The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Wen, Peng; Tonks, Michael R.; Phillpot, Simon R.; Spearot, Douglas E.

doi:10.1016/j.commatsci.2022.111392

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Journal Article · Tue Apr 05 00:00:00 EDT 2022 · Computational Materials Science

DOI:https://doi.org/10.1016/j.commatsci.2022.111392· OSTI ID:1977006

Wen, Peng ^[1]; Tonks, Michael R. ^[2]; Phillpot, Simon R. ^[2]; Spearot, Douglas E. ^[2]

University of Florida, Gainesville, FL (United States); Nanjing University of Science and Technology (China); OSTI
University of Florida, Gainesville, FL (United States)

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO₂. It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

View Accepted Manuscript (DOE)

Research Organization:: University of Florida, Gainesville, FL (United States)

Sponsoring Organization:: USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP); University of Florida

Grant/Contract Number:: NE0008883

OSTI ID:: 1977006

Journal Information:: Computational Materials Science, Journal Name: Computational Materials Science Journal Issue: C Vol. 209; ISSN 0927-0256

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (65)

Three-dimensional phase field simulation of intragranular void formation and thermal conductivity in irradiated α-Fe Wang, Yuanyuan; Ding, Jianhua; Chen, Yonggang Journal of Materials Science, Vol. 53, Issue 15 https://doi.org/10.1007/s10853-018-2376-3	journal	May 2018
On spinodal decomposition Cahn, John W. Acta Metallurgica, Vol. 9, Issue 9 https://doi.org/10.1016/0001-6160(61)90182-1	journal	September 1961
The kinetics of pore movement in UO2 fuel rods Sens, P. F. Journal of Nuclear Materials, Vol. 43, Issue 3 https://doi.org/10.1016/0022-3115(72)90061-X	journal	June 1972
On the thermal gradient migration of lenticular voids Nichols, F. A. Journal of Nuclear Materials, Vol. 84, Issue 1-2 https://doi.org/10.1016/0022-3115(79)90171-5	journal	October 1979
Nucleation of helium bubbles on dislocations, dislocation networks and dislocations in grain boundaries during 600 MeV proton irradiation of aluminium Singh, B. N.; Leffers, T.; Green, W. V. Journal of Nuclear Materials, Vol. 125, Issue 3 https://doi.org/10.1016/0022-3115(84)90556-7	journal	August 1984
High temperature embrittlement of metals due to helium: is the lifetime dominated by cavity growth or crack growth? Trinkaus, H.; Ullmaier, H. Journal of Nuclear Materials, Vol. 212-215 https://doi.org/10.1016/0022-3115(94)90076-0	journal	September 1994
Formation and migration of helium bubbles in Fe and Fe–9Cr ferritic alloy Ono, K.; Arakawa, K.; Hojou, K. Journal of Nuclear Materials, Vol. 307-311 https://doi.org/10.1016/S0022-3115(02)01268-0	journal	December 2002
Weldability of neutron irradiated austenitic stainless steels Asano, Kyoichi; Nishimura, Seiji; Saito, Yoshiaki Journal of Nuclear Materials, Vol. 264, Issue 1-2 https://doi.org/10.1016/S0022-3115(98)00491-7	journal	January 1999
Phase-field simulation of void migration in a temperature gradient Hu, S. Y.; Henager Jr., C. H. Acta Materialia, Vol. 58, Issue 9 https://doi.org/10.1016/j.actamat.2010.01.043	journal	May 2010
A molecular dynamics simulation of self-diffusion on Fe surfaces Wang, Changqing; Qin, Zhen; Zhang, Yongsheng Applied Surface Science, Vol. 258, Issue 10 https://doi.org/10.1016/j.apsusc.2011.12.084	journal	March 2012
A temperature-dependent surface free energy model for solid single crystals Cheng, Tianbao; Fang, Daining; Yang, Yazheng Applied Surface Science, Vol. 393 https://doi.org/10.1016/j.apsusc.2016.09.147	journal	January 2017
Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements Lu, Xiao-Gang; Selleby, Malin; Sundman, Bo Calphad, Vol. 29, Issue 1 https://doi.org/10.1016/j.calphad.2005.05.001	journal	March 2005
An introduction to phase-field modeling of microstructure evolution Moelans, Nele; Blanpain, Bart; Wollants, Patrick Calphad, Vol. 32, Issue 2 https://doi.org/10.1016/j.calphad.2007.11.003	journal	June 2008
Diffusion of a vacancy on Fe(1 0 0): A molecular-dynamics study Papanicolaou, N. I.; Chamati, H. Computational Materials Science, Vol. 44, Issue 4 https://doi.org/10.1016/j.commatsci.2008.09.006	journal	February 2009
Phase-field modeling of temperature gradient driven pore migration coupling with thermal conduction Zhang, Liangzhe; Tonks, Michael R.; Millett, Paul C. Computational Materials Science, Vol. 56 https://doi.org/10.1016/j.commatsci.2012.01.002	journal	April 2012
The formation energy and bonding characteristics of small helium–vacancy clusters on the low-index surface of α-Fe by first principles calculations Cai, Jun; Lu, Daogang Computational Materials Science, Vol. 92 https://doi.org/10.1016/j.commatsci.2014.05.064	journal	September 2014
A quantitative phase-field model for two-phase elastically inhomogeneous systems Durga, A.; Wollants, P.; Moelans, N. Computational Materials Science, Vol. 99 https://doi.org/10.1016/j.commatsci.2014.11.057	journal	March 2015
Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT Schwen, D.; Aagesen, L. K.; Peterson, J. W. Computational Materials Science, Vol. 132 https://doi.org/10.1016/j.commatsci.2017.02.017	journal	May 2017
Quantifying elastic energy effects on interfacial energy in the Kim-Kim-Suzuki phase-field model with different interpolation schemes Aagesen, Larry K.; Schwen, Daniel; Ahmed, Karim Computational Materials Science, Vol. 140 https://doi.org/10.1016/j.commatsci.2017.08.005	journal	December 2017
How to apply the phase field method to model radiation damage Tonks, Michael R.; Cheniour, Amani; Aagesen, Larry Computational Materials Science, Vol. 147 https://doi.org/10.1016/j.commatsci.2018.02.007	journal	May 2018
Phase field study the effects of interfacial energy anisotropy on the thermal migration of voids Chen, W. J.; Zhou, Y. A.; Wang, S. X. Computational Materials Science, Vol. 159 https://doi.org/10.1016/j.commatsci.2018.12.020	journal	March 2019
Phase-field modeling of fission gas bubble growth on grain boundaries and triple junctions in UO2 nuclear fuel Aagesen, Larry K.; Schwen, Daniel; Tonks, Michael R. Computational Materials Science, Vol. 161 https://doi.org/10.1016/j.commatsci.2019.01.019	journal	April 2019
The effects of introducing elasticity using different interpolation schemes to the grand potential phase field model Simon, Pierre-Clément A.; Aagesen, Larry K.; Motta, Arthur T. Computational Materials Science, Vol. 183 https://doi.org/10.1016/j.commatsci.2020.109790	journal	October 2020
A phase field study of the thermal migration of gas bubbles in UO2 nuclear fuel under temperature gradient Wang, Yafeng; Xiao, Zhihua; Hu, Shenyang Computational Materials Science, Vol. 183 https://doi.org/10.1016/j.commatsci.2020.109817	journal	October 2020
A quantitative phase-field model of gas bubble evolution in UO2 Xiao, Zhihua; Wang, Yafeng; Hu, Shenyang Computational Materials Science, Vol. 184 https://doi.org/10.1016/j.commatsci.2020.109867	journal	November 2020
Helium accumulation in metals during irradiation – where do we stand? Trinkaus, H.; Singh, B. N. Journal of Nuclear Materials, Vol. 323, Issue 2-3 https://doi.org/10.1016/j.jnucmat.2003.09.001	journal	December 2003
Ferritic/martensitic steels for next-generation reactors Klueh, R. L.; Nelson, A. T. Journal of Nuclear Materials, Vol. 371, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2007.05.005	journal	September 2007
Phase-field modeling of gas bubbles and thermal conductivity evolution in nuclear fuels Hu, Shenyang; Henager, Charles H.; Heinisch, Howard L. Journal of Nuclear Materials, Vol. 392, Issue 2 https://doi.org/10.1016/j.jnucmat.2009.03.017	journal	July 2009
Study by EELS of helium bubbles in a martensitic steel Fréchard, S.; Walls, M.; Kociak, M. Journal of Nuclear Materials, Vol. 393, Issue 1 https://doi.org/10.1016/j.jnucmat.2009.05.011	journal	August 2009
Phase-field modeling of void migration and growth kinetics in materials under irradiation and temperature field Li, Yulan; Hu, Shenyang; Sun, Xin Journal of Nuclear Materials, Vol. 407, Issue 2 https://doi.org/10.1016/j.jnucmat.2010.09.048	journal	December 2010
A new Fe–He interatomic potential based on ab initio calculations in α-Fe Gao, F.; Deng, Huiqiu; Heinisch, H. L. Journal of Nuclear Materials, Vol. 418, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2011.06.008	journal	November 2011
Properties of Helium bubbles in Fe and FeCr alloys Caro, A.; Hetherly, J.; Stukowski, A. Journal of Nuclear Materials, Vol. 418, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2011.07.010	journal	November 2011
Radiation damage in helium ion irradiated nanocrystalline Fe Yu, K. Y.; Liu, Y.; Sun, C. Journal of Nuclear Materials, Vol. 425, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2011.10.052	journal	June 2012
Diffusion of small He clusters in bulk and grain boundaries in α-Fe Deng, H. Q.; Hu, W. Y.; Gao, F. Journal of Nuclear Materials, Vol. 442, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2013.02.063	journal	November 2013
He-induced vacancy formation in bcc Fe solid from first-principles simulation Zhang, Pengbo; Zhang, Chong; Li, Ruihuan Journal of Nuclear Materials, Vol. 444, Issue 1-3 https://doi.org/10.1016/j.jnucmat.2013.09.048	journal	January 2014
The role of grain size in He bubble formation: Implications for swelling resistance El-Atwani, O.; Nathaniel, J. E.; Leff, A. C. Journal of Nuclear Materials, Vol. 484 https://doi.org/10.1016/j.jnucmat.2016.12.003	journal	February 2017
Phase-field simulations of pore migration and morphology change in thermal gradients Vance, Ian W.; Millett, Paul C. Journal of Nuclear Materials, Vol. 490 https://doi.org/10.1016/j.jnucmat.2017.04.027	journal	July 2017
Effects of temperature on helium bubble behaviour in Fe–9Cr alloy Yan, Zhanfeng; Yang, Tengfei; Lin, Yanru Journal of Nuclear Materials, Vol. 532 https://doi.org/10.1016/j.jnucmat.2020.152045	journal	April 2020
Phase-field simulations of intergranular fission gas bubble behavior in U3Si2 nuclear fuel Aagesen, Larry K.; Andersson, David; Beeler, Benjamin W. Journal of Nuclear Materials, Vol. 541 https://doi.org/10.1016/j.jnucmat.2020.152415	journal	December 2020
Phase-field simulations of fission gas bubbles in high burnup UO2 during steady-state and LOCA transient conditions Aagesen, Larry K.; Biswas, Sudipta; Jiang, Wen Journal of Nuclear Materials, Vol. 557 https://doi.org/10.1016/j.jnucmat.2021.153267	journal	December 2021
Microstructure and microchemistry of laser welds of irradiated austenitic steels Mao, Keyou S.; French, Aaron J.; Liu, Xiang Materials & Design, Vol. 206 https://doi.org/10.1016/j.matdes.2021.109764	journal	August 2021
Phase-field simulations of intragranular fission gas bubble evolution in UO2 under post-irradiation thermal annealing Li, Yulan; Hu, Shenyang; Montgomery, Robert Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 303 https://doi.org/10.1016/j.nimb.2012.11.028	journal	May 2013
MOOSE: A parallel computational framework for coupled systems of nonlinear equations Gaston, Derek; Newman, Chris; Hansen, Glen Nuclear Engineering and Design, Vol. 239, Issue 10 https://doi.org/10.1016/j.nucengdes.2009.05.021	journal	October 2009
Effect of stress on self-diffusion in bcc Fe: An atomistic simulation study Jang, Je-Wook; Kwon, Junhyun; Lee, Byeong-Joo Scripta Materialia, Vol. 63, Issue 1 https://doi.org/10.1016/j.scriptamat.2010.02.045	journal	July 2010
Size and mechanics effects in surface-induced melting of nanoparticles Levitas, Valery I.; Samani, Kamran Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1275	journal	April 2011
Atomic transport properties in UO2 and mixed oxides (U, Pu)O2 Matzke, Hansjoachim Journal of the Chemical Society, Faraday Transactions 2, Vol. 83, Issue 7 https://doi.org/10.1039/f29878301121	journal	January 1987
Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress Wang, Yu U.; Jin, Yongmei M.; Khachaturyan, Armen G. Journal of Applied Physics, Vol. 91, Issue 10 https://doi.org/10.1063/1.1471389	journal	January 2002
Elastic constants of monocrystal iron from 3 to 500 K Adams, J. J.; Agosta, D. S.; Leisure, R. G. Journal of Applied Physics, Vol. 100, Issue 11 https://doi.org/10.1063/1.2365714	journal	January 2006
Binding energetics of substitutional and interstitial helium and di-helium defects with grain boundary structure in α-Fe Tschopp, M. A.; Gao, F.; Yang, L. Journal of Applied Physics, Vol. 115, Issue 3 https://doi.org/10.1063/1.4861719	journal	January 2014
Phase-field study on geometry-dependent migration behavior of voids under temperature gradient in UO ₂ crystal matrix Chen, Weijin; Peng, Yuyi; Li, Xu'an Journal of Applied Physics, Vol. 122, Issue 15 https://doi.org/10.1063/1.4996692	journal	October 2017
Heat transfer and fluid flow during laser spot welding of 304 stainless steel He, X.; Fuerschbach, P. W.; DebRoy, T. Journal of Physics D: Applied Physics, Vol. 36, Issue 12 https://doi.org/10.1088/0022-3727/36/12/306	journal	May 2003
Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti–6Al–4V, 304L stainless steel and vanadium Rai, R.; Elmer, J. W.; Palmer, T. A. Journal of Physics D: Applied Physics, Vol. 40, Issue 18 https://doi.org/10.1088/0022-3727/40/18/037	journal	August 2007
The influence of helium on the bulk properties of fusion reactor structural materials Ullmaier, H. Nuclear Fusion, Vol. 24, Issue 8 https://doi.org/10.1088/0029-5515/24/8/009	journal	August 1984
Molecular dynamics simulations of grain boundary mobility in Al, Cu and γ -Fe using a symmetrical driving force Ulomek, F.; Mohles, V. Modelling and Simulation in Materials Science and Engineering, Vol. 22, Issue 5 https://doi.org/10.1088/0965-0393/22/5/055011	journal	May 2014
Ab initio study of helium in α − Fe : Dissolution, migration, and clustering with vacancies Fu, Chu-Chun; Willaime, F. Physical Review B, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevB.72.064117	journal	August 2005
Molecular dynamics study of self-diffusion in bcc Fe Mendelev, Mikhail I.; Mishin, Yuri Physical Review B, Vol. 80, Issue 14 https://doi.org/10.1103/PhysRevB.80.144111	journal	October 2009
Unified derivation of phase-field models for alloy solidification from a grand-potential functional Plapp, Mathis Physical Review E, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevE.84.031601	journal	September 2011
Grand-potential-based phase-field model for multiple phases, grains, and chemical components Aagesen, Larry K.; Gao, Yipeng; Schwen, Daniel Physical Review E, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevE.98.023309	journal	August 2018
Stability and Mobility of Mono- and Di-Interstitials in α -Fe Fu, Chu-Chun; Willaime, F.; Ordejón, P. Physical Review Letters, Vol. 92, Issue 17 https://doi.org/10.1103/PhysRevLett.92.175503	journal	April 2004
The Soret Effect: A Review of Recent Experimental Results Platten, Jean K. Journal of Applied Mechanics, Vol. 73, Issue 1 https://doi.org/10.1115/1.1992517	journal	April 2005
Thermal Physics, 2nd ed. Kittel, Charles; Kroemer, Herbert; Scott, H. L. American Journal of Physics, Vol. 66, Issue 2 https://doi.org/10.1119/1.19072	journal	February 1998
Designing Radiation Resistance in Materials for Fusion Energy Zinkle, S. J.; Snead, L. L. Annual Review of Materials Research, Vol. 44, Issue 1 https://doi.org/10.1146/annurev-matsci-070813-113627	journal	July 2014
Welding residual stresses in ferritic power plant steels Francis, J. A.; Bhadeshia, H. K. D. H.; Withers, P. J. Materials Science and Technology, Vol. 23, Issue 9 https://doi.org/10.1179/174328407X213116	journal	September 2007
Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media Ammar, Kais; Appolaire, Benoît; Cailletaud, Georges European Journal of Computational Mechanics, Vol. 18, Issue 5-6 https://doi.org/10.3166/ejcm.18.485-523	journal	January 2009
Molecular Dynamics Calculations of Grain Boundary Mobility in CdTe Aguirre, Rodolfo; Abdullah, Sharmin; Zhou, Xiaowang Nanomaterials, Vol. 9, Issue 4 https://doi.org/10.3390/nano9040552	journal	April 2019

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36 MATERIALS SCIENCE
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