Abstract
The induction of eddy currents in a conducting, non-magnetic plate containing a through-the-thickness crack is considered in the limit where the plate thickness (
h
) is small compared with the electromagnetic skin depth (
δ
). The plate is represented by a current sheet and the crack by a distribution of generalized current vortices. The current density for these vortices must differ from that of conventional hydrodynamic vortices so as to be consistent with Faraday’s law for self-induction. The vortex density, and hence the induced current in the cracked plate, can be obtained by solving a one-dimensional singular integral equation involving the current density for the uncracked plate which is assumed to be known. The case where the induced currents are produced by a probe coil, as in eddy-current non destructive inspection, is investigated in detail and a simple expression is derived for ∆
Z
, the change in coil impedance due to the crack. The formalism is applied to the specific problem of an infinite plate containing a straight crack. Analytical results are presented for the limiting cases of long and short cracks, and a numerical method based on Gauss-Chebyshev quadrature is used for intermediate crack length. These theoretical results are compared with experimental measurements of ∆
Z
and the thin-plate theory is found to be in excellent agreement with experiment (to within 5% or better) for values of
h
/
δ
up to 0.4.
Reference9 articles.
1. Abramowitz M. & Stegun I. A. 1965 Handbook of mathematical functions. New York: Dover.
2. Auld B. A. 1981 In Eddy current characterization of materials and structures pp. 332-347. P hiladelphia: American Society for Testing and Materials.
3. Auld B. A. Muennemann F. & Riaziat M. 1984 In Research techniques in nondestructive testing (ed. R. Sharpe) vol. 7 ch. 2. London: Academic Press.
4. Repair of cracked or defective metallic aircraft components with advanced fibre composites—an overview of Australian work
5. Bilby B. A. & Eshelby J. D. 1968 In Fracture (ed. H. Liebowitz) vol. 1 ch. 2. New York: Academic Press.
Cited by
20 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献