考虑微结构特征的陶瓷材料含损伤本构模型

刘慕皓; 张先锋; 谈梦婷; 包阔; 韩国庆; 李逸; 孙伟境

doi:10.11883/bzycj-2023-0237

考虑微结构特征的陶瓷材料含损伤本构模型

doi: 10.11883/bzycj-2023-0237

1.
南京理工大学机械工程学院，江苏南京 210094
2.
北京机电工程总体设计部，北京 100854

基金项目: 国家自然科学基金(12102200, 12141202)；江苏省自然科学基金(BK20210320)

详细信息

作者简介:
刘慕皓（1997－　），男，硕士研究生，1437966356@njust.edu.cn

通讯作者:
张先锋（1978－　），男，博士，教授，博士生导师，lynx@njust.edu.cn

中图分类号: O347.3; TQ174.7
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- 被引次数: 0
出版历程
- 收稿日期: 2023-07-04
- 修回日期: 2023-09-06
- 网络出版日期: 2023-10-30
- 刊出日期: 2024-01-11

A constitutive model for ceramic materials including microstructural features and damage factor

1.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangshu, China
2.
Beijing System Design Institute of the Electro-mechanic Engineering, Beijing 100854, China

摘要

摘要: 为了研究不同微结构陶瓷材料的冲击破坏特征，以从微结构角度出发、描述陶瓷材料非弹性变形和断裂行为的Deshpande-Evan模型为基础构建本构模型，计算了无约束条件下材料的应力状态。为了验证改进模型的有效性，将VUMAT子程序编程方法将与ABAQUS有限元软件相结合，并将其应用于典型陶瓷材料（YAG透明陶瓷）冲击破坏过程的分析模拟。采用改进模型分析应变率、应力三轴度、晶粒尺寸及初始缺陷分布密度对YAG透明陶瓷动态力学行为和损伤演化机制的影响规律。结果表明：随着晶粒尺寸和裂纹分布密度的增加，YAG透明陶瓷破坏程度随之加剧，完全损伤区域面积也随之增加，晶粒尺寸对YAG透明陶瓷宏观破坏特征的影响程度要大于裂纹分布密度；YAG透明陶瓷失效强度以及断裂应变随着晶粒尺寸以及初始缺陷分布密度的增大而减小；随着应变率不断增加，YAG透明陶瓷在不同晶粒尺寸以及初始缺陷分布密度下的峰值应力和断裂应变均随之增加；裂纹扩展速度会随着晶粒尺寸的增加呈现出先增加而后平缓的趋势，裂纹扩展速度与初始缺陷分布密度系数成线性关系。改进模型可以描述YAG透明陶瓷微结构对其宏观破坏特征的影响，为进一步分析微结构对陶瓷材料宏观破坏特征的影响提供支撑。
- 含损伤本构 /
- 陶瓷材料 /
- 冲击破坏 /
- YAG透明陶瓷 /
- 微结构特征
Abstract: In order to study the impact failure characteristics of ceramic materials with different microstructures, a constitutive model was constructed based on the Deshpande-Evan model which describes the inelastic deformation and fracture behavior of ceramic materials from the perspective of microstructure and the stress state of the material is calculated without considering the constraint condition. In order to verify the validity of the improved model, VUMAT subroutine programming method was used to combine it with ABAQUS finite element software, and it was applied to the analysis and simulation of the impact failure process of typical ceramic materials (YAG transparent ceramics). The effects of strain rate, stress triaxiality, grain size and crack distribution density on the dynamic mechanical behavior and damage evolution mechanism of YAG transparent ceramics were analyzed by using the improved model. The results show that with the increase of grain size and crack distribution density, the damage degree of YAG transparent ceramics increases, and the area of complete damage area increases. The influence of grain size on the macroscopic failure characteristics of YAG transparent ceramics is greater than that of crack distribution density. The failure strength and fracture strain of YAG transparent ceramics decrease with the increase of grain and crack distribution density. With the increase of the strain rate, the peak stress and fracture strain of YAG transparent ceramics under the influence of different factors (grain size as well as initial defect distribution density) increase. With the increase of grain size, the crack propagation speed of YAG transparent ceramics increases first and then flattens out, which is linearly related to the crack distribution density coefficient. The improved model can describe the influence of YAG transparent ceramic microstructure on its macroscopic failure characteristics, and provide support for further analysis of the influence of microstructure on the macroscopic failure characteristics of ceramic materials.
- constitutive model involving damage factor /
- ceramic materials /
- impact failure /
- YAG transparent ceramics /
- microstructure characteristics

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图 1 陶瓷的典型微结构特征及缺陷

Figure 1. Typical microstructure characteristics and defects of ceramics

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图 2 考虑微结构特征的陶瓷材料本构模型理论体系

Figure 2. Constitutive model theory system of ceramic materials considering microstructure characteristics

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图 3 裂纹受力示意图

Figure 3. Stress diagram of crack

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图 4 裂纹相互作用

Figure 4. Crack interaction

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图 5 程序计算流程

Figure 5. Program calculation flowts

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图 6 不同应变率下YAG透明陶瓷的应力-应变响应及损伤演化过程

Figure 6. Stress-strain response and damage evolution of YAG transparent ceramics at different strain rates

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图 7 不同应力三轴度下YAG透明陶瓷的应力应变响应

Figure 7. Stress-strain response of YAG transparent ceramics under different stress triaxialities

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图 8 不同晶粒度下YAG透明陶瓷的应力应变曲线

Figure 8. Stress-strain curves of YAG transparent ceramics with different grain sizes

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图 9 不同裂纹分布密度下YAG透明陶瓷的应力应变曲线

Figure 9. Stress-strain curves of YAG transparent ceramics with different crack distribution densities

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图 10 边缘冲击试验照片^[26]

Figure 10. Edge impact test photos^[26]

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图 11 边缘冲击试验仿真模型

Figure 11. Simulation model of edge impact test

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图 12 YAG透明陶瓷损伤演化过程

Figure 12. Damage evolution process of YAG transparent ceramics

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图 13 主裂纹扩展长度模拟结果与试验对比图

Figure 13. Comparison between simulation and test results of main crack propagation length

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图 14 YAG透明陶瓷破坏特征，d=40 μm

Figure 14. Damage characteristics of YAG transparent ceramics while d=40 μm

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图 15 YAG透明陶瓷破坏特征，d=100 μm

Figure 15. Damage characteristics of YAG transparent ceramics while d=100 μm

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图 16 YAG透明陶瓷破坏特征，d=150 μm

Figure 16. Damage characteristics of YAG transparent ceramics while d=150 μm

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图 17 裂纹扩展速度随晶粒度变化

Figure 17. Variation of crack propagation velocity with grain size

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图 18 YAG透明陶瓷破坏特征，g₂=6

Figure 18. Damage characteristics of YAG transparent ceramics, g₂=6

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图 19 YAG透明陶瓷破坏特征，g₂=10

Figure 19. Damage characteristics of YAG transparent ceramics, g₂=10

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图 20 YAG透明陶瓷破坏特征，g₂=12

Figure 20. Damage characteristics of YAG transparent ceramics, g₂=12

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图 21 裂纹扩展速度与裂纹密度系数的关系

Figure 21. Relationship of crack propagation velocity with crack density coefficient

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表 1 YAG透明陶瓷弹性阶段材料参数

Table 1. Material parameters of YAG transparent ceramics in elastic stage

密度/（kg·m³）	剪切模量/GPa	泊松比	$ {\sigma }_{\rm{Y}} $/GPa
4550	113	0.25	1.58

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表 2 YAG透明陶瓷塑性阶段材料参数

Table 2. Material parameters of transparent YAG ceramic in plastic stage

$ {\sigma }_{\rm{Y}} $/GPa	$ {\varepsilon }_{\rm{Y}} $	$ {\dot{{ \varepsilon }}}_0 $/s⁻¹	$ {\dot{\varepsilon }}_{\rm{t}} $/s⁻¹	n	M
1.58	5.6×10⁻³	1×10⁻³	1×10⁶	34	0.1

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表 3 YAG透明陶瓷裂纹扩展阶段材料参数^[19-20]

Table 3. Material parameters of YAG transparent ceramics in crack propagation stage

d/μm	摩擦因数	K_ⅠC/（MPa·m^1/2）	β	γ	g₁	g₂	m	$ {\dot{l}}_{0} $/（m·s⁻¹）
100	0.75	1.27	0.45	2	0.5	6	30	0.01

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表 4 YAG透明陶瓷颗粒相互作用阶段材料参数^[19-20]

Table 4. Material parameters of YAG transparent ceramic particle interaction stage

摩擦损伤角/（°）	强度指数	颗粒塑性应变指数	颗粒塑性参考应变率/（s⁻¹）	初始流动膨胀角/（°）	相对密实度	剩余强度系数
70	5	10	2×10⁴	0	0.99	1

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