The self-consistent dynamic problem of estimating the damage of a material by an acoustic method

An approach is proposed for formulating the self-consistent problem on the basis of equations that describe the dynamics of a material and the state of its defects. It is shown that the damage of the material gives rise to frequency-dependent attenuation and phase velocity dispersion of an ultrasonic wave propagating in it. This makes it possible to estimate the damage by means of the acoustic method. The applied deformation field leads to accumulation of defects. A kinetic equation is derived for describing the damage growth, which proves to be an exponential process. The parameters of the system for which the accumulation of defects can approximately be considered as linear are estimated.