Phase-field simulation of void evolution in UO<sub>2</sub> under applied stress

Jiang Yan-Bo; Liu Wen-Bo; Sun Zhi-Peng; La Yong-Xiao; Yun Di

doi:10.7498/aps.71.20211440

Abstract

Owing to the migration and aggregation of point defects produced by cascade collision, a large number of cavities form easily during irradiation of the uranium dioxide (UO₂) that is an important nuclear fuel. In addition, cavities are also inevitably introduced into the ceramic fuel during sintering. Moreover, the creep strain and thermal strain, caused by the extreme environment of high temperature and strong irradiation, significantly increase the applied stress of nuclear fuel. Therefore, it is crucial to investigate the microstructure evolution of the cavities in UO₂ fuel under applied stress. In this work, a phase-field model of void evolution in UO₂ under applied stress is established. Firstly, the elastic equilibrium equation is solved by the perturbation-iterative method, and the stress distribution around a single void under applied stress is calculated. The results show that the stress concentration is observed at the edge of the void, and the simulated stress distribution is consistent with the theoretically analytical results. Then, the evolution processes of a single void under different applied stresses are simulated by the phase-field model. The results show that the growth rate of void increases with the augment of applied stress. Finally, the effect of applied stress on grain growth and void evolution in polycrystalline are also studied. The results show that the applied stress will accelerate the void growth. With the increase of the applied stress, the effect of the applied stress on accelerating the void evolution increases.

Keywords:

Authors and contacts

1.
Institute of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China
2.
Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu 610213, China

Corresponding author: Liu Wen-Bo, liuwenbo@xjtu.edu.cn

Funds: Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant Nos. U1830124, U2130105) and the Innovative Scientific Program of China National Nuclear Corporation.

FullText HTML : translate this paragraph

References

[1]	Govers K, Lemehov S, Hou M, Verwerft M 2007 J. Nucl. Mater. 366 161 Google Scholar
[2]	杨辉, 冯泽华, 王贺然, 张云鹏, 陈铮, 信天缘, 宋小蓉, 吴璐, 张静 2021 70 054601 Google Scholar Yang H, Feng Z H, Wang H R, Zhang Y P, Chen Z, Xin T Y, Song X R, Wu L, Zhang J 2021 Acta Phys. Sin. 70 054601 Google Scholar
[3]	孙正阳, 杨超, 柳文波 2020 金属学报 56 1295 Sun Z Y, Yang C, Liu W B 2020 Acta Metall. Sin. 56 1295
[4]	Solomon A A 1973 J. Am. Ceram. Soc. 56 164 Google Scholar
[5]	Brask D N 1979 J. Nucl. Mater. 83 265 Google Scholar
[6]	Porter D L, Takata M L, Wood E L 1983 J. Nucl. Mater. 116 272 Google Scholar
[7]	Sahu H K, Jung P 1985 J. Nucl. Mater. 136 154 Google Scholar
[8]	Brager H R, Garner F A, Guthrie G L 1977 J. Nucl. Mater. 66 301 Google Scholar
[9]	Jiang Y, Liu W, Li W, Sun Z, Xin Y, Chen P, Yun D 2021 Comput. Mater. Sci. 188 110176 Google Scholar
[10]	Millett P C, Rokkam S, El-Azab A, Tonks M, Wolf D 2009 Model. Simul. Mater. Sci. Eng. 17 64003 Google Scholar
[11]	Brailsford A D, Bullough R, Hayns M R 1976 J. Nucl. Mater. 60 246 Google Scholar
[12]	Wiedersich H 1972 Radiat. Eff. Defect. S. 12 111 Google Scholar
[13]	Millett P C, El-Azab A, Rokkam S, Tonks M, Wolf D 2011 Comput. Mater. Sci. 50 949 Google Scholar
[14]	Millett P C, El-Azab A, Wolf D 2011 Comput. Mater. Sci. 50 960 Google Scholar
[15]	Liu W B, Wang N, Ji Y Z, Song P C, Zhang C, Yang Z G, Chen L Q 2016 J. Nucl. Mater. 479 316 Google Scholar
[16]	杨朝曦, 柳文波, 张璁雨, 贺新福, 孙正阳, 贾丽霞, 师田田, 恽迪 2021 70 116101 Google Scholar Yang Z X, Liu W B, Zhang C Y, He X F, Sun Z Y, Jia L X, Shi T T, Yun D 2021 Acta Phys. Sin. 70 116101 Google Scholar
[17]	Hu S Y, Chen L Q 2001 Acta Mater. 49 1879 Google Scholar
[18]	Wang J J, Bhattacharyya S, Li Q, Heo T W, Ma X Q, Chen L 2012 Phil. Mag. Lett. 92 327
[19]	Kim D, Kim S G, Kim W T, Cho J, Han H N, Cha P 2011 Scr. Mater. 64 1079 Google Scholar
[20]	Chang K, Lee G, Kwon J 2016 Radiat. Eff. Defect. S. 171 242 Google Scholar
[21]	Salvo M, Sercombe J, Ménard J, Julien J, Helfer T, Désoyer T 2015 J. Nucl. Mater. 456 54 Google Scholar
[22]	Cahn J W, Hilliard J E 1958 J. Chem. Phys. 28 258 Google Scholar
[23]	Tonks M R, Zhang Y, Butterfield A, Bai X 2015 Model. Simul. Mater. Sci. Eng. 23 45009 Google Scholar
[24]	Wang Y U, Jin Y M, Khachaturyan A G 2002 J. Appl. Phys. 92 1351 Google Scholar
[25]	Sheng G, Bhattacharyya S, Zhang H, Chang K, Shang S L, Mathaudhu S N, Liu Z K, Chen L Q 2012 Mater. Sci. Eng. A 554 67 Google Scholar
[26]	Tonks M, Millett P 2011 Mater. Sci. Eng. A 528 4086 Google Scholar
[27]	Yan L L, Liu C Z, Ying Y Z, Zheng C 2014 Chinese Phys. B 23 69102 Google Scholar
[28]	Wang Y U, Jin Y M, Khachaturyan A G 2002 J. Appl. Phys. 91 6435 Google Scholar
[29]	Moelans N, Blanpain B, Wollants P 2008 Calphad 32 268 Google Scholar
[30]	Chen L Q, Shen J 1998 Comput. Phys. Commun. 108 147 Google Scholar
[31]	Kang K H, Ryu H J, Song K C, Yang M S 2002 J. Nucl. Mater. 301 242 Google Scholar
[32]	Aagesen L K, Schwen D, Tonks M R, Zhang Y 2019 Comput. Mater. Sci. 161 35 Google Scholar
[33]	Kinoshita M 1997 J. Nucl. Mater. 248 185 Google Scholar
[34]	Freyss M, Petit T, Crocombette J 2005 J. Nucl. Mater. 347 44 Google Scholar
[35]	Xiao H, Long C, Chen H, Tian X, Wei T, Zhao Y, Gao W 2015 Appl. Surf. Sci. 351 517 Google Scholar
[36]	Chen T, Chen D, Sencer B H, Shao L 2014 J. Nucl. Mater. 452 364 Google Scholar
[37]	Fritz I J 1976 J. Appl. Phys. 47 4353 Google Scholar
[38]	Jin Y M, Wang Y U, Khachaturyan A G 2003 Philos. Mag. 83 1587 Google Scholar
[39]	徐芝纶 1982 弹性力学(上卷) (北京: 高等教育出版社) 第89页 Xu Z L 1982 Elasticity (Vol. 1) (Beijing: Higher Education Press) p89 (in Chinese)
[40]	Wang H, Biswas S, Han Y, Tomar V 2018 Comput. Mater. Sci. 150 169 Google Scholar
[41]	Heo T W, Bhattacharyya S, Chen L 2013 Philos. Mag. 93 1468 Google Scholar
[42]	Aagesen L K, Gao Y, Schwen D, Ahmed K 2018 Phys. Rev. E 98 23309 Google Scholar
[43]	孙正阳, 王昱天, 柳文波 2020 金属学报 56 1643 Google Scholar Sun Z Y, Wang L T, Liu W B 2020 Acta Metall. Sin. 56 1643 Google Scholar
[44]	Liu W B, Ji Y Z, Tan P K, Zang H, He C H, Yun D, Zhang C, Yang Z G 2016 Materials 9 105 Google Scholar

Cited By

图 1 (a) 初始空洞示意图; (b) 空洞周围应力分布

Figure 1. (a) Schematic diagram of the initial void; (b) stress distribution with the void.

DownLoad: Full-Size Img PowerPoint

图 2 三个典型截面上的应力分布

Figure 2. Stress distribution along three typical cross sections.

DownLoad: Full-Size Img PowerPoint

图 3 模拟结果与解析解的应力分布比较

Figure 3. Comparison of stress distribution between simulation results and analytical solutions.

DownLoad: Full-Size Img PowerPoint

图 4 (a)−(c)无应力下空洞演化; (d)−(f) 100 MPa附加应力下空洞演化; (g)−(i)应力分布随时间演化

Figure 4. (a)−(c) The evolution of void without stress; (d)−(f) the evolution of void with 100 MPa applied stress; (g)−(i) the distribution of stress during the evolution.

DownLoad: Full-Size Img PowerPoint

图 5 不同应力下空洞半径随时间变化

Figure 5. The change of void radius with time under different stresses.

DownLoad: Full-Size Img PowerPoint

图 6 (a)中线应力分布; (b)中线弹性能密度分布

Figure 6. (a) Stress distribution in the center line; (b) elastic energy density distribution in the center line.

DownLoad: Full-Size Img PowerPoint

图 7 (a)初始结构示意图; (b)模拟区域的水平中线上的弹性模量分布

Figure 7. (a) Schematic of initial structure; (b) elastic constants distribution in the center line.

DownLoad: Full-Size Img PowerPoint

图 8 (a)−(c)晶粒和空洞随时间演化; (d)−(f)演化过程中的应力分布

Figure 8. (a)−(c) Evolution of grains and void with time; (d)−(f) the distribution of stress during the evolution.

DownLoad: Full-Size Img PowerPoint

图 9 晶间空洞演化中三个典型截面上应力分布

Figure 9. Stress distribution along three typical cross sections during intergranular void evolution.

DownLoad: Full-Size Img PowerPoint

图 10 无外加应力下的双晶组织

Figure 10. The twin-crystal microstructure without applied stress.

DownLoad: Full-Size Img PowerPoint

图 11 不同外加应力下的双晶组织((a)—(c))及对应的应力分布((d)—(f))　(a), (d) 50 MPa; (b), (e) 100 MPa; (c), (f) 150 MPa

Figure 11. The twin-crystal microstructure ((a)–(c)) and the corresponding stress distribution with different applied stresses ((d)–(f)): (a), (d) 50 MPa; (b), (e) 100 MPa; (c), (f) 150 MPa.

DownLoad: Full-Size Img PowerPoint

图 12 无外加应力下的多晶组织

Figure 12. The polycrystal microstructure without applied stress.

DownLoad: Full-Size Img PowerPoint

图 13 不同外加应力下的多晶组织((a)—(c))和对应的应力分布((d)—(f))　(a), (d) 50 MPa; (b), (e) 100 MPa; (c), (f) 150 MPa

Figure 13. The polycrystal microstructure ((a)–(c)) and the corresponding stress distribution with different applied stresses ((d)–(f)): (a), (d) 50 MPa; (b), (e) 100 MPa; (c), (f) 150 MPa.

DownLoad: Full-Size Img PowerPoint

图 14 平均空洞半径随外加应力变化

Figure 14. The change of applied stress on average void radius

DownLoad: Full-Size Img PowerPoint

表 1 模拟中使用的UO₂参数

Table 1. Parameters of UO₂ used in the simulation

参量	符号	取值	参考文献
绝对温度	T	1173 K
玻尔兹曼常数	k_B	1.381 × 10^–23 J/K
晶格常数	a	0.552 nm	[31]
迁移率	L	1.56 × 10^–11 m³/(J·s)	[32]
梯度自由能参数	κ	3.38 × 10^–8 J/m	[32]
空位扩散系数	$ {D_{\text{v}}} $	5.586 × 10^–18 m²/s	[33]
空位形成能	$ E_{\text{v}}^{\text{f}} $	5.10 eV	[34]
表面能	${\gamma _{\text{s}}}$	1.76 eV	[35]
晶界能	${\gamma _{{\text{GB}}}}$	1.67 eV	[36]
弹性模量	C₁₁	389.3 GPa	[37]
	C₁₂	118.7 GPa	[37]
	C₄₄	59.7 GPa	[37]

DownLoad: CSV

map

[1]	Govers K, Lemehov S, Hou M, Verwerft M 2007 J. Nucl. Mater. 366 161 Google Scholar
[2]	杨辉, 冯泽华, 王贺然, 张云鹏, 陈铮, 信天缘, 宋小蓉, 吴璐, 张静 2021 70 054601 Google Scholar Yang H, Feng Z H, Wang H R, Zhang Y P, Chen Z, Xin T Y, Song X R, Wu L, Zhang J 2021 Acta Phys. Sin. 70 054601 Google Scholar
[3]	孙正阳, 杨超, 柳文波 2020 金属学报 56 1295 Sun Z Y, Yang C, Liu W B 2020 Acta Metall. Sin. 56 1295
[4]	Solomon A A 1973 J. Am. Ceram. Soc. 56 164 Google Scholar
[5]	Brask D N 1979 J. Nucl. Mater. 83 265 Google Scholar
[6]	Porter D L, Takata M L, Wood E L 1983 J. Nucl. Mater. 116 272 Google Scholar
[7]	Sahu H K, Jung P 1985 J. Nucl. Mater. 136 154 Google Scholar
[8]	Brager H R, Garner F A, Guthrie G L 1977 J. Nucl. Mater. 66 301 Google Scholar
[9]	Jiang Y, Liu W, Li W, Sun Z, Xin Y, Chen P, Yun D 2021 Comput. Mater. Sci. 188 110176 Google Scholar
[10]	Millett P C, Rokkam S, El-Azab A, Tonks M, Wolf D 2009 Model. Simul. Mater. Sci. Eng. 17 64003 Google Scholar
[11]	Brailsford A D, Bullough R, Hayns M R 1976 J. Nucl. Mater. 60 246 Google Scholar
[12]	Wiedersich H 1972 Radiat. Eff. Defect. S. 12 111 Google Scholar
[13]	Millett P C, El-Azab A, Rokkam S, Tonks M, Wolf D 2011 Comput. Mater. Sci. 50 949 Google Scholar
[14]	Millett P C, El-Azab A, Wolf D 2011 Comput. Mater. Sci. 50 960 Google Scholar
[15]	Liu W B, Wang N, Ji Y Z, Song P C, Zhang C, Yang Z G, Chen L Q 2016 J. Nucl. Mater. 479 316 Google Scholar
[16]	杨朝曦, 柳文波, 张璁雨, 贺新福, 孙正阳, 贾丽霞, 师田田, 恽迪 2021 70 116101 Google Scholar Yang Z X, Liu W B, Zhang C Y, He X F, Sun Z Y, Jia L X, Shi T T, Yun D 2021 Acta Phys. Sin. 70 116101 Google Scholar
[17]	Hu S Y, Chen L Q 2001 Acta Mater. 49 1879 Google Scholar
[18]	Wang J J, Bhattacharyya S, Li Q, Heo T W, Ma X Q, Chen L 2012 Phil. Mag. Lett. 92 327
[19]	Kim D, Kim S G, Kim W T, Cho J, Han H N, Cha P 2011 Scr. Mater. 64 1079 Google Scholar
[20]	Chang K, Lee G, Kwon J 2016 Radiat. Eff. Defect. S. 171 242 Google Scholar
[21]	Salvo M, Sercombe J, Ménard J, Julien J, Helfer T, Désoyer T 2015 J. Nucl. Mater. 456 54 Google Scholar
[22]	Cahn J W, Hilliard J E 1958 J. Chem. Phys. 28 258 Google Scholar
[23]	Tonks M R, Zhang Y, Butterfield A, Bai X 2015 Model. Simul. Mater. Sci. Eng. 23 45009 Google Scholar
[24]	Wang Y U, Jin Y M, Khachaturyan A G 2002 J. Appl. Phys. 92 1351 Google Scholar
[25]	Sheng G, Bhattacharyya S, Zhang H, Chang K, Shang S L, Mathaudhu S N, Liu Z K, Chen L Q 2012 Mater. Sci. Eng. A 554 67 Google Scholar
[26]	Tonks M, Millett P 2011 Mater. Sci. Eng. A 528 4086 Google Scholar
[27]	Yan L L, Liu C Z, Ying Y Z, Zheng C 2014 Chinese Phys. B 23 69102 Google Scholar
[28]	Wang Y U, Jin Y M, Khachaturyan A G 2002 J. Appl. Phys. 91 6435 Google Scholar
[29]	Moelans N, Blanpain B, Wollants P 2008 Calphad 32 268 Google Scholar
[30]	Chen L Q, Shen J 1998 Comput. Phys. Commun. 108 147 Google Scholar
[31]	Kang K H, Ryu H J, Song K C, Yang M S 2002 J. Nucl. Mater. 301 242 Google Scholar
[32]	Aagesen L K, Schwen D, Tonks M R, Zhang Y 2019 Comput. Mater. Sci. 161 35 Google Scholar
[33]	Kinoshita M 1997 J. Nucl. Mater. 248 185 Google Scholar
[34]	Freyss M, Petit T, Crocombette J 2005 J. Nucl. Mater. 347 44 Google Scholar
[35]	Xiao H, Long C, Chen H, Tian X, Wei T, Zhao Y, Gao W 2015 Appl. Surf. Sci. 351 517 Google Scholar
[36]	Chen T, Chen D, Sencer B H, Shao L 2014 J. Nucl. Mater. 452 364 Google Scholar
[37]	Fritz I J 1976 J. Appl. Phys. 47 4353 Google Scholar
[38]	Jin Y M, Wang Y U, Khachaturyan A G 2003 Philos. Mag. 83 1587 Google Scholar
[39]	徐芝纶 1982 弹性力学(上卷) (北京: 高等教育出版社) 第89页 Xu Z L 1982 Elasticity (Vol. 1) (Beijing: Higher Education Press) p89 (in Chinese)
[40]	Wang H, Biswas S, Han Y, Tomar V 2018 Comput. Mater. Sci. 150 169 Google Scholar
[41]	Heo T W, Bhattacharyya S, Chen L 2013 Philos. Mag. 93 1468 Google Scholar
[42]	Aagesen L K, Gao Y, Schwen D, Ahmed K 2018 Phys. Rev. E 98 23309 Google Scholar
[43]	孙正阳, 王昱天, 柳文波 2020 金属学报 56 1643 Google Scholar Sun Z Y, Wang L T, Liu W B 2020 Acta Metall. Sin. 56 1643 Google Scholar
[44]	Liu W B, Ji Y Z, Tan P K, Zang H, He C H, Yun D, Zhang C, Yang Z G 2016 Materials 9 105 Google Scholar

[1]	Liu Xu-Xi, Gao Shi-Sen, La Yong-Xiao, Yu Dong-Liang, Liu Wen-Bo. Phase-field simulation of high-temperature corrosion of binary Zr-2.5Sn alloy. Acta Physica Sinica, 2024, 73(14): 148201. doi: 10.7498/aps.73.20240393
[2]	Liao Yu-Xuan, Shen Wen-Long, Wu Xue-Zhi, La Yong-Xiao, Liu Wen-Bo. Phase-field simulation of sintering process of ceramic composite fuel. Acta Physica Sinica, 2024, 73(21): 210201. doi: 10.7498/aps.73.20241112
[3]	Geng Xiao-Bin, Li Ding-Gen, Xu Bo. Mechanical stress-thermodynamic phase-field simulation of lithium dendrite growth in solid electrolyte battery. Acta Physica Sinica, 2023, 72(22): 220201. doi: 10.7498/aps.72.20230824
[4]	Yang Zhao-Xi, Liu Wen-Bo, Zhang Cong-Yu, He Xin-Fu, Sun Zheng-Yang, Jia Li-Xia, Shi Tian-Tian, Yun Di. Phase field simulation of grain boundary segregation and radiation-enhanced segregation in Fe-Cr alloys. Acta Physica Sinica, 2021, 70(11): 116101. doi: 10.7498/aps.70.20201840
[5]	Song Yan, Jiang Hong-Xiang, Zhao Jiu-Zhou, He Jie, Zhang Li-Li, Li Shi-Xin. Numerical simulations of solidification microstructure evolution process for commercial-purity aluminum alloys inoculated by Al-Ti-B refiner. Acta Physica Sinica, 2021, 70(8): 086402. doi: 10.7498/aps.70.20201431
[6]	Yang Hui, Feng Ze-Hua, Wang He-Ran, Zhang Yun-Peng, Chen Zheng, Xin Tian-Yuan, Song Xiao-Rong, Wu Lu, Zhang Jing. Phase-field modeling of irradiated void microstructure evolution of Fe-Cr alloy. Acta Physica Sinica, 2021, 70(5): 054601. doi: 10.7498/aps.70.20201457
[7]	Liu Di, Wang Jing, Wang Jun-Sheng, Huang Hou-Bing. Phase field simulation of misfit strain manipulating domain structure and ferroelectric properties in PbZr_(1–x)Ti_xO₃ thin films. Acta Physica Sinica, 2020, 69(12): 127801. doi: 10.7498/aps.69.20200310
[8]	Duan Pei-Pei, Xing Hui, Chen Zhi, Hao Guan-Hua, Wang Bi-Han, Jin Ke-Xin. Phase-field modeling of free dendritic growth of magnesium based alloy. Acta Physica Sinica, 2015, 64(6): 060201. doi: 10.7498/aps.64.060201
[9]	Du Li-Fei, Zhang Rong, Xing Hui, Zhang Li-Min, Zhang Yang, Liu Lin. Phase-field simulation of solidified microstructure evolution in the presence of lateral constraint. Acta Physica Sinica, 2013, 62(10): 106401. doi: 10.7498/aps.62.106401
[10]	Chen Xi, Lin Zheng-Zhe, Yin Cong, Tang Hao, Hu Yun-Cheng, Ning Xi-Jing. Theoretical prediction of the growth and surface structure of platinum nanoparticles. Acta Physica Sinica, 2012, 61(7): 076801. doi: 10.7498/aps.61.076801
[11]	Pan Shi-Yan, Zhu Ming-Fang. Quantitative phase-field model for dendritic growth with two-sided diffusion. Acta Physica Sinica, 2012, 61(22): 228102. doi: 10.7498/aps.61.228102
[12]	Wei Cheng-Yang, Li Sai-Yi. Effect of temperature gradient on grain growth behavior from phase field simulations. Acta Physica Sinica, 2011, 60(10): 100701. doi: 10.7498/aps.60.100701
[13]	Chen Yun, Kang Xiu-Hong, Xiao Na-Min, Zheng Cheng-Wu, Li Dian-Zhong. Phase field modelling of grain growth in polycrystalline material. Acta Physica Sinica, 2009, 58(13): 124-S131. doi: 10.7498/aps.58.124
[14]	Wang Gang, Xu Dong-Sheng, Yang Rui. Phase field simulation on sideplates formation in Ti-6Al-4V alloy. Acta Physica Sinica, 2009, 58(13): 343-S348. doi: 10.7498/aps.58.343
[15]	Feng Li, Wang Zhi-Ping, Lu Yang, Zhu Chang-Sheng. Phase-field model of isothermal solidification of binary alloy with multiple grains. Acta Physica Sinica, 2008, 57(2): 1084-1090. doi: 10.7498/aps.57.1084
[16]	Lu Yang, Wang Fan, Zhu Chang-Sheng, Wang Zhi-Ping. Simulation of multiple grains for isothermal solidification of binary alloy using phase-field model. Acta Physica Sinica, 2006, 55(2): 780-785. doi: 10.7498/aps.55.780
[17]	Duan He, Zheng Yu-Feng, Zhang Xiao-Gang, Sun Yan-Fei, Dong You-Zhong. Hydrothermal synthesis of iron pyrite (FeS22) crystalpowder and the rmal-kinetic study on crystal growth. Acta Physica Sinica, 2005, 54(4): 1659-1664. doi: 10.7498/aps.54.1659
[18]	Huang Rui, Lin Xuan-Ying, Yu Yun-Peng, Lin Kui-Xun, Yao Ruo-He, Huang Wen-Yong, Wei Jun-Hong, Wang Zhao-Kui, Yu Chu-Ying. Control of grain size during low-temperature growth of polycrystalline silicon films. Acta Physica Sinica, 2004, 53(11): 3950-3955. doi: 10.7498/aps.53.3950
[19]	Zhang Jian-Min, Xu Ke-Wei. Investigation of abnormal grain growth andtexture change in Ag and Cu films. Acta Physica Sinica, 2003, 52(1): 145-149. doi: 10.7498/aps.52.145
[20]	Zhang Jian-Min, Xu Ke-Wei. . Acta Physica Sinica, 2002, 51(11): 2562-2566. doi: 10.7498/aps.51.2562

Catalog

Vol. 71, Issue 2 - 2022-01-20

Metrics

Abstract views: 4540
PDF Downloads: 91
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Phase-field simulation of void evolution in UO₂ under applied stress

Abstract

Authors and contacts

Corresponding author: Liu Wen-Bo, liuwenbo@xjtu.edu.cn

FullText HTML : translate this paragraph

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Phase-field simulation of void evolution in UO2 under applied stress

Abstract

Authors and contacts

Corresponding author: Liu Wen-Bo, liuwenbo@xjtu.edu.cn

FullText HTML : translate this paragraph

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About

Phase-field simulation of void evolution in UO₂ under applied stress