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金属学报  2020, Vol. 56 Issue (12): 1643-1653    DOI: 10.11900/0412.1961.2020.00120
  本期目录 | 过刊浏览 |
气孔与晶界相互作用的相场模拟
孙正阳1,2, 王昱天3, 柳文波1,2()
1 西安交通大学核科学与技术学院 西安 710049
2 西安交通大学陕西省先进核能工程研究中心陕西省先进核能技术重点实验室 西安 710049
3 西安交通大学机械工程学院 西安 710049
Phase-Field Simulation of the Interaction Between Pore and Grain Boundary
SUN Zhengyang1,2, WANG Yutian3, LIU Wenbo1,2()
1 School of Nuclear Science and Technology, Xi'an Jiaotong University, Xi'an 710049, China
2 Shaanxi Key Laboratory of Advanced Nuclear Energy and Technology, Shaanxi Engineering Research Center of Advanced Nuclear Energy, Xi'an Jiaotong University, Xi'an 710049, China
3 School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
引用本文:

孙正阳, 王昱天, 柳文波. 气孔与晶界相互作用的相场模拟[J]. 金属学报, 2020, 56(12): 1643-1653.
Zhengyang SUN, Yutian WANG, Wenbo LIU. Phase-Field Simulation of the Interaction Between Pore and Grain Boundary[J]. Acta Metall Sin, 2020, 56(12): 1643-1653.

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摘要: 

对现有的气孔与晶界相互作用的相场模型进行改进,提出了新形式的自由能密度函数,并采用了张量形式的扩散系数。分析了相场模型中唯象参数的选择依据,并讨论了模型中界面能和界面宽度等物理参数的影响因素。气孔和晶界相互作用的相场模拟结果表明:晶界的曲率是晶界移动的动力,而气孔是晶界移动的阻力;当气孔施加的最大阻力大于等于晶界移动的动力时,气孔会随晶界一起运动;而当气孔施加的最大阻力小于晶界移动的动力时,气孔与晶界分离。若气孔与晶界未发生分离,体系的演化将由晶界主导转变为气孔主导,演化速率显著下降。含气孔UO2多晶体系的晶粒生长的相场模拟结果表明:气孔率越大,晶粒生长速率越慢;UO2平均晶粒直径与时间成幂函数关系,幂指数随气孔率的增大而增大。

关键词 相场模拟气孔晶界晶粒生长扩散    
Abstract

The grain boundary (GB) and average grain size considerably affect the properties of materials, such as the fracture strength, dielectric constant, and thermal conductivity. For instance, when subjected to irradiation at 1750 ℃, the swelling of the UO2 pellets and the release of fission gas from them decrease significantly with the increasing average grain size. However, several second-phase particles, such as pores, are inevitably introduced into a material during the solid-phase sintering or neutron radiation processes. Therefore, studying the interaction between the pores and GBs is considerably important. In this study, a phase-field model of the interaction between the pores and GBs is developed. Subsequently, the free-energy density function was modified, where the diffusion coefficient was incorporated in the tensor form. In addition, the selection of the phenomenological parameters, such as the coefficient in the free-energy density function of the phase-field model, was analyzed, and the influencing factors of interface energy and interface width were discussed. The phase-field model simulation results of the interaction between the pores and GBs show that the curvature of GB was the major driving force associated with the movement of GB and that pores resisted the movement of GB. Accordingly, the pores moved together with the GBs when the maximum pinning force exerted by the pores was larger than the driving force produced by the curvature of GB; however, the pores and GBs separated in the opposite case, during which the GB moved much faster than pores. The results of the phase-field simulation of the grain growth of the pore-containing UO2 show that the grain growth speed decreases with the increasing porosity. The average grain size of UO2 is a power function of time, the exponent of which increases with the increasing porosity.

Key wordsphase field simulation    pore    grain boundary    grain growth    diffusion
收稿日期: 2020-04-16     
ZTFLH:  TG148  
基金资助:国家自然科学基金委员会与中国工程物理研究院联合基金项目(U1830124);国家自然科学基金青年项目(11705137);中国博士后科学基金项目(2019M663738);清华大学新型陶瓷与精细工艺国家重点实验室项目(KF201713)
作者简介: 孙正阳,男,1998年生,本科生
图1  相场模型示意图
ParameterSymbolValue
Phenomenological parameterA2.5
Dα, Dβ1.08
γα, γβ1.04
ε3
Kinetic parameterLα, Lβ1
M5
Gradient parameterκα, κβ, κc2
Space stepΔx1
Time stepΔt0.001
表1  模拟选取的无量纲参数
图2  不同梯度参数κα下取向场变量η1α、η2α和浓度场变量C的平衡取值
图3  晶界能量密度σgb和晶界宽度l与κα1/2的线性拟合
图4  不同梯度参数κc下相场变量的平衡取值
图5  相界能量密度σint与κα1/2 (κβ1/2)、κc1/2的线性拟合
图6  双晶粒体系演化的相场模拟Color online(a) 1×104 step (b) 3×104 step (c) 4×104 step (d) 5×104 step
图7  晶界移动速率和中心晶粒尺寸随时间演化的动力学曲线
图8  单气孔体系演化的相场模拟Color online(a) 1×104 step (b) 3×104 step (c) 4×104 step (d) 5×104 step
图9  双气孔体系演化的相场模拟Color online(a) 1×104 step (b) 5×104 step (c) 7.5×104 step (d) 10×104 step
图10  四气孔体系演化的相场模拟Color online(a) 1×104 step (b) 2×104 step (c) 10×104 step (d) 25×104 step
图11  气孔率fp=2%时含气孔多晶UO2演化的相场模拟Color online(a) 0.1×104 step (b) 0.5×104 step (c) 1×104 step (d) 2×104 step
图12  不同气孔率下的晶粒生长曲线
fpnR2
02.050.990
2%2.440.997
4%3.150.992
8%4.190.995
表2  不同气孔率下的晶粒生长指数
[1] Rahaman M N. Ceramic Processing and Sintering [M]. New York: Marcel Dekker, 1995: 540
[2] Turnbull J A. The effect of grain size on the swelling and gas release properties of UO2 during irradiation [J]. J. Nucl. Mater., 1974, 50: 62
doi: 10.1016/0022-3115(74)90061-0
[3] Ahmed K, Tonks M, Zhang Y F, et al. Particle-grain boundary interactions: A phase field study [J]. Comput. Mater. Sci., 2017, 134: 25
doi: 10.1016/j.commatsci.2017.03.025
[4] Zhao Y, Zhang H Y, Wei H, et al. A phase field study for scaling rules of grain coarsening in polycrystalline system containing second-phase particles [J]. Acta Metall. Sin., 2013, 49: 981
doi: 10.3724/SP.J.1037.2013.00164
[4] (赵 彦, 张洪宇, 韦 华等. 相场法研究含第二相颗粒多晶体系的晶粒粗化标度律 [J]. 金属学报, 2013, 49: 981)
doi: 10.3724/SP.J.1037.2013.00164
[5] Zhou G Z, Wang Y X, Chen Z. Phase-field method simulation of the effect of hard particles with different shapes on two-phase grain growth [J]. Acta Metall. Sin., 2012, 48: 227
doi: 10.3724/SP.J.1037.2011.00609
[5] (周广钊, 王永欣, 陈 铮. 相场法模拟不同形状的硬质颗粒对两相晶粒长大的影响 [J]. 金属学报, 2012, 48: 227)
doi: 10.3724/SP.J.1037.2011.00609
[6] Gao Y J, Zhang H L, Jin X, et al. Phase-field simulation of two-phase grain growth with hard particles [J]. Acta Metall. Sin., 2009, 45: 1190
[6] (高英俊, 张海林, 金 星等. 相场方法研究硬质颗粒钉扎的两相晶粒长大过程 [J]. 金属学报, 2009, 45: 1190)
[7] Ahmed K, Yablinsky C A, Schulte A, et al. Phase field modeling of the effect of porosity on grain growth kinetics in polycrystalline ceramics [J]. Model. Simul. Mater. Sci. Eng., 2013, 21: 065005
doi: 10.1088/0965-0393/21/6/065005
[8] Moelans N, Blanpain B, Wollants P. Pinning effect of second-phase particles on grain growth in polycrystalline films studied by 3-D phase field simulations [J]. Acta Mater., 2007, 55: 2173
doi: 10.1016/j.actamat.2006.11.018
[9] Moelans N, Blanpain B, Wollants P. A phase field model for the simulation of grain growth in materials containing finely dispersed incoherent second-phase particles [J]. Acta Mater., 2005, 53: 1771
doi: 10.1016/j.actamat.2004.12.026
[10] Chang K, Feng W M, Chen L Q. Effect of second-phase particle morphology on grain growth kinetics [J]. Acta Mater., 2009, 57: 5229
doi: 10.1016/j.actamat.2009.07.025
[11] Hötzer J, Rehn V, Rheinheimer W, et al. Phase-field study of pore-grain boundary interaction [J]. J. Ceram. Soc. Jpn., 2016, 124: 329
doi: 10.2109/jcersj2.15266
[12] Kundin J, Sohaib H, Schiedung R, et al. Phase-field modelling of pores and precipitates in polycrystalline systems [J]. Model. Simul. Mater. Sci. Eng., 2018, 26: 065003
doi: 10.1088/1361-651X/aacb94
[13] Nichols F A. Theory of grain growth in porous compacts [J]. J. Appl. Phys., 1966, 37: 4599
doi: 10.1063/1.1708102
[14] Brook R J. Pore-grain boundary interactions and grain growth [J]. J. Am. Ceram. Soc., 1969, 52: 56
doi: 10.1111/jace.1969.52.issue-1
[15] Riedel H, Svoboda J. A theoretical study of grain growth in porous solids during sintering [J]. Acta Metall. Mater., 1993, 41: 1929
doi: 10.1016/0956-7151(93)90212-B
[16] Petrishcheva E, Renner J. Two-dimensional analysis of pore drag and drop [J]. Acta Mater., 2005, 53: 2793
doi: 10.1016/j.actamat.2005.02.040
[17] Klinger L, Rabkin E, Shvindlerman L S, et al. Grain growth in porous two-dimensional nanocrystalline materials [J]. J. Mater. Sci., 2008, 43: 5068
doi: 10.1007/s10853-008-2678-y
[18] Fan D, Chen L Q. Computer simulation of grain growth using a continuum field model [J]. Acta Mater., 1997, 45: 611
doi: 10.1016/S1359-6454(96)00200-5
[19] Moelans N, Blanpain B, Wollants P. An introduction to phase-field modeling of microstructure evolution [J]. Calphad, 2008, 32: 268
doi: 10.1016/j.calphad.2007.11.003
[20] Krivilyov M D, Mesarovic S D, Sekulic D P. Phase-field model of interface migration and powder consolidation in additive manufacturing of metals [J]. J. Mater. Sci., 2017, 52: 4155
doi: 10.1007/s10853-016-0311-z
[21] Lin M Z, Zhang R J, Fang W, et al. Phase field simulation of sintering process in biphasic porous material [J]. Acta Metall. Sin., 2012, 48: 1207
doi: 10.3724/SP.J.1037.2012.00353
[21] (刘明治, 张瑞杰, 方 伟等. 相场法模拟两相多孔组织烧结 [J]. 金属学报, 2012, 48: 1207)
doi: 10.3724/SP.J.1037.2012.00353
[22] Chen Y, Kang X H, Xiao N M, et al. Phase field modelling of grain growth in polycrystalline material [J]. Acta Phys. Sin., 2009, 58: 124
[22] (陈 云, 康秀红, 肖纳敏等. 多晶材料晶粒生长粗化过程的相场方法模拟 [J]. 物理学报, 2009, 58: 124)
doi: 10.7498/aps.58.124
[23] Jing X N, Ni Y, He L H, et al. 2-D phase-field simulation of pore evolution in sintering ceramics [J]. J. Inorg. Mater., 2002, 17: 1078
[23] (景晓宁, 倪 勇, 何陵辉等. 陶瓷烧结过程孔隙演化的二维相场模拟 [J]. 无机材料学报, 2002, 17: 1078)
[24] Deng J. A phase field model of sintering with direction-dependent diffusion [J]. Mater. Trans., 2012, 53: 385
doi: 10.2320/matertrans.M2011317
[25] Sun Z Y, Yang C, Liu W B. Phase-field simulations of the sintering process of uranium dioxide [J]. Acta Metall. Sin., 2020, 56: 1295
[25] (孙正阳, 杨 超, 柳文波. UO2烧结过程的相场模拟 [J]. 金属学报, 2020, 56: 1295)
[26] Lu D, Jiang P, Xu Z Z. Solid State Physics [M]. 2nd Ed., Shanghai: Shanghai Scientific and Technical Publishers, 2010: 364
[26] (陆 栋, 蒋 平, 徐至中. 固体物理学 [M]. 第2版. 上海: 上海科学技术出版社, 2010: 364)
[27] Chen L Q, Fan D N. Computer simulation model for coupled grain growth and Ostwald ripening—Application to Al2O3-ZrO2 two-phase systems [J]. J. Am. Ceram. Soc., 1996, 79: 1163
doi: 10.1111/jace.1996.79.issue-5
[28] Cahn J W. On spinodal decomposition [J]. Acta Metall., 1961, 9: 795
doi: 10.1016/0001-6160(61)90182-1
[29] Moelans N, Blanpain B, Wollants P. Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems [J]. Phys. Rev., 2008, 78B: 024113
[30] Hsueh C H, Evans A G, Coble R L. Microstructure development during final/intermediate stage sintering—I. Pore/grain boundary separation [J]. Acta Metall., 1982, 30: 1269
doi: 10.1016/0001-6160(82)90145-6
[31] Ahmed K, Allen T, El-Azab A. Phase field modeling for grain growth in porous solids [J]. J. Mater. Sci., 2016, 51: 1261
doi: 10.1007/s10853-015-9107-9
[32] Ahmed K, Pakarinen J, Allen T, et al. Phase field simulation of grain growth in porous uranium dioxide [J]. J. Nucl. Mater., 2014, 446: 90
doi: 10.1016/j.jnucmat.2013.11.036
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