Huang M, Sha G, Huthwaite P, Rokhlin S I, Lowe M J S
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom.
Department of Materials Science and Engineering, Edison Joining Technology Center, The Ohio State University, 1248 Arthur E. Adams Drive, Columbus, Ohio 43221, USA.
J Acoust Soc Am. 2020 Dec;148(6):3645. doi: 10.1121/10.0002916.
The phase velocity dispersion of longitudinal waves in polycrystals with elongated grains of arbitrary crystallographic symmetry is studied in all frequency ranges by the theoretical second-order approximation (SOA) and numerical three-dimensional finite element (FE) models. The SOA and FE models are found to be in excellent agreement for three studied polycrystals: cubic Al, Inconel, and a triclinic material system. A simple Born approximation for the velocity, not containing the Cauchy integrals, and the explicit analytical quasi-static velocity limit (Rayleigh asymptote) are derived. As confirmed by the FE simulations, the velocity limit provides an accurate velocity estimate in the low-frequency regime where the phase velocity is nearly constant on frequency; however, it exhibits dependence on the propagation angle. As frequency increases, the phase velocity increases towards the stochastic regime and then, with further frequency increase, behaves differently depending on the propagation direction. It remains nearly constant for the wave propagation in the direction of the smaller ellipsoidal grain radius and decreases in the grain elongation direction. In the Rayleigh and stochastic frequency regimes, the directional velocity change shows proportionalities to the two elastic scattering factors even for the polycrystal with the triclinic grain symmetry.
利用理论二阶近似（SOA）和数值三维有限元（FE）模型，在所有频率范围内研究了具有任意晶体对称性的细长晶粒多晶体中纵波的相速度色散。对于三种研究的多晶体：立方铝、因科镍合金和三斜材料体系，发现SOA模型和FE模型具有极好的一致性。推导了一个不包含柯西积分的简单速度玻恩近似以及显式解析准静态速度极限（瑞利渐近线）。有限元模拟证实，在低频区域，当相速度随频率几乎恒定时，速度极限提供了准确的速度估计；然而，它表现出对传播角度的依赖性。随着频率增加，相速度朝着随机区域增加，然后随着频率进一步增加，根据传播方向表现出不同的行为。对于沿较小椭球晶粒半径方向传播的波，相速度几乎保持恒定，而在晶粒伸长方向上相速度减小。在瑞利和随机频率区域，即使对于具有三斜晶粒对称性的多晶体，方向速度变化也与两个弹性散射因子成比例。
