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A hardening model considering grain size effect for ion-irradiated polycrystals under nanoindentation

  • Liu, Kai (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University) ;
  • Long, Xiangyun (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University) ;
  • Li, Bochuan (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University) ;
  • Xiao, Xiazi (Department of Mechanics, School of Civil Engineering, Central South University) ;
  • Jiang, Chao (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University)
  • Received : 2020.08.18
  • Accepted : 2021.03.07
  • Published : 2021.09.25

Abstract

In this work, a new hardening model is proposed for the depth-dependent hardness of ion-irradiated polycrystals with obvious grain size effect. Dominant hardening mechanisms are addressed in the model, including the contribution of dislocations, irradiation-induced defects and grain boundaries. Two versions of the hardening model are compared, including the linear and square superposition models. A succinct parameter calibration method is modified to parametrize the models based on experimentally obtained hardness vs. indentation depth curves. It is noticed that both models can well characterize the experimental data of unirradiated polycrystals; whereas, the square superposition model performs better for ion-irradiated materials, therefore, the square superposition model is recommended. In addition, the new model separates the grain size effect from the dislocation hardening contribution, which makes the physical meaning of fitted parameters more rational when compared with existing hardness analysis models.

Keywords

Acknowledgement

This work was supported by the National Science Fund for Distinguished Young Scholars, China (Grant No. 51725502), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004), the National Nature Science foundation of China (NSFC) under Contract No, 11802344, and Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50809).

References

  1. S.J. Zinkle, J.T. Busby, Structural materials for fission & fusion energy, Mater. Today 12 (11) (2009) 12-19. https://doi.org/10.1016/S1369-7021(09)70294-9
  2. W.Q. Chen, X.Z. Xiao, B. Pang, S.S. Si, Y.Z. Jia, B. Xu, T.W. Morgan, W. Liu, Y.L. Chiu, Irradiation hardening induced by blistering in tungsten due to low-energy high flux hydrogen plasma exposure, J. Nucl. Mater. 522 (2019) 11-18. https://doi.org/10.1016/j.jnucmat.2019.05.004
  3. S.I. Kim, B.H. Kim, J.L. Kim, J.I. Lee, A review of neutron scattering correction for the calibration of neutron survey meters using the shadow cone method, Nuclear Engineering and Technology 47 (7) (2015) 939-944. https://doi.org/10.1016/j.net.2015.07.005
  4. G.S. Was, Z. Jiao, E. Getto, K. Sun, A.M. Monterrosa, S.A. Maloy, O. Anderoglu, B.H. Sencer, M. Hackett, Emulation of reactor irradiation damage using ion beams, Scripta Mater. 88 (2014) 33-36. https://doi.org/10.1016/j.scriptamat.2014.06.003
  5. C. Heintze, F. Bergner, S. Akhmadaliev, E. Altstadt, Ion irradiation combined with nanoindentation as a screening test procedure for irradiation hardening, J. Nucl. Mater. 472 (2016) 196-205. https://doi.org/10.1016/j.jnucmat.2015.07.023
  6. R. Kasada, S. Konishi, K. Yabuuchi, S. Nogami, M. Ando, D. Hamaguchi, H. Tanigawa, Depth-dependent nanoindentation hardness of reduced-activation ferritic steels after MeV Fe-ion irradiation, Fusion Eng. Des. 89 (7) (2014) 1637-1641. https://doi.org/10.1016/j.fusengdes.2014.03.068
  7. Z. Fan, S. Zhao, K. Jin, D. Chen, Y.N. Osetskiy, Y. Wang, H. Bei, K.L. More, Y. Zhang, Helium irradiated cavity formation and defect energetics in Ni-based binary single-phase concentrated solid solution alloys, Acta Mater. 164 (2019) 283-292. https://doi.org/10.1016/j.actamat.2018.10.040
  8. C.D. Hardie, S.G. Roberts, A.J. Bushby, Understanding the effects of ion irradiation using nanoindentation techniques, J. Nucl. Mater. 462 (2015) 391-401. https://doi.org/10.1016/j.jnucmat.2014.11.066
  9. P. Sun, Y. Wang, M. Frost, C. Schonwalder, A.L. Levitan, M. Mo, Z. Chen, J.B. Hastings, G.R. Tynan, S.H. Glenzer, P. Heimann, Characterization of defect clusters in ion-irradiated tungsten by X-Ray diffuse scattering, J. Nucl. Mater. 510 (2018) 322-330. https://doi.org/10.1016/j.jnucmat.2018.07.062
  10. A. Prasitthipayong, S.J. Vachhani, S.J. Tumey, A.M. Minor, P. Hosemann, Indentation size effect in unirradiated and ion-irradiated 800H steel at high temperatures, Acta Mater. 144 (2018) 896-904. https://doi.org/10.1016/j.actamat.2017.11.001
  11. C. Xu, L. Zhang, W. Qian, J. Mei, X. Liu, The studies of irradiation hardening of stainless steel reactor internals under proton and xenon irradiation, Nuclear Engineering and Technology 48 (3) (2016) 758-764. https://doi.org/10.1016/j.net.2016.01.007
  12. C. Heintze, F. Bergner, M. Hernandez-Mayoral, Ion-irradiation-induced damage in Fe-Cr alloys characterized by nanoindentation, J. Nucl. Mater. 417 (1) (2011) 980-983. https://doi.org/10.1016/j.jnucmat.2010.12.196
  13. X. Xiao, L. Chen, L. Yu, H. Duan, Modelling nano-indentation of ion-irradiated FCC single crystals by strain-gradient crystal plasticity theory, Int. J. Plast. 116 (2019) 216-231. https://doi.org/10.1016/j.ijplas.2019.01.005
  14. C. Yan, R. Wang, Y. Wang, X. Wang, G. Bai, Effects of ion irradiation on microstructure and properties of zirconium alloys-a review, Nuclear Engineering and Technology 47 (3) (2015) 323-331. https://doi.org/10.1016/j.net.2014.12.015
  15. D. Chen, K. Murakami, K. Dohi, K. Nishida, N. Soneda, Z. Li, L. Liu, N. Sekimura, Depth distribution of Frank loop defects formed in ion-irradiated stainless steel and its dependence on Si addition, Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms 365 (2015) 503-508. https://doi.org/10.1016/j.nimb.2015.08.029
  16. Z.Y. Fu, P.P. Liu, F.R. Wan, Q. Zhan, Helium and hydrogen irradiation induced hardening in CLAM steel, Fusion Eng. Des. 91 (2015) 73-78. https://doi.org/10.1016/j.fusengdes.2015.01.001
  17. Y. Huang, F. Zhang, K.C. Hwang, W.D. Nix, G.M. Pharr, G. Feng, A model of size effects in nano-indentation, J. Mech. Phys. Solid. 54 (8) (2006) 1668-1686. https://doi.org/10.1016/j.jmps.2006.02.002
  18. W.D. Nix, H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity, J. Mech. Phys. Solid. 46 (3) (1998) 411-425. https://doi.org/10.1016/S0022-5096(97)00086-0
  19. E. Orowan, A type of plastic deformation new in metals, Nature 149 (3788) (1942) 643-644. https://doi.org/10.1038/149643a0
  20. X. Xiao, Q. Chen, H. Yang, H. Duan, J. Qu, A mechanistic model for depthdependent hardness of ion irradiated metals, J. Nucl. Mater. 485 (2017) 80-89. https://doi.org/10.1016/j.jnucmat.2016.12.039
  21. X. Xiao, L. Yu, A hardening model for the cross-sectional nanoindentation of ion-irradiated materials, J. Nucl. Mater. 511 (2018) 220-230. https://doi.org/10.1016/j.jnucmat.2018.09.019
  22. X. Xiao, L. Yu, Comparison of linear and square superposition hardening models for the surface nanoindentation of ion-irradiated materials, J. Nucl. Mater. 503 (2018) 110-115. https://doi.org/10.1016/j.jnucmat.2018.02.047
  23. J.F. Nye, Some geometrical relations in dislocated crystals, Acta Metall. 1 (2) (1953) 153-162. https://doi.org/10.1016/0001-6160(53)90054-6
  24. G.J. Weng, A micromechanical theory of grain-size dependence in metal plasticity, J. Mech. Phys. Solid. 31 (3) (1983) 193-203. https://doi.org/10.1016/0022-5096(83)90021-2
  25. E.O. Hall, The deformation and ageing of mild steel: III discussion of results, Proc. Phys. Soc. B 64 (9) (1951) 747-753. https://doi.org/10.1088/0370-1301/64/9/303
  26. A. Singh, Y. Osawa, H. Somekawa, T. Mukai, Effect of microstructure on strength and ductility of high strength quasicrystal phase dispersed Mg-Zn-Y alloys, Mater. Sci. Eng., A 611 (2014) 242-251. https://doi.org/10.1016/j.msea.2014.05.091
  27. Y. Wang, H. Choo, Influence of texture on Hall-Petch relationships in an Mg alloy, Acta Mater. 81 (2014) 83-97. https://doi.org/10.1016/j.actamat.2014.08.023
  28. H. Yu, Y. Xin, M. Wang, Q. Liu, Hall-Petch relationship in Mg alloys: a review, J. Mater. Sci. Technol. 34 (2) (2018) 248-256. https://doi.org/10.1016/j.jmst.2017.07.022
  29. B. Guan, Y. Xin, X. Huang, P. Wu, Q. Liu, Quantitative prediction of texture effect on Hall-Petch slope for magnesium alloys, Acta Mater. 173 (2019) 142-152. https://doi.org/10.1016/j.actamat.2019.05.016
  30. X. Hou, N.M. Jennett, Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects, Acta Mater. 60 (10) (2012) 4128-4135. https://doi.org/10.1016/j.actamat.2012.03.054
  31. Y. Ha, A. Kimura, Effect of recrystallization on ion-irradiation hardening and microstructural changes in 15Cr-ODS steel, Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms 365 (2015) 313-318. https://doi.org/10.1016/j.nimb.2015.07.076
  32. G.M. Cheng, W.Z. Xu, Y.Q. Wang, A. Misra, Y.T. Zhu, Grain size effect on radiation tolerance of nanocrystalline Mo, Scripta Mater. 123 (2016) 90-94. https://doi.org/10.1016/j.scriptamat.2016.06.007
  33. E. Hug, R. Prasath Babu, I. Monnet, A. Etienne, F. Moisy, V. Pralong, N. Enikeev, M. Abramova, X. Sauvage, B. Radiguet, Impact of the nanostructuration on the corrosion resistance and hardness of irradiated 316 austenitic stainless steels, Appl. Surf. Sci. 392 (2017) 1026-1035. https://doi.org/10.1016/j.apsusc.2016.09.110
  34. C. Heintze, I. Hilger, F. Bergner, T. Weissgarber, B. Kieback, Nanoindentation of single- (Fe) and dual-beam (Fe and He) ion-irradiated ODS Fe-14Cr-based alloys: effect of the initial microstructure on irradiation-induced hardening, J. Nucl. Mater. 518 (2019) 1-10. https://doi.org/10.1016/j.jnucmat.2019.02.037
  35. G. Monnet, C. Mai, Prediction of irradiation hardening in austenitic stainless steels: analytical and crystal plasticity studies, J. Nucl. Mater. 518 (2019) 316-325. https://doi.org/10.1016/j.jnucmat.2019.03.001
  36. G.I. Taylor, The mechanism of plastic deformation of crystals. Part I. Theoretical, Proc. Roy. Soc. Lond. 145 (855) (1934) 362-387.
  37. G.I. Taylor, Plastic strain in metals, J. Inst. Met. 62 (1938) 307-324.
  38. M. Ashby, The deformation of plastically non-homogeneous materials, Phil. Mag.: A Journal of Theoretical Experimental and Applied Physics 21 (170) (1970) 399-424. https://doi.org/10.1080/14786437008238426
  39. T. Miura, K. Fujii, K. Fukuya, K. Takashima, Influence of crystal orientation on hardness and nanoindentation deformation in ion-irradiated stainless steels, J. Nucl. Mater. 417 (1-3) (2011) 984-987. https://doi.org/10.1016/j.jnucmat.2010.12.197
  40. H. Huang, J. Li, D. Li, R. Liu, G. Lei, Q. Huang, L. Yan, TEM, XRD and nanoindentation characterization of Xenon ion irradiation damage in austenitic stainless steels, J. Nucl. Mater. 454 (1-3) (2014) 168-172. https://doi.org/10.1016/j.jnucmat.2014.07.033
  41. A.L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yield Criteria and Flow Rules for Porous Ductile Media, 1977.
  42. D. Tabor, A simple theory of static and dynamic hardness, Proc. Roy. Soc. Lond. Math. Phys. Sci. 192 (1029) (1948) 247-274.
  43. D. Whitley, A genetic algorithm tutorial, Stat. Comput. 4 (2) (1994) 65-85. https://doi.org/10.1007/BF00175354
  44. X. Xiao, D. Terentyev, L. Yu, A. Bakaev, Z. Jin, H. Duan, Investigation of the thermo-mechanical behavior of neutron-irradiated Fe-Cr alloys by self-consistent plasticity theory, J. Nucl. Mater. 477 (2016) 123-133. https://doi.org/10.1016/j.jnucmat.2016.05.012
  45. M. Dade, J. Malaplate, J. Garnier, F. De Geuser, F. Barcelo, P. Wident, A. Deschamps, Influence of microstructural parameters on the mechanical properties of oxide dispersion strengthened Fe-14Cr steels, Acta Mater. 127 (2017) 165-177. https://doi.org/10.1016/j.actamat.2017.01.026
  46. P. Song, J. Gao, K. Yabuuchi, A. Kimura, Ion-irradiation hardening accompanied by irradiation-induced dissolution of oxides in FeCr(Y, Ti)-ODS ferritic steel, J. Nucl. Mater. 511 (2018) 200-211. https://doi.org/10.1016/j.jnucmat.2018.09.007

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