MSSMat Laboratory, CentraleSupélec, CNRS UMR8579, Université Paris-Saclay, 3 Rue Joliot Curie, 91190 Gif-sur-Yvette, France; Laser Institute, Qilu University of Technology (Shandong Academy of Sciences), 250103 Shandong, China.
MSSMat Laboratory, CentraleSupélec, CNRS UMR8579, Université Paris-Saclay, 3 Rue Joliot Curie, 91190 Gif-sur-Yvette, France.
Ultrasonics. 2020 Jan;100:105980. doi: 10.1016/j.ultras.2019.105980. Epub 2019 Aug 19.
An analytical approach to develop explicit formulas of attenuation coefficient in both 2D and 3D cases is proposed. It results in a better understanding of the grain scattering mechanisms within a polycrystalline material and the grain size effects on the attenuation of an ultrasonic wave. It is based on the Stanke and Kino's model and uses the Born approximation. An explicit formula is deduced for untextured polycrystals with equiaxed grains of cubic symmetry and allows a rigorous comparison of the attenuation coefficient between both 2D and 3D cases. It confirms that the attenuation in the Rayleigh region is higher in 2D simulation than in 3D one, while very similar coefficients are obtained in the stochastic region for both cases. The study of the explicit formula allows the decomposition of the attenuation coefficient into various scattering-induced components, which leads to a better understanding of different grain scattering mechanisms. The reflection/transmission at grain boundaries between wave modes of a same type mainly explains a same attenuation coefficient in the stochastic region for both 2D and 3D modelings. The conversion at grain boundaries between different types of wave modes provides some explanations for a higher attenuation value given by the 2D modeling in the Rayleigh region. The effect of the grain size on the attenuation coefficient is then predicted by the 2D analytical calculation and by the FE simulation. The analytical-numerical comparison validates the numerical calculations and the approach suggests a way of using the 2D FE calculations to predict the evolution of the attenuation coefficient with the wave frequency in 3D.
提出了一种在 2D 和 3D 情况下开发衰减系数显式公式的分析方法。这有助于更好地理解多晶材料内部晶粒散射机制以及晶粒尺寸对超声波衰减的影响。该方法基于 Stanke 和 Kino 的模型，并使用 Born 近似。推导了具有各向同性立方对称晶粒的无织构多晶材料的显式公式，可实现 2D 和 3D 情况之间衰减系数的严格比较。结果表明，在瑞利区，2D 模拟中的衰减高于 3D 模拟，而在随机区，两种情况下的系数非常相似。显式公式的研究允许将衰减系数分解为各种散射引起的分量，从而更好地理解不同的晶粒散射机制。同一类型波模式的晶粒边界处的反射/透射主要解释了 2D 和 3D 建模中随机区的相同衰减系数。不同类型波模式之间的边界转换为 2D 建模在瑞利区给出的更高衰减值提供了一些解释。然后通过 2D 分析计算和有限元模拟预测晶粒尺寸对衰减系数的影响。分析-数值比较验证了数值计算，该方法提出了一种使用 2D FE 计算预测 3D 中衰减系数随波频率变化的方法。
