A Method for the Localization of an Elongated Subsurface Defect in a Conducting Material
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A METHOD FOR THE LOCALIZATION OF AN ELONGATED SUBSURFACE DEFECT IN A CONDUCTING MATERIAL Ya. P. Kulynych and I. I. Tryhub
UDC 537.874: 621.317
We propose a method for the localization of a long subsurface defect in a conducting material by using the magnetic field measured on the surface of the analyzed object. It is shown that, to find the point of localization of the defect, it suffices to know the value of one component of the magnetic field at the points of measurements. The numerical testing of the proposed method is performed.
In estimating the residual service life of conducting structures, it is necessary to detect defects affecting the physical characteristics of the material (strength, conductivity, etc.). Electromagnetic nondestructive testing is one of the methods used to reveal defects of this sort. In the collection of cracklike defects, we select subsurface defects whose length is much larger then the other dimensions. For conducting materials, the electromagnetic field of this defect at points of measurement can be approximately described by the field of an infinitely long thread with current located at a certain point of the defect (localization point) [3, 4]. The determination of this point is the first stage of the solution of the inverse problem of evaluation of the sizes of the crack. In the present work, we construct an algorithm of localization of elongated subsurface defects in conducting materials in the case of weak signals of the defects or signals with high levels of noise. Statement of the Problem We consider two media separated by a horizontal plane. The upper and lower media are characterized by wave numbers k1 and k 2 , respectively. The magnetic permeabilities of the media are equal. We introduce a rectangular coordinate system whose z-axis is directed into the lower medium and the x-axis lies in the plane separating the media. An infinitely long nonconducting inclusion placed in the lower medium is parallel to the y-axis. The x-component of the magnetic field of the inclusion in the plane z = 0 denoted by H xin ( x ) is regarded as known. It is necessary to determine the location of the thread with electric current for which the xcomponent of the magnetic field in the plane z = 0 is approximately equal to H xin ( x ). We are not interested in the current strength. Algorithm of Localization In the upper medium, the x-component of the magnetic field induced by the thread conducting a current Jy is given by the formula [5] H xm ( x˜ ; x˜ ′, z˜ ′) =
Jy 4π
∞
k2
∫
−∞
˜ ˜ ˜ k˜x2 − k˜12 ˜ e − ik x ( x − x ′)− z ′ ˜k 2 − i + k˜ 2 − k˜ 2 x x 1
k˜ x2 − i
dk˜x ,
(1)
Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Lviv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 5, pp. 73–76, September–October, 2004. Original article submitted June 17, 2004. 656
1068–820X/04/4005–0656
© 2005
Springer Science+Business Media, Inc.
A METHOD FOR
THE
LOCALIZATION
OF AN
ELONGATED SUBSURFACE DEFECT
IN A
CONDUCTING MATERIAL
657
where k˜1 =
k1 , k2
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