Eddy-current interaction with an ideal crack. I. The forward problem

Abstract

The impedance of an eddy-current probe changes when the current it induces in an electrical conductor is perturbed by a flaw such as a crack. In predicting the probe signals, it is expedient to introduce idealizations about the nature of the flaw. Eddy-current interaction is considered with an ideal crack having a negligible opening and acting as a impenetrable barrier to electric current. The barrier gives rise to a discontinuity in the electromagnetic field that has been calculated by finding an equivalent electrical source distribution that produces the same effect. The choice of source is between a current dipole layer or a magnetic dipole layer; either will give the required jump in the electric field at the crack. Here a current dipole layer is used. The strength of the equivalent source distribution has been found by solving a boundary integral equation with a singular kernel. From the solution, the probe impedance due to the crack has been evaluated. Although analytical solutions are possible for special cases, numerical approximations are needed for cracks of arbitrary shape. Following a moment method scheme, numerical predictions have been made for both rectangular and semielliptical ideal cracks. These predictions have been compared with experiments performed on narrow slots used to simulate ideal cracks. Good agreement has been found between the calculations and the measurements.

Magnetic flux distortion in two-phase liquid metal flow: Model experiment

“…5 Using the reciprocity theorem and an expansion of magnetic vector potential, Bowler et al have estimated the perturbation in impedance due to a single small defect in a conducting medium. 6,7 This result is only valid for small skin depths and does not allow to predict the perturbation in magnetic flux due to the distribution of voids in the core of a conducting flow. For single phase conducting flow in a circular cylinder at constant or very slowly varying magnetic fields (i.e., x 100 rad s À1 ), the electrical potential is given by a Poisson equation: r 2 V ¼ r Á ðŨ ÂBÞ.…”

New Method for Estimating the Depth of Small Surface-Breaking Cracks from Photo Inductive Data

“…+ I GpndS, (3) crack_face where Eno crack is the electric field in the absence ofthe crack, Gis the (dyadic) half-space Green's function to the (vector) Helmholtz's equation, p is a concept known as the current dipole density and n is the unit vector normal to the crack. Formulas for Eno_crack and for G have been given in the literature [6][7][8]. As to p, it is usually not known beforehand, but there is a fact that is useful in determining it.…”

“…The work of Bowler [6] shows that the electric field E is given by E = Eno_cruc.l. + I GpndS, (3) crack_face where Eno crack is the electric field in the absence ofthe crack, Gis the (dyadic) half-space Green's function to the (vector) Helmholtz's equation, p is a concept known as the current dipole density and n is the unit vector normal to the crack.…”

Prediction of Eddy-Current Probe Impedance Due to Surface Cracks in Ferromagnetic Steels

“…where p('f) is a current dipole density on the surface of the crack [6]. In the thin-skin regime, the current dipole density on the crack cau be related to the TM potential as follows [5):…”