Journal of Materials Science

, Volume 51, Issue 5, pp 2540–2549 | Cite as

Modeling of structural hardening in oxide dispersion-strengthened (ODS) ferritic alloys

  • S. Y. Zhong
  • V. Klosek
  • Y. de Carlan
  • M. H. Mathon
Original Paper


Based on a rather simple macroscopic and statistical model, experimentally observed variations of yield stress at room temperature in various ODS alloys were theoretically reproduced. For the first time, yield stress values of ODS steels were calculated by taking into account: (1) two interaction mechanisms between dislocations and nanoprecipitates (shearing or bypassing, simultaneously, depending on the particle size); and (2) the whole, possibly multimodal, nanoparticle distributions experimentally determined by SANS. The relative importances of the various strengthening mechanisms can be easily deduced from these calculations.


Critical Resolve Shear Stress Small Angle Neutron Scattering Fiber Texture Nanoparticle Distribution Orowan Strengthen 


  1. 1.
    Bacon DJ, Kocks UF, Scattergood RO (1973) Effect of dislocation self-interaction on Orowan stress. Philos Mag 28:1241–1263CrossRefGoogle Scholar
  2. 2.
    Brown LM, Ham RK (1971) Dislocation-particle interactions. In: Kelly A, Nicholson RB (eds) Strengthening methods in crystals. Applied Science Publishers, London, p 9Google Scholar
  3. 3.
    de Carlan Y, Béchade JL, Dubuisson P, Seran JL, Billot P, Bougault A, Cozzika T, Doriot S, Hamon D, Henry J, Ratti M, Lochet N, Nunes D, Olier P, Leblond T, Mathon MH (2009) CEA developments of new ferritic ODS alloys for nuclear applications. J Nucl Mater 386–388:430–443CrossRefGoogle Scholar
  4. 4.
    Deschamps A, Brechet Y (1998) Influence of predeformation and ageing of an Al-Zn-Mg alloy—II. Modeling of precipitation kinetics and yield stress. Acta Mater 47(1):293–305CrossRefGoogle Scholar
  5. 5.
    Friedel J (1964) Dislocations. Pergamon Press, OxfordGoogle Scholar
  6. 6.
    Hall EO (1951) The deformation and ageing of mild steel.3. Discussion of results. Proc Phys Soc Lond Sect B 64(381):747–753CrossRefGoogle Scholar
  7. 7.
    Hanson K, Morris JW (1975) Limiting configuration in dislocation glide through a random array of point obstacles. J Appl Phys 46(3):983–990CrossRefGoogle Scholar
  8. 8.
    Hin C, Wirth BD (2010) Formation of Y2O3 nanoclusters in nano-structured ferritic alloys: modeling of precipitation kinetics and yield strength. J Nucl Mater 402:30–37CrossRefGoogle Scholar
  9. 9.
    Hirata A, Fujita T, Wen YR, Schneibel JH, Liu CT, Chen MW (2011) Atomic structure of nanoclusters in oxide-dispersion-strengthened steels. Nat Mater 10:922–926CrossRefGoogle Scholar
  10. 10.
    Hirsch PB, Humphreys FJ (1969) In: Argon AS (ed) Physics of strength and plasticity. MIT Press, Cambridge, p 189Google Scholar
  11. 11.
    Hoelzer DT, Bentley J, Sokolov MA, Miller MK, Odette GR, Alinger MJ (2007) Influence of particle dispersions on the high-temperature strength of ferritic alloys. J Nucl Mater 367–370:166–172CrossRefGoogle Scholar
  12. 12.
    Klueh RL, Maziasz PJ, Kim IS, Heatherly L, Hoelzer DT, Hashimoto N, Kenik EA, Miyahara K (2002) Tensile and creep properties of an oxide dispersion- strengthened ferritic steel. J Nucl Mater 307–311:773–777CrossRefGoogle Scholar
  13. 13.
    Klueh RL, Shingledecker JP, Swindeman RW, Hoelzer DT (2005) Oxide dispersion-strengthened steels: a comparison of some commercial and experimental alloys. J Nucl Mater 341:103–114CrossRefGoogle Scholar
  14. 14.
    Kocks UF, Argon AS, Ashby MF (1975) Thermodynamics and kinetics of slip. Prog Mater Sci 19:1–281CrossRefGoogle Scholar
  15. 15.
    Koppenaal TJ, Kuhlmann-Wilsdorf D (1964) The effect of prestressing on the strength of neutron-irradiated copper single crystals. Appl Phys Lett 4:59–61CrossRefGoogle Scholar
  16. 16.
    Larson DJ, Maziasz PJ, Kim IS, Miyahara K (2001) Three-dimensional atom probe observation of nanoscale titanium-oxygen clustering in an oxide-dispersion-strengthened Fe-12Cr-3W-0.4Ti+Y2O3 ferritic alloy. Scr Mater 44(2):359–364CrossRefGoogle Scholar
  17. 17.
    Lim H, Lee MG, Kim JH, Adams BL, Wagoner RH (2011) Simulation of polycrystal deformation with grain and grain boundary effects. Int J Plast 27:1328–1354CrossRefGoogle Scholar
  18. 18.
    Lindau R, Molang A, Schirra M, Schlossmacher P, Klimenkov M (2002) Mechanical and microstructural properties of a hipped RAFM ODS-steel. J Nucl Mater 307–311:769–772CrossRefGoogle Scholar
  19. 19.
    Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming (111)-pensil glide. Int J Mech Sci 22:419CrossRefGoogle Scholar
  20. 20.
    Miller MK, Russell KF, Hoelzer DT (2006) Characterization of precipitates in MA/ODS ferritic alloys. J Nucl Mater 351:261–268CrossRefGoogle Scholar
  21. 21.
    Nan C, Clarke D (1996) The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites. Acta Mater 44(9):3801–3811CrossRefGoogle Scholar
  22. 22.
    Nedelcu S, Kizler P, Schmauder S, Moldovan N (2000) Atomic scale modelling of edge dislocation movement in the alpha-Fe-Cu system. Model Simul Mater Sci Eng 8(2):181–191CrossRefGoogle Scholar
  23. 23.
    Nembach E (1996) Particle strengthening of metals and alloys. Wiley, New-YorkGoogle Scholar
  24. 24.
    Orowan E (1948) Discussion. In: Symposium on internal stresses in metals and alloys, Institute of Metals, London, p 451Google Scholar
  25. 25.
    Pavlina EJ, Van Tyne CJ (2008) Correlation of yield strength and tensile strength with hardness for steels. J Mater Eng Perform 17:888–893CrossRefGoogle Scholar
  26. 26.
    Petch NJ (1953) The cleavage strength of polycrystals. J Iron Steel Inst 174(1):25–28Google Scholar
  27. 27.
    Praud M, Mompiou F, Malaplate J, Caillard D, Garnier J, Steckmeyer A, Fournier B (2012) Study of the deformation mechanisms in a Fe-14 % Cr ODS alloy. J Nucl Mater 428:90–97CrossRefGoogle Scholar
  28. 28.
    Preininger D (2004) Effect of particle morphology and microstructure on strength, work-hardening and ductility behaviour of ODS-(7-13)Cr steels. J Nucl Mater 329(Part a):362–368CrossRefGoogle Scholar
  29. 29.
    Queyreau S, Monnet G, Devincre B (2009) Slip systems interactions in alpha-iron determined by dislocation dynamics simulations. Int J Plast 25:361–377CrossRefGoogle Scholar
  30. 30.
    Queyreau S, Monnet G, Devincre B (2010) Orowan strengthening and forest hardening superposition examined by dislocation dynamics simulations. Acta Mater 58:5586–5595CrossRefGoogle Scholar
  31. 31.
    Ratti M (2010) Développement de nouvelles nuances d’aciers ferritiques / martensitiques pour le gainage d’éléments combustibles des réacteurs à neutrons rapides au sodium. PhD thesis, CEA, Institut National Polytechnique de GrenobleGoogle Scholar
  32. 32.
    Ratti M, Leuvrey D, Mathon MH, de Carlan Y (2009) Influence of titanium on nano-cluster (Y, Ti, O) stability in ODS ferritic materials. J Nucl Mater 386–388:540–543CrossRefGoogle Scholar
  33. 33.
    Raynor D, Silcock JM (1970) Strengthening mechanisms in gamma precipitating alloys. Met Sci J 4:121–130CrossRefGoogle Scholar
  34. 34.
    Ribis J, de Carlan Y (2012) Interfacial strained structure and orientation relationships of the nanosized oxide particles deduced from elasticity-driven morphology in oxide dispersion strengthened materials. Acta Mater 60:238–252CrossRefGoogle Scholar
  35. 35.
    Schneibel JH, Heilmaier M, Blum W, Hasemann G, Shanmugasundaram T (2011) Temperature dependence of the strength of fine- and ultrafine-grained materials. Acta Mater 59(3):1300–1308CrossRefGoogle Scholar
  36. 36.
    Schwarz RB, Labusch R (1978) Dynamic simulation of solution hardening. J Appl Phys 49(10):5174–5187CrossRefGoogle Scholar
  37. 37.
    Steckmeyer A, Praud M, Fournier B, Malaplate J, Garnier J, Béchade JL, Tournié I, Tancray A, Bougault A, Bonnaillie P (2010) Tensile properties and deformation mechanisms of a 14Cr ODS ferritic steel. J Nucl Mater 405:95–100CrossRefGoogle Scholar
  38. 38.
    Takaki S, Kawasaki K, Kimura Y (2001) Mechanical properties of ultra fine grained steels. J Mater Process Technol 117(3, SI):359–363CrossRefGoogle Scholar
  39. 39.
    Taylor GI (1934) The mechanism of plastic deformation of crystals. Proc R Soc 145:362–387CrossRefGoogle Scholar
  40. 40.
    Taylor GI (1956) Strains in polycrystalline aggreggates. In: Grammel R (ed) Deformation and flow of solids. Springer, Berlin, p 3Google Scholar
  41. 41.
    Toloczko MB, Gelles DS, Garner FA, Kurtz RJ, Abe K (2004) Irradiation creep and swelling from 400 to 600 degrees C of the oxide dispersion strengthened ferritic alloy MA957. J Nucl Mater 329–333:352–355CrossRefGoogle Scholar
  42. 42.
    Tsuji N, Ito Y, Ueji R, Minamino Y, Koizumi Y, Saito Y (2001) Mechanical properties of ultrafine grained ferritic steels produced by accumulative roll-bonding (ARB) process. In: International symposium on ultrafine grained steels (ISUGS), FukuokaGoogle Scholar
  43. 43.
    Ukai S, Mizuta S, Fujiwara M, Okuda T, Kobayashi T (2002a) Development of 9Cr-ODS martensitic steel claddings for fuel pins by means of ferrite to austenite phase transformation. J Nucl Sci Technol 39:778–788CrossRefGoogle Scholar
  44. 44.
    Ukai S, Okuda T, Fujiwara M, Kobayashi T, Mizuta S, Nakashima H (2002b) Characterization of high temperature creep properties in recrystallized 12Cr-ODS ferritic steel claddings. J Nucl Sci Technol 39:872–879CrossRefGoogle Scholar
  45. 45.
    Zhang Z, Chen D (2006) Consideration of Orowan strengthening effect in particulate-reinforced metal matrix nanocomposites: a model for predicting their yield strength. Scr Mater 54(7):1321–1326CrossRefGoogle Scholar
  46. 46.
    Zhao MC, Hanamura T, Qiu H, Nagai K, Yang K (2006) Grain growth and Hall-Petch relation in dual-sized ferrite/cementite steel with nano-sized cementite particles in a heterogeneous and dense distribution. Scr Mater 54:1193–1197CrossRefGoogle Scholar
  47. 47.
    Zhong SY (2012) Etude des évolutions microstructurales á haute température en fonction des teneurs initiales en Y, Ti, et O et de leur incidence sur les hétérogénéités de déformation dans les aciers ODS Fe-14Cr1W. PhD thesis, U. Paris-SudGoogle Scholar
  48. 48.
    Zhong SY, Ribis J, Klosek V, de Carlan Y, Lochet N, Ji V, Mathon MH (2012) Study of the thermal stability of nanoparticle distributions in an oxide dispersion strengthened (ODS) alloy. J Nucl Mater 428:154–159CrossRefGoogle Scholar
  49. 49.
    Zhong SY, Ribis J, Baudin T, Lochet N, de Carlan Y, Klosek V, Mathon MH (2014a) The effect of Ti/Y ratio on the recrystallisation behaviour of Fe-14 %Cr oxide dispersion-strengthened alloys. J Nucl Mater 452:359–363CrossRefGoogle Scholar
  50. 50.
    Zhong SY, Ribis J, Lochet N, de Carlan Y, Klosek V, Mathon MH (2014b) Influence of nano-particle coherency degree on the coarsening resistivity of the nano-oxide particles of Fe-14Cr-1W ODS alloys. J Nucl Mater 455:618–623CrossRefGoogle Scholar
  51. 51.
    Zhong SY, Ribis J, Lochet N, de Carlan Y, Klosek V, Ji V, Mathon MH (2015) The effect of Y/Ti ratio on oxide precipitate evolution in ODS Fe-14 Wt Pct Cr alloys. Metall Mater Trans A 46A:1413–1418CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • S. Y. Zhong
    • 1
    • 2
  • V. Klosek
    • 1
  • Y. de Carlan
    • 3
  • M. H. Mathon
    • 1
  1. 1. Laboratoire Léon BrillouinCEA, IRAMISGif-sur-Yvette CedexFrance
  2. 2.Shanghai Jiaotong UniversityShanghaiChina
  3. 3.CEA, DEN, SRMAGif-sur-Yvette CedexFrance

Personalised recommendations