Functionally graded

Media with a continuous dependence of the elastic properties on the depth are usually called functionally graded materials (FGMs). The necessity of solving wave problems for FGMs occurs in hydro-, seismo-, and physical acoustics, as well as in connection with the appearance of new composite materials, film microelectronic piezoelectric structures, and materials with protective micro- and nanocoatings. The elastic properties of such materials gradually vary due to the technology of their fabrication (sputtering, sintering) or diffusion processes in the interlayer gluing of dissimilar module layers. In some cases, it is a special task to reduce the contrast of the elastic properties of a composite (for example, metal ceramics) in order to reduce internal stresses occurring under temperature and force loads. Materials with strengthening gradient coatings are widely used; accordingly, there is an increasing need to develop reliable nondestructive wave methods for their control.

To determine the elastic properties of FGMs or different damages in the material, indentation or ultrasonic probing data are used. The theoretical analysis of indentation results is based on solving the corresponding contact problems, while remote ultrasonic control is based on analysis of surface acoustic waves (SAWs).The IMMI develops integral approach to solve wave problems for half-spaces, cylindrical and periodical FGM structures. Within this approach, the total wave field (displacement field) is represented as a convolution of the Green’s matrix of the considered waveguide with the surface load vector. Methods of construction of the Fourier transform of Green’s matrix and algorithms of the search for the real and close-to-real axis poles of its element are developed that is of key importance for implementing integral approach.

FGM coating under surface load

Influence of thickness (h_g) of FGM interlayer on slowness of surface waves in layered half-space