Stress-dependent elastic moduli of polycrystalline materials are used in a statistically based model for the scattering of ultrasonic waves from randomly oriented grains that are members of a stressed polycrystal. The stress is assumed to be homogeneous and can be either residual or generated from external loads. The stress-dependent elastic properties are incorporated into the definition of the differential scattering cross-section, which defines how strongly an incident wave is scattered into various directions. Nine stress-dependent differential scattering cross-sections or scattering coefficients are defined to include all possibilities of incident and scattered waves, which can be either longitudinal or (two) transverse wave types. The evaluation of the scattering coefficients considers polycrystalline aluminum that is uniaxially stressed. An analysis of the influence of incident wave propagation direction, scattering direction, frequency, and grain size on the stress-dependency of the scattering coefficients follows. Scattering coefficients for aluminum indicate that ultrasonic scattering is much more sensitive to a uniaxial stress than ultrasonic phase velocities. By developing the stress-dependent scattering properties of polycrystals, the influence of acoustoelasticity on the amplitudes of waves propagating in stressed polycrystalline materials can be better understood. This work supports the ongoing development of a technique for monitoring and measuring stresses in metallic materials.
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