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The paper presents an efficient numerical method to simulate eddy-current testing (ECT) of ferromagnetic steel parts. The method is based on the nonlinear integral equation for quasi-stationary electromagnetic field with gauge condition based on tree/cotree decomposition. The eddy-current density in the conductive domain and the magnetization in the ferromagnetic domain are discretized with edge elements and vectorial volume elements, respectively. A simple, but very effective magnetization model of steel in a low field is also presented. The algorithm convergence for solving the forward ECT nonlinear problem with time-periodic boundary conditions is proved.

In this paper, new progress on the ECT-based crack sizing techniques is presented. At first, a fast and accurate forward simulator, which is indispensable in the inversion of ECT signals, is briefly introduced. Several schemes for inversion of crack signals are presented then for EDM cracks, stress corrosion cracks (SCC) respectively. In addition, scheme and reconstruction results for multiple cracks, deep cracks and cracks in the welding part are also given. From the numerical results, it is demonstrated that sizing of single crack from ECT signals has become possible even for a natural crack or a crack as deep as 10 mm. For multiple cracks, more effort is necessary for its modelization and reconstruction.

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