.144 in. (24-ply) respectively. All of the panels were subjected to c-scan examination for uniformity and integrity. The properties of the material are presented in Table 1. A schematic of the unidirectional composite is shown in Fig. 1.

Composite materials are gaining popularity in the aerospace industry because of their light weight and high strength, and the possibility to fabricate pieces to meet specific design needs. With the anticipated increase in usage, including the use in critical parts, it is essential to develop methods and techniques to determine the soundness of a structure fabricated from these materials.

The determination of levels of porosity is important in the engineering uses of graphite fiber/polymer matrix composites, since the interlaminar shear strength can be greatly reduced by excessive porosity [1]. Research in making nondestructive evaluations using ultrasonics as the probing energy has taken many directions. Hsu [2] has successfully modeled the frequency dependent attenuation to predict porosity levels in composites. Kline [3] has extended the work of Hashsin and Rosen [4] to determine the porosity and fiber volume fraction of composites by solving for the elastic coefficients of the composite structure. The propagation of leaky Lamb waves [5] has also been used to model porosity levels.

Porosity is a defect which can arise from moisture or gases being introduced to the resin system before cure and also during the curing process when poor bagging techniques are used. The effect of porosity results in a degradation in compressive, transverse tensile, and interlaminar shear strengths. For example, for a 1% porosity level there is approximately a 7% decrease in the interlaminar shear strength [1]. Ultrasonics is the current state of the art NDE method for the characterization of porosity in composites using the back scatter and frequency dependent attenuation measurements. In this work a thermal diffusivity technique is investigated for the characterization of porosity in graphite composite parts. The advantages of using thermal techniques is the noncontacting nature of the measurements and the ability to capture large areas using a thermal imager.

Honeycomb structures are often used because they are light in weight, yet able to bear large pressure loads. Because weight is such a major consideration in the aerospace industry, honeycomb is used in many non-load bearing structures such as control surfaces, access doors, floors, and speed brakes. As may be expected in a complicated structure, there are many possibilities for defects or damage to be induced into these parts, both during the fabrication process and while the part is in service. The presence of these defects necessitate that honeycomb structures be inspected. Film radiography is often used as the primary inspection technique for honeycomb. Alternatively, real time imaging is a filmless radiographic inspection technique which has speed and arbitrary orientation of the sample as its primary advantage. This technique has not been widely used, primarily because of poor image quality. The first point is poor spatial resolution, and the second is poor contrast sensitivity, as compared to film. When a microfocus x-ray source is used in conjunction with a real time system, the result is a marked improvement of the image resolution. The use of image processing can significantly improve the contrast sensitivity. The result is a real time system with resolution equivalent to the present film inspection techniques thus allowing for quicker and less costly inspections, so long a the sensitivity requirements are not too stringent.

Materials characterization exemplifies quantitative NDE because it demands quantitative measurements of basic physical properties and quantitative theoretical models that relate the physical properties to the service requirements. One of the most important applications of quantitative NDE is the prediction of mechanical strength of a structural material from measurements that do not mechanically deform it. This can only be accomplished through an understanding of the microstructural sources of strengthening followed by carefully designed measurements of those physical properties that reflect the key microstructures. An examination of the content of this volume shows many papers devoted to predicting hardness, strength, drawability and residual stresses from physical property measurements that can be made nondestructively under field conditions. Most of these papers conclude that more accurate predictions can be made if more than one physical property is measured because the correlations observed are limited in the range of alloys and heat treatments over which reliable results can be obtained.

The most common technique to determine the elastic constants of anisotropic materials from ultrasonic wave speed measurements requires that the material be cut into samples such that particular symmetry directions can be accessed for normal incidence wave speed measurements.[1,2] This is a destructive technique and is not feasible for thin or inhomogeneous materials. A truly nondestructive technique is needed. Recent work along these lines has addressed composite materials using ultrasonic immersion techniques.[3–7] However these methods have been limited to measurements in symmetry planes. Due to this limitation, all of the elastic constants can not be obtained by this technique alone. Two of the limiting factors are: the lack of a general analytic closed form solution for elastic wave propagation in anisotropic materials and that the energy vector does not, in general, lie in the plane formed by the incident wave and the refracted phase velocity. However, general analytic closed form solutions have been recently reported, removing the first of the limitations.[8,9] The second limitation greatly complicates the analysis of the problem.

Along with a wide application of nondestructive evaluation methods by ultrasonic techniques, Rayleigh surface waves are being studied for their applications in material characterization. Because surface waves can offer some sensitive measurement features of wave propagation, it is suggested that surface waves be conveniently used as an experimental technique for the solution of the inverse problem of determining elastic constants and/or other characteristics in materials [1–3]. The most common direct problem is to obtain wave propagation features by theoretical analysis, experimental measurement, or numerical calculation. A desired problem in material evaluation however, is to solve an inverse problem to find material characteristics from a set of field measurement data. In surface wave problems, the closed form solutions may not even exist for some direct problems. Moreover, often material constants collectively influence the ultrasonic wave propagation in anisotropic medium, and we can not decouple them and evaluate them individually by each single ultrasonic measurement. Therefore, a numerical computational procedure is proposed.

The nondestructive determination of mechanical properties of materials is desirable because of the rising cost of both materials and labor as well as safety concerns. In most alloys, changes in thermal and/or mechanical history results in microstructural changes and consequently different mechanical properties. Thermal or mechanical cycles may result from processing or occur in service. Therefore nondestructive detection of microstructure and mechanical properties would prove useful in all phases of metallurgical use. This paper reports on efforts to determine selected mechanical properties of structural materials by nondestructive means such as electrical, acoustic and magnetic techniques as well as hardness. Various thermal and mechanical conditions have been imposed on aluminum, titanium and ferrous alloys to arrive at a wide range of mechanical properties. It is concluded that the intimate knowledge of the microstructure and environmental effects are essential to select the nondestructive method that is most sensitive to property changes.

Growth of a fatigue crack is modified according to the development of contacts between the crack faces [1,2] creating shielding, thus canceling a portion of the crack driving force. These contacts develop through a number of mechanisms, including plastic deformation, sliding of the faces with respect to each other and the collection of debris such as oxide particles [3]. Compressive stresses are created on either side of the partially contacting crack faces resulting in opening loads that must be overcome in order to apply a driving force at the crack tip. In this way, the crack tip is shielded from a portion of the applied load, thus creating the need for modification [1] of the applied stress intensity range from ΔK = K_Imax − K_Imin to ΔK_eff = K_Imax − K_Ish. Determination of the contact size and density in the region of closure from ultrasonic transmission and diffraction experiments [4] has allowed estimation of the magnitude of Kish on a crack grown under constant ΔK conditions. The calculation has since [5] been extended to fatigue cracks grown with a tensile overload block. The calculation was also successful in predicting the growth rate of the crack after reinitiation had occurred. This paper reports the further extension to the effects of a variable ΔK on fatigue crack growth. In addition, this paper presents preliminary results on detection of the tightly closed crack extension present during the growth retardation period after application of a tensile overload as well as an observation of the crack surface during reinitiation of growth that presents some interesting questions.

The absorption of acoustic energy by a rubber sheet containing a single cylindrical hole was reported in reference 1. In that case, the hole was sited so that the top of the hole was located in the middle of the rubber sheet and the bottom of the hole was against an infinitely hard surface upon which the sheet was mounted. There were two resonant systems, the first being the walls of the holes vibrating radially as the thickness of the rubber varied and the second being the motion of the top of the hole normal to the hard surface, similar to a drum-head. We have extended this work to the case where the hole entends through the rubber sheet and is capped with a steel plate. The additional mass of the steel plate causes the resonant frequency of the rubber-steel-hole system to be at a much lower frequency than the rubber alone and also eliminates the drum-head resonance. We have analyzed this system using a dedicated, time dependent finite element program and have also verified the results of the finite element program by use of a small water-filled guided wave tube. The results show that the impedance is a useful parameter which is both sensitive to the geometry of the entire system and is a good descriptor of the resonant system.

Surface hardening is a usual treatment to increase the tolerance for fatigue, fretting corrosion, and wear of steel parts such as gears and axles. Typical operation is the induction hardening, in which the surface is heated using a high-frequency AC current and then quenched to form a “hard” layer of martensite on the surface. At the same time, the volume expansion associated with the martensite transformation generates the compressive residual stress, which works to restrain the crack initiation and progression.

The internal friction (Q-1), electric resistance (r), shape change (X), and temperature (T) in TiNi alloys during phase transformation have been measured simultaneously [1]. A. Ghilarducci and, M. Ahlers [2] have studied the internal friction in Cu-Zn and Cu-Zn-Al alloys and have shown that the Q-1 peaks are not due to the phase transformation but due to point defects. The electric resistance during thermoelastic martensite (TEM) phase transformation has been studied by K. Otsuka, et.al, [3] and I. Cornelis and, C. M. Wayman showed that the TEM phase transformation temperature M_s, M_f, A_s and A_f can be obtained from the electric resistance R vs. temperature T curves (R-T curve) [4]. The quantitative relation between the electric resistance change and the amount of martensite is not yet known. Now, the Q-1, R, X, frequency f and T during TEM transformation in Cu-Zn and Cu-Zn-Al alloys have been measured simultaneously as has been done in a TiNi alloy [1,5]. The amount of martensite at every temperature from M_s to M_f and A_s to A_f was calculated by Delorme’s formula of internal friction [6], so that the change of R can be calculated.

The shape memory effect (SME) is generally recognized to be caused by the reverse transformation of the deformed thermoelastic martensite (TEM); in a TiNi alloy, however, it has been reported that the SME is not related to the thermoelastic martensite but is caused by stress--induced martensite (SIM) [1]. The SME is mainly related to the R-phase transformation [2].

There are several microwave techniques and probes available for characterizing inner properties of materials [1]. Microstrip patches operating in cavity modes are well suited for determining the dielectric properties of materials. A microstrip patch can be characterized by its resonant frequency and quality factor (Q-factor) when operating in free-space. When the patch is covered by another material whose dielectric properties (real and imaginary parts) are different than that of free-space, resonant frequency and Q-factor of the patch will change. The changes in these two parameters are then related to the real and imaginary parts of the material permittivity. Subsequently, the permittivity of the material is related to its moisture content, density, temperature, grain size, etc. via available dielectric mixing models [2]. Such a device can be placed inside a material temporarily (snow pack for avalanche prediction) or permanently (concrete structures for water content and crack detection).

Formation by anodization of a thin porous layer of aluminum oxide (Al₂0₃) on an aluminum surface prior to bonding is required for adhesive joining of aluminum alloys [1,2]. The properties of this layer have major importance for joint strength [1,2].

Turbine blades in an aircraft engine are typically made of a nickel-based alloy, and covered with a protective coating to increase oxidation and hot corrosion resistance. The coating is on the order of 50–100 μm thick. There is currently no nondestructive method available to verify that the blade coating thickness is within specifications, or that the proper interfacial boundary has been set up between the coating and base alloy.

Embrittlement of Zr−2.5%Nb pressure tubes from CANDU nuclear reactors has recently become a concern in the Canadian nuclear industry. While a full understanding of the mechanisms involved has not yet been achieved, it is known that hydrogen/deuterium, liberated through oxidization of the tube’s inner surface, is absorbed into the metal where it eventually precipitates out as weak, brittle hydride platelets. Knowledge of the nature and extent of oxide formation may thus give indications about the degree of hydrogen uptake and embrittlement in the tubes. In particular, a reliable, nondestructive technique for determining the thickness and integrity of these oxide layers is needed. Theoretically, such an evaluation is possible using ultrasonic spectroscopy.

If we include consideration of wave propagation in an ideal gas, we can trace the origin of theoretical nonlinear acoustics, at least as far back as Poisson’s work in 1808 [1]. The first experiments in air were done 1.27 centuries later [2]. With liquids Fox and Wallace [3] tried to explain experimental results on sound attenuation with a correct, but somewhat inadequate nonlinear theory. Keck and Beyer [4] used the equations of hydrodynamics and showed that nonlinear considerations lead to the prediction of nonlinear distortion, something that had been observed in fluids by optical techniques [5] and showed that the nonlinear equation for wave propagation in fluids has the same form as that for an ideal gas. Different thermodynamical quantities appeared in the nonlinear equations, however. It is significant that Keck and Beyer were able to perceive the inherent similarity of the two descriptions without becoming confused by the dissimilarities of certain details of equations describing ideal gases compared with those describing liquids.

The importance of nonlinearity in the description of material behavior is gaining widespread attention. Nonlinearity plays a major, if not dominating, role in a number of material properties. For example, properties that are important in engineering design such as thermal expansion or the pressure dependence of optical refraction are inherently nonlinear [1]. New assembley techniques such as the use of ultrasonic gauges to determine the loading of critical fasteners depend upon nonlinear properties of the fasteners [2]. Areas of considerable fundamental interest in nonlinearity include lattice dynamics [3], radiation stress in solids [4,5], and nonlinear optics [6].

Most of the NDE effort using ultrasonics to assess engineering materials has been in the detection of cracks or crack-related phenomena. Other questions involving, for example, NDE measurements of temper or the state of fatigue prior to cack initiation, while very important to material scientists and design engineers, are not easily investigated using ultrasonic techniques based on linear theory. Recent work indicates, however, that the use of ultrasonics based on nonlinear concepts provides potentially useful information about material processing and certain pathological states that develop in materials as they are used.

One of the most obvious manifestations of the nonlinear stress-strain relation in elastic solids is the existence of thermal expansion due to a non-parabolic atomic potential. From the acoustic point of view, this nonlinearity immediately explains a variety of observations such as stress effects on the sound propagation velocities and acoustic harmonic generation, which is basically a distortion of the wave. Additional nonlinearities come about due to dislocation motion, or the initiation of plastic flow, and the nucleation of a new phase, such as in the case of a martensitic transformation, e.g. Other examples are nonlinear acoustic effects that are induced at free and internal surfaces caused for a variety of reasons. Detailed acoustic experiments on these phenomena have been made over the past forty years but the ideas have not been applied seriously in NDE. The present paper is a short review of work, some of which this author has been involved in. The objective is to show the utility of nonlinear acoustics for NDE of structural materials.

Ultrasonic techniques have been used successfully to measure important bond parameters and to detect various defects in adhesive joints for about twenty years. Recent reviews of nondestructive testing of adhesively bonded structures can be found in the literature [1–3]. For direct strength assessment, the reliability of these techniques leaves much to be desired. Linear acoustic parameters are only indirectly correlated to material and bond strength, therefore we must rely on dubious empirical relations between the measured parameter (e.g., velocity or attenuation) and the sought strength parameter on a case-to-case basis. On the other hand, it is well known that failure of most materials and bonds is usually preceded by some kind of nonlinear mechanical behavior, well before appreciable plastic deformation occurs, i.e. within the range of nondestructive testing. This macroscopic nonlinearity is due to a number of different causes such as weakening of covalent bonds with increased atomic spacing, reduction in the number of these bonds, etc. It seems to be reasonable to assume that nonlinear parameters measured at approximately 10–20% of the ultimate stress level are more directly correlated to mechanical strength than linear ones measured at negligibly low ultrasonic amplitudes:

A major unresolved problem of the ultrasonic testing of adhesive bonds concerns the relation between quantities measured by ultrasonic methods and the actual ultimate strength of the bond. In this paper it is postulated that adhesive failure is preceded by nonlinear behavior which can be represented by a simple relation between tractions and gross displacement increments across the adhesive layer. The effects of this nonlinear behavior on various wave phenomena, including reflection for normal incidence, interface waves, and antiplane transverse wave have been investigated. The overall objective is to obtain information when the adhesive is pulled in the nonlinear range, either by the wave system itself or by the application of a large static deformation on which the ultrasonic wave motion has been superimposed. The nonlinear parameters which can be extracted from the ultrasonic data, in principle allow an extrapolation to the point of adhesive failure. For a detailed discussion of adhesive failure and other failure mechanisms in adhesives, we refer to Ref. [1].

One effect of nonlinear elasticity on elastic wave propagation is that the velocity of the elastic wave is a function of the applied stress on the material. This effect has been used to characterize the nonlinear elastic properties of numerous materials and is also important in attempts to nondestructively characterize residual and applied stress in materials. In addition, investigations have established a possible correlation between the nonlinear elastic properties and ultimate strength in conventional materials such as aluminum [1] and carbon steel [2].

When natural materials are loaded by a stress field, dramatic changes in modulus occur as the microstructure deforms, even if there is no permanent macroscopic damage. The effect is primarily due to pervasive, thin microfractures which easily close under load. The pressure derivative of a generalized elastic modulus, M=dC/dP, for most intact solids equals ~5, but can be two orders of magnitude higher for rocks and soils [1]. Nonlinear terms in the stress strain relation that governs material response can therefore be very important. Measurements of longitudinal and shear velocity under hydrostatic and uniaxial loading for various rocks are reported to illustrate these phenomena. Observations of amplitude dependent attenuation are presented to show direct evidence of nonlinear behavior. New results presented here for partially saturated rocks show the strongest nonlinear response yet reported.

Scattering of ultrasonic energy by discrete and random discontinuities has been studied on a number of scales in geophysics, submarine warfare, mine-hunting, weld inspection, medicine, and materials characterization, to name but a few application areas. This study belongs to the latter category, materials characterization, and is specifically directed towards establishing correlations between metallurgical microstructure and the observable backscatter that is produced when high frequency ultrasonic energy interacts with crystalline grain structures in an immersion test. Wave propagation near liquid-solid interfaces has been described in considerable mathematical detail [2–4], as has propagation in crystalline solids [5–7], but the scattering of sound from grain structure into a liquid half-space is complex, and has received little theoretical treatment. Adler and Bolland [8] measured backscattering from isotropic and anisotropic materials, but with beam diameters and wavelengths far greater than common metallic grain sizes. In studies of backscattering from annealed aluminum samples Bridge and Bin Saffiey [9] presented theoretical and empirical results relating attenuation to microstructure for relatively low frequencies. They noted that leaky waves, propagating both forward and backward, were generated at all angles of incidence; this finding complements the observation by Diachok and Mayer [10] that leaky waves propagate in a conical pattern (not just forward and backwards) when a liquid-solid interface is excited by a longitudinal wave incident at the Rayleigh angle. Because backscattered energy can exist in an acoustic environment which is free from specularly reflected signals, relatively high signal-to-noise ratios can be easily achieved, even from scatterers of microscopic dimensions. A wide range of signal processing tools are available to extract from the backscattered signals features which may correlate with microstructure [11–12]. Saniie and Bilgutay [13] applied several of these tools, including homomorphic deconvolution, to backscattered signals produced in normal incidence contact testing of stainless steel samples with a variety of grain sizes, with some success. The homomorphic deconvolution technique was also used by Kechter and Achenbach [14] to extract single-scatterer characteristics from the complex sound field produced by multiple scatterers.

The use of reflection acoustic microscopy with spherical lens for quantitative nondestructive evaluation has been studied in the past both from the experimental and theoretical point of view. The basic results have shown that the output of the microscope’s transducer is sensitive to the near-surface material’s elastic properties. Based on this, a variety of applications of the acoustic microscope to material science study have been developed [1]. Measurements of surface wave velocity and elastic constants in solids [2,3,4], detection and characterization of discontinuities of the elastic constants in solids due to cracks, interfaces, etc. [5], and measurements of dispersion relation for leaky Rayleigh wave in simple and layered systems [4,6] are a few examples of problems which can be investigated by means of the acoustic microscope.

The physical and chemical processes taking place during intergranular stress corrosion cracking (IGSCC), in particular the effects of impurities on cracking mechanisms, have been the subjects of a research program sponsored by the Division of Materials Science, Office of Basic Energy Science, U. S. Department of Energy at Pacific Northwest Laboratory (PNL), operated by Battelle Memorial Institute. Acoustic emission (AE) was brought into the program because of the unique ability of AE methods to detect dynamic microscopic fracture processes. In this paper, the results of these tests are presented.

The uses of laser speckle photography are widespread in mechanics and metrology[1][2]. Most, if not all, of the applications of laser speckle involve the comparison of two correlated speckle patterns of a given field before and after some perturbation to the system has occurred. From the relative displacement of the correlated patterns either Young’s fringes or isothetic fringes may be produced when the specklegram is processed[3]. It is from these fringes that one quantitatively determines the speckle spacing from which such information as displacement and displacement gradient (strain) can be calculated. However, if the displacement, displacement gradient, surface tilt, or surface out-of-plane displacement is excessive, or if the surface morphology changes, the correlation of the speckle patterns is lost and the fringes are either distorted or simply no longer visible. In this case the speckle patterns are said to be decorrelated and accurate quantitative information about changes to the system is no longer available.

Separation of crack growth signals is of fundamental importance for detecting, locating, and determining the significance of an internal flaw. The difficulty associated with modeling acoustic emission is not only in providing an accurate representation of the source mechanism, but also in determining the effect of the specimen geometry and the sensor on the acoustic emission signal.

The stress level in a material is usually measured with an electrical resistance strain gage attached permanently to the object. Such an approach actually yields only the change in stress when a load is applied and thus gives no information on the state of residual or thermal stresses that may be present in the unloaded material. X-ray methods can be made to yield absolute stress levels but they are time consuming and only give values characteristic of the first few microns of the surface layer. Elsewhere in this volume, several articles {1} can be found that describe magnetic methods that infer stress in steel from the magnetic field dependence of certain magnetic properties. Not only are these methods applicable only to steel but they suffer from the fact that they must be calibrated for the specific alloy being used and are based on experimentally established correlations between the stress and the particular quantity being measured. Ultrasonic techniques, on the other hand, are generally applicable to any material and are much less susceptible to uncertainties arising from the empirical tests used to calibrate them. However, like the electrical resistance strain gage, they are normally used to measure only relative changes in stress because the rolling textures that are often present in commercial structural materials introduce effects that cannot be distinguished from residual or thermal stresses.

The ultrasonic NDT community has been aware for several years that a different Index Point is found for angle beam search units when comparing aluminum IIW type calibration blocks with steel blocks of identical design. Brissaud and Kleiman [1,2] and Watson [3] have discussed anisotropy texture as a possible cause of the differerence.

Considerable attention has been given recently to techniques for predicting stress and texture from the angular dependence of the velocity of guided ultrasonic modes in plates [1–4]. The analysis on which the measurements are interpreted is based on the continuum theory of elasticity. No influence of stress induced dislocation motion on the velocity is considered and plastic deformation only enters the theory through the changes in texture sensitive elastic constants, induced by such processes as grain rotation.

In the last decade, ultrasonic techniques have been shown to have considerable promise for the rapid and nondestructive determination of the texture of metal plates [1–3]. In addition, ultrasonics provides texture information on the bulk of material, instead of a local, near surface region as characterized by the X-ray diffraction technique [4].

Ultrasonic velocity and attenuation of ultrasound are usually strongly affected by grain boundaries, porosity, texture and various structural defects. This is the reason why ultrasound is often used in nondestructive testing of materials.

It has recently been shown that one can measure stress, in the presence of texture, or other metallurgical variables, by comparing the velocities of horizontally polarized (SH) ultrasonic waves propagating in orthogonal directions [1,2].

The global competition for the production of high quality oriented Fe-Si steel and other magnetic materials is increasing, and therefore, there is demand for the characterization of the materials’ properties and crystallographic texture. Because it is important to minimize down time in any manufacturing process, it is logical that these demands should be met with on-line systems using non-destructive evaluation techniques. To this end, we have been designing on-line NDE systems for use throughout the manufacturing process to quantitatively understand the affects of different processing conditions on the texture of the material. As the texture is one of the most dominant characteristics of both steels and the new hard magnetic materials, the information can be used to tune the processing conditions to attain optimum end result material properties. Ultimately, the on-line texture analyzing systems will be used in a feed back loop for the on-line control of material properties.

The influence of texture on forming properties of metals has widely been recognized [l–4]. Preferred orientation of the crystallites (grains) in polycrystalline aggregates results in anisotropy of the mechanical properties. The desired degree of, or absence of, anisotropy depends on the particular process of forming, and any subsequent manufacturing process requires certain material properties for satisfactory performance. For example, the type of texture desired in deep drawing is quite different from the one necessary for simple stamping or multiaxial bending. Thus, in-process texture monitoring is receiving increased interest, both from manufacturers and researchers [4,5].

This paper is concerned with recent investigations of the effects of both microstructure and stress on the magnetic properties of steels. In particular the paper focuses on how the changes in material condition due to differences in microstructure and stress lead to changes in magnetic NDE measurements using techniques such as Barkhausen effect sensors, magneto acoustic emission sensors, hysteresis and the magnetoelastic (magnetically induced velocity change) method.

There are a lot of experimental results concerning the effect of stress, elastic and plastic deformation and dislocation structure on the magnetic properties of ferromagnetic material. Atherton et al. measured stress induced changes in the magnetization of steel pipesl. Schroeder et al. studied domain arrangement in plastically deformed iron single crystals2. Hayashi et al. found that the application of an oscillating magnetic field during tensile testing reduced the flow stress of nickel3. Jiles and Atherton4,5D reported changes in magnetization during one stress cycle as a function of an external magnetic field. They have also reported a theory that describes ferromagnetic hysteresis and the effect of stress on magnetization. This theory is based on the Langevins theory of paramagnetism. Jiles and Atherton4 have experimentally shown that the modified Langevins equation gives the change in magnetization as a function of the applied magnetic field.

The change in the microstructure state (lattice defects, especially dislocations, precipitations and thus the stress fields) with the addition of alloying elements plays an important role for the strength and the toughness of a material. In order to determine these microstructural parameters, up to now the electron microscopy and similar methods are used. X-ray methods are normally used to determine residual stresses.

Barkhausen noise is generated by abrupt changes in the magnetization of materials under applied AC magnetizing field /1/. These changes are known to be affected by residual and/or applied stresses /2, 3/. Monitoring the Barkhausen noise under controlled conditions then provides a means of evaluating the stress state of the material /4/. The relation between stress and Barkhausen noise level is illustrated in Figure 1: the lower the compressive stress or the higher the tensile stress, the higher the Barkhausen noise level.

Our previous work has shown that magnetoacoustic emission (MAE) is mainly contributed by the motion of 90° domain walls which lags behind that of 180° domain walls in phase [1]. The amplitude of MAE burst is always higher in the embrittled samples than in unembrittled one for a sufficient level of internal magnetic field. It has been also shown that for a small internal magnetic field, the MAE activity is higher in an unembrittled sample than is in embrittled ones. This is a direct evidence of the effect of potential barriers at the grain boundaries that determine the amplitude of the MAE burst under given conditions [2]. The pulse height analysis of the MAE spectral pattern has been included in our more recent work (3]. The results have shown that the Gaussian- like distribution broadens upon the decrease in impact strength of HY-80 steel samples due to embrittlement up to a certain level.

The use of eddy currents to measure the depth of surface modified layers in ferromagnetic materials has been the subject of numerous studies which are generally based on changes in impedance associated with differences in permeability (and to a lesser extent resistivity) in the surface modified layer compared to the core material (see for example reference 1). By changing the frequency, the material can be probed at different depths. Recently a different approach has been studied by Theiner et al[2] and others[3, 4] based on using eddy currents of different frequencies to probe spatial distributions of magnetic coercivity. This is obtained by measuring eddy current response while simultaneously cycling an externally applied magnetic field to near saturation. For a uniform material the impedance of the eddy current coil reaches a maximum at a field equal to the coercivity of the material, H_c.

Pipelines are subjected to a number of different sources of stress. The principal in-service stress component is due to line pressure, with operating stresses commonly about 60% of the yield strength. Pipelines may also be subjected to considerable bending stresses, particularly when constructed on unstable terrain such as permafrost. Residual stresses may also be present, generally resulting from processing or welding, but more seriously as a consequence of mechanical damage. Anomalously high stress levels, whether residual or applied, may lead to pipeline failure; as a result serious efforts are being made to develop on-line stress detection methods. It is well established that stress is a major factor affecting magnetic properties of ferromagnetic materials, however the effects are complex and have only recently begun to be understood [1,2]. Because of the strong influence of stress on magnetic properties, magnetic NDE techniques are being considered as potential methods for the detection of stress.

Magnetic properties of ferromagnetic materials are often sensitive to residual and applied stresses principally through the effect of magnetostriction. Each magnetic domain within the material is strained along its direction of magnetization. Consequently a change in the stress level will result in a modification to the domain configuration so as to reduce the elastic and magnetoelastic energy. The gross magnetic properties such as coercivity, hysteresis, permeability and remanence are intimately related to the microscale of domain sizes and orientations, and so measurement of such properties can be used to infer the stress state [1–4]. Other magnetic techniques used for stress measurement include Barkhausen emission (BE) [5–7], magnetoacoustic emission (MAE) [8] and magnetoacoustic response [9]. A number of these magnetic techniques are currently being developed for stress measurement with a wide range of applications in the energy supply, aerospace, materials, fabrication, construction and engineering industries.

The possibility of monitoring material properties during the early stages of processing is an area of growing interest which offers potential not only for improving quality but also productivity. Of particular interest is the monitoring of mechanical properties on-line either during intermediate stages of processing or prior to shipping[1, 2].

Track buckling in continuously welded rail is a significant problem in the railroad industry [1–3]. Buckling is caused by the buildup of compressive stress (longitudinal force), which is primarily caused by an increase in rail temperature while the rail is constrained and cannot expand longitudinally. The buckling is typically manifested in the wavy lateral displacement of the track over a distance of approximately 100 feet [3]. Because buckling can cause the derailment of a passing train, extensive efforts are spent on preventive maintenance of the track. If a region of rail is known to be in a high state of compressive stress, the rail can be de-stressed by cutting it, allowing it to expand, and then welding it back together. Currently, one of the major difficulties in preventing track buckling is lack of a means for detecting the highly stressed areas.

The magneto-acoustic stress measurement technique has been evaluated by the authors as a means of revealing information on residual and applied stresses in ferromagnetic materials. Past work has included: documentation of the response of carbon steels to various test configurations [1], the effect of grain size and cooling rates in medium carbon alloy steels [2], test results obtained with a railroad rail sample [3], and investigations performed with a prototype device for examining full railroad wheels [4]. Other published papers have sought to provide detailed reviews of the test theory and model behind this technique in light of the accumulated test data [5,6].

Among the several unique phenomena observed during the irreversible domain wall motion in a ferromagnet, the Barkhausen and AE-type effects have been extensively studied due to their sensitivity to the material properties and residual stress state [1,2]. Between these two effects, the former is based on the abrupt motion of domain walls over pinning sites and the latter is based on the progressive rearrangement of domain structure following the magnetization process. A series of acoustic noise events, which occurs almost simultaneously with the magnetic Barkhausen noise, provides a separate methodology with unique capabilities and is the base of the magnetoacoustic emission (MAE) technqiue. The practical application of the ∆E-type effect to NDE residual stress measurement involves measuring ∆F(B)/F, fractional changes in frequency of phase-locked acoustic waves as a function of net magnetic induction, and the method has been called the low-field magnetoacoustic (MAC) technique by some of us [3].

During the past several years, many reports have been published concerning the sad state of deterioration of the nation’s public works, such as, bridges, roadways, water and sewer systems, ports, harbors, airports, and buildings of all types. According to the 1988 National Research Council Report on “Building for Tomorrow” estimates of public infrastructure amounted to $49 trillion in 1984, and growing rapidly. The infrastructure ages and deteriorates with time. The deterioration is mostly a result of aging of the materials, excessive use, overloading, climatic conditions, lack of sufficient maintenance, and difficulties encountered in proper inspection methods. All of these factors contribute to the obsolescence of the structural system as a whole. As a result, repair, retrofit, rehabilitation, and replacement become necessary actions to be taken to insure the safety of the public.

A large inventory of unreinforced masonry buildings exists in the United States many of which may be structurally marginal or inadequate for their present or proposed use. Recent advances in seismic hazard mapping have resulted in more stringent design requirements in many parts of the country. Changed functional use of masonry structures can also impose increased design loadings.

An ongoing research program initiated in 1983 by Carino and Sansalone has been aimed at developing the theoretical basis and practical applications for a new nondestructive technique for detecting flaws in reinforced concrete structures. The technique, known as impact-echo, is well documented [1–6] and only a brief overview of the principle of the method, signal processing techniques, and instrumentation is presented. This paper highlights the results of a recent investigation into the feasibility of using the impact-echo technique to detect voids in plates containing thin layers of materials having different acoustic impedances.

In 1965 J. W. Cooly and J. W. Tukey published their famous paper “The Calculation of Fourier Series by Computer”. This allowed model identification and measurement technology to be developed to a new stage. After inputting stimulus and response signals, the whole model and physical parameters can be obtained from computer calculations.