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

刘慕皓, 张先锋, 谈梦婷, 包阔, 韩国庆, 李逸, 孙伟境. 考虑微结构特征的陶瓷材料含损伤本构模型[J]. 爆炸与冲击, 2024, 44(1): 013102. doi: 10.11883/bzycj-2023-0237
引用本文: 刘慕皓, 张先锋, 谈梦婷, 包阔, 韩国庆, 李逸, 孙伟境. 考虑微结构特征的陶瓷材料含损伤本构模型[J]. 爆炸与冲击, 2024, 44(1): 013102. doi: 10.11883/bzycj-2023-0237
LIU Muhao, ZHANG Xianfeng, TAN Mengting, BAO Kuo, HAN Guoqing, LI Yi, SUN Weijing. A constitutive model for ceramic materials including microstructural features and damage factor[J]. Explosion And Shock Waves, 2024, 44(1): 013102. doi: 10.11883/bzycj-2023-0237
Citation: LIU Muhao, ZHANG Xianfeng, TAN Mengting, BAO Kuo, HAN Guoqing, LI Yi, SUN Weijing. A constitutive model for ceramic materials including microstructural features and damage factor[J]. Explosion And Shock Waves, 2024, 44(1): 013102. 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
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

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

  • 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。
  • 图  1  陶瓷的典型微结构特征及缺陷

    Figure  1.  Typical microstructure characteristics and defects of ceramics

    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

    图  3  裂纹受力示意图

    Figure  3.  Stress diagram of crack

    图  4  裂纹相互作用

    Figure  4.  Crack interaction

    图  5  程序计算流程

    Figure  5.  Program calculation flowts

    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

    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

    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

    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

    图  10  边缘冲击试验照片[26]

    Figure  10.  Edge impact test photos[26]

    图  11  边缘冲击试验仿真模型

    Figure  11.  Simulation model of edge impact test

    图  12  YAG透明陶瓷损伤演化过程

    Figure  12.  Damage evolution process of YAG transparent ceramics

    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

    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

    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

    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

    图  17  裂纹扩展速度随晶粒度变化

    Figure  17.  Variation of crack propagation velocity with grain size

    图  18  YAG透明陶瓷破坏特征,g2=6

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

    图  19  YAG透明陶瓷破坏特征,g2=10

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

    图  20  YAG透明陶瓷破坏特征,g2=12

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

    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

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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 KⅠC/(MPa·m1/2 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
    下载: 导出CSV

    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
    下载: 导出CSV
  • [1] 胡泽望, 陈肖朴, 刘欣, 等. 微量SiO2添加对Pr: Lu3Al5O12陶瓷光学及闪烁性能的影响 [J]. 无机材料学报, 2020, 35(7): 796–802. DOI: 10.15541/jim20190418.

    HU Z W, CHEN X P, LIU X, et al. Trace SiO2 addition on optical and scintillation property of Pr: Lu3Al5O12 ceramics [J]. Journal of Inorganic Materials, 2020, 35(7): 796–802. DOI: 10.15541/jim20190418.
    [2] 卢绪高. 轧膜成型氮化硅陶瓷的组织结构与导热性能研究 [D]. 哈尔滨: 哈尔滨工业大学, 2019.
    [3] TAYLOR L M, CHEN E P, KUSZMAUL J S. Microcrack-induced damage accumulation in brittle rock under dynamic loading [J]. Computer Methods in Applied Mechanics and Engineering, 1986, 55(3): 301–320. DOI: 10.1016/0045-7825(86)90057-5.
    [4] RAJENDRAN A M, KROUPA J L. Impact damage model for ceramic materials [J]. Journal of Applied Physics, 1989, 66(8): 3560–3565. DOI: 10.1063/1.344085.
    [5] STEINBERG D J. Computer studies of the dynamic strength of ceramics [C]//Proceedings of the 18th International Symposium on Shock Waves. Senda: Springer, 1991: 415–422. DOI: 10.1007/978-3-642-77648-9_64.
    [6] JOHNSON G R, HOLMQUIST T J. A computational constitutive model for brittle materials subjected to large strains, high strain rates, and high pressures [M]// Shock Wave and High-Strain-Rate Phenomena in Materials. CRC Press, 1992: 1075–1082. DOI: 10.1115/1.4004326.
    [7] JOHNSON G R, HOLMQUIST T J. An improved computational constitutive model for brittle materials [J]. AIP Conference Proceedings, 1994, 309(1): 981–984. DOI: 10.1063/1.46199.
    [8] JOHNSON G R, HOLMQUIST T J, BEISSEL S R. Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures [J]. Journal of Applied Physics, 2003, 94(3): 1639–1646. DOI: 10.1063/1.1589177.
    [9] WILKINS M. Second progress report of light armor program [R]. Livermore: Lawrence Livermore National Laboratory, 1967. DOI: 10.2172/7156835.
    [10] CHAKRABORTY S, ISLAM R I, SHAW A, et al. A computational framework for modelling impact induced damage in ceramic and ceramic-metal composite structures [J]. Composite Structures, 2017, 164: 263–276. DOI: 10.1016/j.compstruct.2016.12.064.
    [11] REN H L, ZHUANG X Y, RABCZUK T. Implementation of GTN model in dual-horizon peridynamics [J]. Procedia Engineering, 2017, 197: 224–232. DOI: 10.1016/j.proeng.2017.08.099.
    [12] 唐瑞涛, 徐柳云, 文鹤鸣, 等. 陶瓷材料宏观动态新本构模型 [J]. 高压物理学报, 2020, 34(4): 044201. DOI: 10.11858/gywlxb.20190863.

    TANG R T, XU L Y, WEN H M, et al. A macroscopic dynamic constitutive model for ceramic materials [J]. Chinese Journal of High Pressure Physics, 2020, 34(4): 044201. DOI: 10.11858/gywlxb.20190863.
    [13] RAJENDRAN A M. Modeling the impact behavior of AD85 ceramic under multiaxial loading [J]. International Journal of Impact Engineering, 1994, 15(6): 749–768. DOI: 10.1016/0734-743x(94)90033-h.
    [14] RAJENDRAN A M, GROVE D J. Modeling the shock response of silicon carbide, boron carbide and titanium diboride [J]. International Journal of Impact Engineering, 1996, 18(6): 611–631. DOI: 10.1016/0734-743x(96)89122-6.
    [15] ESPINOSA H D, ZAVATTIERI P D, DWIVEDI S K. A finite deformation continuum\discrete model for the description of fragmentation and damage in brittle materials [J]. Journal of the Mechanics and Physics of Solids, 1998, 46(10): 1909–1942. DOI: 10.1016/s0022-5096(98)00027-1.
    [16] 任会兰, 宁建国. 冲击压缩下准脆性材料含微裂纹损伤的本构模型 [J]. 材料工程, 2007(3): 18–21. DOI: 10.3969/j.issn.1001-4381.2007.03.005.

    REN H L, NING J G. Micro-cracks damage constitutive model of quasi-brittle materials subjected to shock compression [J]. Journal of Materials Engineering, 2007(3): 18–21. DOI: 10.3969/j.issn.1001-4381.2007.03.005.
    [17] 任会兰, 宁建国. 强冲击载荷下氧化铝陶瓷的力学特性及本构模型 [J]. 北京理工大学学报, 2007, 27(9): 761–764, 796. DOI: 10.3969/j.issn.1001-0645.2007.09.003.

    REN H L, NING J G. Mechanical characteristics and constitutive model of alumina ceramic subjected to shock loading [J]. Transactions of Beijing Institute of Technology, 2007, 27(9): 761–764, 796. DOI: 10.3969/j.issn.1001-0645.2007.09.003.
    [18] ASHBY M F, SAMMIS C G. The damage mechanics of brittle solids in compression [J]. Pure and Applied Geophysics, 1990, 133(3): 489–521. DOI: 10.1007/BF00878002.
    [19] WANG D, ZHAO J, ZHOU Y H, et al. Extended finite element modeling of crack propagation in ceramic tool materials by considering the microstructural features [J]. Computational Materials Science, 2013, 77: 236–244. DOI: 10.1016/j.commatsci.2013.04.045.
    [20] VIGLIOTTI A, DESHPANDE V S, PASINI D. Non linear constitutive models for lattice materials [J]. Journal of the Mechanics and Physics of Solids, 2014, 64: 44–60. DOI: 10.1016/j.jmps.2013.10.015.
    [21] DESHPANDE V S, EVANS A G. Inelastic deformation and energy dissipation in ceramics: a mechanism-based constitutive model [J]. Journal of the Mechanics and Physics of Solids, 2008, 56(10): 3077–3100. DOI: 10.1016/j.jmps.2008.05.002.
    [22] DESHPANDE V S, GAMBLE E A N, COMPTON B G, et al. A constitutive description of the inelastic response of ceramics [J]. Journal of the American Ceramic Society, 2011, 94(S1): s204–s214. DOI: 10.1111/j.1551-2916.2011.04516.x.
    [23] LAHIRI S K, SHAW A, RAMACHANDRA L S. On performance of different material models in predicting response of ceramics under high velocity impact [J]. International Journal of Solids and Structures, 2016, 176-177: 96–107. DOI: 10.1016/j.ijsolstr.2019.05.024.
    [24] GAMBLE E A, COMPTON B G, DESHPANDE V S, et al. Damage development in an armor ceramic under quasi-static indentation [J]. Journal of the American Ceramic Society, 2011, 94(S1): s215–s225. DOI: 10.1111/j.1551-2916.2011.04472.x.
    [25] ASHBY M F, HALLAM S D. The failure of brittle solids containing small cracks under compressive stress states [J]. Acta Metallurgica, 1986, 34(3): 497–510. DOI: 10.1016/0001-6160(86)90086-6.
    [26] 韩国庆, 张先锋, 谈梦婷, 等. 边缘冲击(EOI)作用下透明陶瓷破坏特性研究 [J]. 爆炸与冲击, 2022, 42(5): 053102. DOI: 10.11883/bzycj-2021-0292.

    HAN G Q, ZHANG X F, TAN M T, et al. Failure characteristics of three transparent ceramics materials under the edge-on impact loading [J]. Explosion and Shock Waves, 2022, 42(5): 053102. DOI: 10.11883/bzycj-2021-0292.
    [27] 马坤, 李名锐, 陈春林, 等. 修正金属本构模型在超高速撞击模拟中的应用 [J]. 爆炸与冲击, 2022, 42(9): 091406. DOI: 10.11883/bzycj-2021-0315.

    MA K, LI M R, CHEN C L, et al. The application of a modified constitutive model of metals in the simulation of hypervelocity impact [J]. Explosion and Shock Waves, 2022, 42(9): 091406. DOI: 10.11883/bzycj-2021-0315.
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  • 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

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