Extremum method: Inverse solution of the two-layer thermal wave problem

Abstract

An inverse solution of the two-layer thermal wave problem has been derived, which allows us to determine the relevant thermal transport parameters, the thermal diffusion time and the thermal reflection coefficient, respectively, the ratio of the effusivities of the two layers, deduced from the relative minimum or maximum of the calibrated phase lags measured between the periodically modulated excitation of the thermal wave and the detected thermal response. Applying a functional transformation by multiplying the calibrated phase lags with the variable (1∕f1∕2)q, where f is the modulation frequency of excitation and q a positive or negative real number close to zero, the inversion method is extended to other values of the calibrated phase lags measured in the neighborhood of the phase minimum or maximum. The application potential of these two solution methods is studied by analyzing the phase lags measured as a function of frequency for two-layer systems of technological importance, e.g., different plasma-deposited hard coatings on tool steel, coated cutting tools after friction wear, and a sample of a shape memory alloy (NiTi) after mechanical surface treatment.