Degree Type


Date of Award


Degree Name

Master of Science


Electrical and Computer Engineering


Transducer response in nondestructive evaluation (NDE) requires fundamental knowledge of the field interaction with the material under test. Specifically, in eddy current NDE the transducer is an inductive coil or some combination of coils with an electromagnetic induction field surrounding the coil. The coil is used predominantly for surface or near-surface inspection of electrical conductors (metals). The change of impedance of the coil at its terminals is used as the criterion for defect detection. The impedance change due to a defect depends upon the relative disruption of the steady state field configuration in a given testing situation. A spatially smaller defect relative to the coil dimensions usually causes a smaller impedance change, therefore, it is more difficult to detect. The eddy currents induced in the metal by the exciting coil decay with distance into the metal due to energy loss in the form of Ohmic heating. Consequently, a defect easily detected at the surface with a given coil becomes undetectable at some distance beneath the metal surface. The distance at which a given defect becomes "invisible" is directly related to the rate of decay of the induced currents and their spatial distribution. The classical skin depth, δδ= √2/ωμσ, is the usual measure of the decay rate of currents in metals, but it is derived assuming a source field of infinite spatial extent and no inhomogeneity. In contrast, coils are often very small relative to the metal object under test and their useful fields are confined to a finite region surrounding the coil; therefore, assuming the classical skin depth in place of the actual skin depth may lead to erroneous conclusions about a coil's ability to detect and size the defect.

This thesis compares the actual decay of induced time-harmonic, steady-state current densities in conductors to the classical skin depth for an air-core coil over a conductor of both infinite (half-space) and finite thickness and for a pair of differential coils inside a conducting tube of infinite and finite thickness. In each case the finite element method (FEM) in its axisymmetric form is used to solve for the magnetic vector potential, A, from which all relevant quantities such as coil impedance and eddy current density are computed. For the coil over a half-space, the FEM is compared to an exact integral solution to confirm the validity of the FEM, while the FEM alone is used to compute quantities for coils in a tube. Actual current densities are computed and their rate of decay versus depth in the conductor, distance from exciting coil, and variations in coil and material parameters are investigated. The normalized coil impedance is computed versus coil proximity to the conductor (liftoff) and changing dimensionless parameter RSS (RS = coil mean radius). For the coil over a half-space, experimental measurements of coil impedance were performed and compared with the computed analytical solution and the FEM. In general, the experimental measurements show the range of validity of the analytical and FEM solutions.

The experiments and computer simulations show the actual eddy current density distribution and decay is significantly different from the classical exponential decay in regions of operation where the coil is most useful for NDE but does approach the classical solution in the extreme region RS / δS>> 1. Caution should therefore be used when applying the classical skin depth approximation when RSS ~ 1. This study also shows the validity and usefulness of the axisymmetric FEM for modelling field/material interaction in spite of inherent simplifying assumptions. The analytical solution, while elegant and important in its own right, cannot model complex defects or material inhomogeneities in general, yet the FEM handles these situations with relative ease.



Digital Repository @ Iowa State University,

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Paul A. Stucky



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117 pages