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Mechanical properties of irradiated multi-phase polycrystalline BCC materials

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Abstract

Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility, resulting from irradiation-induced defects such as vacancies, interstitials and dislocation loops, etc. In this paper, we develop an elastic–viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored. At the microscopic grain scale, we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop, which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions. At the macroscopic polycrystal scale, the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties. Based on the proposed model, we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops, and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors. At the polycrystalline scale, numerical results for pure Fe match well with the irradiation experiment data. The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing. The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.

Graphical Abstract

Comparison of numerical modeling results (solid lines) with experimental results (square lines) for the polycrystalline BCC iron. We develop an elastic–viscoplastic model for irradiated multiphase polycrystalline BCC materials, based on a dislocation-based model at the grain scale, and the self-consistent scheme at the macroscopic scale. This model can be easily applied to predict the hardening behaviors of irradiated multi-phase polycrystalline materials.

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References

  1. Bruemmer, S.M., Simonen, E.P., Scott, P.M., et al.: Radiation-induced material changes and susceptibility to intergranular failure of light-water-reactor core internals. J. Nucl. Mater. 274, 299–314 (1999)

    Google Scholar 

  2. Byun, T.S., Farrell, K.: Plastic instability in polycrystalline metals after low temperature irradiation. Acta Mater. 52, 1597–1608 (2004)

    Google Scholar 

  3. Luppo, M.I., Bailat, C., Schaublin, R., et al.: Tensile properties and microstructure of 590 MeV proton-irradiated pure Fe and a Fe–Cr alloy. J. Nucl. Mater. 283, 483–487 (2000)

    Google Scholar 

  4. Singh, B.N., Horsewell, A., Toft, P.: Effects of neutron irradiation on microstructure and mechanical properties of pure iron. J. Nucl. Mater. 271, 97–101 (1999)

    Google Scholar 

  5. Barton, N.R., Arsenlis, A., Marian, J.: A polycrystal plasticity model of strain localization in irradiated iron. J. Mech. Phys. Solids 61, 341–351 (2013)

    Google Scholar 

  6. Krishna, S., Zamiri, A., De, S.: Dislocation and defect density-based micromechanical modeling of the mechanical behavior of fcc metals under neutron irradiation. Philos. Mag. 90, 4013–4025 (2010)

    Google Scholar 

  7. Patra, A., Mcdowell, D.L.: Crystal plasticity-based constitutive modelling of irradiated bcc structures. Philos. Mag. 92, 861–887 (2012)

    Google Scholar 

  8. Zinkle, S.J., Farrell, K.: Void swelling and defect cluster formation in reactor-irradiated copper. J. Nucl. Mater. 168, 262–267 (1989)

    Google Scholar 

  9. Ghaly, M., Nordlund, K., Averback, R.S.: Molecular dynamics investigations of surface damage produced by kiloelectronvolt self-bombardment of solids. Philos. Mag. Phys. Condens. Matter Struct. Defects Mech. Prop. 79, 795–820 (1999)

    Google Scholar 

  10. Osetsky, Y.N., Bacon, D.J., Serra, A., et al.: One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper. Philos. Mag. 83, 61–91 (2003)

    Google Scholar 

  11. Arakawa, K., Ono, K., Isshiki, M., et al.: Observation of the one-dimensional diffusion of nanometer-sized dislocation loops. Science 318, 956–959 (2007)

    Article  Google Scholar 

  12. Matsukawa, Y., Zinkle, S.J.: One-dimensional fast migration of vacancy clusters in metals. Science 318, 959–962 (2007)

    Article  Google Scholar 

  13. Uberuaga, B.P., Hoagland, R.G., Voter, A.F.: Direct transformation of vacancy voids to stacking fault tetrahedra. Phys. Rev. Lett. 99, 135501 (2007)

    Google Scholar 

  14. Wirth, B.D.: How does radiation damage materials? Science 318, 923–924 (2007)

    Article  Google Scholar 

  15. Bacon, D.J., Osetsky, Y.N., Stoller, R., et al.: MD description of damage production in displacement cascades in copper and alpha-iron. J. Nucl. Mater. 323, 152–162 (2003)

    Google Scholar 

  16. Seeger, A.K.: On the theory of radiation damage and radiation hardening (No. A/CONF. 15/P/998). Max-Planck-Inst. fur Metallforschung, Technischen Hochschule, Stuttgart (1959)

  17. Odette, G.R., Frey, D.: Development of mechanical property correlation methodology for fusion environments. J. Nucl. Mater. 85, 817–822 (1979)

    Google Scholar 

  18. Blewitt, T.H., Coltman, R.R., Jamison, R.E., et al.: Radiation hardening of copper single crystals. J. Nucl. Mater. 2, 277–298 (1960)

    Google Scholar 

  19. Singh, B.N., Foreman, A.J.E., Trinkaus, H.: Radiation hardening revisited: role of intracascade clustering. J. Nucl. Mater. 249, 103–115 (1997)

    Google Scholar 

  20. Arsenlis, A., Wirth, B.D., Rhee, M.: Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu. Philos. Mag. 84, 3617–3635 (2004)

    Google Scholar 

  21. Robach, J.S., Robertson, I.M., Wirth, B.D., et al.: In-situ transmission electron microscopy observations and molecular dynamics simulations of dislocation-defect interactions in ion-irradiated copper. Philos. Mag. 83, 955–967 (2003)

    Google Scholar 

  22. Lee, H., Wirth, B.D.: Molecular dynamics simulation of dislocation-void interactions in BCC Mo. J. Nucl. Mater. 386–88, 115–118 (2009)

    Google Scholar 

  23. Osetsky, Y.N., Stoller, R.E., Rodney, D., et al.: Atomic-scale details of dislocation-stacking fault tetrahedra interaction. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 400, 370–373 (2005)

    Google Scholar 

  24. Krishna, S., De, S.: A temperature and rate-dependent micromechanical model of molybdenum under neutron irradiation. Mech. Mater. 43, 99–110 (2011)

    Google Scholar 

  25. Patra, A., Mcdowell, D.L.: Continuum modeling of localized deformation in irradiated bcc materials. J. Nucl. Mater. 432, 414–427 (2013)

    Google Scholar 

  26. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 241, 376–396 (1957)

    MATH  MathSciNet  Google Scholar 

  27. Kroner, E.: Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls. Z. Phys. 151, 504–518 (1958) (in German)

  28. Hill, R.: Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89 (1965)

    MATH  Google Scholar 

  29. Iwakuma, T., Nematnasser, S.: Finite elastic plastic-deformation of polycrystalline metals. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 1984, 87–119 (1806)

    Google Scholar 

  30. Clausen, B., Tome, C.N., Brown, D.W., et al.: Reorientation and stress relaxation due to twinning: modeling and experimental characterization for Mg. Acta Mater. 56, 2456–2468 (2008)

    Google Scholar 

  31. Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 348, 101–127 (1976)

    MATH  Google Scholar 

  32. Molinari, A., Canova, G.R., Ahzi, S.: A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. 35, 2983–2994 (1987)

    Google Scholar 

  33. Weng, G.J.: A self-consistent scheme for the relaxation behavior of metals. J. Appl. Mech. Trans. Asme. 48, 779–784 (1981)

    Google Scholar 

  34. Weng, G.J.: Self-consistent determination of time-dependent behavior of metals. J. Appl. Mech. Trans. Asme 48, 41–46 (1981)

    MATH  Google Scholar 

  35. Nematnasser, S., Obata, M.: Rate-dependent, finite elastoplastic deformation of polycrystals. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 1986, 343–375 (1833)

    Google Scholar 

  36. Li, J., Weng, G.J.: A secant-viscosity approach to the time-dependent creep of an elastic-viscoplastic composite. J. Mech. Phys. Solids 45, 1069–1083 (1997)

    MATH  Google Scholar 

  37. Turner, P.A., Tome, C.N.: Self-consistent modeling of viscoelastic polycrystals—application to irradiation creep and growth. J. Mech. Phys. Solids 41, 1191–1211 (1993)

    MATH  Google Scholar 

  38. Wang, H., Wu, P.D., Tome, C.N., et al.: A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials. J. Mech. Phys. Solids 58, 594–612 (2010)

    MATH  MathSciNet  Google Scholar 

  39. Molinari, A.: Averaging models for heterogeneous viscoplastic and elastic viscoplastic materials. J. Eng. Mater. Technol. Trans. Asme. 124, 62–70 (2002)

    Google Scholar 

  40. Mercier, S., Molinari, A.: Homogenization of elastic-viscoplastic heterogeneous materials: self-consistent and Mori–Tanaka schemes. Int. J. Plast. 25, 1024–1048 (2009)

    MATH  Google Scholar 

  41. Berbenni, S., Favier, V., Lemoine, X., et al.: Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels having different microstructures. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 372, 128–136 (2004)

    Google Scholar 

  42. Mercier, S., Molinari, A., Berbenni, S.: Comparison of different homogenization approaches for elastic-viscoplastic materials. Model. Simul. Mater. Sci. Eng. 20, 024004 (2012)

    Google Scholar 

  43. Paquin, A., Berbenni, S., Favier, V., et al.: Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels. Int. J. Plast. 17, 1267–1302 (2001)

    MATH  Google Scholar 

  44. Paquin, A., Sabar, H., Berveiller, M.: Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials. Arch. Appl. Mech. 69, 14–35 (1999)

    MATH  Google Scholar 

  45. Sabar, H., Berveiller, M., Favier, V., et al.: A new class of micro–macro models for elastic-viscoplastic heterogeneous materials. Int. J. Solids Struct. 39, 3257–3276 (2002)

    MATH  MathSciNet  Google Scholar 

  46. Coulibaly, M., Sabar, H.: New integral formulation and self-consistent modeling of elastic-viscoplastic heterogeneous materials. Int. J. Solids Struct. 48, 753–763 (2011)

    MATH  Google Scholar 

  47. Xiao, X., Song, D., Xue, J., et al.: A self-consistent plasticity theory for modeling the thermo-mechanical properties of irradiated FCC metallic polycrystals. J. Mech. Phys. Solids 78, 1–16 (2015)

    Google Scholar 

  48. Kiener, D., Hosemann, P., Maloy, S.A., et al.: In situ nanocompression testing of irradiated copper. Nat. Mater. 10, 608–613 (2011)

    Google Scholar 

  49. Gussev, M.N., Byun, T.S., Busby, J.T.: Description of strain hardening behavior in neutron-irradiated fcc metals. J. Nucl. Mater. 427, 62–68 (2012)

    Google Scholar 

  50. Klueh, R.L., Nelson, A.T.: Ferritic/martensitic steels for next-generation reactors. J. Nucl. Mater. 371, 37–52 (2007)

    Google Scholar 

  51. Chen, C.Q., Cui, J.Z., Duan, H.L., et al.: Perspectives in mechanics of heterogeneous solids. Acta Mech. Solida Sin. 24, 1–26 (2011)

    MATH  Google Scholar 

  52. Duan, H.L., Weissmüller, J., Wang, Y.: Instabilities of core-shell heterostructured cylinders due to diffusions and epitaxy: spheroidization and blossom of nanowires. J. Mech. Phys. Solids 56, 1831–1851 (2008)

    MATH  MathSciNet  Google Scholar 

  53. Duan, H.L., Yi, X., Huang, Z.P., et al.: A unified scheme for prediction of effective moduli of multiphase composites with interface effects. Part I: theoretical framework. Mech. Mater. 39, 81–93 (2007)

  54. Duan, H.L., Yi, X., Huang, Z.P., et al.: A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part II—application and scaling laws. Mech. Mater. 39, 94–103 (2007)

    Google Scholar 

  55. Berbenni, S., Favier, V., Berveiller, M., et al.: Micromechanical modelling of the elastic-viscoplastic behaviour of interstitial-free and dual-phase steels. Revue De Metall. Cah. D Info. Tech. 101, 381 (2004)

    Google Scholar 

  56. Seeger, A.: Why anomalous slip in body-centred cubic metals? Mater. Sci. Eng. A 319–321, 254–260 (2001)

    Google Scholar 

  57. Kothari, M., Anand, L.: Elasto-viscoplastic constitutive equations for polycrystalline metals: applications to tantalum. J. Mech. Phys. Solids 46, 51 (1998)

    MATH  Google Scholar 

  58. Robertson, I.M., Jenkins, M.L., English, C.A.: Low-dose neutron-irradiation damage in alpha-iron. J. Nucl. Mater. 108–109, 209–221 (1982)

    Google Scholar 

  59. Little, E.A.: Neutron-irradiation hardening in irons and ferritic steels. Int. Metall. Rev. 21, 25–60 (1976)

    MathSciNet  Google Scholar 

  60. Xiao, X., Song, D., Xue, J., et al.: A size-dependent tensorial plasticity model for FCC single crystal with irradiation. Int. J. Plast. 65, 152–167 (2015)

    Google Scholar 

  61. Arsenlis, A., Rhee, M., Hommes, G., et al.: A dislocation dynamics study of the transition from homogeneous to heterogeneous deformation in irradiated body-centered cubic iron. Acta Mater. 60, 3748–3757 (2012)

    Google Scholar 

  62. Wang, Y., Weissmüller, J., Duan, H.L.: Mechanics of corrugated surfaces. J. Mech. Phys. Solids 58, 1552–1566 (2010)

    MATH  MathSciNet  Google Scholar 

  63. Mecking, H., Kocks, U.F.: Kinetics of flow and strain-hardening. Acta Metall. 29, 1865–1875 (1981)

    Google Scholar 

  64. Gilbert, M.R., Queyreau, S., Marian, J.: Stress and temperature dependence of screw dislocation mobility in alpha-Fe by molecular dynamics. Phys. Rev. B 84, 174103 (2011)

    Google Scholar 

  65. Konobeev, Y.V., Dvoriashin, A.M., Porollo, S.I., et al.: Swelling and microstructure of pure Fe and Fe–Cr alloys after neutron irradiation to similar to 26 dpa at 400 degrees C. J. Nucl. Mater. 355, 124–130 (2006)

    Google Scholar 

  66. Oksiuta, Z., Olier, P., de Carlan, Y., et al.: Development and characterisation of a new ODS ferritic steel for fusion reactor application. J. Nucl. Mater. 393, 114–119 (2009)

    Google Scholar 

  67. de Carlan, Y., Bechade, J.L., Dubuisson, P., et al.: CEA developments of new ferritic ODS alloys for nuclear applications. J. Nucl. Mater. 386–88, 430–432 (2009)

  68. Asgharzadeh, H., Kim, H.S., Simchi, A.: Microstructure, strengthening mechanisms and hot deformation behavior of an oxide-dispersion strengthened UFG Al6063 alloy. Mater. Charact. 75, 108–114 (2013)

    Google Scholar 

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Acknowledgments

The authors would like to thank the support provided by the Major State Basic Research Development Program of China (Grant 2011CB013101), and the National Natural Science Foundation of China (NSFC) (Grants 11225208 and 91226202). Duan acknowledges support from the key subject “Computational Solid Mechanics” of the China Academy of Engineering Physics. Chu acknowledges the support provided by the Shanghai Eastern-Scholar Plan and by the State Key Laboratory for Mechanical Behavior of Materials.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Dingkun Song, Xiazi Xiao, Jianming Xue & Huiling Duan

  2. CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing, 100871, China

    Xiazi Xiao, Jianming Xue & Huiling Duan

  3. Department of Mechanics, College of Sciences, Shanghai University, Shanghai, 200444, China

    Haijian Chu

  4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai, 200444, China

    Haijian Chu

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  1. Dingkun Song
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  2. Xiazi Xiao
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  3. Jianming Xue
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  5. Huiling Duan
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Correspondence to Huiling Duan.

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Song, D., Xiao, X., Xue, J. et al. Mechanical properties of irradiated multi-phase polycrystalline BCC materials. Acta Mech Sin 31, 191–204 (2015). https://doi.org/10.1007/s10409-015-0447-0

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