A benchmark problem for computation of ΔZ in eddy-current nondestructive evaluation (NDE)

Experimental results are presented for the change in coil impedance Z when a circular air-cored coil carrying an alternating current of fixed frequency is scanned across a rectangular slot in an aluminium alloy plate. It is proposed that these measurements be used as a benchmark test to verify theoretical calculations of probe response in eddy-current NDE.     

Eddy-current reflection probes: Theory and experiment

A general Z theory of reflection-type eddy-current probes was recently developed for new types of robotic proximity sensors. In this paper, the theory is applied to the characterization of surface-connected flaws. Flaw signals were calculated using a finite-difference implementation of the Z theory developed at Stanford University. A special air-core eddy-current reflection probe was fabricated at the National Institute of Standards and Technology (NIST) and used to obtain flaw signals for a number of rectangular-shaped electrical-discharge-machined (EDM) notches in aluminum. An automatic impedance analyzer was used to measure flaw signals as the probe was scanned over the length of the flaw. Experimental results were then compared to predictions of the theory.This paper is a contribution of the National Institute of Standards and Technology, not subject to copyright in the United States.     

Selection of ferrite powder for thermal coagulation therapy with alternating magnetic field

Selection of ferrite powder was carried out to realize a thermal coagulation technique in which tumors are locally heated by an application of alternating magnetic field from external coils. Magnesium ferrite (MgFe₂O₄) showed the largest increase in temperature (T) under an alternating magnetic field in all the ferrites examined. For all the samples, T value under alternating magnetic field was increased with an increase in frequency (200–500 kHz). The heating ability for the Mg-ferrite was ca. 1.4 W/g under alternating magnetic field of 4.0 kA/m (200 W, 370 kHz). The heating ability in alternating magnetic field was clearly depended on the magnitude of the hysteresis loss for the ferrite powder.     

Measurement of angle errors of mutual inductance coils by means of an alternating current bridge

Summary In using the described method for the measurement of angle errors of mutual inductance coils, it should be kept in mind that the error is determined by a number of factors, of which eddy currents in windings and the distributed capacitance are the most important. The presence of distributed capacitance leads to a situation where, in transition from the accordant connection of windings to connection in opposition, the leakage current changes. Therefore, the measured value of the angle error can be, generally speaking, substantially different from the value obtained if the given coil is used as an actual measure of the 90° phase shift. Consequently, the described method of measuring the angle error is suitable for those mutual inductance coils where the capacitance leakage is sufficiently small or does not change to a great extent when the coil connections are interchanged.It should be remarked that this circumstance affects the measured value of the coefficient of mutual inductance to a certain extent if the measurement results are obtained by using (6).Finally, we shall make another remark regarding the difference (R₂-R₁). In deriving (7), it was assumed that the resistance of both coils remained unchanged during the measurements. As the resistance corresponding to the loss angle is small, in order that the above condition be satisfied, it is necessary, in particular, to keep the temperature conditions of the coils under careful control by not overloading them with a current which would cause appreciable heating.The requirement for the stability of resistances can be set forth in a concrete manner by assigning a certain given error caused by their instability.Denoting the change in resistance by R, we obtain accordingly:Thus, for R=1000 cps, M=0.01 h, and for =5·10^–5, we have R=3·10^–3 ohm.     

Characterizing the performance of eddy current probes using photoinductive field-mapping

We present a new method for characterizing the performance of eddy current probes by mapping their electromagnetic fields. The technique is based on the photoinductive effect, the change in the impedance of an eddy current probe induced by laser heating of the material under the probe. The instrument we developed maps a probe's electric field distribution by scanning an infrared laser beam over a thin film of gold lying underneath the probe. Measurements of both photoinductive signals and flaw signals for a series of similar probes demonstrate that the impedance change caused by an electrical-discharge-machined (EDM) notch or a fatigue crack is proportional to the strength of the photoinductive signal. Thus, photoinductive measurements can supplant the use of artifact standards to calibrate eddy current probes. Furthermore, the shape and symmetry of the probe's field pattern can reveal defects in probe construction. By combining photoinductive measurements of a probe's field strength with a theoretical model, we are able to quantitatively predict the probe's performance under hypothetical conditions. To model commercial eddy current probes with ferrite cores, we developed a procedure to treat them as effective air-core probes. We obtained good agreement between the flaw signals calculated using this effective-coil approach and actual fatiguecrack signals measured with commercial probes. We also calculated probabilities of detection for target flaws in titanium alloys for a series of commercial probes. The results reveal how probe sensitivity can affect the reliability of an eddy current inspection.This article is dedicated to Professor Bertram A. Auld on the occasion of his 70th birthday and his retirement from Stanford University.     

Inductances,loss resistances and Q-factors of induction coils

Conclusions The suggested new method of determining L_c, R_c and Q_c is applicable to all direct and indirect methods of measuring inductances. Since the values of the latter are very close to each other and are determined in a relatively narrow frequency band by means of the same measuring device, their relative errors L₁/L₁ and L₂/L₂ are of the same order and according to (18) and (19) will not have an appreciable effect on the value of 1–k².For coils with cores whose permeability varies with frequency the ratio n=f₂/f₁ should be selected in such a way that in the measured frequency range the permeability should remain practically unchanged. For coils with cores whose permeability does not vary with frequency,n can be chosen so as to obtain values of L₁ and L₂, suitable for measuring purposes.The new method requires only one additional measurement of the coil inductance, and is simpler than any other method. Providing all the above mentioned conditions are observed and a measuring generator whose f₁/f₁ f₂/f₂ is used, this method can provide a far more precise determination of L_c, R_c and Q_c.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

The rate of transverse propagation of normal zone in aluminum-stabilized superconducting windings

Transverse propagation of the normal zone in superconducting windings of a conductor with a copper-aluminum stabilizing matrix was measured in compounded and uncompounded model coils. The special coil design enables one to simulate the one-dimensional propagation of normal zone in the winding in the radial direction.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Design and operation of a protection system for transformers with superconducting windings

Power transformers with superconducting windings need a protection system to prevent damage to the low-loss superconducting winding by an abnormally high current. The generally accepted protection technique which uses auxiliary coils has been analysed using a network representation. The current distribution between main and auxiliary coil is expressed in terms of geometrical parameters. Experimental data on current transfer and main coil recovery in a test transformer are presented and a method of obtaining a very low auxiliary coil current is suggested.     

Split-type magnetic field generator with wide homogeneous region

This paper discusses the homogeneity of a magnetic field generator for measurement of nuclear magnetic resonance (NMR). It shows that inhomogeneity is caused by an excess number of turns and a discrepancy from the design dimensions. A control circuit consisting of a pair of shim coils and a few Hall elements can improve the homogeneity. With it, a homogeneity of the magnetic field in the split coil of better than ±0.05% over 50 mm was obtained     

The Calculation of an?Air Gap Between Pancake Windings in?a?Superconducting Magnet by Using the Response Surface Method

The effects of a gap at a high temperature superconducting magnet which has an insert magnet and an outsert magnet are examined. Both magnets consist of pancake windings. The optimum gap of an insert magnet and an outsert magnet are calculated by using the response surface method. The insert magnet consists of 8 YBCO pancake windings. The number of turns of a pancake winding and the inner diameter of the insert magnet are 60 turns and 40 mm, respectively. The outsert magnet consists of 12 BSCCO-2223 pancake windings. The number of turns of a pancake winding and the inner diameter of the outsert magnet are 100 turns and 115 mm, respectively. The calculation results show the optimum gap of the insert magnet and the outsert magnet are 0 and 10.3 mm, respectively. When there is a gap of 10.3 mm in the outsert magnet the central magnetic field increased by 11.4% from 604.2 to 542.6 mT. RSM is proved to be an effective mean for finding optimum gaps in a shorter time comparing with other non-deterministic optimization technique.     

The effects of the air gap between pancake windings on the central magnetic field in a high temperature superconducting magnet

In an HTS magnet consisting of pancake windings, an air gap between the pancake windings can be used to increase the central magnetic field because the air gap increases the critical current of pancake windings. The effects of an air gap on the central magnetic field of an HTS magnet are discussed in this paper according to the various number of turns and also to the number of pancake windings. Results of calculation show the air gap could increase the central magnetic field and the field uniformity simultaneously. The optimum air gap which maximized the central magnetic field was about 4 mm at eight pancake windings and 50 turns per pancake winding. The central magnetic field increased 6.2% from 0.225 T (no air gap) to 0.239 T (4 mm air gap) at that case.     

Upgraded coil configuration for ISABELLE magnets

Achievement of the design field of 5 T in the ISABELLE dipole magnets is turning out to be more arduous than expected and several avenues of improvement are being pursued. One possibility for improving training and peak field performance is discussed in this paper. It has been recognized that the inert spacers with their adjacent active turns in the cosine magnet windings can be replaced by a double thickness braid operating at approximately half-current density in 46 of the 190 turns. Since the high-field region occurs in the low current density turns near the poles, a performance improvement can be expected. It has been verified that the proposed coil configuration satisfies the field requirements and details thereof are given. Results from an experimental magnet in which superconducting spacer turns are used to simulate half-current density windings are presented. Construction of thick braid coils is being planned and the status of these magnets is reviewed.     

Bolt-Hole Corner Crack Inspection Using the Photoinductive Imaging Method

We applied a laser-excited eddy current (EC) imaging technique, or so-called photoinductive (PI) imaging, to characterize corner cracks at the edge of a bolt hole. Crack images with excellent signal-to-noise-ratios were obtained. The PI signals revealed the geometrical shape of the electrical-discharge-machined (EDM) notches that were either triangular or rectangular. The results show that this technique is promising to characterize the length, as well as possibly the depth and shape, of corner cracks. In this paper we present measurement results of 0.25-mm, 0.50-mm, and 0.75-mm rectangular and triangular EDM notches. We also show measurement results of a very small notch (<0.25 mm) which would be difficult to detect with conventional eddy current techniques. The dependencies of PI signals on laser chopping frequencies and eddy current frequencies are also examined. To demonstrate the photoinductive imaging capabilities to image actual cracks, we display images of fatigue cracks grown in a Ti-6Al-4V hole specimen. Finally, we present comparisons of the photoinductive imaging results with usual eddy current images obtained from a 0.75-mm triangular EDM notch using a rotating bolt-hole scanner. This article intends to verify experimentally that the photoinductive imaging technique has a potential to become a useful nondestructive testing method.Deceased.     

Methodic error of conversion of analog signals into frequency-modulated pulse signals

Conclusions For an equiprobable distribution of the position of the beginning of interval T_i on the time axis, _m manifests itself as an uncorrelated random error.If the pulse duration is negligible in comparison with the time interval between adjacent pulses, the ME of the error _m is equal to zero for AFC's with uniform or nonuniform pulse sequences.The RMSD of the error _m varies with T_i, assuming a number of extremum values [_m]_max. For the same values of T_i andf, [_mn]_max exceeds [_mu]_max by a factor of not more than 2. If the maximum allowable values of the RMSD of the methodic error _m are assigned on the basis of experimental conditions, the minimum allowable measurement time of the secondary instrument which receives the AFC signal can be found by means of (7) and (11).Translated from Izmeritel'naya Tekhnika, No. 12, pp. 53–55, December, 1972.     

On the Method of Determination of Strain Energy Release Rate During Fatigue Delamination in Composite Materials

In this paper, the problem of calculation of the energy release rate for a fatigue test on composite material has been investigated. The application of the Linear Elastic Failure Mechanics (LEFM) leads to the use of varation of the energy release rate ( G). As the energy release rate is a function of the load squared, the variation of G becomes either a function of variation of the load squared ( G = f((P²))) or a function of the square of the load variation ( G = f(( P)²)).In this paper, we determine, by different fatigue tests, which of the two theoretical results is the best to describe the experiments. These fatigue tests have been made on DCB test-specimen in mode I with different R ratios (R = P_max / P_min) and different maximum loads. The material was a unidirectionnal glass-epoxy.The results show that considering G as a function of ( P)² seems more appropriated to describe a cracking test in fatigue.     

Behavior of short fatigue cracks initiated from a notch in 8090 Al-Li alloy

The rates of growth of short fatigue cracks initiated from a notch are much greater than the rates of growth of long fatigue cracks for the same values of K. A decrease in the strength of materials caused by aging affects the behavior of long cracks. The geometric form of the notch strongly affects the behavior of short cracks. The growth rate of a short crack initiated from a sharp notch decreases and attains a minimum value at a length of 0.45 mm, which is far beyond the region of its influence. However, short cracks initiated from blunt notches exhibit slower growth in the region of stress concentration than outside this region. Strain fields induced by deformation of the tip of the notch are not the only factor inhibiting the propagation of short cracks from notches. To explain the behavior of a short crack initiated at a notch, one must take into account some other factors, in particular, crack closure.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 39–44, January – February, 1995.     

Comparator attachment to spectrophotometer SF-2M for measuring color differences

Conclusions The SF-2M spectrophotometers' colorimetric attachment made by the VNIIM is a simple and convenient device for evaluating chromacity coordinates of transparent and reflecting specimens.The first selection of correcting filters provides measurements of large chromatic differences with an error of the same order as that of the objective colorimeters KNO-3.The same filters used in measuring small chromatic differences provide a measurement precision of the chromatic sensitivity threshold of x, y=0.005, and ¯y/¯y=0.5%. The measurements on the attachment are made under illumination conditions which correspond to those adopted at the VNIIM for certifying standard color specimens. Therefore, the attachment can be used for testing purposes. The attachment is also intended for carrying out further experimental investigations of the relationship of the color measurement error to the width of the tolerances for the correcting filters.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 44–47, January, 1969.     

Fatigue crack closure and crack growth behaviour in a titanium alloy with different microstructures

Fatigue crack closure and crack growth behaviour in Ti–2.5 wt % Cu alloy with two equiaxed and two lamellar microstructures have been investigated by constant-load amplitudetests. Plasticity-induced crack closure and roughness-induced crack closure have been characterized separately by experimental methods. A change in closure mechanism from plasticity-induced crack closure at high K values (region of high stress intensity ranges)to roughness-induced crack closure at low K values occurs in a solution-annealed equiaxed microstructure, while plasticity-induced crack closure is the operative closure mechanism in an over-aged equiaxed microstructure over the whole range of K and roughness-induced crack closure occurs in two lamellar microstructures. The crack closing stress intensity factor for plasticity-induced crack closure increases continuously with increasing maximum stress intensity. The crack closing stress intensity factor for roughness-induced crack closure increases with increasing maximum stress intensity at low K, and remains constant at high K. Crack closure and crack path deflection have a significant influence on the crack growth rates. © 1998 Kluwer Academic Publishers