氮化硅陶瓷微观结构的有限元建模方法

doi:10.12382/bgxb.2024.0407

摘要/Abstract

摘要：

陶瓷在长时高温和高应力下工作时会发生蠕变,蠕变损伤累积将最终导致失效发生。蠕变损伤的演化与陶瓷的微结构有十分密切的关系,建立陶瓷材料的微观有限元模型有助于更深入地了解这一关系。以氮化硅陶瓷为研究对象,提出一种基于动力学的三维晶体沉积数值模型,结合Monte Carlo Potts结晶生长模型对氮化硅陶瓷的烧结过程进行模拟,力求还原氮化硅陶瓷的动态生长过程以及结晶后晶体大小、形状、取向分布以及空洞的大小、形状、分布等微观结构特征。基于该模拟生成的几何边界描述自动生成Python脚本,在有限元软件中完成建模。利用该有限元模型对氮化硅陶瓷的统计弹性常数进行验证,计算结果与试验数据对比,相对误差约为4.5%,吻合良好。

关键词: 氮化硅陶瓷, 沉积算法, 动态模型, Monte Carlo Potts模型, 有限元模型

Abstract:

Ceramics will undergo when operating under long-term high temperature and high stress conditions,which promotes the generation and propagation of cracks and eventually leads to failure.The evolution of creep damage is closely related to the microstructure of ceramics.Establishing a microscopic finite element model of ceramic materials is conducive to a more in-depth understanding of this relationship.For this purpose,a dynamics-based 3D crystal deposition model is proposed by taking Si₃N₄ ceramics as the research object.The sintering process of Si₃N₄ ceramics is simulated by the Monte Carlo Potts crystal growth model,striving to reproduce the dynamic growth process of Si₃N₄ceramics as well as the microstructure characteristics,such as the size,shape and orientation distribution of crystals after crystallization,and the size,shape and distribution of pores.Based on the geometric boundary description generated by this simulation,a Python script is automatically generated to complete the finite element modeling in a FEA software.The statistical elastic constants of Si₃N₄ ceramics are verified using this finite element model.By comparing the calculated results with the experimental data,it is shown rhat the relative error is approximately 4.5%,which shows a good agreement.

Key words: Si₃N₄ ceramics, deposition algorithm, dynamic model, Monte Carlo Potts model, finite element model

中图分类号:

TQ174.1+5

周迅, 王洪武, 王旭升, 王正, 曲俊峰, 孙孟勇, 潘骏. 氮化硅陶瓷微观结构的有限元建模方法[J]. 兵工学报, 2025, 46(4): 240407-.

ZHOU Xun, WANG Hongwu, WANG Xusheng, WANG zheng, QU Junfeng, SUN Mengyong, PAN Jun. Finite Element Modeling of Si₃N₄ Ceramic Microstructure[J]. Acta Armamentarii, 2025, 46(4): 240407-.

图/表 17

图1 β-氮化硅陶瓷结构显微形貌

Fig.1 Microscopic morphology of β-Si3N4 ceramics structure

图2 β-氮化硅陶瓷XRD分析结果

Fig.2 XRD analysis results of β-Si3N4 ceramics

表1 样品成分及比例

Table 1 Sample composition and proportion

比例类型	β-氮化硅	晶间相
比例类型	β-氮化硅	Lu₄Si₂O₇N₂	空洞
质量比例/%	88.4	11.6	0
体积比例/%	93.3	5.2	1.5

图3 晶粒的几何模型简化

Fig.3 Simplified geometric model of crystal grains

图4 晶粒的位置及姿态

Fig.4 The position and posture of crystal grains

图5 晶粒的受力分析

Fig.5 Stress analysis of crystal grains

图6 晶粒间的接触计算

Fig.6 Contact of crystal grains

图7 沉积模拟中的晶粒群

Fig.7 Crystal grains in deposition simulation

图8 沉积模型剖面局部图像

Fig.8 A profile image of the deposition model

图9 晶体取向角分布直方图

Fig.9 Histogram of crystal orientation angle distribution

图10 晶体生长示意图

Fig.10 Schematic diagram of crystal growth

图11 晶体二维剖面生长速度计算

Fig.11 Crystal growth rate diagram

图12 Monte Carlo Potts模型模拟流程

Fig.12 Monte Carlo Potts model simulation flow chart

图13 晶体粗化后的氮化硅陶瓷剖面图像

Fig.13 Profile image of ceramics after crystal coarsening

图14 有限元网格

Fig.14 Finite element mesh

表2 β-氮化硅晶体的弹性刚度矩阵常数

Table 2 Elastic stiffness matrix constants of β-Si3N4 crystal

常数	C₁₁	C₃₃	C₄₄	C₆₆	C₁₂	C₁₃
数值/GPa	434	577	109	120	197	130

图15 数值模拟结果与试验结果

Fig.15 Numerically simulated results and experimental results

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