Eur. Phys. J. Appl. Phys. 28, 355–360 (2004) DOI: 10.1051/epjap:2004185 T HE EUROPEAN P HYSICAL JOURNAL APPLIED PHYSICS Calculation of the ECT signal of a minute crack by a FEM-BIM hybrid method Y. Le Bihan 1, a , J. Pavo 2, b , and C. Marchand 1, c 1 Laboratoire de G´ enie ´ Electrique de Paris, UMR 8507 CNRS, SUPELEC, Universit´ es de Paris XI et Paris VI, Plateau de Moulon, 91192 Gif-sur-Yvette Cedex, France 2 Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics, 1521 Budapest, Egry J. u. 18., Hungary Received: 22 January 2004 / Received in final form: 1st April 2004 / Accepted: 25 June 2004 Published online: 30 August 2004 – c  EDP Sciences Abstract. A hybrid method is presented for the calculation of the interaction of a complicated shape ferrite-core eddy current testing probe with extremely small size cracks in a plate. The method is obtained by blending the boundary integral (BIM) and finite element (FEM) methods preserving their attractive properties, that is, the fast and accurate evaluation of the defect field and the versatility in specimen and probe geometry, respectively. FEM is applied for the computation of the electric field induced in the specimen without cracks. Using the obtained, so-called, incident field the BIM is used for the calculation of the field perturbation due to the presence of the cracks in the tested specimen. With the application of the presented hybrid calculations, a very fast and accurate method is developed for the solution of a problem that would pose considerable difficulties for either the FEM or the BIM if they were applied purely alone in the conventional way. The results of the calculations are compared with a large number of experimental data. The very good correlation between the measured and simulated probe responses proves the applicability of the presented method. PACS. 81.70.Ex Nondestructive testing: electromagnetic testing, eddy-current testing – 07.05.Tp Computer modeling and simulation 1 Introduction The calculation of the signal of eddy current testing (ECT) probe due to a crack in a conducting plate has been stud- ied extensively. Usually integral or variational methods are applied [1–6]. Both methods have their advantages and disadvantages. The finite element method (FEM) is flexi- ble in specimen and probe geometry, while it might require very dense discretization at the vicinity of the crack. In the same time signal calculated in different probe posi- tions are calculated independently, so the evaluation of a scan line by FEM is time consuming. In the case of bound- ary integral method (BIM) only the crack (that is actually assumed as an infinitesimally thin surface) is discretized. The calculations related to different probe positions result in the same system matrix, consequently the evaluation of the signal related to the different probe positions is very fast once the system matrix is established. The difficulties with the BIM are the lack of flexibility in specimen and probe geometry. The specimen geometries usually handled a e-mail: le-bihan@lgep.supelec.fr b e-mail: pavo@evtsz1.evt.bme.hu c e-mail: marchand@lgep.supelec.fr by BIM are infinite plate and cylinder and in most cases cylindrical air core impedance probes are considered. An interesting class of signal calculation methods can be formed from a blend of BIM and FEM preserving their attractive properties that is the fast evaluation of the de- fect field and the versatility in specimen and probe geom- etry, respectively. A simple example for such methods is proposed in [7] where the probe response due to a crack in a finite size plate has been calculated by superimposing the signal due to a crack in an infinite plate calculated by BIM and the signal due to the presence of the boundaries of the finite plate calculated by FEM. In this paper we report the results of an hybrid method developed for the calculation of the crack signal of a novel type industrial probe [8]. The investigated geometry posed special problems either for FEM and BIM methods be- cause the size of the crack was extremely small (requiring extremely dense mesh for FEM) and a special two-coil ferrite core probe (difficult to model by BIM) has been applied. These are the reasons why a new hybrid method has been developed where the incident field due to the interaction of the probe and the crack-free specimen has been calculated by FEM and the signal variation due to the presence of the crack has been analyzed by BIM.