IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010 3037 3-D Numerical Modeling of the Thermo-Inductive Technique Using Shell Elements Brahim Ramdane, Didier Trichet, Mohamed Belkadi, and Javad Fouladgar Institut de Recherche en Electrotechnique et Electronique de Nantes Atlantique (IREENA), 37, Boulevard de l’université, BP 406-44600 Saint Nazaire Cedex, France Thermo-inductive testing is a new technique used for health investigations on different components of automotive and aeronautic in- dustries. In this technique, eddy current deviation around the default creates local heating which can be detected by an infrared camera. The purpose of this work is to develop a 3-D finite-element model as a support tool to study the reliability of the technique. To reduce the number of unknowns, shell elements are introduced to model defects or thin conductive regions. Inspected materials are classified into metallic and composites. Investigations on various parameters of the technique and crack dimensions are performed in order to optimize the method. Experimental and simulation results show that the method is well suited. Index Terms—Eddy current testing, finite-element methods, induction heating, infrared measurements, nondestructive testing. I. INTRODUCTION C RACKS constitute one of the major problems threatening the security of systems subjected to mechanical, thermal or chemical constraints. In order to detect and characterize these defects in different materials and situations, researches try to combine the NDT techniques to obtain the best performances. In this context, we propose a new method called thermo-inductive technique, which combines the advantages of both eddy current and infrared thermography techniques [1]. This technique is recent and little researches are carried out on it in the literature. In addition, most of these works are based on simplified models which limit the study to simple types of defects and pieces [2]. Our objective is then to develop a 3-D numerical model as a support tool to analysz and optimize this new technique. The ability of thermo-inductive method to detect the defects depends on electromagnetic and thermal properties of the mate- rial under investigation. In automotive and aeronautic industry, two principal groups of material are used: metallic pieces and carbon fiber reinforced polymer composite sheets. The first group has a linear or non linear magnetic permeability, a small electromagnetic skin depth and high thermal diffusivity. The second group has non isotropic physical properties, high skin depth and low thermal diffusivity. The material investigated by this technique present a scale factor problem at two levels. The cracks but also the material itself which may be large and thin such as aluminium plates or composite sheets. Modeling such regions involves difficulties due to their small thickness compared to other dimensions. This is expressed by mesh problems such as high density or deformed elements leading to a prohibitive computing time or ill-condi- tioned matrix systems. In literature, many researches have been carried out to model thin regions. Among the various proposed methods, the shell elements, which derive from degeneration of Whitney prism elements, is well suited for our problem [3]. Manuscript received December 18, 2009; accepted February 13, 2010. Current version published July 21, 2010. Corresponding author: B. Ramdane (e-mail: brahim.ramdane@univ-nantes.fr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2044022 Fig. 1. Schematic of experimental system. To consider all these constraints, we have developed a 3-D finite-element method based on Whitney’s elements under a Matlab environment as a support tool to model the different phe- nomena involved in this technique. This model takes into ac- count the anisotropy, the nonlinearity of materials, and the pres- ence of thin regions which are modeled by the shell elements. The new technique is applied to defects detection in mate- rials used in automotive and aeronautic industries. Due to their anisotropic properties and scale factor, composite materials are modeled after a preliminary homogenization stage. The sensi- bility of the defect detection towards some parameters such as electromagnetic frequency, heating time, or defect dimensions has been investigated. II. PROBLEM DESCRIPTION A typical measurement installation for the thermo-inductive method is shown in Fig. 1. In this technique, the electromagnetic and thermal fields penetrations have a great influence on the defect detection. These two parameters depend on the field and thermal frequencies as well as the material physical properties. This is why the optimal field and thermal frequencies depend on the material under investigation. The induction frequency may vary from 50 Hz to 2 MHz and the thermal frequency from 0.1 to 20 Hz. III. NUMERICAL MODELING The study of the NDT by thermo-inductive technique in- volves both thermal and electromagnetic phenomena. A. Electromagnetic Model The electromagnetic problem defined by Maxwell’s equa- tions is solved with the 3-D finite-element method. The weak 0018-9464/$26.00 © 2010 IEEE