Acoustoelasticity in cracked solids

A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov's approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated.