Inverse Heat Conduction Approach for Infrared Non-destructive Testing of Single and Multi-layer Materials

Abstract

The focus of this thesis is to derive analytical tools for the design of infrared nondestructive tests in single and multi layer material bodies. This requires the predetermination of the parameters of the experiment such that the infrared image has the required resolution for defect detection. Inverse heat conduction in single and multi-layer materials is investigated to determine the required frequency of excitation in order to obtain a desired temperature at the observation point. We use analytical quadrupole representation to derive a polynomial relation to estimate the frequency of the periodic excitation as a function of the temperature amplitude at a given observation point within the body. The formula includes characteristic geometric and material parameters of the system. The polynomial formula can be an e ective design tool for quick frequency predetermination in the design of non-destructive testing experiments with infrared thermography. The convergence and accuracy of the formula is assessed by comparison with the analytical thermal quadrupole solution and experimental results. We also investigate the e ect of the nite length of the material domain in order to establish the range of applicability of a simpli ed formula based on semi-in nite domain assumption. The e ect of nite length is investigated analytically by using (i) Fourier series which accounts for transients and (ii) Time varying solution associated to the steady state solution when a purely periodic excitation is applied. These results are also compared with numerical solution obtained with commercial nite element software ANSYSTM.