Phase field simulation of intra/intergranular pore morphology evolution in neutron-irradiated austenitic stainless steel

Cheng Da-Zhao; Liu Cai-Yan; Zhang Chao-Ran; Qu Jia-Hui; Zhang Jing

doi:10.7498/aps.73.20241353

Abstract

Intergranular or intragranular anisotropic pores can be easily observed in the FCC structure of nuclear reactor core structural materials, such as austenitic stainless steel or nickel-based alloys. Austenitic stainless steel contains a certain amount of nickel (Ni), and Ni undergoes transmutation reaction under neutron irradiation to produce helium. Helium combines with vacancy and continuously absorbs more helium and vacancy, evolving into under pressure pores filled with a small amount of helium. The morphology of pores is influenced by both the surface anisotropy of the crystal and grain boundary characteristic because pore nucleation predominantly occurs at grain boundary. The swelling effect caused by pores and the embrittlement effect of high temperature helium are related to the morphology, size and distribution of pores. The phase field method can couple multiple physical fields and accurately describe the effects of material microscopic defects on pores. In this study, we use the phase field method to simulate the evolution and morphology of pores, establishing a free energy functional coupling between crystal plane anisotropy and pore-grain boundary interactions. Our results demonstrate that helium gas induces pore nucleation, with higher concentrations leading to shorter incubation period, faster nucleation rate, and greater growth rate. Grain boundaries act as heterogeneous nucleation sites for helium pores, leading to the formation of pores along these boundaries and high-density diffusion pores within the grains. The intragranular pores exhibit anisotropic characteristics regulated by interfacial energy’s anisotropic modulus, the strength of the anisotropy, and crystal orientation. The high-density intergranular pores interact with each other significantly and are influenced by grain boundaries, while the anisotropic morphology is negligible. Additionally, it has been observed that the pores located in the middle of grain boundaries tend to become an elliptical. The stress inside the pores that contain a small amount of helium gas is negative, which is lower than the value in the matrix. These findings presented herein align well with experimental results, which inspires the prediction of service life of core components and the design of core materials.

Keywords:

Authors and contacts

1.
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2.
School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, China

Corresponding author: Zhang Jing, jingzhang@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U2267253, 51704243) and the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2022JM-238).

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References

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图 1 不同各向异性模数N和不同各向异性强度$ \delta $情况下演化结果及实验观察到的各向异性孔隙　(a) 2.0×10⁴t₀时空位浓度场; (b) $ \delta $为0.2, 2.0×10⁴t₀时不同各向异性孔隙周围的应力场分布; (c) 辐照下奥氏体不锈钢中观察到的孔隙^[8]; (d)不同各向异性模数N下孔隙半径随演化时间的变化曲线; (e)不同各向异性强度$ \delta $下孔隙半径随演化时间的变化曲线

Figure 1. Evolution results under different anisotropic modulus N and anisotropic strength $ \delta $ and anisotropic pores observed experimentally: (a) 2.0×10⁴t₀ vacancy concentration field; (b) distribution of stress field around different anisotropic pores when $ \delta $ is 0.2 and time is 2.0×10⁴t₀; (c) the pores observed in irradiated austenitic stainless steel^[8]; (d) variation curve of pore radius with evolution time under different anisotropy modulus N; (e) variation curve of pore radius with evolution time under different anisotropy intensities $ \delta $.

DownLoad: Full-Size Img PowerPoint

图 2 He气体浓度$ {c_{\text{g}}} $和各向异性模数N对孔隙的形核与长大的影响　(a) N为0, He气体浓度$ {c_{\text{g}}} $不同情况下孔隙的形核与长大; (b) He气体浓度$ {c_{\text{g}}} $为1.04×10^–1, 各向异性模数N为0, 4和6情况下孔隙的形核与长大; (c) 实验中1023 K温度下辐照25 h的AISI 316 SS不锈钢中观测到的孔隙形貌^[36]; (d) 不同He气体浓度$ {c_{\text{g}}} $下孔隙面积分数随时间的变化曲线; (e) 不同各向异性模数N下孔隙面积分数随时间的变化曲线

Figure 2. Influence of He gas concentration $ {c_{\text{g}}} $ and anisotropy modulus N on pores nucleation and growth: (a) Pores nucleation and growth when N is 0 and He gas concentration $ {c_{\text{g}}} $is different; (b) pores nucleation and growth when He gas concentration $ {c_{\text{g}}} $ is 1.04×10^–1 and anisotropy modulus N is 0, 4 and 6; (c) pores morphology was observed in AISI 316 SS stainless steel irradiated for 25 h at 1023 K temperature^[36]; (d) variation curve of pore area fraction with time under different He gas concentration $ {c_{\text{g}}} $; (e) variation curve of pore area fraction with time under different anisotropy modulus N.

DownLoad: Full-Size Img PowerPoint

图 3 晶粒取向角$ {\theta _0} $对孔隙演化的影响　(a)晶粒取向角$ {\theta _0} $为0°, 30°, 45°和60°时晶内孔隙长大; (b)右侧晶粒${\varphi _2}$取向角$ {\theta _0} $为30°, 45°和60°时双晶体系中孔隙演化(图左侧标注$ {\theta _0} $为右侧晶粒${\varphi _2}$的取向角); (c)不同晶粒取向角$ {\theta _0} $情况下晶内孔隙半径随演化时间变化曲线; (d)右侧晶粒取向角不同时孔隙面积分数随演化时间变化曲线

Figure 3. Effect of grain orientation angle $ {\theta _0} $ on pore evolution: (a) When the grain orientation angles are 0°, 30°, 45° and 60°, the intrachrystalline pores growth; (b) pores evolution in the twin-crystal system when the right grain orientation angle $ {\theta _0} $ is 30°, 45° and 60° (the left side of the figure is marked with the right grain orientation angle $ {\theta _0} $); (c) variation curve of the pores radius with evolution time under different grain orientation angles $ {\theta _0} $; (d) variation curve of the area fraction of pores with evolution time when the orientation angle of the right grain is different.

DownLoad: Full-Size Img PowerPoint

表 1 模型中采用的无量纲化参数

Table 1. Dimensionless parameters used in the model.

参数	值	参数	值
特征时间t₀/s	5×10^–3	空位迁移率$M_{\text{v}}^{\text{*}}$	1
特征长度l₀/nm	20	间隙原子迁移率$M_{\text{i}}^{\text{*}}$	1
空位梯度系数$\kappa _{\text{v}}^{\text{*}}$	1	He气体迁移率$M_{\text{g}}^{\text{*}}$	2
间隙原子梯度系数$\kappa _{\text{i}}^{\text{*}}$	1	He气体形成能$E_{\text{g}}^{\text{f}}$/eV	4^[33]
He气体扩散系数$\kappa _{\text{g}}^{\text{*}}$	1	空位形成能$E_{\text{v}}^{\text{f}}$/eV	2^[33]
表面能系数$\gamma _{_0}^*$	1	间隙原子形成能$E_{\text{i}}^{\text{f}}$/eV	2^[33]
He气体化学势$\mu _{\text{g}}^{\circ}$/eV	0.4^[26]	弹性模量$ C_{11}^0 $($ C_{1111}^0 $)/GPa	169^[3]
相互作用系数$ {a_{\text{s}}} $	1.1	弹性模量$ C_{12}^0 $($ C_{1122}^0 $)/GPa	131^[3]
绝对温度T/K	710	弹性模量$ C_{44}^0 $($ C_{1212}^0 $)/GPa	84.5^[3]
动力学系数${L^*}$	1

DownLoad: CSV

map

[1]	杨文斗 2000 反应堆材料学(北京: 原子能出版社) 第18—19页 Yang W D 2000 Reactor Materials Science (Beijing: Atomic Energy Press) pp18–19
[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]	刘彩艳, 冯泽华, 张云鹏, 余康, 吴璐, 马聪, 张静 2024 金属学报 60 1279 Google Scholar Liu C Y, Feng Z H, Zhang Y P, Yu K, Wu L, Ma C, Zhang J 2024 Acta Metall. Sin. 60 1279 Google Scholar
[4]	Wang H R, Yu K, Wang J C, Wu L, Zhang W, Zhang J 2024 Mech. Mater. 189 104865 Google Scholar
[5]	Zinkle S J, Busby J T 2009 Mater. Today 12 12 Google Scholar
[6]	Nazarov A V, Mikheev A A, Melnikov A P 2020 J. Nucl. Mater. 532 152067 Google Scholar
[7]	Zinkle S J, Farrell K 1989 J. Nucl. Mater 168 262 Google Scholar
[8]	Was G S 2017 Fundamentals of Radiation Materials Science: Metals and Alloys (New York: Springer) pp379–484
[9]	Chen C W 1973 Phys. Status Solidi. A 16 197 Google Scholar
[10]	Niwase K, Ezawa T, Tanabe T, Fujita F E 1988 J. Nucl. Mater. 160 229 Google Scholar
[11]	Griffiths M, Styles R C, Woo C H, Phillipp F, Frank W 1994 J. Nucl. Mater 208 324 Google Scholar
[12]	El-Atwani O, Hattar K, Hinks J A, Greaves G, Harilal S S, Hassanein A 2015 J. Nucl. Mater 458 216 Google Scholar
[13]	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
[14]	Han G M, Wang H, Lin D Y, Zhu X Y, Hu S Y, Song H F 2017 Comp. Mater. Sci. 133 22 Google Scholar
[15]	Vitos L, Ruban A V, Skriver H L, Kollár J 1998 Surf. Sci. 411 186 Google Scholar
[16]	Tschopp M A, Solanki K N, Gao F, Sun X, Khaleel M A, Horstemeyer M F 2012 Phys. Rev. B 85 064108 Google Scholar
[17]	Gao Z Y, Huang J, Liu H C, Ge W, Luo F P, Zhang B W, Liu G Y, Sun B R, Shen T D, Xue J M, Wang Y G, Wang C X 2023 Scripta Mater. 232 115497 Google Scholar
[18]	Yan Z F, Yang T F, Lin Y R, Lu Y P, Su Y, Zinkle S J, Wang Y G 2020 J. Nucl. Mater. 532 152045 Google Scholar
[19]	Hirth J P, Pond R C, Lothe J 2007 Acta Mater. 55 5428 Google Scholar
[20]	Jiang Y B, Liu W B, Li W J, Sun Z Y, Xin Y, Chen P H, Yun D 2021 Comp. Mater. Sci. 188 110176 Google Scholar
[21]	戚晓勇, 柳何, 王恽 2023 金属学报 59 1513 Google Scholar Qi X Y, Liu H, Wang Y 2023 Acta Metall. Sin. 59 1513 Google Scholar
[22]	刘续希, 柳文波, 李博岩, 贺新福, 杨朝曦, 恽迪 2022 金属学报 58 943 Google Scholar Liu X X, Liu W B, Li B Y, He X F, Yang C X, Yun D 2022 Acta Metall. Sin. 58 943 Google Scholar
[23]	Moladje G F B, Thuinet L, Becquart C S, Legris A 2022 Acta Mater. 225 117523 Google Scholar
[24]	Sakaël C, Domain C, Ambard A, Thuinet L, Legris A 2023 Int. J. Plast. 168 103699 Google Scholar
[25]	Liu C Y, Zhang Y P, Cheng D Z, Yu K, Teng C Q, Wu L, Zhang J 2024 Nucl. Eng. Des. 425 113321 Google Scholar
[26]	Millett P C, El-Azab A, Wolf D 2011 Comp. Mater. Sci. 50 960 Google Scholar
[27]	Bhattacharyya S, Heo T W, Chang K, Chen L Q 2011 Model. Simul. Mater. Sc. 19 035002 Google Scholar
[28]	姜彦博, 柳文波, 孙志鹏, 喇永孝, 恽迪 2022 71 026103 Google Scholar Jiang Y B, Liu W B, Sun Z P, La Y X, Yun D 2022 Acta Phys. Sin. 71 026103 Google Scholar
[29]	Greenwood M, Hoyt J J, Provatas N 2009 Acta Mater. 57 2613 Google Scholar
[30]	Tonks M R, Zhang Y, Butterfield A, Bai X M 2015 Model. Simul. Mater. Sc. 23 045009 Google Scholar
[31]	Golubov S I, Ovcharenko A M, Barashev A V, Singh B N 2001 Philos. Mag. 81 643 Google Scholar
[32]	Russell K C 1971 Acta Mater. 19 753 Google Scholar
[33]	Wen P, Tonks M R, Phillpot S R, Spearot D E 2022 Comp. Mater. Sci. 209 111392 Google Scholar
[34]	Wang Y Y, Zhao J J, Ding J H, Zhao J J 2022 Int. J. Refract. Met. H. 105 105824 Google Scholar
[35]	Lin Y R, Chen W Y, Tan L, Hoelzer D T, Yan Z, Hsieh C Y, Huang C W, Zinkle S J 2021 Acta Mater. 217 117165 Google Scholar
[36]	Schroeder H, Kesternich W, Ullmaier H 1985 Fusion Eng. Des. 2 65 Google Scholar

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