Skip to main content

Multiscale Modeling of Radiation Hardening

  • Reference work entry
  • First Online:
Handbook of Mechanics of Materials
  • 4489 Accesses

Abstract

All materials used in nuclear reactors experience radiation hardening, thus altering significantly their mechanical behavior. Despite the large efforts made by the scientific community to correctly predict the radiation effects on nuclear materials, many difficulties persist in modeling radiation defects. Although radiation hardening is responsible for macroscopic consequences such as embrittlement, its fundamental mechanisms prevail at the atomic scale. The fast development of simulation techniques, especially atomistic simulations, helped in exploring many features of dislocation interactions with radiation-induced defects. For a long time, the obtained results were used to validate theoretical models and to qualitatively explain and rationalize experimental observations.

More recently, with the ubiquity of simulation results and techniques at different scales, quantitative physically based predictions of the mechanical behavior became a realistic objective. Efforts were made to couple simulation results at different scales through the development of scale transition methods and the construction of constitutive equations of the local mechanical behavior. The objective of this chapter is to trace the evolution and progress of this strategy, thus enabling the construction of a chain of physical knowledge across the scales. Details of simulations techniques and methods are not presented. We emphasize on basic achievements of simulations and on the treatment of results with the aim to bridge the different scales of interest for the mechanical behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 919.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Konings R. Comprehensive nuclear materials. 1st ed. Amsterdam: Elsevier Science; 2011. 3560 p.

    Google Scholar 

  2. Fukuya K. Current understanding of radiation-induced degradation in light water reactor structural materials. J Nucl Sci Technol. 2013;50(3):213–54.

    Article  Google Scholar 

  3. Kenik EA, Busby JT. Radiation-induced degradation of stainless steel light water reactor internals. Mater Sci Eng R: Rep. 2012;73(7–8):67–83.

    Article  Google Scholar 

  4. Weeks RW, Pati SR, Ashby MF, Barrand P. The elastic interaction between a straight dislocation and a bubble or a particle. Acta Metall. 1969;17(12):1403–10.

    Article  Google Scholar 

  5. Kroupa F. Circular edge dislocation loop. Czechoslov J Phys. 1960;10(4):284–93.

    Article  MathSciNet  Google Scholar 

  6. Hu S y, Schmauder S, Chen L q. Atomistic simulations of interactions between cu precipitates and an edge dislocation in a B.C.C. Fe single crystal. phys stat sol (b). 2000;220(2):845–6.

    Article  Google Scholar 

  7. Bacon DJ, Osetsky YN, Rodney D. Dislocation–obstacle interactions at the atomic level. In: JP Hirth, L Kubin, editor. Dislocations in solids [Internet]. Elsevier; 2009.

    Google Scholar 

  8. Haile JM. Molecular dynamics simulation: elementary methods. New York: Wiley; 1997.

    Google Scholar 

  9. Devincre B, Condat M. Model validation of a 3D simulation of dislocation dynamics: discretization and line tension effects. Acta Metall Mater. 1992;40(10):2629–37.

    Article  Google Scholar 

  10. Ghoniem NM, Huang J, Wang Z. Affine covariant-contravariant vector forms for the elastic field of parametric dislocations in isotropic crystals. Philos Mag Lett. 2002;82(2):55–63.

    Article  Google Scholar 

  11. Wang YU, Jin YM, Cuitiño AM, Khachaturyan AG. Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations. Acta Mater. 2001;49(10):1847–57.

    Article  Google Scholar 

  12. Devincre B, Madec R, Monnet G, Queyreau S, Gatti R, Kubin L. Modeling crystal plasticity with dislocation dynamics simulations: the «MICROMEGAS» code. In: Forest S, Ponchet A, Thomas O, editors. Mechanics of Nano-objects. Presses des mines. Mechanics of Nano-objects; 2011. p. 81–100.

    Google Scholar 

  13. Bulatov VV, et al. Scalable line dynamics in ParaDiS. Supercomputing. http://www.sc-conference.org/sc2004/schedule/pdfs/pap206.pdf (2004).

  14. Pavia F, Curtin WA. Parallel algorithm for multiscale atomistic/continuum simulations using LAMMPS. Modelling Simul. Mater Sci Eng. 2015;23(5):55002.

    Google Scholar 

  15. Vattré A, Devincre B, Feyel F, Gatti R, Groh S, Jamond O, et al. Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: the discrete-continuous model revisited. J Mech Phys Solids. 2014;63:491–505.

    Article  MathSciNet  Google Scholar 

  16. Cai W. Computer simulations of dislocations. Oxford: Oxford University Press; 2013.

    MATH  Google Scholar 

  17. Osetsky YN, Bacon DJ, Mohles V. Atomic modelling of strengthening mechanisms due to voids and copper precipitates in α-iron. Philos Mag. 2003;83(31–34):3623–41.

    Article  Google Scholar 

  18. Kohler C, Kizler P, Schmauder S. Atomistic simulation of the pinning of edge dislocations in Ni by Ni3Al precipitates. Mater Sci Eng A. 2005;400–401:481–4.

    Article  Google Scholar 

  19. Bacon DJ, Osetsky YN. Hardening due to copper precipitates in α-iron studied by atomic-scale modelling. J Nucl Mater. 2004, Part B:1233–1237.

    Article  Google Scholar 

  20. Okita T. Effect of the Stacking Fault Energy on Interactions Between an Edge Dislocation and a Spherical Void in FCC Metals at Various Spatial Geometries. Fusion Sci Technol [Internet], (2014); 66(1).

    Article  Google Scholar 

  21. Terentyev D, Malerba L, Bonny G, Al-Motasem AT, Posselt M. Interaction of an edge dislocation with Cu–Ni-vacancy clusters in bcc iron. J Nucl Mater. 2011;419(1–3):134–9.

    Article  Google Scholar 

  22. Prakash A, Guénolé J, Wang J, Müller J, Spiecker E, Mills MJ, et al. Atom probe informed simulations of dislocation–precipitate interactions reveal the importance of local interface curvature. Acta Mater. 2015;92:33–45.

    Article  Google Scholar 

  23. Caillard D. Kinetics of dislocations in pure Fe. Part I. In situ straining experiments at room temperature. Acta Mater. 2010;58(9):3493–503.

    Article  Google Scholar 

  24. Rodney D, Martin G. Dislocation pinning by small interstitial loops: a molecular dynamics study. Phys Rev Lett. 1999;82(16):3272–5.

    Article  Google Scholar 

  25. Liu X-Y, Biner SB. Molecular dynamics simulations of the interactions between screw dislocations and self-interstitial clusters in body-centered cubic Fe. Scr Mater. 2008;59(1):51–4.

    Article  Google Scholar 

  26. Nogaret T, Robertson C, Rodney D. Atomic-scale plasticity in the presence of frank loops. Philos Mag. 2007;87(6):945–66.

    Article  Google Scholar 

  27. Monnet G, Osetsky YN, Bacon DJ. Mesoscale thermodynamic analysis of atomic-scale dislocation–obstacle interactions simulated by molecular dynamics. Philos Mag. 2010;90(7–8):1001–18.

    Article  Google Scholar 

  28. Nembach E. Particle strengthening of metals and alloys. New York: Wiley Professional Software; 1997.

    Google Scholar 

  29. Bacon DJ, Kocks UF, Scattergood RO. The effect of dislocation self-interaction on the orowan stress. Philos Mag. 1973;28(6):1241–63.

    Article  Google Scholar 

  30. Hazzledine PM, Karnthaler HP, Korner A. The application of the Wulff construction to dislocation problems. phys stat sol (a). 1984;81(2):473–84.

    Article  Google Scholar 

  31. Osetsky YN, Bacon DJ. Void and precipitate strengthening in α-iron: what can we learn from atomic-level modelling? J Nucl Mater. 2003;323(2–3):268–80.

    Article  Google Scholar 

  32. Shin CS, Fivel MC, Verdier M, Oh KH. Dislocation–impenetrable precipitate interaction: a three-dimensional discrete dislocation dynamics analysis. Philos Mag. 2003;83(31–34):3691–704.

    Article  Google Scholar 

  33. Hafez Haghighat SM, Fivel MC, Fikar J, Schaeublin R. Dislocation–void interaction in Fe: a comparison between molecular dynamics and dislocation dynamics. J Nucl Mater. 2009;386–388:102–5.

    Article  Google Scholar 

  34. Mohles V, Rönnpagel D, Nembach E. Simulation of dislocation glide in precipitation hardened materials. Comput Mater Sci. 1999;16(1–4):144–50.

    Article  Google Scholar 

  35. Monnet G. Multiscale modeling of precipitation hardening: application to the Fe–Cr alloys. Acta Mater. 2015;95:302–11.

    Article  Google Scholar 

  36. Terentyev DA, Bonny G, Malerba L. Strengthening due to coherent Cr precipitates in Fe–Cr alloys: atomistic simulations and theoretical models. Acta Mater. 2008;56(13):3229–35.

    Article  Google Scholar 

  37. Ngan AHW, Zuo L, Wo PC. Probabilistic nature of the nucleation of dislocations in an applied stress field. Scr Mater. 2006;54:589–93.

    Article  Google Scholar 

  38. Vineyard GH. Frequency factors and isotope effects in solid state rate processes. J Phys Chem Solids. 1957;3(1):121–7.

    Article  Google Scholar 

  39. Spitzig WA, Keh AS. The effect of orientation and temperature on the plastic flow properties of iron single crystals. Acta Metall. 1970;18:611–22.

    Article  Google Scholar 

  40. Monnet G. Transition methods in the multiscale simulation framework: from the atomic to the continuum scale. In: Ionescu I, Bouvier S, editors. Plasticity of crystalline materials: from dislocations to continuum. Hoboken: ISTE Ltd.; 2011. p. 3–36.

    Google Scholar 

  41. Monnet G. Determination of the activation energy by stochastic analyses of molecular dynamics simulations of dislocation processes. Philos Mag. 2011;91(29):3810–29.

    Article  Google Scholar 

  42. Rodney D. Activation enthalpy for kink-pair nucleation on dislocations: comparison between static and dynamic atomic-scale simulations. Phys Rev B. 2007;76(14):144108.

    Article  Google Scholar 

  43. Kuksenko V, Pareige C, Genevois C, Cuvilly F, Roussel M, Pareige P. Effect of neutron-irradiation on the microstructure of a Fe–12at.%Cr alloy. J Nucl Mater. 2011;415(1):61–6.

    Article  Google Scholar 

  44. Shi XJ, Dupuy L, Devincre B, Terentyev D, Vincent L. Interaction of 〈100〉 dislocation loops with dislocations studied by dislocation dynamics in α-iron. J Nucl Mater. 2015;460:37–43.

    Article  Google Scholar 

  45. Terentyev D, Grammatikopoulos P, Bacon DJ, Osetsky YN. Simulation of the interaction between an edge dislocation and a 〈1 0 0〉 interstitial dislocation loop in α-iron. Acta Mater. 2008;56:5034–46.

    Article  Google Scholar 

  46. Diaz de la Rubia T, Zbib HM, Khraishi TA, Wirth BD, Victoria M, Caturla MJ. Multiscale modelling of plastic flow localization in irradiated materials. Nature. 2000;406:871–4.

    Article  Google Scholar 

  47. Crosby T, Po G, Ghoniem NM. Modeling plastic deformation of post-irradiated copper micro-pillars. J Nucl Mater. 2014;455(1–3):126–9.

    Article  Google Scholar 

  48. Terentyev D, Monnet G, Grigorev P. Transfer of molecular dynamics data to dislocation dynamics to assess dislocation–dislocation loop interaction in iron. Scr Mater. 2013;69(8):578–81.

    Article  Google Scholar 

  49. Hiratani M, Zbib HM, Khaleel MA. Modeling of thermally activated dislocation glide and plastic flow through local obstacles. Int J Plast. 2003;19(9):1271–96.

    Article  MATH  Google Scholar 

  50. Arsenlis A, Rhee M, Hommes G, Cook R, Marian JA. Dislocation dynamics study of the transition from homogeneous to heterogeneous deformation in irradiated body-centered cubic iron. Acta Mater. 2012;60(9):3748–57.

    Article  Google Scholar 

  51. Mohles V. Computer simulations of the glide of dissociated dislocations in lattice mismatch strengthened materials. Mater Sci Eng A. 2002;324(1–2):190–5.

    Article  Google Scholar 

  52. Monnet G, Naamane S, Devincre B. Orowan strengthening at low temperatures in bcc materials studied by dislocation dynamics simulations. Acta Mater. 2011;59(2):451–61.

    Article  Google Scholar 

  53. Monnet G. New insights into radiation hardening in face-centered cubic alloys. Scr Mater. 2015;100:24–7.

    Article  Google Scholar 

  54. Friedel J. Dislocations. Oxford: Pergamon Press; 1964.

    MATH  Google Scholar 

  55. Bergner F, Pareige C, Hernández-Mayoral M, Malerba L, Heintze C. Application of a three-feature dispersed-barrier hardening model to neutron-irradiated Fe–Cr model alloys. J Nucl Mater. 2014;448(1–3):96–102.

    Article  Google Scholar 

  56. Queyreau S, Monnet G, Devincre B. Orowan strengthening and forest hardening superposition examined by dislocation dynamics simulations. Acta Mater. 2010;58(17):5586–95.

    Article  Google Scholar 

  57. Libert M, Rey C, Vincent L, Marini B. Temperature dependant polycrystal model application to bainitic steel behavior under tri-axial loading in the ductile-brittle transition. Int J Solids Struct. 2011;48(14–15):2196–208.

    Article  Google Scholar 

  58. Monnet G, Vincent L. Crystalline plasticity constitutive equations for BCC steel at low temperature. Mec. Ind. 2011;12(3):193–8.

    Google Scholar 

  59. Franciosi P, Berveiller M, Zaoui A. Latent hardening in copper and aluminium single crystals. Acta Metall. 1980;28(3):273–83.

    Article  Google Scholar 

  60. Wulfinghoff S, Forest S, Böhlke T. Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures. J Mech Phys Solids. 2015;79:1–20.

    Article  MathSciNet  MATH  Google Scholar 

  61. Auger P, Pareige P, Welzel S, Van Duysen J-C. Synthesis of atom probe experiments on irradiation-induced solute segregation in French ferritic pressure vessel steels. J Nucl Mater. 2000;280(3):331–44.

    Article  Google Scholar 

  62. Mecking H, Kocks UF. Kinetics of flow and strain-hardening. Acta Metall. 1981;29(11):1865–75.

    Article  Google Scholar 

  63. Code_Aster [Internet]. [cited 2016 Sep 4]. Available from: http://www.code-aster.org/spip.php?rubrique1

  64. AMITEX_FFTP 2.3 documentation [Internet]. [cited 2016 Sep 4]. Available from: http://www.maisondelasimulation.fr/projects/amitex/html/

  65. Taylor GI. Plastic Strain in metals [Internet]. 1938. Available from: http://books.google.fr/books?id=I50lAQAAIAAJ

  66. Berveiller M, Zaoui A. An extension of the self-consistent scheme to plastically-flowing polycrystals. J Mech Phys Solids. 1978;26(5–6):325–44.

    Article  MATH  Google Scholar 

  67. Buswell JT, Phythian WJ, McElroy RJ, Dumbill S, Ray PHN, Mace J, et al. Irradiation-induced microstructural changes, and hardening mechanisms, in model PWR reactor pressure vessel steels. J Nucl Mater. 1995;225:196–214.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ghiath Monnet .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Monnet, G., Vincent, L. (2019). Multiscale Modeling of Radiation Hardening. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6884-3_8

Download citation

Publish with us

Policies and ethics