基于自洽聚类分析的2D C/SiC压缩性能快速预报

戴新航; 许承海; 王琨杰; 高博

doi:10.13801/j.cnki.fhclxb.20231206.002

基于自洽聚类分析的2D C/SiC压缩性能快速预报

doi: 10.13801/j.cnki.fhclxb.20231206.002

哈尔滨工业大学　特种环境复合材料技术国家级重点实验室，哈尔滨 150001

详细信息

通讯作者:
高博，博士，助理教授，研究方向为复合材料热结构力学行为研究与不确定性量化　E-mail: 20230194@hit.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2023-10-11
- 修回日期: 2023-11-09
- 录用日期: 2023-11-29
- 网络出版日期: 2023-12-07
- 刊出日期: 2024-08-15

Fast prediction of 2D C/SiC compression performance based on self-consistent clustering analysis

National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150001, China

摘要

摘要: 本文利用自洽聚类分析(Self-consistent clustering analysis，SCA)方法研究了2D C/SiC在单轴压缩载荷下的渐进损伤行为，SCA方法通过应变集中张量对网格单元进行聚类，在不显著降低计算精度的前提下，大幅度降低了模型的自由度，使模型的计算效率得以提高。整个方法由离线和在线两个阶段组成：离线阶段，利用 k-means算法对高保真度的复合材料单胞进行分解、聚类并计算不同聚类间的相互作用张量，最终生成降阶模型；在线阶段，基于降阶模型求解离散的Lippmann-Schwinger方程组获取力学响应。将SCA方法应用于2D C/SiC压缩强度的预报，当聚类总数量为64时，与试验相比，压缩强度求解的计算精度与传统有限元相比降低了1%，但整体计算效率提升了34倍。当不考虑离线阶段花费的聚类时间，即事先已知材料的细观构型对其力学行为进行求解时，其一次在线计算的时间仅为6 s，计算效率比传统有限元提升了10 ⁴倍，在结构性能快速设计、结构状态快速预报等领域，有着广阔的应用前景。
- 2D C/SiC /
- 自洽聚类分析 /
- 渐进损伤 /
- 压缩强度 /
- 细观模型
Abstract: In this paper, the self-consistent clustering analysis (SCA) method was used to investigate the progressive damage behavior of 2D C/SiC under uniaxial compression load. The SCA method clusters the grid elements by strain concentration tensor, which greatly reduces the degree of freedom of the model and improves the computational efficiency of the model without significantly reducing the computational accuracy. The whole method consists of two stages: Offline and online. In the offline stage, the k-means algorithm was used to decompose and cluster the high-fidelity composite unit cells and calculate the interaction tensor between different clusters, and finally the reduced-order model was generated. At the online stage, the mechanical response was obtained by solving the discrete Lippmann-Schwinger equations based on the reduced-order model. The SCA method was applied to predict the compressive strength of 2D C/SiC. When the total number of clusters is 64, compared with the experiment, the calculation accuracy of the compressive strength solution is reduced by 1% compared with the traditional finite element method, but the overall calculation efficiency is improved by 34 times. When the clustering time spent in the offline stage is not considered, that is, the meso-structure of the material is known in advance to solve its mechanical behavior, the time of one-time online calculation is only 6 s, and the calculation efficiency is 10 ⁴ times higher than that of the traditional finite element method. It has broad application prospects in the fields of rapid design of structural performance and rapid prediction of structural state.
- 2D C/SiC /
- self-consistent clustering analysis /
- progressive damage /
- compressive strength /
- mesoscopic model

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图 1 自洽聚类分析(SCA)计算流程图

RVE—Representative volume element; FEM—

Figure 1. Self-consistent clustering analysis (SCA) calculation flow chart

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图 2 聚类算法示意图

Figure 2. Clustering analysis diagram

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图 3 2D C/SiC复合材料的显微形貌

Figure 3. Microstructure of 2D C/SiC composites

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图 4 2D C/SiC的RVE

Figure 4. RVE of 2D C/SiC

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图 5 2D C/SiC纤维束的微观结构

Figure 5. Microstructure of 2D C/SiC fiber bundles

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图 6 2D C/SiC断裂表面的SEM图像

Figure 6. SEM image of 2D C/SiC fracture surface

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图 7 2D C/SiC试样的原位变形

Figure 7. In-situ deformation of 2D C/SiC specimen

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图 8 碳化硅基体聚类可视化结果

Figure 8. Visualization results of silicon carbide matrix clustering

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图 9 碳纤维束两次聚类示意图

Figure 9. Twice clustering diagram of carbon fiber bundles

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图 10 碳纤维束聚类可视化结果

Figure 10. Visualization results of carbon fiber bundle clustering

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图 11 2D C/SiC单轴压缩试验、FEM、SCA应力-应变曲线

Figure 11. Test, FEM, SCA stress-strain curves of 2D C/SiC under uniaxial compression load

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图 12 碳纤维束和碳化硅基体损伤变量

Figure 12. Damage variables of carbon fiber bundles and silicon carbide matrix

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图 13 2D C/SiC的应力云图

Figure 13. Stress cloud of 2D C/SiC

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表 1 代表性体积单元(RVE)几何参数

Table 1. Representative volume element (RVE) geometric parameters

Parameter	Mean value/mm
Long axis of fiber bundle 2 a	0.80
Short axis of fiber bundle 2 b	0.24
Unit cell side length c	1.85
Unit cell height	0.26

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表 2 SiC基体和T300弹性常数

Table 2. SiC matrix and T300 elastic constants

Elastic constant	SiC	T300 carbon fiber
E ₁(compress)/GPa	300.00	130.00
E ₂/GPa	300.00	40.00
G ₁₂/GPa	120.00	24.00
ν ₁₂	0.25	0.26
ν ₂₃	0.25	0.44

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表 3 纤维束弹性常数

Table 3. Elastic constant of fiber bundle

Parameter	E ₁/GPa	E ₂/GPa	G ₁₂/GPa	ν ₁₂	ν ₂₃
Value	173.38	66.80	40.06	0.25	0.43

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表 4 有限元与SCA对2D C/SiC刚度性能的计算结果

Table 4. Results of FEM and SCA calculations for stiffness of 2D C/SiC

Method	Clustering combination	E ₁₁/GPa	G ₁₂/GPa
FEM	—	130.8	46.2
SCA	Matrix: 32, Yarn: 32	127.6(2.5%)	45.9(0.6%)
	Matrix: 64, Yarn: 32	127.7(2.4%)	46.0(0.4%)
	Matrix: 128, Yarn: 32	128.1(2.1%)	46.0(0.4%)
	Matrix: 32, Yarn: 64	128.6(1.7%)	46.0(0.4%)
	Matrix: 32, Yarn: 128	128.8(1.5%)	46.1(0.2%)

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表 5 2D C/SiC试验、FEM、SCA计算时间与计算结果

Table 5. Calculation time and results of test, FEM and SCA for 2D C/SiC

Method	Clustering combination	Time/s		Strength/MPa	Error
Experiment	—	—		382.7	—
FEM	—	61200		364.4	4.8%
		Offline	Online
SCA	Matrix: 32, Yarn: 32	1800	6	361.0	5.7%
	Matrix: 64, Yarn: 32		11	367.9	3.9%
	Matrix: 128, Yarn: 32		25	367.4	4.0%
	Matrix: 32, Yarn: 64		11	361.3	5.6%
	Matrix: 32, Yarn: 128		29	360.7	5.7%

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