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We have derived analytical expressions for the quasi-static time-harmonic electromagnetic field of a circular coil used to induce eddy currents in a tube or pipe, the axis of the coil being perpendicular to that of the conductor. The results are used to determine coil impedance variations with frequency and position due to induced current. The analysis is based on a derivation of the transverse electric field of a circular current filament in free space expressed as a single layer potential. Integration of the filament field yields the coil field and its impedance in the presence of a tube. We have used the theory and a numerical approximation in fitting the frequency dependence of experimental coil impedance and thereby determined accurate estimates of the electrical conductivity of an inconel tube and the coil lift-off. Finding these parameters is a preliminary step in evaluating coil interactions with flaws. [ABSTRACT FROM AUTHOR]

In eddy current testing, a flaw in a metal is detected when it gives rise to a change in the electrical impedance of the probe that induces current in the material. Theoretical models and computer codes have been developed to predict the probe signals as an aid to improving inspections and the interpretation of measurements. Model calculations can be efficient for a restricted class of problems in which the conductor geometry is simple, such as an infinite plate or tube. The computational cost is usually low in such cases because dedicated Green's kernels are available, allowing numerical approximations of integral equations to be found using only a few unknowns to represent the field in the flaw region. In this study, the aim has been to perform eddy current calculations on corner cracks efficiently using an approximate Green's function for a conductive quarter-space, thereby extending the class of problems that benefit from the use of a dedicated kernel. The properties of the kernel mean that numerical solutions based on boundary or volume elements can be found for an edge crack by rendering as a discrete approximation only the field at the surface of the flaw or the field within it respectively. Volume element calculations have been carried out to determine the field at a corner crack and from it the probe response. Comparisons of the calculated probe impedance due to edge notches show good agreement with experimental measurements. [ABSTRACT FROM AUTHOR]

Cracks in conductors are detected through changes in the impedance of a coil that induces current in the material. In order to gain insight into the physics of the inspection, we have developed a theoretical and computational model that predicts the signals due to cracks in circular cylindrical holes using a boundary element calculation. In formulating the problem, the electromagnetic field is decomposed into transverse electric and transverse magnetic scalar modes. The effect of a planar crack in an electromagnetic field is represented by an electric current dipole layer orientated normal to the crack surface. The dipole density is determined by the integral equation whose dyadic kernel ensures that the tangential electric and magnetic fields are continuous at the surface of the hole. Instead of solving this equation, a numerical approximation is found in the form of a discrete system of linear algebraic equations formed using either boundary and volume elements depending respectively, on whether the crack opening is negligible or not. Because the kernel embodies the interface conditions at the surface of the hole, a discrete approximation of the field is only necessary in the flaw domain which means that relatively few unknowns are needed. The probe impedance variation has been computed for both ideal cracks, defined as having negligible opening but impenetrable to current, and open cracks/slots. Open crack model predictions of coil impedance variations with position relative to a semi-elliptical axial crack are in good agreement with measurements. [ABSTRACT FROM PUBLISHER]

A fundamental problem in eddy-current nondestructive evaluation is one of finding the quasi-static electromagnetic field of a cylindrical coil in the vicinity of the edge of a metal block. Although the field can be calculated numerically, an effective analytical approach can potentially provide a better understanding of the edge fields and form the basis of a procedure for solving a whole class of related edge problems including edge structures that contain corner cracks. One can represent the metal block as a conductive quarter space in an unbounded region. However, it has been found that the analysis is more straightforward if the problem domain is truncated in two dimensions. With the domain boundaries far from both the coil and the corner, the truncation has a negligible effect on the solution near the edge but the field calculation becomes much easier. A double Fourier series representation of the field is used, as in the case of a rectangular waveguide problem. The field in the conductor is then matched at the interfaces with that in air to determine the expansion coefficients that are used to represent the field in different parts of the domain. In this way we have derived expressions for the magnetic field, the induced eddy-current density and the coil impedance at arbitrary position and orientation of the coil. [ABSTRACT FROM AUTHOR]

Electromagnetic fields due to excitation coils in boreholes containing cracks have been calculated using a boundary element method formulated in terms of a scalar decomposition of the field. By using a Green's kernel that ensures continuity of the tangential electric and magnetic field at the cylindrical surface, it is only necessary to render the flaw region in a discrete form. The effect of an ideal crack, one with zero opening but acting as a perfect barrier to eddy currents, is here represented by a current dipole layer orientated normal to the crack surface. An integral equation determines the source density on the crack and a numerical solution is found using boundary elements. The coil impedance change due to the crack is then computed using an expression based on a reciprocity principle. [ABSTRACT FROM AUTHOR]