Please wait a minute...
Acta Metall Sin  2020, Vol. 56 Issue (5): 753-759    DOI: 10.11900/0412.1961.2019.00324
Current Issue | Archive | Adv Search |
Numerical Simulation of Nanohardness in Hastelloy N Alloy After Xenon Ion Irradiation
LIU Jizhao1,2,3, HUANG Hefei1,2(), ZHU Zhenbo1,2, LIU Awen1,2,3, LI Yan1,2,3()
1.Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
2.School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
3.School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
Download:  HTML  PDF(2120KB) 
Export:  BibTeX | EndNote (RIS)      

Ion irradiation experiments are of importance for investigating irradiation damage of reactor structural materials. However, estimating the irradiation hardening of ion-irradiated materials is difficult due to the limitation of ion penetration depth. In recent years, nanoindentation test has been widely used to study the irradiation hardening of materials, because the continuous stiffness measurement (CSM) mode can obtain the relationship between nanohardness and indentation depth at a very small penetration depth. In this work, the average nanohardness of Hastelloy N alloy irradiated by xenon ion at room temperature was tested by this mode. The results showed that the nanohardness in the irradiated samples was larger than that in the unirradiated sample and this value of irradiated samples is saturated when the irradiation dose is in the range of 0.5~3.0 dpa. Based on the Nix-Gao model, the indentation size effects (ISE) of unirradiated and irradiated samples were separated from nanohardness measured by nanoindentation. The volume law of mixture model (VLM) was subsequently applied to simulate the measured nanohardness. As the depth of indentation increases, the plasticity affected region (PAR) includes both irradiation damage layer and matrix. Interface parameter was introduced to correct the volume of matrix deformation. The results indicated that the improved VLM model leads to a characteristic relation for the depth dependence of nanohardness that is in excellent agreement with nanoindentation experiments.

Key words:  irradiation hardening      nanoindentation      volume law of mixture (VLM) model      numerical simulation     
Received:  26 September 2019     
ZTFLH:  TL341  
Fund: National Natural Science Foundation of China(11605271);National Natural Science Foundation of China(11975304);National Natural Science Foundation of China(91126012)
Corresponding Authors:  HUANG Hefei,LI Yan     E-mail:;

Cite this article: 

LIU Jizhao, HUANG Hefei, ZHU Zhenbo, LIU Awen, LI Yan. Numerical Simulation of Nanohardness in Hastelloy N Alloy After Xenon Ion Irradiation. Acta Metall Sin, 2020, 56(5): 753-759.

URL:     OR

Fig.1  SRIM calculation of the damage profiles as a function of the depth for irradiated samples (SRIM —stopping and range of ions in matter)
Fig.2  OM image of indentation shape of sample after nanoindentation experiment
Fig.3  Indentation depth dependence of the average nanohardness of the unirradiated and irradiated samples
Fig.4  Curves of H2-h-1 for average nanohardness of the unirradiated and irradiated samples (H—nanohardness, h—indentation depth)
SampleH0 / GPah* / nm
Xe 0.5 dpa4.69±0.0358±2
Xe 1.0 dpa4.87±0.0840±5
Xe 3.0 dpa4.65±0.0457±3
Table 1  The values of the hardness in the limit of in?nite depth (H0) and the characteristic length (h*) for unirradiated and irradiated samples
Fig.5  The indentation size effects for the unirradiated and irradiated samples (HISE—the indentation size effect)
Fig.6  Schematic drawing of the nanohardness measurement (I—the thickness of irradiation damage layer, R—the radius of plasticity affected region, T—the difference between R and I)
Fig.7  Calculated volume fraction of matrix in the plasticity affected region
Fig.8  Comparison of nanohardness calculated by different models with the measured nanohardness of the samples before (a) and after Xe26+ ion irradiation with 0.5 dpa (b), 1.0 dpa (c) and 3.0 dpa (d) (HMeasured—the measured nanohardness, HVLM—the nanohardness calculated by VLM model, H0—the nanohardness in the limit of in?nite depth, HNG—the nanohardness calculated by Nix-Gao model)
Fig.9  Comparisons of nanohardness calculated by the modified VLM model with the measured nanohardness of the samples after Xe26+ ion irradiation with 0.5 dpa (a), 1.0 dpa (b) and 3.0 dpa (c)
1 Liu P P, Wan F R, Zhan Q. A model to evaluate the nano-indentation hardness of ion-irradiated materials [J]. Nucl. Instrum. Methods Phys. Res., 2015, 342B: 13
2 Gao J, Huang H F, Liu J Z, et al. Synergistic effects on microstructural evolution and hardening of the Hastelloy N alloy under subsequent He and Xe ion irradiation [J]. J. Appl. Phys., 2018, 123: 205901
doi: 10.1063/1.5030028
3 Huang H F, Li J J, Li D H, et al. TEM, XRD and nanoindentation characterization of xenon ion irradiation damage in austenitic stainless steels [J]. J. Nucl. Mater., 2014, 454: 168
doi: 10.1016/j.jnucmat.2014.07.033
4 Lu Y P, Huang H F, Gao X Z, et al. A promising new class of irradiation tolerant materials: Ti2ZrHfV0.5Mo0.2 high-entropy alloy [J]. J. Mater. Sci. Technol., 2019, 35: 369
5 Liu X B, Wang R S, Ren A, et al. Evaluation of radiation hardening in ion-irradiated Fe based alloys by nanoindentation [J]. J. Nucl. Mater., 2014, 444: 1
doi: 10.1016/j.jnucmat.2013.09.026
6 Takayama Y, Kasada R, Sakamoto Y, et al. Nanoindentation hardness and its extrapolation to bulk-equivalent hardness of F82H steels after single- and dual-ion beam irradiation [J]. J. Nucl. Mater., 2013, 442(Suppl.1): S23
7 Huang H F, Li D H, Li J J, et al. Nanostructure variations and their effects on mechanical strength of Ni-17Mo-7Cr alloy under xenon ion irradiation [J]. Mater. Trans., 2014, 55: 1243
8 Nix W D, Gao H J. Indentation size effects in crystalline materials: A law for strain gradient plasticity [J]. J. Mech. Phys. Solids, 1998, 46: 411
9 Yang Y T, Zhang C H, Meng Y C, et al. Nanoindentation on V-4Ti alloy irradiated by H and He ions [J]. J. Nucl. Mater., 2015, 459: 1
10 Wei Y P, Liu P P, Zhu Y M, et al. Evaluation of irradiation hardening and microstructure evolution under the synergistic interaction of He and subsequent Fe ions irradiation in CLAM steel [J]. J. Alloys Compd., 2016, 676: 481
doi: 10.1016/j.jallcom.2016.03.167
11 Xu C L, Zhang L, Qian W J, et al. The studies of irradiation hardening of stainless steel reactor internals under proton and xenon irradiation [J]. Nucl. Eng. Technol., 2016, 48: 758
12 Kasada R, Takayama Y, Yabuuchi K, et al. A new approach to evaluate irradiation hardening of ion-irradiated ferritic alloys by nano-indentation techniques [J]. Fusion Eng. Des., 2011, 86: 2658
13 Xiao X Z, Yu L. Comparison of linear and square superposition hardening models for the surface nanoindentation of ion-irradiated materials [J]. J. Nucl. Mater., 2018, 503: 110
14 Kareer A, Prasitthipayong A, Krumwiede D, et al. An analytical method to extract irradiation hardening from nanoindentation hardness-depth curves [J]. J. Nucl. Mater., 2018, 498: 274
15 Hosemann P, Kiener D, Wang Y Q, et al. Issues to consider using nano indentation on shallow ion beam irradiated materials [J]. J. Nucl. Mater., 2012, 425: 136
16 Burnett P J, Rickerby D S. The mechanical properties of wear-resistant coatings: I: Modelling of hardness behaviour [J]. Thin Solid Films, 1987, 148: 41
17 Olivier W C, Pharr G M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments [J]. J. Mater. Res., 1992, 7: 1564
18 Zhu Z B, Huang H F, Liu J Z, et al. Xenon ion irradiation induced hardening in inconel 617 containing experiment and numerical calculation [J]. J. Nucl. Mater., 2019, 525: 32
19 Lee E H, Oliver W C, Mansur L K. Hardness measurements of Ar+-beam treated polyimide by depth-sensing ultra low load indentation [J]. J. Mater. Res., 1993, 8: 377
20 Chen H C, Hai Y, Liu R D, et al. The irradiation hardening of Ni-Mo-Cr and Ni-W-Cr alloy under Xe26+ ion irradiation [J]. Nucl. Instrum. Methods Phys. Res., 2018, 421B: 50
21 Liu J Z, Huang H F, Gao J, et al. Defects evolution and hardening in the Hastelloy N alloy by subsequent Xe and He ions irradiation [J]. J. Nucl. Mater., 2019, 517: 328
doi: 10.1016/j.jnucmat.2019.02.022
22 Sammuels L E, Mulhearn T O. An experimental investigation of the deformed zone associated with indentation hardness impressions [J]. J. Mech. Phys. Solids, 1957, 5: 125
doi: 10.1016/0022-5096(57)90056-X
23 Saleh M, Zaidi Z, Ionescu M, et al. Relationship between damage and hardness profiles in ion irradiated SS316 using nanoindentation―Experiments and modelling [J]. Int. J. Plast., 2016, 86: 151
24 Zhang Z X, Hasenhuetl E, Yabuuchi K, et al. Evaluation of helium effect on ion-irradiation hardening in pure tungsten by nano-indentation method [J]. Nucl. Mater. Energy, 2016, 9: 539
25 Rickerby D S, Burnett P J. Correlation of process and system parameters with structure and properties of physically vapour-deposited hard coatings [J]. Thin Solid Films, 1988, 157: 195
[1] WANG Bo,SHEN Shiyi,RUAN Yanwei,CHENG Shuyong,PENG Wangjun,ZHANG Jieyu. Simulation of Gas-Liquid Two-Phase Flow in Metallurgical Process[J]. 金属学报, 2020, 56(4): 619-632.
[2] XU Qingyan,YANG Cong,YAN Xuewei,LIU Baicheng. Development of Numerical Simulation in Nickel-Based Superalloy Turbine Blade Directional Solidification[J]. 金属学报, 2019, 55(9): 1175-1184.
[3] Peiyuan DAI,Xing HU,Shijie LU,Yifeng WANG,Dean DENG. Influence of Size Factor on Calculation Accuracy of Welding Residual Stress of Stainless Steel Pipe by 2D Axisymmetric Model[J]. 金属学报, 2019, 55(8): 1058-1066.
[4] Sensen HUANG,Yingjie MA,Shilin ZHANG,Min QI,Jiafeng LEI,Yaping ZONG,Rui YANG. Influence of Alloying Elements Partitioning Behaviors on the Microstructure and Mechanical Propertiesin α+β Titanium Alloy[J]. 金属学报, 2019, 55(6): 741-750.
[5] LU Shijie, WANG Hu, DAI Peiyuan, DENG Dean. Effect of Creep on Prediction Accuracy and Calculating Efficiency of Residual Stress in Post Weld Heat Treatment[J]. 金属学报, 2019, 55(12): 1581-1592.
[6] ZHANG Qingdong, LIN Xiao, LIU Jiyang, HU Shushan. Modelling of Q&P Steel Heat Treatment Process Based on Finite Element Method[J]. 金属学报, 2019, 55(12): 1569-1580.
[7] Pengyue ZHAO, Yongbo GUO, Qingshun BAI, Feihu ZHANG. Research of Surface Defects of Polycrystalline Copper Nanoindentation Based on Microstructures[J]. 金属学报, 2018, 54(7): 1051-1058.
[8] Jun LI, Mingxu XIA, Qiaodan HU, Jianguo LI. Solutions in Improving Homogeneities of Heavy Ingots[J]. 金属学报, 2018, 54(5): 773-788.
[9] Xinhua LIU, Huadong FU, Xingqun HE, Xintong FU, Yanqing JIANG, Jianxin XIE. Numerical Simulation Analysis of Continuous Casting Cladding Forming for Cu-Al Composites[J]. 金属学报, 2018, 54(3): 470-484.
[10] Zheng LIU, Zhiping CHEN, Tao CHEN. Effects of Crucible Size and Electromagnetic Frequency on Flow During Fabrication of Semisolid A356 Al Alloy Slurry[J]. 金属学报, 2018, 54(3): 435-442.
[11] Jincheng WANG, Can GUO, Qi ZHANG, Sai TANG, Junjie LI, Zhijun WANG. Recent Progresses in Modeling of Nucleation During Solidification on the Atomic Scale[J]. 金属学报, 2018, 54(2): 204-216.
[12] Shiping WU, Rujia WANG, Wei CHEN, Guixin DAI. Progress on Numerical Simulation of Vibration in the Metal Solidification[J]. 金属学报, 2018, 54(2): 247-264.
[13] Chuansong WU, Hao SU, Lei SHI. Numerical Simulation of Heat Generation, Heat Transfer and Material Flow in Friction Stir Welding[J]. 金属学报, 2018, 54(2): 265-277.
[14] Miaoyong ZHU, Wentao LOU, Weiling WANG. Research Progress of Numerical Simulation in Steelmaking and Continuous Casting Processes[J]. 金属学报, 2018, 54(2): 131-150.
[15] Dunming LIAO, Liu CAO, Fei SUN, Tao CHEN. Research Status and Prospect on Numerical Simulation Technology of Casting Macroscopic Process[J]. 金属学报, 2018, 54(2): 161-173.
No Suggested Reading articles found!