AC Magnetic Fields in the Vicinity of a Crack Calculated by Analytic and Numerical Methods

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

Frequency Dependence of Electric Current Perturbation Probe Response

The electric current perturbation (ECP) probe1–3 is similar to a conventional eddy current probe in that a coil, typically a cylindrical winding, is used to induce current in the test piece. The ECP probe differs in the use of a separate differential sensor coil, with axis parallel to the surface of the piece, and usually located just outside the induction coil winding. We have found that this sensor orientation tends to minimize probe-to-surface coupling and therefore minimizes liftoff noise

Eddy-Current Detection Methods for Surface-Breaking Tight Cracks

The eddy-current (EC) NDE method has been in use for quite some time, and efforts have been made to make it a fully quantitative method. To evaluate impedance signals for a given EC inspection system, one has to characterize the system as a whole, including both probes and specimens. In particular, until probes are characterized, the electromagnetic fields cannot be calculated. Naturally, the amount of numerical computation becomes a serious issue during the course of development. It is necessary to choose probes carefully so as to maximize the flaw-characterization capability, while keeping numerical tasks within a reasonable size. Probes that are suitable for quantitative assessment are presumably different in nature from those with maximum detection capability. Among all kinds of existing probes, the simplest characterizable probe is the uniform-field-eddy-current (UFEC) probe. In fact, a series of studies, both theoretical and experimental, were devoted to demonstrating potential capabilities of UFEC probes [1–9]. The present theoretical work is another entry in this series. The numerical procedure developed in this work is limited to the case where cracks are tightly closed. The procedure is nevertheless capable, in principle, of dealing with an arbitrary range of frequencies

AC Magnetic Fields in the Vicinity of a Crack Calculated by Analytic and Numerical Methods

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.</p

AC Magnetic Fields in the Vicinity of a Crack Calculated by Analytic and Numerical Methods

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.</p