4. Eddy Currents, Techniques and Phenomena
We report calculations of the impedance of a long solenoid which surrounds a cylinder of conducting material containing a radial surface crack. The calculation is accomplished by two independent methods. The first method expresses the field in the interior of the "cracked" cylinder as an infinite series of cylindrical Bessel functions. The coefficients in the series are determined in principle by boundary conditions; the most significant terms are calculated by solving the finite set of equations obtained by truncation of the series. The second method, applicable to any uniform geometric cross-section, obtains the impedance from the normal derivative of the field on the boundary of the conductor. This normal derivative satisfies a (boundary) Fredholm integral equation of the first kind; a solution is obtained by discretizing and solving the resulting linear system of algebraic equations. The impedance is calculated for a wide range of values of the ratios of crack depth-to-radius and radius-to-skin depth. The results are displayed in graphical form giving the fractional charges of the real and imaginary parts of the complex impedance induced by the presence of the crack.
Kahn, A. H. and Spal, R., "AC Magnetic Fields in the Vicinity of a Crack Calculated by Analytic and Numerical Methods" (1980). Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE, July 1978–September 1979. 7.