The fast computation of eddy current distribution and probe response in homogenized composite material based on semi-analytical approach

Houssem Chebbi,Denis Prémel

doi:10.1051/epjap/2020190220

Houssem Chebbi, Denis Prémel

Open Access

https://doi.org/10.1051/epjap/2020190220

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Abstract

Due to the excessive use of composites in the industrial field, many numerical modeling approaches dedicated to the characterization of such complex material by means of Non Destructive Testing Techniques were developed. In this paper, we present a numerical model dedicated to simulate the inspection of unidirectional Carbon Fiber Reinforced Polymer using Eddy Current technique for detecting fiber disorientation. A semi-analytical model based on a modal approach is developed for the fast computation of quasi-static field induced by an arbitrary 3D Eddy Current probe in the material. Because of the high anisotropy and strong heterogeneity of such material, a prior phase of homogenization is assumed and the material is then considered as homogeneously anisotropic. The modal approach consists in resolving Maxwell’s equations in the Fourier domain. Therefore, the electromagnetic field is expressed as a sum of eigen-modes. To take into account the wave propagation through the multilayered structure and boundary conditions at each separating interface, a stable and recursive scattering matrix algorithm has been implemented. The impedance of the probe is computed analytically using Auld’s formula in orders to identify the main orientation of the fibers in the inspected zone. For numerical validation, simulated data provided by the model are compared to finite element data.

Highlights

The use of unidirectional composite materials as Carbon Fiber Reinforced Polymer (CFRP) in manufacturing aeronautical structure has been significantly increased during the last decades thanks to their lightness and stiffness characteristics
We present a Semi-Analytical (S-A) model based on a modal approach dedicated to the fast computation of quasi static fields and EC density distribution induced by an arbitrary EC probe
We adopt a semi-analytical approach to simulate the response of an anisotropic, planar and multilayered structure to the excitation of 3D Eddy current probe

Summary

Introduction

The use of unidirectional composite materials as Carbon Fiber Reinforced Polymer (CFRP) in manufacturing aeronautical structure has been significantly increased during the last decades thanks to their lightness and stiffness characteristics. A wide variety of NDT techniques have been used, including ultrasonic testing, infrared thermography testing, radiographic testing, shearography testing, and Eddy Current Testing [1], for the characterization and the detection of defects such fiber disorientation in intermediate layers, delamination, out-of-plan waviness or fiber breakage. Despite of the low electrical conductivity along carbon fibers with respect to metallic structure, eddy currents remain sensitive to the abrupt variation of the conductivity and sufficiently enough for detecting eventual damages. This method has an ability of fast and contact-free inspection of defects in conductive materials and the global characterization of the sample as the estimation of the bulk conductivity using a multi-frequency analysis and the identification of fiber orientation [2]. CFRP is a non-homogeneous and highly anisotropic conductive material due to the random positioning of the carbon

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