Polycrystals Modeling And Micromechanical Analysis Of Ceramics
Shengqiang Xue - M.S. Thesis Defense
Advisor: Dr. Ruqiang Feng
Date: Tuesday, April 22, 2003
Time: 11:00 a.m.
Place: W183 Nebraska Hall
A computational modeling technique for analyzing the microstructural effects on the elastic response of polycrystalline materials is successfully developed. The technique uses two-dimensional (2-D) and three-dimensional (3-D) Voronoi tessellations for topologically accurate modeling of polycrystalline microstructures. A new efficient algorithm and its computer program are developed and used to simulate 2-D and 3-D Voronoi polycrystals with as many as 10,000 grains. The topological properties of these Voronoi polycrystals are studied statistically and compared with the available data in the literature.
To implement the Voronoi polycrystal model into the commercial finite element (FE) code ABAQUS/Standard for micromechanical analysis, a method for generating special meshes that preserve the polycrystalline microstructure is developed. Model simulations are carried out: (1) to study the micromechanical states in fully-dense and slightly-porous polycrystalline a-6H silicon carbide (SiC) and a-phase aluminum oxide (Al2O3) under macroscopically uniaxial-strain elastic compression, and (2) to determine the stress and strain fields in nanocrystalline zirconium oxide (ZrO2) nanofibers under uniaxial-stress tension as well as the statistical elastic properties of these nanofibers.
The results on SiC and Al2O3 show that: (1) statistically accurate representation is achieved with a Voronoi polycrystal model containing 1000 grains; (2) the distributions of stresses and strain energy density are Gaussian-like and their mean values are independent of loading direction and distributions of crystal size and orientation; and (3) the results of 2-D calculations are statistically consistent with those of 3-D simulations. The results on Al2O3 also indicate that the commonly used simplification, i.e., treating a trigonal Al2O3 polycrystal as an aggregate of transversely isotropic grains underestimates the microstructural stress variation in the material.
The analysis for nanocrystalline ZrO2 nanofibers uses models containing 330~650 3-D Voronoi crystals and covers a number of length-to-width ratios. The results show that: 1) microstructural axial stress varies significantly (±40%); 2) for a sufficiently large length-to-width ratio, the axial stress and strain distributions are Gaussian-like; and 3) the fiber’s nominal Young’s modulus varies between 210 and 220 GPa. The modulus results are very close to the lower Hashin-Shtrikman bound for the material in its polycrystalline bulk form.
