Acoustoelastic Birefringences in Plastically Deformed Solids: Part I—Theory

Abstract

A modified theory of acoustoelasticity is proposed to include the effect of small plastic deformation on propagational speeds of elastic waves in orthotropic media. In the constitutive equation for the incremental stresses of a predeformed body, the elastic moduli are modified by elastic deformation and plastic strains. The latter is related to the texture of the material. Several formulae for the acoustoelastic birefringences (differences of two shear wave speeds polarized at perpendicular directions) are derived. They can be applied to measure residual stresses and plastic strains by ultrasonic techniques.