Eur. Phys. J. Appl. Phys. (2012) 57: 10601 DOI: 10.1051/epjap/2011100483 THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS Regular Article Pulsed eddy current non-destructive evaluation based on coupled electromagnetic quantities method A. Bouzidi 1, a , B. Maouche 1 , M. Feliachi 2 , and G. Berthiau 2 1 Laboratoire de G´ enie ´ Electrique (LGE), Universit´ e A. Mira, route de Mezaia-Targa-Ouzamour, 6000 Beja¨ ıa, Algeria 2 IREENA-IUT, CRTT, University Boulevard, BP 406, 44602 Saint-Nazaire Cedex, France Received: 3 December 2010 / Received in final form: 2 June 2011 / Accepted: 19 September 2011 Published online: 28 November 2011 – c  EDP Sciences 2011 Abstract. This paper proposes a semi-analytical model for Pulsed Eddy Current Non-Destructive Eval- uation (PEC-NDE) based on the Coupled Electromagnetic Quantities Method (CEQM). The proposed formulation is developed from coupled electric circuit’s approach in which the Crank Nicholson formula is used to derive the transient behavior. The computational model makes use of current excitation allowing the determination of the sensor voltage in the case of an axisymmetric device. The feature of the variation of voltage provides information on the electromagnetic and geometrical properties of the device. So, the second peak of voltage variation (SPVV) and second ratio between the minimum and maximum (RMM2) are used to determine these properties. The proposed model is validated by comparison with Fourier re- constitution obtained from measurements on one hand and with finite element calculations on the other hand. The developed model, associated to an inversion technique, is applied to evaluate the lift-off and the work piece thickness. 1 Introduction The Eddy Current Non-Destructive Testing and Evalua- tion (EC-NDT&E) is used in all industrial pieces made of electrical conducting materials. It operates in a pro- duction line, in an installation under operation, and at maintenance time. What is more important in the process control is how the eddy currents are induced and inter- act with the examined piece. That depends on the phys- ical properties of the sensor and the injected signal, as well as the electromagnetic and geometrical properties of the piece to control. The EC-NDT&E interest is due to its technical characteristics such as speed, sensitivity, and feasibility. To study the EC-NDT&E, some exper- imental models, numerical, mainly that using the finite element method, analytical or semi-analytical ones, were developed in harmonic cases [1–3]. Recently, the works are directed toward the transient eddy currents for which ex- perimental models [4–6], numerical ones [7–10], and some other analytical or semi-analytical models [11–13] are developed. In the case of the harmonic EC-NDT&E, semi- analytical formulation based on the Coupled Electromag- netic Quantities Model (CEQM) was previously developed [2]. In such a case, the general inspection of pieces and the detection of defects require the use of a multi-frequencies excitation mode. Let us notice that the pulsed model is a e-mail: athmane bouzidi@yahoo.fr well adapted for such investigations [4–13]. In this con- text, we propose the generalization of the CEQM to the case of the pulsed eddy current analysis. The proposed formulation is based on the use of the coupled electric circuits governed by Biot-Savart and Maxwell Faraday’s laws. The spatial integration is cal- culated by the first and second kinds Legendre’s elliptic functions [14]. The adaptation to the transient case and its application to the PEC determination are obtained by using Crank Nicholson’s formula to represent the temporal term. The proposed approach provides various information obtained from the voltage variation. Particularly the SPVV and the RMM2 parameters translate the electro- magnetic and geometrical properties which can be deter- mined using an inversion technique. The P-CEQM is compared to Fourier Reconstitution of Measured Harmonic Signals (FRMHS) on one hand and to finite element method on the other hand. The applica- tion concerns an axisymmetric device with absolute sensor excited by a half-sinusoidal current. 2 Coupled electromagnetic equations for pulsed eddy current To describe the phenomena by coupling electromagnetic quantities, the Maxwell equations are considered in terms 10601-p1