The role of sensitivity matrix formulation on damage detection via EIT in non-planar CFRP laminates with surface-mounted electrodes

Abstract

Carbon fibre reinforced polymers (CFRPs) are extensively used in aerospace, automotive and other weight-conscious applications for their high strength-to-weight ratio. Utilization of these lightweight materials unfortunately also involves dealing with damages unlike those seen in traditional monolithic materials. This includes invisible, below-the-surface damages such as matrix cracking, delaminations, fibre breakage, etc. that are difficult to spot outwardly in their early stages. Robust methods of damage detection and health monitoring are hence important. With the intention of avoiding weight addition to the structure to monitor its usability, it would be desirable to utilize an inherent property of these materials, such as its electrical conductivity, as an indicator of damage to render the material as self-sensing. To this end, electrical impedance tomography (EIT) has been explored for damage detection and health monitoring in self-sensing materials due to its ability to spatially localize damage via non-invasive electrical measurements. Presently, EIT has been applied mainly to materials possessing lesser electrical anisotropy than is encountered in CFRPs (e.g. nanofiller-modified polymers and cements), with experimental setups involving electrodes placed at the edges of plates. The inability of EIT to effectively tackle electrical anisotropy limits its usage in CFRP structures. Moreover, most real structures of complex geometries lack well-defined edges on which electrodes can be placed. Therefore, in this thesis, we confront these limitations by presenting a study into the effect of EIT sensitivity matrix formulation and surface-mounted electrodes on damage detection and localization in CFRPs. In this work, the conductivity is modeled as being anisotropic, and the sensitivity matrix is formed using three approaches – with respect to i) a scalar multiple of the conductivity tensor, ii) the in-plane conductivity, and iii) the through-thickness conductivity. It was found that through-hole damages can be adeptly identified with a combination of surface-mounted electrodes and a sensitivity matrix formed with respect to either a scalar multiple of the conductivity tensor or the in-plane conductivity. This theory was first validated on a CFRP plate to detect a single through-hole damage. Furthermore, EIT was also used to successfully detect both through-hole and impact damages on a non-planar airfoil shaped structure. Singular value decomposition (SVD) analysis revealed that the rank of the sensitivity matrix is not affected by the conductivity term with respect to which the sensitivity matrix is formed. The results presented here are an important step towards the transition of EIT based diagnostics to real-life CFRP structures.