Irradiation hardening for metallic materials

Xiazi XIAO; Dingkun SONG; Haijian CHU; Jianming XUE; Huiling DUAN

doi:10.6052/1000-0992-14-071

Volume 45 Issue 1

Aug. 2015

Turn off MathJax

Article Contents

Article Navigation > Advances in Mechanics > 2015 > 45(1): 201505

Xiazi XIAO, Dingkun SONG, Haijian CHU, Jianming XUE, Huiling DUAN. Irradiation hardening for metallic materials[J]. Advances in Mechanics, 2015, 45(1): 201505. doi: 10.6052/1000-0992-14-071

Citation:

Xiazi XIAO, Dingkun SONG, Haijian CHU, Jianming XUE, Huiling DUAN. Irradiation hardening for metallic materials[J]. Advances in Mechanics, 2015, 45(1): 201505. doi: 10.6052/1000-0992-14-071

Xiazi XIAO, Dingkun SONG, Haijian CHU, Jianming XUE, Huiling DUAN. Irradiation hardening for metallic materials[J]. Advances in Mechanics, 2015, 45(1): 201505. doi: 10.6052/1000-0992-14-071

Citation:

Xiazi XIAO, Dingkun SONG, Haijian CHU, Jianming XUE, Huiling DUAN. Irradiation hardening for metallic materials[J]. Advances in Mechanics, 2015, 45(1): 201505. doi: 10.6052/1000-0992-14-071

PDF( 28358 KB)

Irradiation hardening for metallic materials

doi: 10.6052/1000-0992-14-071

1 State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking Universitity, Beijing 100871, China
2 HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, China
3 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200444, China
4 Department of Mechanics, College of Sciences, Shanghai 200444, China
5 Physics School of Peking University, Beijing 100871, China

More Information

Corresponding author: Huiling DUAN
Received Date: 2014-11-27
Publish Date: 2015-08-30

Abstract

Abstract

Investigations on irradiation hardening of metallic materials have much sig- nificance for the design of anti-irradiation materials and engineering applications. Both irradiation-induced defects and gaseous impurities produced by nuclear reactions have dra- matic irradiation effects on the mechanical properties of materials, which include irradiation hardening, irradiation embrittlement and irradiation creep, etc. In this paper we are con- cerned with irradiation hardening, i.e., the strength of materials increases with irradiation, under low irradiation doses and low temperatures of T < 0.3 T_m with T_m the melting temper- ature. Besides, other factors such as the grain size, the grain boundary and the temperature affect mechanical behaviors of irradiated polycrystalline materials. The study of irradia- tion hardening of metallic materials is a multi-scale problem, for which the macroscopic mechanical behaviors of irradiated materials are determined by both the change of interior structures with irradiation at micro-scale and the interactions among irradiated grains at meso-scale. This paper reviews experimental results, numerical simulations and theoretical models for irradiation hardening of metallic materials. Some scientific problems for future study are also presented.
- metallic materials,
- irradiation hardening,
- temperature effect,
- size effect,
- mechanical behaviors

FullText(HTML)

References(113)

References

[1]	Alsabbagh A, Valiev R Z, Murty K L. 2013. Influence of grain size on radiation effects in a low carbon steel. Journal of Nuclear Materials, 443: 302-310.
[2]	Arsenlis A, Rhee M, Hommes G, Cook R, Marian J. 2012. A dislocation dynamics study of the transition from homogeneous to heterogeneous deformation in irradiated body-centered cubic iron. Acta Materialia, 60: 3748-3757.
[3]	Arsenlis A, Wirth B D, Rhee M. 2004. Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu. Philosophical Magazine, 84: 3617-3635.
[4]	Asaro R J, Rice J R. 1977. Strain localiazation in ductile single-crystals. Journal of the Mechanics and Physics of Solids, 25: 309-338.
[5]	Bai X M, Uberuaga B P. 2013. The influence of grain boundaries on radiation-induced point defect produc- tion in materials: A review of atomistic studies. Jom, 65: 360-373.
[6]	Bai X M, Voter A F, Hoagland R G, Nastasi M, Uberuaga B P. 2010. E±cient annealing of radiation damage near grain boundaries via interstitial emission. Science, 327: 1631-1634.
[7]	Barton N R, Arsenlis A, Marian J. 2013. A polycrystal plasticity model of strain localization in irradiated iron. Journal of the Mechanics and Physics of Solids, 61: 341-351.
[8]	Beamish E, Campañá C, Woo T K. 2010. Grain boundary sliding in irradiated stressed Fe-Ni bicrystals: a molecular dynamics study. Journal of Physics: Condensed Matter, 22: 345006.
[9]	Beyerlein I J, Caro A, Demkowicz M J, Mara N A, Misra A, Uberuaga B P. 2013. Radiation damage tolerant nanomaterials. Materials Today, 16: 443-449.
[10]	Beyerlein I J, Tome C N. 2008. A dislocation-based constitutive law for pure Zr including temperature effects. International Journal of Plasticity, 24: 867-895.
[11]	Blewitt T H, Coltman R R, Jamison R E, Redman J K. 1960. Radiation hardening of copper single crystals. Journal of Nuclear Materials, 2: 277-298.
[12]	Borovikov V, Tang X Z, Perez D, Bai X M, Uberuaga B P, Voter A F. 2013. Influence of point defects on grain boundary mobility in bcc tungsten. Journal of Physics-Condensed Matter, 25: 035402.
[13]	Briceno M, Kacher J, Robertson I M. 2013. Dynamics of dislocation interactions with stacking-fault tetra- hedra at high temperature. Journal of Nuclear Materials, 433: 390-396.
[14]	Brimbal D, Decamps B, Barbu A, Meslin E, Henry J. 2011. Dual-beam irradiation of alpha-iron: Heteroge- neous bubble formation on dislocation loops. Journal of Nuclear Materials, 418: 313-315.
[15]	Bullough R, Wood M H. 1980. Mechanisms of radiation-induced creep and grouth. Journal of Nuclear Materials, 90: 1-21.
[16]	Campañá C, Boyle K, Miller R. 2008. Grain boundary motion assisted via radiation cascades in bcc Fe. Physical Review B, 78: 134114.
[17]	Cottrell A H. 1958. The 1958 institute of metals division lecture-theory of brittle fracture in steel and similar metals. Transactions of the American Institute of Mining and Metallurgical Engineers, 212: 192-203.
[18]	Coulibaly M, Sabar H. 2011. New integral formulation and self-consistent modeling of elastic-viscoplastic heterogeneous materials. International Journal of Solids and Structures, 48: 753-763.
[19]	de la Rubia T D, Zbib H M, Khraishi T A, Wirth B D, Victoria M, Caturla M J. 2000. Multiscale modelling of plastic flow localization in irradiated materials. Nature, 406: 871-874.
[20]	Demkowicz M J, Bellon P, Wirth B D. 2010. Atomic-scale design of radiation-tolerant nanocomposites. Mrs Bulletin, 35: 992-998.
[21]	Demkowicz M J, Hoagland R G, Hirth J P. 2008. Interface structure and radiation damage resistance in Cu-Nb multilayer nanocomposites. Physical Review Letters, 100: 136102.
[22]	Demkowicz M J, Thilly L. 2011. Structure, shear resistance and interaction with point defects of interfaces in Cu-Nb nanocomposites synthesized by severe plastic deformation. Acta Materialia, 59: 7744-7756.
[23]	Drouet J, Dupuy L, Onimus F, Mompiou F, Perusin S, Ambard A. 2014. Dislocation dynamics simulations of interactions between gliding dislocations and radiation induced prismatic loops in zirconium. Journal of Nuclear Materials, 449: 252-262.
[24]	Fabritsiev S A, Pokrovsky A S. 2003. The effects of grain size and helium accumulation on radiation hardening and loss of ductility of pure copper for ITER application. Fusion Engineering and Design, 65: 545-559.
[25]	Fabritsiev S A, Pokrovsky A S. 2007. Effect of irradiation temperature on microstructure, radiation hard- ening and embrittlement of pure copper and copper-based alloy. Journal of Nuclear Materials, 367: 977-983.
[26]	Fabritsiev S A, Pokrovsky A S. 2009. Effect of irradiation temperature and dose on SHC of pure Cu. Journal of Nuclear Materials, 386-88: 268-272.
[27]	Fabritsiev S A, Pokrovsky A S. 2011. Effect of irradiation temperature and dose on radiation hardening of some pure metals. Journal of Nuclear Materials, 417: 940-943.
[28]	Fabritsiev S A, Pokrovsky A S, Ostrovsky S E. 2004. Effect of the irradiation-annealing-irradiation cycle on the mechanical properties of pure copper and copper alloy. Journal of Nuclear Materials, 324: 23-32.
[29]	Hall E O. 1951. The deformation and ageing of mild steel. 3. Discussion of results. Proceedings of the Physical Society of London Section B, 64: 747-753.
[30]	Hill R. 1966. Generalized constitutive relations for incremental deformation of metal crystals by multislip. Journal of the Mechanics and Physics of Solids, 14: 95.
[31]	Hill R, Rice J R. 1972. Constitutive analysis of elastic-plastic crystals at arbitrary strain. Journal of the Mechanics and Physics of Solids, 20: 401.
[32]	Hutchinson J W. 1976. Bounds and self-consistent estimates for creep of polycrystalline metarials. Proceed- ings of the Royal Society of London Series a-Mathematical and Physical Sciences, 348: 101-127.
[33]	Jiao Z, Was G S. 2010. The role of irradiated microstructure in the localized deformation of austenitic stainless steels. Journal of Nuclear Materials, 407: 34-43.
[34]	Khraishi T A, Zbib H M, De La Rubia T D, Victoria M. 2002. Localized deformation and hardening in irradiated metals: Three-dimensional discrete dislocation dynamics simulations. Metallurgical and Materials Transactions B-Process Metallurgy and Materials Processing Science, 33: 285-296.
[35]	Kiener D, Hosemann P, Maloy S A, Minor A M. 2011. In situ nanocompression testing of irradiated copper. Nature Materials, 10: 608-613.
[36]	Kocks U F. 1977. Theory of an obstacle-controlled yield strength-report after an international workshop. Materials Science and Engineering, 27: 291-298.
[37]	Kojima S, Zinkle S J, Heinisch H L. 1991. Radiation hardening in neutron-irradiated polycrystalline copper: Barrier strength of defect clusters. Journal of Nuclear Materials, 179: 982-985.
[38]	Kraft O, Gruber P A, Moenig R, Weygand D. 2010. Plasticity in confined dimensions. Annual Review of Materials Research, 40: 293-317.
[39]	Krishna S, De S. 2011. A temperature and rate-dependent micromechanical model of molybdenum under neutron irradiation. Mechanics of Materials, 43: 99-110.
[40]	Krishna S, Zamiri A, De S. 2010. Dislocation and defect density-based micromechanical modeling of the mechanical behavior of fcc metals under neutron irradiation. Philosophical Magazine, 90: 4013-4025.
[41]	Lee E H, Byun T S, Hunn J D, Yoo M H, Farrell K, Mansur L K. 2001a. On the origin of deformation microstructures in austenitic stainless steel: Part I-Microstructures. Acta Materialia, 49: 3269-3276.
[42]	Lee E H, Yoo M H, Byun T S, Hunn J D, Farrell K, Mansur L K. 2001b. On the origin of deformation microstructures in austenitic stainless steel: Part II-Mechanisms. Acta Materialia, 49: 3277-3287.
[43]	Lee H J, Shim J H, Wirth B D. 2007. Molecular dynamics simulation of screw dislocation interaction with stacking fault tetrahedron in face-centered cubic Cu. Journal of Materials Research, 22: 2758-2769.
[44]	Lee H J, Wirth B D. 2009. Molecular dynamics simulation of the interaction between a mixed dislocation and a stacking fault tetrahedron. Philosophical Magazine, 89: 821-841.
[45]	Li D, Zbib H, Garmestani H, Sun X, Khaleel M. 2011. Modeling of irradiation hardening of polycrystalline materials. Computational Materials Science, 50: 2496-2501.
[46]	Li J C M. 1963. Petch relation and grain boundary sources. Transactions of the Metallurgical Society of Aime, 227: 239.
[47]	Li W, Sun L, Xue J, Wang J, Duan H. 2013. Influence of ion irradiation induced defects on mechanical properties of copper nanowires. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, 307: 158-164.
[48]	Li W N, Xue J M, Wang J X, Duan H L. 2014. Mechanical properties of self-irradiated single-crystal copper. Chinese Physics B, 23: 036101.
[49]	Lu K, Lu L, Suresh S. 2009. Strengthening materials by engineering coherent internal boundaries at the nanoscale. Science, 324: 349-352.
[50]	Lucas G E. 1993. The evolution of mechanical property change in irradiated austenitic stainless-steels. Journal of Nuclear Materials, 206: 287-305.
[51]	Luppo M I, Bailat C, Schaublin R, Victoria M. 2000. Tensile properties and microstructure of 590 MeV proton-irradiated pure Fe and a Fe-Cr alloy. Journal of Nuclear Materials, 283: 483-487.
[52]	Mansur L K. 1979. Irradiation creep by climb-enable glide of dislocations resulting from preferred ab- sorption of point-defects. Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, 39: 497-506.
[53]	Matsukawa Y, Osetsky Y N, Stoller R E, Zinkle S J. 2006. Destruction processes of large stacking fault tetrahedra induced by direct interaction with gliding dislocations. Journal of Nuclear Materials, 351: 285-294.
[54]	Matsukawa Y, Osetsky Y N, Stoller R E, Zinkle S J. 2008. Mechanisms of stacking fault tetrahedra destruc- tion by gliding dislocations in quenched gold. Philosophical Magazine, 88: 581-597.
[55]	Matsukawa Y, Zinkle S J. 2004. Dynamic observation of the collapse process of a stacking fault tetrahedron by moving dislocations. Journal of Nuclear Materials, 329: 919-923.
[56]	Matsuoka H, Yamasaki T, Zheng Y J, Mitamura T, Terasawa M, Fukami T. 2007. Microstructure and me- chanical properties of neutron-irradiated ultra-fine-grained SUS316L stainless steels and electrodeposited nanocrystalline Ni and Ni-W alloys. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 449: 790-793.
[57]	Matthews J R, Finnis M W. 1988. Irradiation creep models-An overview. Journal of Nuclear Materials, 159: 257-285.
[58]	Mecking H, Kocks U F. 1981. Kinetics of flow and strain-hardening. Acta Metallurgica, 29: 1865-1875.
[59]	Nita N, Schaeublin R, Victoria M. 2004. Impact of irradiation on the microstructure of nanocrystalline materials. Journal of Nuclear Materials, 329-333: 953-957.
[60]	Nita N, Schaeublin R, Victoria M, Valiev R Z. 2005. Effects of irradiation on the microstructure and mechanical properties of nanostructured materials. Philosophical Magazine, 85: 723-735.
[61]	Nogaret T, Robertson C, Rodney D. 2007. Atomic-scale plasticity in the presence of Frank loops. Philo- sophical Magazine, 87, 945-966.
[62]	Odette G R, Alinger M J, Wirth B D. 2008. Recent developments in irradiation-resistant steels. Annual Review of Materials Research, 38: 471-503.
[63]	Odette G R, Frey D. 1979. Development of mechanical property correlation methodology for fusion envi- ronments. Journal of Nuclear Materials, 85-6: 817-822.
[64]	Odette G R, Lucas G E. 2001. Embrittlement of nuclear reactor pressure vessels. Jom-Journal of the Minerals Metals & Materials Society, 53: 18-22.
[65]	Orowan E. 1942. A type of plastic deformation new in metals. Nature, 149: 643-644.
[66]	Osetsky Y N, Bacon D J. 2001. Defect cluster formation in displacement cascades in copper. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, 180: 85-90.
[67]	Osetsky Y N, Bacon D J. 2003. Atomic-scale modelling of primary damage and properties of radiation defects in metals. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, 202: 31-43.
[68]	Osetsky Y N, Bacon D J, Serra A, Singh B N, Golubov S I. 2000. Stability and mobility of defect clusters and dislocation loops in metals. Journal of Nuclear Materials, 276: 65-77.
[69]	Osetsky Y N, Rodney D, Bacon D J. 2006. Atomic-scale study of dislocation-stacking fault tetrahedron interactions. Part I: mechanisms. Philosophical Magazine, 86: 2295-2313.
[70]	Osetsky Y N, Stoller R E, Rodney D, Bacon D J. 2005. Atomic-scale details of dislocation-stacking fault tetrahedra interaction. Materials Science and Engineering a-Structural Materials Properties Microstruc- ture and Processing, 400: 370-373.
[71]	Paquin A, Berbenni S, Favier V, Lemoine X, Berveiller M. 2001. Micromechanical modeling of the elastic- viscoplastic behavior of polycrystalline steels. International Journal of Plasticity, 17: 1267-1302.
[72]	Paquin A, Sabar H, Berveiller M. 1999. Integral formulation and self-consistent modelling of elastoviscoplas- tic behavior of heterogeneous materials. Archive of Applied Mechanics, 69: 14-35.
[73]	Patra A, McDowell D L. 2012. Crystal plasticity-based constitutive modelling of irradiated bcc structures. Philosophical Magazine, 92: 861-887.
[74]	Patra A, McDowell D L. 2013. Continuum modeling of localized deformation in irradiated bcc materials. Journal of Nuclear Materials, 432: 414-427.
[75]	Peirce D, Asaro R J, Needleman A. 1982. An analysis of nonuniform and localized deformation in ductile single-crystals. Acta Metallurgica, 30: 1087-1119.
[76]	Perez-Perez F J, Smith R. 2000. Structural changes at grain boundaries in bcc iron induced by atomic colli- sions. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, 164: 487-494.
[77]	Petch N J. 1953. The cleavage strength of polycrystals. Journal of the Iron and Steel Institute, 174: 25-28.
[78]	Rhee M, Zbib H M, Hirth J P, Huang H, de la Rubia T. 1998. Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals. Modelling and Simulation in Materials Science and Engineering, 6: 467-492.
[79]	Robach J S, Robertson I M, Lee H J, Wirth B D. 2006. Dynamic observations and atomistic simulations of dislocation-defect interactions in rapidly quenched copper and gold. Acta Materialia, 54: 1679-1690.
[80]	Robach J S, Robertson I M, Wirth B D, Arsenlis A. 2003. In-situ transmission electron microscopy ob- servations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper. Philosophical Magazine, 83: 955-967.
[81]	Rose M, Balogh A G, Hahn H. 1997. Instability of irradiation induced defects in nanostructured materials. Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, 127: 119-122.
[82]	Sabar H, Berveiller M, Favier V, Berbenni S. 2002. A new class of micro-macro models for elastic-viscoplastic heterogeneous materials. International Journal of Solids and Structures, 39: 3257-3276.
[83]	Saintoyant L, Lee H J, Wirth B D. 2007. Molecular dynamics study of the interactions between dislocation and imperfect stacking fault tetrahedron in Cu. Journal of Nuclear Materials, 361: 206-217.
[84]	Samaras M, Derlet P M, Van Swygenhoven H, Victoria M. 2002. Computer simulation of displacement cascades in nanocrystalline Ni. Physical Review Letters, 88: 125505.
[85]	Samaras M, Derlet P M, Van Swygenhoven H, Victoria M. 2003. Radiation damage near grain boundaries. Philosophical Magazine, 83: 3599-3607.
[86]	Sharma G, Mukherjee P, Chatterjee A, Gayathri N, Sarkar A, Chakravartty J K. 2013. Study of the effect of alpha irradiation on the microstructure and mechanical properties of nanocrystalline Ni. Acta Materialia, 61: 3257-3266.
[87]	Sharma G, Sarkar A, Varshney J, Ramamurty U, Kumar A, Gupta S K, Chakravartty J K. 2011. Effect of irradiation on the microstructure and mechanical behavior of nanocrystalline nickel. Scripta Materialia, 65: 727-730.
[88]	Sharp J V, Makin, M J. 1965. Microstrain in neutron irradiated copper crystals. Philosophical Magazine, 12: 427.
[89]	Shimada M, Campbell D J, Mukhovatov, V, Fujiwara, M, Kirneva, N, Lackner, K, Nagami, M, Pustovitov, V.D, Uckan N, Wesley J, Asakura N, Costley A E, Donne A J H, Doyle E J, Fasoli A, Gormezano C, Gribov Y, Gruber O, Hender T C, Houlberg W, Ide S, Kamada Y, Leonard A, Lipschultz B, Loarte A, Miyamoto K, Osborne T H, Polevoi A, Sipps A C C. 2007. Progress in the ITER Physics Basis - Chapter 1: Overview and summary. Nuclear Fusion, 47: S1-S17.
[90]	Singh A, Tao N R, Dao M, Suresh S. 2012. Repeated frictional sliding properties of copper containing nanoscale twins. Scripta Materialia, 66: 849-853.
[91]	Singh B N, Edwards D J, Toft P. 2001. Effect of neutron irradiation and post-irradiation annealing on microstructure and mechanical properties of OFHC-copper. Journal of Nuclear Materials, 299: 205-218.
[92]	Singh B N, Foreman A J E, Trinkaus H. 1997. Radiation hardening revisited: role of intracascade clustering. Journal of Nuclear Materials, 249: 103-115.
[93]	Singh B N, Horsewell A, Toft P, Edwards D J. 1995. Temperature and dose dependencies of microstructure and hardness of neutron-irradiated OFHC copper. Journal of Nuclear Materials, 224: 131-140.
[94]	Singh B N, Zinkle S J. 1993. Defect accumulation in pure FCC metals in the transient regime - A review. Journal of Nuclear Materials, 206: 212-229.
[95]	Song D K, Li X G, Xue J M, Duan H L, Jin Z H. 2014. Irradiation-enhanced twin boundary migration in BCC Fe. Philosophical Magazine Letters, 94: 361-369.
[96]	Sugio K, Shimomura Y, de la Rubia T D. 1998. Computer simulation of displacement damage cascade formation near sigma 5 twist boundary in silver. Journal of the Physical Society of Japan, 67: 882-889.
[97]	Taylor, G I. 1938. Plastic strain in metals. Journal of the Institute of Metals, 62: 307-324.
[98]	Terentyev D, Bakaev A. 2013. Interaction of a screw dislocation with Frank loops in Fe-10Ni-20Cr alloy. Journal of Nuclear Materials, 442: 208-217.
[99]	Terentyev D, Bakaev A, Osetsky Y N. 2013. Interaction of dislocations with Frank loops in Fe-Ni alloys and pure Ni: An MD study. Journal of Nuclear Materials, 442: S628-S632.
[100]	Uchic M D, Shade P A, Dimiduk D M. 2009. Plasticity of micrometer-scale single crystals in compression. Annual Review of Materials Research, 39: 361-386.
[101]	Varshni Y P. 1970. Temperature dependence of the elastic constants. Physical Review B-Solid State, 2: 3952-3958.
[102]	Victoria M, Baluc N, Bailat C, Dai Y, Luppo M I, Schaublin R, Singh B N. 2000. The microstructure and associated tensile properties of irradiated fcc and bcc metals. Journal of Nuclear Materials, 276: 114-122.
[103]	von Blanckenhagen B, Gumbsch P, Arzt E. 2001. Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation. Modelling and Simulation in Materials Science and Engineering, 9: 157-169.
[104]	von Blanckenhagen, B, Gumbsch, P, Arzt, E. 2003. Dislocation sources and the flow stress of polycrystalline thin metal films. Philosophical Magazine Letters, 83: 1-8.
[105]	Wang H, Wu P D, Tome C N, Huang Y. 2010a. A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials. Journal of the Mechanics and Physics of Solids, 58: 594-612.
[106]	Wang Y, Weissmuller J, Duan H L. 2010b. Mechanics of corrugated surfaces. Journal of the Mechanics and Physics of Solids, 58: 1552-1566.
[107]	Wirth B D, Bulatov V V, de la Rubia T D. 2002. Dislocation-stacking fault tetrahedron interactions in Cu. Journal of Engineering Materials and Technology-Transactions of the Asme, 124: 329-334.
[108]	Wirth B D, Odette G R, Marian J, Ventelon L, Young-Vandersall J A, Zepede-Ruiz L A. 2004. Multiscale modeling of radiation damage in Fe-based alloys in the fusion environment. Journal of Nuclear Materials, 329: 103-111.
[109]	Xiao X Z, Song D K, Xue J M, Chu H J, Duan H L. 2015a. A size-dependent tensorial plasticity model for FCC singlecrystal with irradiation. International Journal of Plasticity, 65: 152-167.
[110]	Xiao X Z, Song D K, Xue J M, Chu H J, Duan H L. 2015b. A self-consistent plasticity theory for modeling the thermo-mechanical properties of irradiated FCC metallic polycrystals. Journal of the Mechanics and Physics of Solids, 78: 1-16.
[111]	Yu K Y, Bufford D, Sun C, Liu Y, Wang H, Kirk M A, Li M, Zhang X. 2013. Removal of stacking-fault tetrahedra by twin boundaries in nanotwinned metals. Nature Communications, 4: 1377-1377.
[112]	Zhang H M, Dong X H, Du D P, Wang Q. 2013. A unified physically based crystal plasticity model for FCC metals over a wide range of temperatures and strain rates. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 564: 431-441.
[113]	Zinkle S J, Singh B N. 1993. Analysis of displacement damage and defect production under cascade damage conditions. Journal of Nuclear Materials, 199: 173-191.