Dependence of the magnetic field of eddy currents on the parameters of a crack in aluminum alloys
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DEPENDENCE OF THE MAGNETIC FIELD OF EDDY CURRENTS ON THE PARAMETERS OF A CRACK IN ALUMINUM ALLOYS A. Ya. Teterko and V. I. Hutnyk
UDC 620.179.14
On the basis of rigorous solutions of diffraction problems, we calculate the dependences of the magnetic field strength of eddy currents on changes in the length of an extended undersurface crack, the depth of its occurrence, and inclination to the surface as well as on a local change in the specific conductance of the base material. We determine the structural features of the field induced by a defect of the type of an arbitrarily oriented crack for the solution of defectometry problems.
For the development of eddy current methods of finding defects and evaluating their parameters, it is important to study the specific features of the structure of abnormal electromagnetic field (AF), induced by a defect, on the basis of solutions of diffraction problems [1 – 3]. In [1, 4 – 6], one can find the solutions of two problems key for eddy current flaw detection, namely, determination of the vectors of abnormal electromagnetic field for a thin longitudinal crack-like defect (Fig. 1a) [4, 6] and a circular cylindrical inclusion of radius a [1, 5] in an electricity-conductive half-space. In the general case, a defect can have an arbitrary cross-sectional shape and be represented by a superposition of elementary cylindrical inclusions (Fig. 1b) [1]. Defects are situated in an electricity-conductive nonferromagnetic medium with a wave number k2 = ωσ 2μ0 , where σ2 ≠ 0 is the specific conductance (SC) of material of the medium, μ0 = 4π ⋅ 10– 7 H / m, and ω = 2π f is the angular frequency of electromagnetic field (EMF). We consider the primary EMF as an E-polarized plane wave ( Ez ≠ 0, Ex = 0, Ey = 0 ). For a thin crack, the components of the strength of electric and magnetic fields are determined from the solution of the corresponding integral equation [6] and, for a circular cylindrical inclusion, are calculated by series, using rapidly convergent Bessel functions [5]. According to the statement of the problem [4, 6], the wave number of the medium inside the crack is k3 = 0 (the SC of the material is σ3 = 0), and the AF vectors are proportional to its opening d. A crack is characterized by the depth of its occurrence h, length L = 2l, the angle of inclination to the surface α, and curvature ε. The parameters of a circular cylindrical inclusion are the depth of its occurrence h, radius a, and the SC of its material, which can change from zero to the SC of the base material 0 ≤ σ 3 ≤ σ 2 (in particular, σ3 > σ2 ). The latter is important for studying the influence of local changes in the SC of the base material on the resultant EMF. In particular, due to the accumulation of structural changes in the material in the course of crack initiation, the SC of the material changes significantly (by tens of percent) in a local domain, and, for ferromagnetic materials, their magnetic permeability varies as well. Obviously, knowing the sizes of this domain and changes in the SC of the base mat
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