Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

• Published in: Ultrasonics 2011-08, Vol.51 (6), p.697-708
• Main Authors: Yang, L., Lobkis, O.I., Rokhlin, S.I.
• Format: Article
• Language: English
• Subjects: Acoustical properties of solids; Acoustics; Attenuation; Attenuation in polycrystals; Condensed matter: structure, mechanical and thermal properties; Cross sections; Ellipsoids; Elongated grains; Elongation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Grains; Mechanical and acoustical properties of condensed matter; Models, Theoretical; Physics; Rayleigh and stochastic limits; Stochastic Processes; Stochasticity; Ultrasonic attenuation; Ultrasonic scattering; Ultrasonics; Ultrasonics, quantum acoustics, and physical effects of sound; Wave propagation
• ISSN: 0041-624X; 1874-9968
• DOI: 10.1016/j.ultras.2011.02.002

► Attenuation coefficients are obtained for cubic polycrystalline materials with elongated grains. ► The Rayleigh and stochastic frequency limits are given for propagation in an arbitrary direction. ► In the stochastic limits the attenuation depends only on the grain size in the propagation direction. ► In the Rayleigh region the attenuation is proportional to grain volume is independent of its shape. ► The relation to backscattering coefficient in polycrystallite medium with elongated grains is obtained. Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.