Eddy current induced in a metal by a coil carrying an alternating current may be perturbed by the presence of any macroscopic defects in the material, such as cracks, surface indentations, or inclusions. In eddy-current nondestructive evaluation, defects are commonly sensed by a change of the coil impedance resulting from perturbations in the electromagnetic field. This paper describes theoretical predictions of eddy-current probe responses for surface cracks with finite opening. The theory expresses the electromagnetic field scattered by a three-dimensional flaw as a volume integral with a dyadic kernel. Probe signals are found by first solving an integral equation for the field at the flaw. The field equation is approximated by a discrete form using the moment method and a numerical solution found using conjugate gradients. The change in probe impedance due to a flaw is calculated from the flaw field. Predictions of the theory are compared with experimental impedances due to eddy-current interaction with a rectangular surface breaking slot. Good agreement is found between predictions and the measurements.
In this report we describe an approach to the reconstruction of flaws, not merely their detection. This will give us the ability to obtain much xoore information about the nature of the flaw. By "flaw" we mean virtually any departure of the medium from a standard condition, which is known a priori, such as may be produced not only by a crack but also by conductivity in homogeneities produced by stresses, magnetite build-up, etc. Our appro~ch is very much in the spirit of contemporary work in inverse methods in electromagnetics [1][2][3] and electromagnetic-geophysical prospecting [4][5][6][7][8][9][10][11].The method of solving this problem is based on minimizing the square of the error between the actual measured data and that produced by the model-system, the model-output (this error is often called the residual). The parameters that are varied to produce the optimum model, in the least-squares sense, are, of course, the conductivities that are assigned to each cell in the mesh of Figure 1.Thus, mathematically, we wish to determine a set of unknown parameters a ., .j=l, . . . , M, where M is the number of cells in the mesh, frdm a set of data, e., i=l, • • • , N, where ei are the voltages induced into the N sen §ing coils. The e. are functionally related to the a. in a known way; that is 1 J
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