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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]