Effective Elastic Stiffness Tensor and Ultrasonic Velocities for 3D Printed Polycrystals with Pores and Texture

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.

KEYWORDS:

• Elastic stiffness tensor
• ultrasonic velocities
• 3D printing
• polycrystals
• pores
• texture

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [92060111].