Rokhlin S I, Li J, Sha G
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. 2015 May;137(5):2655-69. doi: 10.1121/1.4919333.
A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Green's function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.
针对超声波在随机弹性介质中的传播，建立了一个简单的近似模型。该模型包含二阶多重散射，适用于包括几何频段在内的所有频率范围。它基于参考介质格林函数的远场近似以及质量算符的简化，此外还包括一阶平滑近似的简化。在此近似下，得到了扰动波数的色散方程；其解给出了色散超声速度和衰减系数。该近似解具有通用性，适用于具有任意弹性对称性的非等轴晶粒。对于等轴立方晶粒，将该解与现有的二阶模型以及玻恩近似进行了比较。比较结果表明，所得解的误差比玻恩近似小，并且能合理地显示多重散射的起始以及玻恩近似在高频时的适用极限。即使对于任意晶体对称性，所建立模型中的扰动波数也不明确依赖于微晶弹性性质；它取决于两个无量纲散射弹性参数和宏观超声速度（这些参数取决于微晶模量）。这为从衰减到材料微观结构的反演潜在方案提供了优势。
