Calculation of whisker Poisson’s ratio and hardnessprediction of whisker-reinforced ceramic composites
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摘要: 晶须在强化陶瓷材料强度和韧性的同时能显著提高材料硬度，在解决陶瓷硬度不足上具有突出优势。针对目前实验法研究晶须增强陶瓷材料中存在组分设计盲目性大、试样制备耗时费力等问题，以β-Si3N4晶须(β-Si3N4w)增强Si3N4陶瓷为对象，提出了一种计算晶须泊松比的双向随机建模方法，并基于密度泛函理论(DFT)框架下平面超软赝势法和广义梯度近似(GGA)中的Perdew-Wang 91(PW91)函数，对β-Si3N4超晶胞泊松比进行了计算。以此为基础，提出了运用德劳内(Delaunay)三角剖分法和伪随机函数法建立β-Si3N4w增强Si3N4陶瓷微观结构模型的方法，对模型硬度进行了预报并对β-Si3N4w增硬机制进行了探讨。结果表明，β-Si3N4w泊松比约为0.27。β-Si3N4w增强Si3N4陶瓷硬度预报值与相关实验测试值存在较好一致性，这表明了晶须泊松比计算模型和晶须强韧陶瓷微观结构建模法的有效性。在β-Si3N4w含量为3wt%时，硬度达到最大值22.80 GPa。应力分析表明β-Si3N4w各向分布性分散了应力集中作用区并依靠β-Si3N4w高强度特性承载了大量应力的作用，这是硬度提高的主要原因。Abstract: Whisker is able to enhance remarkably the hardness of ceramics while strengthening their strength and toughness, and has outstanding advantages in solving the lack of hardness. Aiming at the problems of high blindness of component design and time-consuming of specimen preparation in the current experimental method to investigate whisker-reinforced ceramics, a bidirectional stochastic modeling method to calculate the whisker Poisson’s ratio was proposed taking β-Si3N4w-reinforced Si3N4 ceramic as the object. Based on the plane super-soft pseudopotential method under the framework of density functional theory (DFT) and Perdew-Wang 91 (PW-91) function in the generalized gradient approximation (GGA), the β-Si3N4 supercell Poisson’s ratio was calculated. Further, an approach to establish the two-dimensional microstructure of β-Si3N4w-reinforced Si3N4 ceramics was presented by using Delaunay triangulation rule and pseudo-random function method. Then, the model hardness was predicted and the hardening mechanism of β-Si3N4w was discussed. Results show that the Poisson’s ratio of β-Si3N4w is about 0.27. The predicted hardness values of β-Si3N4w-reinforced Si3N4 ceramics are in good consistent with the related experimental test values, which demonstrates the validity of whisker Poisson’s ratio calculation model and whisker-reinforced ceramic microstructure modeling method. The hardness of Si3N4-based ceramics reaches the maximum value of 22.80 GPa at 3wt% β-Si3N4w content. Stress analysis shows that the anisotropic distribution of β-Si3N4w disperses the stress concentration area and with stands a large amount of stress depending on its high strength characteristics, which is the main reason for the increase in hardness.
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Key words:
- whisker /
- ceramics /
- Poisson’s ratio /
- first principle /
- hardness
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图 1 β-Si3N4w及其泊松比计算模型
Figure 1. β-Si3N4w and Poisson’s ratio calculation model
NA, NB and NC—Number of cell units in the array along directions A, B and C; A, B, C—Direction of the cell array
图 3 随机种子点集V (a)、Delaunay三角网 (b)、Voronoi 图 (c)、β-Si3N4w种子 (d) 和β-Si3N4w增强Si3N4陶瓷微观结构模型 (e)
Figure 3. Random seed point set V (a), Delaunay triangulation (b), Voronoi diagram (c), β-Si3N4w seeds (d) and β-Si3N4w-reinforced Si3N4 ceramic microstructure model (e)
Pk—Point of kth random seed; Ww—Width of whiskers; Hw—Height of whiskers
图 4 β-Si3N4w增强Si3N4陶瓷硬度预报模型
Figure 4. β-Si3N4w-reinforced Si3N4 ceramic hardness model
Phd—Load
图 5 0wt%~5wt% β-Si3N4w增强Si3N4陶瓷材料Mises等效应力云图
Figure 5. Mises stress cloud diagrams of 0wt%-5wt% β-Si3N4w-reinforced Si3N4 ceramics
图 6 β-Si3N4w增强Si3N4陶瓷载荷-压深曲线
Figure 6. Load-depth curves of β-Si3N4w-reinforced Si3N4 ceramics
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