Development of Time-Domain Models for Nondestructive Testing

The development of a Transmission-Line Matrix (TLM) for the simulation of ultrasound and microwave propagation in structures common in Nondestructive Testing (NDT) is described. The spatial resolution of the proposed model is better than a tenth of a wavelength. Numerical modeling was carried out for frequencies commonly used in ultrasound and microwave nondestructive testing (3.5MHz – 20GHz). The sample results provided here for ultrasonic and microwave testing show the applicability and accuracy of the model. Introduction Many of the methods used in Nondestructive Testing (NDT) are based on wave interaction with the materials under investigation. Elastic and electromagnetic waves are used to identify and characterize the local changes that occur in a materials in response to external excitation. To improve the results obtained in NDT of materials, considerable theoretical effort is involved in developing reliable mathematical models of wave propagation in different media. Due to the complexity of the problems, numerical methods have proven to be an appropriate approach. The Transmission Line Matrix (TLM) is a time domain numerical technique which was found to be particularly suitable for modeling of complex geometries encountered in testing. The TLM method dates back to 1971 [1] and as such is one of the newest numerical methods available yet it has proven both reliable and flexible enough for the demands of many applications including those in NDT. The method is considered to be “a modeling process” rather than a numerical method for solving differential equations [2]. The method is a direct numerical implementation of the Huygens principle [3]. An appropriate field propagator (Green function) is first identified [4]. Then the wave front at each iteration (instant in time) for each point in space is a result produced by the waveforms generated at neighboring points in the previous iteration. The TLM is a physical discretization approach and this method does not require the solution of a differential equation. The TLM requires division of the solution region into a rectangular mesh of transmission lines in ahich the nodes of the mesh are points of discontinuity for impedances. In addition, to solve a problem using the TLM, a set of boundary conditions and material parameters must be provided as well as an initial excitation. Then the impulsess are propagated throughout the mesh using scattering theory on the transmission lines. There is no limitation regarding the frequency of interest, but the size of the mesh imposes an upper limit on the frequency response analysis. Unlike some other numerical techniques, the TLM algorithm does not involve an explicit convergence criterion, a property that makes it an inherently stable method. This stability is reflected in the flexibility of the TLM method when dealing with various types of input signals and boundaries. The present work describes the development of models for microwave and ultrasound NDT and shows that the models are essentially the same for both NDT methods in spite of the inherent differences between acoustic and microwave applications including obvious differences in wavelength, material properties and interpretation of results. The purpose of this general model is to show the applicability, accuracy and flexibility of the method in modeling NDT environments which previously were difficult to model. Results from various configurations including conducting and dielectric objects and practical testing configurations are presented to demonstrate the method’s applicability and flexibility. Extraction of S parameters and prediction of resonant frequencies are also demonstrated.