Modélisation de la propagation ultrasonore en milieu dispersif ; mesure de vitesse et application à la caractérisation des graphites

Abstract
The measurement of the velocity of propagation of ultrasonic pulse in dispersive media gives a quantity which physical meaning is ambiguous. In this paper we simulate a dispersive medium using the Kramers-Krönig relationship which expresses the causality of a linear system. We develope an appropriate signal processing such as Hilbert transform and cross-correlation to measure the time of flight of an ultrasonic impulse propagating in such a medium. This allows to deduce from this simulation the physical significance of the two informations given by two methods. Then these two methods are applied to several categories of graphites with dispersif character. Thus the differences between the measured velocities by Hilbert transform and cross-correlation are correlated to several microstructural properties of the material such as grain size, porosity and to thermal elaboration treatement.