Effective Elastic Stiffness Tensor and Ultrasonic Velocities for 3D Printed Polycrystals with Pores and Texture
Effective Elastic Stiffness Tensor and Ultrasonic Velocities for 3D Printed Polycrystals with Pores and Texture
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DOI：
10.1080/09349847.2022.2151058
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发表时间：
2022-09
影响因子：
1.4
通讯作者：
Ruo-yu Tan;Yongfeng Song;Xiongbing Li;Shu Cheng;Pei-jun Ni
中科院分区：
文献类型：
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作者：
Ruo-yu Tan;Yongfeng Song;Xiongbing Li;Shu Cheng;Pei-jun Ni
摘要 本文重点研究 3D 打印多晶中孔隙和纹理的微机械建模。采用高斯形状近似来描述方向分布函数（ODF）并构建代表体积单元（RVE）的初始均匀化模型。利用改进的 Mori-Tanaka (MT) 方案结合逐步迭代方法，将不同尺寸的球形和椭圆形孔隙分阶段添加到 RVE 中以实现均质化。其中，在建立从微观结构到宏观弹性的跨尺度模型时，可以考虑孔隙之间的力学相互作用和孔隙位置的空间分布。获得最终的弹性刚度张量后，将 Christoffel 方程与 Cardano 公式相结合，得出取决于微观结构的超声波速度的封闭形式解。数值结果表明，该方法能够有效地捕捉孔隙和纹理在弹性刚度张量、平均速度和速度分布上的行为特征。
ABSTRACT This paper focuses on the micromechanical modeling of pores and texture in 3D-printed polycrystals. A Gaussian-shape approximation is used to describe the orientation distribution function (ODF) and construct the initial homogenization model of the representative volume element (RVE). Spherical and ellipsoidal pores of varying sizes are added in stages to the RVE for homogenization, utilizing the modified Mori-Tanaka (MT) scheme in conjunction with the stepwise iterative method. Wherein, the mechanical interactions between pores and the spatial distribution of pore locations could be taken into account, when developing a cross-scale model from microstructure to macroelasticity. After obtaining the final elastic stiffness tensor, the Christoffel equation is combined with the Cardano’s formula to derive a closed form solution for ultrasonic velocities depending on microstructure. According to the numerical results, this method can effectively capture the behavior characteristics of pores and texture on the elastic stiffness tensor, average velocity, and velocity distribution.