Numerical solution of an integral equation for electromagnetic field in conductive medium with crack

Abstract

Introduction. For detecting subsurface cracks in metal constructions broad application have received eddy-current methods of non-destructive testing, which based on the analysis of interaction an eddy-currents and defect induced in conductor [1]. If the crack has sufficiently small opening then it perform function of a surface barrier where the electric field actually suffers break. Therefore for research of an electromagnetic field, scattered such cracks, it is used its model as a cut on some opened surfaces. There is the primary problem to define jumps electromagnetic field vectors jumps at transition through a surface of a crack. Physically this jump can be presented some surface distribution of electric dipoles [2]. Research of the general regularities of forming of this distribution carry out on model problems when the body occupies boundless (half-boundary) domain, and the crack is described by a flat figure of canonical forms (for example, circle). Statement of the problem. Let us consider the ideal crack described by disk of single radius s (fig. 1.) in conductive half-space with flat boundary and //7 7 7 7 7 7 7 7/ / / electroconductivity a . The plain electromagnetic wave (time dependence Ho e-i") is falling on boundary of halfspace under an arbitrary angel. Magnetic conductivity of the crack and E,, medium, which surrounds it, is equal