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This paper presents a modelling procedure to take into account the capacitive effect at high frequencies, in Eddy Current Non-Destructive Characterization (EC-NDC) of Unidirectional Carbon Fiber Reinforcement Composite (UD-CFRC) rods. To simulate the complete EC-NDC systems, first, the multilayer circular air coil is physically modeled by a finite element (FE) axisymmetric eddy current model coupled to equivalent RL circuit. Each layer of the coil is represented by an equivalent resistance (R) in series with the equivalent inductance (L). Secondly, R and L of the coil layers are computed for several frequencies up to 5Mhz, and then introduced into the equivalent RLC circuit with considering inter-turn and interlayer capacitances. Then the inversion problem is solved in order to identify all inner capacitances of the coil. Finally, the UD-CFRC rod is introduced into the FE eddy current axisymmetric model coupled to an equivalent RLC circuit, as a homogenized conductive material with an equivalent transverse conductivity. The coil with the presence of the homogenized UD-CFRC rod is then modeled as a transformer with a secondary connected to a capacitor in parallel with a resistance in order to evaluate the inner capacitor of the UD-CFRC. All evaluated parameters are then introduced in the last model. The comparison between the computed impedance parts and the measured ones shows a mean error less than 2% and a maximum one of 5% according to the frequency.

The analysis of the electrical behavior of a unidirectional (UD) composite material requires a lot of resources and measurement techniques. To overcome this constraint, the real composite material is replaced by a virtual material with same overall behavior. In this article, an approach to determine the setting parameters of the virtual material model is presented to accurately reconstruct the electrical behavior of a real UD material in the three spatial directions.

In this paper, one proposes a model-assisted probability of detection approach to study the reliability of detecting special defects. The approach is based on a 3-D finite-element T– $\Omega $ formulation with circuit coupling. This model is then applied to calculate performances of induction thermography method to detect thin open cracks in vessel reactor shell in nuclear installation.

Numerical simulations by means of finite elements are used to investigate the capacities of the induction thermography technique for the characterization of electrical conductivities of unidirectional carbon fiber reinforced polymer (CFRP) materials. A coupled electromagnetic-thermal model is presented using hexahedral elements to deal with the thin region of fully anisotropic physical properties. Eddy-current problem is solved using the $ {{T}}$ - $\Omega $ formulation to deduce heat source density power. Transient thermal problem is solved with a fixed time step. An error minimization-based method is presented to identify the electrical resistivity of unidirectional CFRP from the induction thermography measurement.

This paper proposes a simple approach to evaluate a transverse electrical resistivity of a rod unidirectional carbon fiber-reinforced composites (UD-CFRCs). The method is based on eddy current technique. The model is associated with inverse problem method that consists of minimizing the difference between the computed and measured resistances. The ant colony algorithm which is a kind of heuristic minimizing algorithm based on population exploration is used to get transverse electrical resistivity. The findings of the work are summarized as the following. First, it was demonstrated that the induced power in the UD-CFRC and the resistance of the coil are independent of the value of longitudinal resistivity. Then, the electrical resistance is computed using direct problem which is formulated with the 2-D axisymmetric finite-element method. After that, the identified resistivity, which obtained with the inverse problem, is introduced in the direct problem to compute resistance. Finally, the confrontation between the computed resistance and the measured one shows a significant concordance between the two.

In this paper, a new multi-scale approach to predict the effective electrical conductivity tensor of a woven-fabric composite layer for frequencies lower than 10 MHz is presented. The result is then used to model the behavior of a stratified composite material composed by a pileup of woven-fabric layers with different relative orientations. To take into account the orientation and the anisotropy of the material, a 3-D multilayer hexahedral degenerated elements method is used to model the anisotropic thin plate. This approach enables to take into account random distribution of carbon fibers in the yarns, 3-D effects, and electric percolation threshold with an acceptable numerical cost. The developed model is then validated by results for one anisotropic thin layer.

We present a lightened 3D finite element model for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing technique to reduce the computation time. The time harmonic electromagnetic problem is expressed in A-ø formulation and lightened by using the Surface Impedance Boundary Condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece under test including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved using surface electromagnetic power density as thermal source. The comparisons with reference analytical solution and full 3D finite element model show the accuracy and performance of the method.

This paper develops a novel method for optimal design of fractional slot with concentrated windings. The basis of this method is a generalized analytical model of the winding magnetomotive force (MMF) combined with a multiobjective genetic algorithm, which searches the optimal winding parameters that maximize the winding factor and minimize the MMF harmonic content. This technique is applied to optimize the winding layout of the permanent magnet synchronous machine with 12 × n slots/10 × n poles combination ( n is an integer number). The electromagnetic performances of the optimized winding are investigated and compared with conventional winding topology. It is found that the proposed approach allows the emergence of new windings with higher performances.

In this paper, degenerated hexahedral Whitney elements are used to model carbon-fiber-reinforced polymer composites in nondestructive testing induction thermography technique. These elements avoid meshing the thin regions of composite and consider the anisotropic multilayer characteristic of the materials and also the flaws inside their volume. The eddy-current problem is solved using $A- \phi $ formulation. The accuracy of this method is shown by comparison with the classical hexahedral elements.

In this paper, the use of a degenerated hexahedral Whitney elements method in the modeling of multi-layer anisotropic regions is presented. The elements degenerated from hexahedral elements are used to model laminated composites at the elementary-ply scale considering the circulation of eddy-currents along the thickness of the material. Eddy-current problem is solved using the $ {{A}}-\phi $ formulation.

This paper presents a fast-numerical approach to optimize the localization of induced power in highly anisotropic composite materials with a large-scale factor. A one-dimensional hybrid multi-physical tool allows us to find the best ply sequence and the best strategy to constrain the induced currents to circulate in an interest area defined respecting specific temperature objectives. A three-dimensional multi-physical modeling is then used on a few selected candidates to refine results.

In this paper, a model is built to evaluate the flaw detection capacity of the induction thermography applied to nondestructive testing (NDT) of carbon-fiber-reinforced polymer composite. A homogenization approach is used to overcome the large-scale factor. The homogenized electric conductivity obtained is used in a 3-D multilayer finite element model. The problem is discretized by hexahedral element to deal with the numeric instability of tetrahedron element in the modeling of thin and strongly anisotropic domain. The distribution of current in the induction coil is also considered to improve the accuracy of the solution. Numerical model is then validated by comparison with measurement. Simulation of an NDT case with induction thermography will be discussed.

In this paper a percolation model is used to determinate the electrical conductivity tensor of one layer of carbon fiber composite. For this kind of material, fibers are randomly distributed in the resin. To take into account this distribution a virtual 3-D material model is developed and coupled with a homogenization method to overcome the scale factor problem. The electrical conductivity tensor is then used to simulate the induction heating of a multilayer composite.

In this paper, a 3-D modeling of a thermo inductive nondestructing testing (NDT) technique applied to carbon fiber reinforced polymer (CFRP) composite is presented. A multiscale approach is used to calculate the electromagnetic and thermal field distribution. The relevance of the technique is then discussed for different positions of flaws and the optimal frequency is estimated.

In this paper, we present some advances in 3D finite element modeling of the induction heating process. Lighten finite element models are used for fast simulation of Carbone Fiber Reinforced Polymers and massive metals at high frequencies. The lightening methods include the use of degenerated hexahedral Whitney elements for very thin anisotropic layers and the impedance boundary condition with external electrical circuit constraint.

Thermo-inductive testing is a new technique used for health investigations on different components of automotive and aeronautic industries. 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.

In this paper, a new multiscale homogenization method is introduced to calculate the field and current distribution inside carbon fiber reinforced polymer composites submitted to an external electromagnetic field. In the microscopic scale, the real structure of the material is taken into account and electromagnetic and electrical equivalent properties are calculated using finite-element method (FEM). In the macroscopic scale, these properties are introduced in an impedance network or in an anisotropic-finite elements method according to the working frequency. The simulating results are in accordance with experimental ones and will allow a better modeling of composites.

A non linear homogenization approach, based on 3D edge finite elements method, is used to determine the equivalent electromagnetic properties of the Soft Magnetic Composites (SMC). A new geometry generation algorithm is introduced to take into account the material density, the randomized size and location of the SMC particles and the insulation layer around the particles. A modified Preisach hysteresis model associated with a new analytical Lorentz function is developed to calculate the homogenized hysteresis loops from intrinsic properties of its constituents.

This paper presents an electrical conductivity identification technique of composite materials based on electrical resistance measurement with a frequency range from 1 kHz to 1 MHz. Resistance is measured by an impedance analyzer and also computed using the 3-D anisotropic shell element model. The inverse problem technique is then applied to identify the conductivity tensor components. This technique is validated using anisotropic materials with known electrical conductivity tensor.

This paper presents the optimal design of a rotating eddy-current probe using the inverse problem method. The probe is dedicated to identify the electrical tensor conductivity of carbon fiber composite materials. A 3-D anisotropic shell elements model associated with annealing optimization algorithm is used to minimize the goal function.

The paper presents a magneto-thermal model of a high-speed synchronous reluctance machine (SRM). Both magnetic and thermal aspects are described using two-dimensional and three-dimensional finite-element method for machine modeling. Additional current harmonics losses, friction losses, and convective exchange coefficients at high speed are estimated. Finally, test results on a 20kW, 20 000rpm SRM are reported and compared with the simulation results

A methodology based on shell elements, to study the electromagnetic and thermal behavior of multilayered anisotropic conductive composite materials, is presented. The anisotropic behavior and orientation of each layer of the composite material has been taken into account. The model is validated with experimental results. It is then applied to study the induction heating of composite materials, and also to detect the delamination in these materials

This paper presents a three-dimensional modeling of induction heating of conductive composite materials using the shell elements. These elements are generalized by taking into account the anisotropic behavior of the load. Magnetic fields and temperatures on the composite load are then calculated and compared with experimental measurements.

In this paper, a method is introduced to calculate the equivalent electromagnetic and thermal properties of nonhomogeneous materials. The study is in large part applied to a bundle of conductors. For a filling rate, the conductors are distributed inside a cylindrical geometry using a Monte-Carlo random algorithm. Electromagnetic and thermal equations are solved in this nonhomogeneous material and the total power, magnetic field and temperature distribution are calculated. Supposing an equivalent homogeneous cylinder, the inverse problem methodology is used to calculate the electromagnetic and thermal properties of the equivalent material which give the same power, mean magnetic field or mean temperature distribution. The validity of these hypotheses are then discussed.

An electromagnetic and thermal model of carbon fiber reinforced polymer composite material is introduced. This model takes into account the influence of different fiber orientations on the electromagnetic parameters. These parameters are defined in microscopic scale and introduced in finite element method model in macroscopic scale.

In this paper, a methodology based on shell elements is presented to model the electromagnetic behavior of multilayered conductive composite materials. The standard 3-D finite-element formulation is accomplished by a multilevel shell element representation. This leads to a reduced number of unknowns which improve the system convergence and consequently the computational time. The model developed will be validated with classical 3-D finite-element method and experimental results.

International audience; In this paper, the asymptotic development method is used to study the electromagnetic and thermal behavior of nonhomogeneous materials. The method, widely used in high frequency applications, is adapted to an induction heating system of partially conducting composites. The asymptotic method, based on the spatial filtering of the electromagnetic field, is applied to study the composite materials with periodic structure. The model is valid when the size of the elementary cell is small compared with the dimensions of the system. For large cells, the model gives an average value of field. A local solution is then used to improve the homogenized field. The conditions of using the model for nonperiodic structures are also discussed.

Purpose This paper aims to present a lightened 3D finite element model (FEM) for coupled electromagnetic thermal simulation of the induction thermography non-destructive testing (NDT) technique to reduce the computation time. Design/methodology/approach The time harmonic electromagnetic problem is expressed in A – ϕ formulation and lightened by using the surface impedance boundary condition (SIBC) applied to both the massive induction coil surface and the surface of conductor workpiece including open cracks. The external circuit is taken into account by using the impressed voltage or the impressed current formulation. The thermal diffusion in the workpiece is solved by using surface electromagnetic power density as thermal source. Findings The accuracy and the usefulness of the method for the design of the induction thermography NDT technique have been shown with acceptable deviation compared with a full FEM model. It is also observed that at high frequency, when the ratio between the local radius of the conductor and the skin depth is high, a very good accuracy can be obtained with the SIBC methods. At lower frequency, the effect of the curvature of the surface becomes significant. In this case, the use of the Mitzner’s impedance can help to correct the error. Originality/value The SIBC can be used for both massive coil and workpieces with open cracks to alleviate 3D FEMs of the coupled electrothermal model. The implementation in matrix form of the coupled electrothermal formulation is given in details. The comparisons with reference analytical solution and full 3D FEM show the accuracy and performance of the method. In the test case presented, the computation time is 6.6 times lower than the classical model.