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考虑损伤判据温度相关性的相场法模拟氧化铝热冲击裂纹扩展

杨国欣 郑世风 李定玉 李卫国

杨国欣,郑世风,李定玉,李卫国. 考虑损伤判据温度相关性的相场法模拟氧化铝热冲击裂纹扩展 [J]. 应用数学和力学,2022,43(11):1259-1267 doi: 10.21656/1000-0887.430133
引用本文: 杨国欣,郑世风,李定玉,李卫国. 考虑损伤判据温度相关性的相场法模拟氧化铝热冲击裂纹扩展 [J]. 应用数学和力学,2022,43(11):1259-1267 doi: 10.21656/1000-0887.430133
YANG Guoxin, ZHENG Shifeng, LI Dingyu, LI Weiguo. Thermal Shock Crack Propagation of Alumina Simulated With the Phase-Field Method Under Temperature-Dependent Damage Criteria[J]. Applied Mathematics and Mechanics, 2022, 43(11): 1259-1267. doi: 10.21656/1000-0887.430133
Citation: YANG Guoxin, ZHENG Shifeng, LI Dingyu, LI Weiguo. Thermal Shock Crack Propagation of Alumina Simulated With the Phase-Field Method Under Temperature-Dependent Damage Criteria[J]. Applied Mathematics and Mechanics, 2022, 43(11): 1259-1267. doi: 10.21656/1000-0887.430133

考虑损伤判据温度相关性的相场法模拟氧化铝热冲击裂纹扩展

doi: 10.21656/1000-0887.430133
基金项目: 国家自然科学基金(11727802)
详细信息
    作者简介:

    杨国欣(1994—),男,硕士生(E-mail:gxyang@cqu.edu.cn

    李卫国(1976—),男,教授,博士,博士生导师(通讯作者. E-mail:wgli@cqu.edu.cn

  • 中图分类号: O34

Thermal Shock Crack Propagation of Alumina Simulated With the Phase-Field Method Under Temperature-Dependent Damage Criteria

  • 摘要:

    氧化铝陶瓷材料的力学性能受温度影响显著,因此使用相场法模拟热冲击裂纹的扩展时有必要考虑损伤判据的温度相关性。在现有热力学相场模型的基础上通过引入温度相关性损伤判据,修正了相场模型的控制方程。利用该模型对氧化铝陶瓷热冲击实验进行有限元模拟,并将模拟结果与氧化铝热冲击实验结果和不考虑温度相关性损伤判据的有限元模拟结果进行对比。结果表明,通过引入温度相关性损伤判据,可实现对热冲击裂纹的萌生和扩展过程更合理的模拟。

  • 图  1  x=0处尖锐和弥散裂纹拓扑:(a)尖锐裂纹;(b) 弥散裂纹,用长度尺度l表示裂纹相场$ \bar{d} $

    Figure  1.  Topologies of sharp and diffuse cracks at x=0: (a) the sharp crack; (b) phase field $ \bar{d} $ of the diffuse crack denoted by length scale l

    图  2  水淬实验几何模型

    Figure  2.  The geometric model for the water quenching experiment

    图  3  收敛性分析

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  3.  Convergence analysis

    图  4  裂纹相场和温度场随时间的演化

    Figure  4.  Evolution of the crack phase field and the temperature field with time

    图  5  水淬实验结果与有无考虑温度相关性损伤判据模拟结果的对比:(a) Chu等[13]的模拟结果;(b)实验结果[6];(c) 本文模拟结果

    Figure  5.  Comparison between water quenching experimental results and simulation results with or without temperature-dependent damage criteria: (a) simulation results of Chu et al [13]; (b) the experimental results [6]; (c) simulation results of this paper

    图  6  圆盘热冲击问题的几何模型和热边界条件(红色区域表示外加热流)

    Figure  6.  The geometric model and thermal boundary conditions for thermal shock problems of disks (the red area represents applied heat flow)

    图  7  圆盘辐射加热实验结果和模拟结果

    Figure  7.  Experimental results of radiation heating and simulation results of the phase field method

    图  8  圆盘辐射加热实验结果和模拟结果: (a)实验结果;(b) 考虑温度相关性临界能量释放率Gc(T)的模拟结果;(c) 不考虑温度相关性临界能量释放率Gc的模拟结果

    Figure  8.  Experimental and simulation results of disk radiation heating: (a) the experimental results; (b) the simulation results with temperature-dependent critical energy release rate Gc(T); (c) the simulation results without temperature-dependent critical energy release rate Gc

    图  9  不同热流密度下的裂纹和裂纹尖端温度随时间的演化:(a) $ \gamma =7.5\times {10}^{5}\;\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3} $;(b) $\gamma =1\times {10}^{6}\;\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3}$

    Figure  9.  Evolution of crack and crack tip temperatures with time under different heat fluxes: (a) $ \gamma =7.5\times {10}^{5}\;\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3} $; (b) $\gamma =1\times {10}^{6}\;\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3}$

    表  1  氧化铝薄板试样材料参数[6]

    Table  1.   Material parameters of the alumina sheet sample[6]

    material parametervalue or expression
    elastic modulus $ E/{\text{GPa}} $$340 - 2.54T{\exp({ - {T_{\rm{m} } } }/T}) + 1.9( {T - 0.363{T_{\rm{m} } } + | {T - 0.363{T_{\rm{m} } } } |} ){\exp ({ { { - {T_{\rm{m} } } } / T} } )}$
    density $ \rho /( {{{\text{g}} / {{\text{c}}{{\text{m}}^{\text{3}}}}}} ) $6.119
    Poisson’s ratio $ \upsilon $0.22
    melting point $ {T_{\rm{m}}}/{\text{K}} $2327.15
    thermal conductivity $ k/( {{{\text{W}} / {( {{\text{m}} \cdot {\text{K}}} )}}} ) $$ 210.75\ln ( T ) - 746.28 $
    heat capacity $ C_p/( {{{\text{J}} / {( {{\text{kg}} \cdot {\text{K}}} )}}} ) $$60.225 - 0.011\;28T + 1.244\;56 \times {10^{ - 6} }\times{T^2}$
    thermal expansion $ \alpha /( {{{\text{1}} / {\text{K}}}} ) $$( {6.52 + 6.811\;4 \times { {10}^{ - 4} }\times T} ){\text{ } } \times {10^{ - 6} }$
    下载: 导出CSV

    表  2  圆盘试样的温度相关性材料参数[7-8]

    Table  2.   Temperature-dependent material parameters of disk samples[7-8]

    material parametervalue or expression
    elastic modulus $ E{\text{/GPa}} $$380 - 2.54T{\exp ({ { { - {T_{\rm{m} } } } / T} } }) + 1.9( {T - 0.363{T_{\rm{m} } } + | {T - 0.363{T_{\rm{m} } } } |} ){\exp( { { { - {T_{\rm{m} } } } / T} } )}$
    density $ \rho /( {{{\text{g}} / {{\text{c}}{{\text{m}}^{\text{3}}}}}} ) $3.90
    Poisson’s ratio $ \upsilon $0.25
    melting point $ {T_{\rm{m}}}/{\text{K}} $2327.15
    thermal conductivity $k/( { { {\text{W} } / ({ {\text{m} } \cdot {\text{K} } } }} ) )$$31.06 - 0.113\;8 T + 2.95 \times {10^{ - 4} } \times {T^2} - 4.43 \times {10^{ - 7} } \times {T^3}$
    heat capacity $ C_p/( {{{\text{J}} / {( {{\text{kg}} \cdot {\text{K}}} )}}} ) $$60.225 - 0.011\;28T + 1.244\;56 \times {10^{ - 6} }\times {T^2}$
    thermal expansion $ \alpha /( {{1 / {\text{K}}}} ) $$60.225 - 0.011\;28T + 1.244\;56 \times {10^{ - 6} }\times {T^2}$
    下载: 导出CSV
  • [1] KINGERY W D. Factors affecting thermal stress resistance of ceramic materials[J]. Journal of the American Ceramic Society, 2010, 38(1): 3-15.
    [2] MENOUILLARD T, BELYTSCHKO T. Analysis and computations of oscillating crack propagation in a heated strip[J]. International Journal of Fracture, 2011, 167: 57-70. doi: 10.1007/s10704-010-9519-0
    [3] 吴大方, 王怀涛, 朱芳卉. 1 200 ℃高温环境下部件受热前表面应变的光学测量[J]. 应用数学和力学, 2018, 39(6): 631-644

    WU Dafang, WANG Huaitao, ZHU Fanghui. Optical measurement of heated-front-surface strains for components in high temperature environments up to 1 200 ℃[J]. Applied Mathematics and Mechanics, 2018, 39(6): 631-644.(in Chinese)
    [4] LI D, WANG R, WANG X, et al. Simulation of the thermal shock cracking behaviors of ceramics under water quenching for 3-dimension conditions[J]. European Journal of Mechanics A: Solids, 2020, 84: 104080. doi: 10.1016/j.euromechsol.2020.104080
    [5] WU J Y. A unified phase-field theory for the mechanics of damage and quasi-brittle failure[J]. Journal of the Mechanics and Physics of Solids, 2017, 103: 72-99. doi: 10.1016/j.jmps.2017.03.015
    [6] SHAO Y, ZHANG Y, XU X. Effect of crack pattern on the residual strength of ceramics after quenching[J]. Journal of the American Ceramic Society, 2011, 94: 72-99.
    [7] HONDA S, OGIHARA Y, KISHI T, et al. Estimation of thermal shock resistance of fine porous alumina by infrared radiation heating method[J]. Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi, 2009, 117(1371): 1208-1215. doi: 10.2109/jcersj2.117.1208
    [8] HONDA S, SUZUKI T, NISHIKAWA T, et al. Estimation of thermal shock properties for silicon nitride having high thermal conductivity[J]. Journal of the Ceramic Society of Japan, 2010, 110(1277): 38-43.
    [9] KARMA A, KESSLER D A, LEVINE H. Phase-field model of mode Ⅲ dynamic fracture[J]. Physical Review Letters, 2001, 87: 045501. doi: 10.1103/PhysRevLett.87.045501
    [10] 李家宇, 曾忠, 乔龙. 相场方法模拟液滴的动态润湿行为[J]. 应用数学和力学, 2019, 40(9): 957-967

    LI Jiayu, ZENG Zhong, QIAO Long. Numerical simulation of droplets’ dynamic wetting process with the phase field method[J]. Applied Mathematics and Mechanics, 2019, 40(9): 957-967.(in Chinese)
    [11] MICHE C, SCHÄNZEL LM, ULMER H. Phase field modeling of fracture in multi-physics problems, part Ⅰ: balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 294: 449-485. doi: 10.1016/j.cma.2014.11.016
    [12] 柳占立, 初东阳, 王涛, 等. 爆炸和冲击载荷下金属材料及结构的动态失效仿真[J]. 应用数学和力学, 2021, 42(1): 1-14 doi: 10.1007/s10483-021-2692-5

    LIU Zhanli, CHU Dongyang, WANG Tao, et al. Dynamic failure simulation of metal materials and structures under blast and impact loading[J]. Applied Mathematics and Mechanics, 2021, 42(1): 1-14.(in Chinese) doi: 10.1007/s10483-021-2692-5
    [13] CHU D, LI X, LIU Z. Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling[J]. International Journal of Fracture, 2017, 208: 115-130. doi: 10.1007/s10704-017-0220-4
    [14] LI D, LI W, WANG R, et al. Simulation of the thermal shock behavior of ultra-high temperature ceramics with the consideration of temperature-dependent crack propagation criterion and interaction between thermal shock cracks evolution and thermal conduction[J]. European Journal of Mechanics A: Solids, 2018, 72: 268-274. doi: 10.1016/j.euromechsol.2018.05.016
    [15] MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45/48): 2765-2778.
    [16] 李定玉. 计及使役环境的高温陶瓷材料抗热震性能及表征方法研究[D]. 博士学位论文. 重庆: 重庆大学, 2015.

    LI Dingyu. Research of thermal shock resistance of high temperature ceramics and its characterization methods with the consideration of different operating environments[D]. PhD Thesis. Chongqing: Chongqing University, 2015. (in Chinese)
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出版历程
  • 收稿日期:  2022-04-13
  • 修回日期:  2022-04-20
  • 网络出版日期:  2022-09-27
  • 刊出日期:  2022-11-30

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