WAVE-PROPAGATION IN DAMAGED SOLIDS

In this paper, a theoretical model is presented for investigating elastic wave propagation in damaged solids. This model is suited for damaged solids with dilutely distributed defects, and it may aid in the design of experimental configurations and in the proper interpretation of measured data from ultrasonic non-destructive evaluation (NDE) for detecting and characterizing the damage states of the solid. The problem of wave scattering by a single defect of arbitrary shape is first formulated as a set of boundary integral equations. whose solution yields the unknown quantities on the boundary of the defect. The scattering cross-section is then introduced as a measure of the overall effects of the defect on the energy withdrawal from the incident wave. The damaged solid is approximated by an equivalent effective medium which is thought of as statistically homogeneous and linearly viscoelastic. By introducing a complex wave number. neglecting interaction effects among individual defects, and using energy considerations, a simple equation is obtained for calculating the attenuation coefficient from the average scattering cross-section and the number density of the defects. Kramers-Kronig relations are subsequently applied to compute the effective wave (phase) velocity from which the group velocity can be immediately calculated. A method for finding the dynamic effective stiffness of the damaged solid from the attenuation coefficient and the effective wave velocity is proposed. Numerical results are presented for a damaged solid permeated by a distribution of completely randomly oriented penny-shaped microcracks.