Issue 39

S. Harzallah et alii, Frattura ed Integrità Strutturale, 39 (2017) 282-290; DOI: 10.3221/IGF-ESIS.39.26 283 related particularly to the health of the matter [1, 2]. The non-destructive testing of materials became a tool impossible to circumvent for the improvement of safety (at the time of the uniform), and of quality (during the development) [3]. Eddy current sensor devices have been used for over a century in the control of conductive parts including metal parts. Nowadays, the theory of Eddy current sensors is already largely developed. We find its applications in various industrial fields, ranging from the measurement of the properties of matter to the detection of flaws in metal parts. Due to their sensitivity to defects (fatigue cracks, inclusions or corrosion effects) [4] their implementation, easy and robust, is widespread in the context of industrial use. However, the growing need for reliability and rapidity of checking operations lead to the development of new sensors [5]. Detection and characterization of a crack in a plate at its initial stage (before propagation), is a real industrial challenge and a major element in safety especially in high-risk areas. It is on the basis of these characterizations that engineers have the means to analyze such crack behavior, predict its spread and eventually assess its harmfulness as well as the life of the inspected body, [6]. In this paper, a numerical model for the assessment of eddy currents in materials, for the detection and characterization of defects is considered. We first describe the physical and geometrical properties of used materials and then, we present, through an example, results of eddy currents obtained using a numerical model that we have developed. The most promising numerical technique for computation of eddy current fields is the FEM. This method has proven usefulness in demonstrating the feasibility of flaw detection under given inspection conditions. The problems studied in this work of this paper are the NDT by EC of ferromagnetic materials. These materials are largely used in various industrial fields, such as aeronautics, metallurgy and rail transport. B ASIC EQUATIONS istribution of the magnetic field and the currents induced in a conducting material, and possibly magnetic, is governed by the fundamental laws of the electromagnetism whose most general formulation is given by the Maxwell's equations [7]: 0 0 0 0 S ρ .E  ε  .  B 0  B   E    t  E    B  μ ε  μ J  t                                (1) where, B   is the magnetic induction and. E  represents the electrical field. The quantities ρ and S J  are the volume charge density and the electrical current density (flux) of any external charges, respectively. P ROPOSED M ODEL ddy current testing systems consist of configurations that are present in Fig. 1 such as the conductor sensor in which c  , nk  represent the sample conducting region and cracks area (a damage region), respectively. On the other hand; k  refers to the conductor region with its normal vector n . In a multi-conductor sensor, a high coupling is considered from the sensor and the tube as a sample. The Primary field resulting from the current source I k includes contribution to the flow of all conductors k  which interact entirely all due to proximity effect. In another mode, every conductor interacts with the secondary field produced by the eddy current induced in the sample. For the massive conductor   k   and   s k I  the interaction from the primary and secondary fields are weak because all considerations on the effects of skin and proximity [8]. D E