Analysis of eddy currents in a bar containing an embedded defect

The eddy current distribution is studied in a metal bar containing an embed ded defect inserted within an encircling coil. Furthermore, the impedance c hange of the coil regarding the characteristics of the defect is determined . The defects investigated are nonmetallic inclusions and embedded cracks w hich may occur during the manufacturing processes of bars. To simulate thes e problems, a two-dimensional transverse-electric model is proposed, and th en a set of coupled surface integral equations are formulated systematicall y. Since the magnetic field is unknown along the boundary of the defect, an additional boundary condition derived from Maxwell's equations is used. Us ing the boundary element method (BEM), these integral equations are solved in terms of nodal unknowns-current density. After the current distribution is obtained, the impedance changes of the coil caused by the defects are ca lculated vs. the configuration of defect for various frequencies. If the in clusion is circular and located at the center of the bar, good agreements a re found by comparing the BEM solutions with the analytical ones. An auxili ary surface integral equation is also derived to further determine the curr ents on both sides of the crack. (C) 1999 Elsevier Science Ltd. All rights reserved.