Stress-dependent ultrasonic scattering in polycrystalline materials

Abstract

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.

Attenuation and velocity of elastic waves in polycrystals with generally anisotropic grains: Analytic and numerical modeling

“…ellipsoidal grain shapes [8,9,13,14,15], crystallographic texture [7,8,12,16] and residual stresses [17]. Also, complex colony microstructure of titanium alloys [18] can be incorporated in the scattering models through the effective grain properties of general anisotropy [8,12].…”

Stress-dependent second-order grain statistics of polycrystals

“…Explicit expressions for the other 43 independent components are given elsewhere. 45 Traditionally, the Voigt index notation is used to represent the components of the elastic moduli C eff IJ ¼ C eff ijkl (see Appendix A for the relation between IJ and ijkl). However, it is customary to present the components of N in full index form, N abdc ijkl .…”

“…The 44 independent components are N Relations between the 44 independent components of N and the remaining 1597 non-zero terms are listed elsewhere. 45 Section III gives quantitative results for these 44 components for polycrystalline iron and aluminum.…”

Attenuation and Phase Velocity of Elastic Wave in Textured Polycrystals with Ellipsoidal Grains of Arbitrary Crystal Symmetry

“…However, FEM is a numerical method and it has limited practical application to the ultrasonic characterization of grain microstructures. Due to the industrial needs of ultrasonic characterization of microstructure characteristics from ultrasound measurements, many studies have strived to develop analytical attenuation models for polycrystalline materials with a variety of complexities such as the low symmetry constituents [7,[24][25][26][27], the duplex microstructure [10] and the columnar grains [28].…”