Study On Analytical Modeling For Eddy Current Testing Of Multi-layered Conductive Structures

Nondestructive testing and evaluation of multilayered conducting structures is demanding urgently in the critically important fields, such as aircraft and nuclear industries. Eddy current (EC) testing has been one of the preferable techniques, because it is a fast, cost-effective and non-contact method. After a general survey of the state of the art of modeling theory in EC testing, the study in this dissertation is deeply developed around analytical modeling and model solution methods for EC inspection of multilayered conductive structures. The main contributions and innovations of this dissertation are summarized as follows:(1) The closed-form analytical model of harmonic eddy currents in layered conductive structures is presented with an integral form. During the model formulation, the net magnetic field in the whole space is divided into the coil excitation field and EC field, and the variation of parameters of multilayered specimen only changes EC field. The application of the concepts above simplifies the analytical model of EC field, and model solutions are also reduced. In comparison with the conventional analytical model, the developed model is more concise and easier to solve.(2) An improved analytical model of harmonic eddy currents in layered conductive structures is established, and the solutions to the presented model take a series form. In the typical model of harmonic EC field, the boundaries of the problem are set to infinity, thus resulting in integral-form solutions. After the analysis of eddy current distribution, it is found that the EC field is mainly confined in a finite domain. Based on the discovery above, the problem region, in this dissertation, is reduced to a cylinder with a finite radius by imposing Dirichlet and Neumann boundary conditions, respectively. Thus the resulting solutions to the improved model take the form of a series rather than an integral. With respect to accuracy, the obtained series-form model is as good as the integral model if the problem region and summation terms are large enough. In terms of computation speed, accuracy control and simplicity in the model's computer implementation, the developed improved model is much better.(3) The reflection-transmission theory based method is put forward to solve the analytical model of harmonic EC problems for inspection of multilayered conductive structures. Compared to the analytical model by the conventional Cheng's matrix method, the model by the presented alternative method has a more clear and concise form. Moreover, it is faster and more reliable in the model's computer implementation. In addition, another model for computing the impedance change, which is established by Luquire using inductive method, has very good performance in engineering application. However, a strict proof of the Luquire's model has not been provided. In this thesis, Luquire's model is proofed using the developed reflection-transmission theory based method.(4) Fourier and Laplace transform based methods are presented to model the transient EC field in time domain for inspection of multilayered conductive structures. In the Fourier-transform based model, an attenuation factor is brought in for better approximation of pulse excitation, thus leading to the suppression of Gibbs effect. In the Laplace-transform based model, the theoretical model of transient EC field in complex-frequency domain is inverted by analytical and numerical method, respectively. Finally, use of the convolution theorem extends the time-domain model of transient EC field to the theoretical analysis of transient EC field in time-domain for arbitrary excitation in EC testing.This dissertation is focused around analytical modeling and model solution methods for EC testing of multilayered conductive structures. All the contributions could help us grasp the essence of eddy-current effect, establish a fast and accurate solver, improve the performance of EC instrument, and form an inverse model. Finally, the progress on analytical modeling in EC testing made by the author improves the evaluation of multilayered conductive structures.