Profile inversion of principal diffusivities through the use of a spatially modulated heating and a Fourier analysis

Kurzfassung

The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximise the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid flash method). When the material presents a transverse gradient of conductivity, we propose, as a first approach, to perform the Fourier analysis over a sliding window corresponding to one period of the grid pattern. This method allowed us to quantify insitu the diffusivity decrease in a tensile composite sample due to the stress-induced density increase of transverse microcracks. We finally analysed a more rigorous method for transverse conductivity profile inversion. It is based on a perturbation method. The analytical expression of the "transfer function" between the Fourier transform of the temperature contrast and the Fourier transform of conductivity was established. We validated the proposed inverse technique on simulated and noise-corrupted thermograms. The approach is robust and the simulated profiles are very well resolved.