Theoretical approach of the characterization of gradients in elastic properties by acoustic microscopy

This study explains processes for the characterization by acoustic microsco py of materials presenting, along a thickness d close to the surface, a gra dient in elastic properties in direction perpendicular to the surface. The method, modelling the non-homogeneous area by a finite number of layers of the same thickness, is sensitive to the factor fd (f is the working frequen cy) and to the nature of the gradient profile. The study of the dispersion of the Rayleigh velocity as a function of frequency shows that the shape of the curve mainly depends on the gradient profile and on the structure (sur face material and bulk material). When the numerical derivative of the disp ersion curves presents inflexion points, they can be linked to the depth an d to the nature of the profile. Modelling of the materials displaying a gra dient shows that, in some cases; the plot of the curvature of the dispersio n curves as a function of frequency is a useful means of characterization.