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In this article, we proposed a novel theoretical electromagnetic model of an eddy current probe used as a position sensor with respect to a tube in a fast reactor under standby conditions. In these circumstances the coil position cannot be guided by optical aids but electromagnetic sensing can be used. Initially, we derived analytical expressions for the quasi-static time-harmonic electromagnetic field of a circular current filament via the transverse magnetic potential expressed in terms of a single layer potential. This is then used to deduce the field of a circular sensor coil near a conductive tube, the axis of the coil having an arbitrary direction with respect to that of the tube. The fields for an external coil have been determined and can be used to deduce coil impedance variations with frequency, location and orientation. The model predictions can be used to guide the probe to a desire position with respect to the tube. [ABSTRACT FROM AUTHOR]

Eddy current testing to evaluate the condition of metallic parts in a sodium cooled fast reactor under standby conditions is challenging due to the presence of liquid sodium at 250 °C. The eddy current test system should be sensitive enough to capture small signal changes and hence an advanced inspection systems is needed. We have developed new hardware and improved numerical models to predict the eddy current probe signal due to cracks in metallic fast reactor parts by using volume integral equation method. The analytical expressions are derived for the quasi-static time-harmonic electromagnetic fields of a circular eddy current coil which interacts with conductive plate. Naturally, the method of moment is used to approximate the integral equation and obtain the discrete approximation of the field in the crack domain. A simple and accurate analytical method for dealing with the hyper-singularity element evaluation is also provided. An accurate controlled experiment is carried out on the ferromagnetic stainless steel plate with precision made notch to obtain reference impedance changes for comparison with the theoretical model predictions. Good agreement between predictions and experiment is obtained. [ABSTRACT FROM AUTHOR]

The feasibility of using eddy current probes for detecting flaws in fast nuclear reactor structures has been investigated with the aim of detecting defects immersed in electrically conductive coolant including under liquid sodium during standby. For the inspections to be viable, there is a need to use an encapsulated sensor system that can be move into position with the aid of visualization tools. The initial objective being to locate the surface to be investigated using, for example, a combination of electromagnetic sensors and sonar. Here we focus on one feature of the task in which eddy current probe impedance variations due to interaction with the external surface of a tube are evaluated in order to monitor the probe location and orientation during inspection. [ABSTRACT FROM AUTHOR]

We present a short theoretical overview of semi-analytical and numerical models of eddy current interactions with flaws in plates and tubes which use volume and boundary integral methods. In the approach taken, dyadic kernels dedicated to a particular geometry are derived based on a decomposition of the field into transverse electric (TE) and transverse magnetic (TM) component express using scalar potentials. Naturally, the method of moments is used to obtain the numerical approximation of the probe measurements. Here we provide a simple method for dealing with the key step of evaluating the singular element required in the numerical approximation of an integral kernel by a matrix operator. Numerical predictions for the rotary probe impedance variation due to a longitudinal notch in a tube have been computed and are compared with experiment showing good agreement. [ABSTRACT FROM AUTHOR]

Multi-frequency alternate current potential drop measurements have been made to estimate the case depth of case hardened steels using four point probes. The probes have four parallel sprung loaded pins in a line with a 1.5 mm separation between the contact points. A printed circuit board has been used to ensure the electrical connections to the pins are close to the surface of the material. This has the effect of reducing the mutual induction between driver and pick-up pins. The case depth is estimated from measurements at frequencies typically from 10 Hz to 10 kHz. The real part of the voltage phasor representing the AC potential drop is used to evaluate the case depth. The imaginary part includes the contribution due to mutual induction. To estimate the case depth of the hardened samples, the measured potential drop has been fitted to theoretical predictions. The substrate material properties of the hardened samples are extracted from multi-frequency potential drop measurements on non-harden samples. The estimated case hardened depths, deduced from potential drop measurements, are similar to those found from destructive measurements. [ABSTRACT FROM AUTHOR]

The four point direct current potential drop (DCPD) technique is used to measure electrical conductivity and crack depth. It is also used, together with Hall voltage measurements, to evaluate carrier concentration and mobility in semiconductors. Here the theory of DCPD is studied for planar structures in which edge effects may have to be taken into account and correction made to ensure accuracy. The current injected at a point on the surface of an infinite plate of finite thickness gives rise to a field that can be expressed as a summation derived using image theory. Because the images are periodic in the direction perpendicular to the plate surface, the field can also be conveniently expressed in the form of a Fourier series. The two basic formulas; image summation and Fourier series, can be modified for the case where the probe points are near the edge of a plate by further applying image theory and summing image/Fourier terms in two dimensions. Both of these approaches agree with measurement results very well. [ABSTRACT FROM AUTHOR]

A number of complex problems in eddy current nondestructive evaluation have been solved recently using the truncated region eigenfunction expansion method. The solution of a boundary value problem is commonly obtained by separation of variables. In a particular unbounded coordinate, the solution is usually expressed as an integral form such as a Fourier or Bessel integral. However, by truncating the domain of the problem, a modified solution is obtained in the form of a series expansion instead of an integral. Although one achieves a gain in computation efficiency in this way, the most significant advantage of the approach is the ability to match interface conditions across several boundaries simultaneously and thus obtain analytical solutions to complex problems. We illustrate the approach by solving the axisymmetric, time harmonic boundary value problem of a coil above a coaxial hole in a plate. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

This article describes a new probe technology with enhanced flaw detection capability, which through the use of multiple magnetic field sensing elements, can also reduce inspection time. The probe contains a linear array of high-sensitivity Hall sensors and a racetrack coil. Instead of using individual Hall sensors to form the array, sensor arrays were fabricated directly on a wafer using photolithography techniques and then mounted in their unencapsulated form. The array dimensions are chosen to achieve high spatial resolution and to limit the overall probe size. Individual active elements have a minimum separation of 400 μm and a sensitive region 50 μm across. Electronic hardware and custom software have been developed to interface the new probes to a computer. Modulation of Hall current was introduced to discriminate the Hall signal from the effects of inductive pick-up and to improve signal to noise ratio. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]