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Three-dimensional analysis of scale dependence of sub-micron polycrystals due to configuration entropy

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Abstract

The authors proposed a plausible explanation for the deviation of experimental data for sub-micron polycrystals from the Hall-Petch relation by introducing the configuration entropy. The present paper extends the previous two-dimensional analysis to the three-dimensional case. The statistical distribution of dislocation lengths within a spherical grain and the bow-out of dislocations are considered. According to Ashby's model, analyses are pursued for the statistically stored dislocations and geometrically necessary dislocations, respectively. It is confirmed that the configuration entropy model can predict the abnormal Hall-Petch dependence for grain sizes in the sub-micron range.

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References

  1. Hall EO. The deformation and aging of mild steel: III discussion of results.Proc Phys Soc, 1951, B64: 747–753

    Article  Google Scholar 

  2. Petch NJ. The cleavage strength of polycrystals.J Iron Steel Inst, 1953; 174: 25–28

    Google Scholar 

  3. Li JCM, Chou YT. The role of dislocations in the flow stress-grain size relationships.Metall Trans, 1970, 1: 1145–1159

    Google Scholar 

  4. Cottrell AH. Theory of brittle fracture in steel and similar metalsTrans Metall Soc AIME, 1958, 212: 192–202

    Google Scholar 

  5. Li JCM. Petch relation and grain boundary sources.Trans Metall Soc, AIME, 1963, 227: 239–247

    Google Scholar 

  6. Phillips WL, Armstrong RW. The strain dependence of the flow stress-grain size relation for 70∶30 brass.Metall Tans, 1972, 3: 2571–2577

    Google Scholar 

  7. Hansen N. The effect of grain size and strain in the tensile flow stress of aluminum at room temperature.Acta Metall, 1977, 25: 863–869

    Article  Google Scholar 

  8. Jiang Zh, Lian J, Baudelet B. A dislocation density approximation for the flow stress-grain size relation of polycrystals.Acta Metall Mater, 1995, 43: 3349–3360

    Article  Google Scholar 

  9. Ashby MF. The deformation of plastically non-homogeneous materials.Phil Mag, 1970, 21: 399–424

    Google Scholar 

  10. Hirth JP. The influence of grain boundaries on mechanical properties.Metall Trans, 1972, 3: 3047–3067

    Google Scholar 

  11. Baldwin Jr WM. Yield strength of metals as a function of grain size.,Acta Metall, 1958, 6: 139–141.

    Article  Google Scholar 

  12. Anderson E, King DWW, Spreadborough J. The relationship between lower yield stress and grain size in Armco iron.Trans TMS-AIME 1968, 242: 115–119

    Google Scholar 

  13. Thompson AW. Effect of grain size on work hardening in nickel.Acta Metall, 1977, 25: 83–86

    Article  Google Scholar 

  14. Fujita H, Tabata T. The effect of grain size and deformation sub-structure on the mechanical properties of polycrystalline aluminum.Acta Metall, 1973, 21: 355–365

    Article  Google Scholar 

  15. Abrahamson II EP. Surfaces and Interfaces II, New York: Syracuse University Press, 1968

    Google Scholar 

  16. Chokshi AH, Rosen A, Karch J, Gleiter H. On the validity of the Hall-Petch relationship in nanocrystalline materials.Scr Metall, 1989, 23: 1679–1684

    Article  Google Scholar 

  17. Meyers MA, Ashworth E. A model for the effect of grain size on the yield stress of metals.Phil Mag, 1982, 46: 737–759

    Google Scholar 

  18. Wang N, Wang Z, Aust KT, Erb U. Effect of grain size on mechanical properties of nanocrystalline materials.Acta Metall, 1995, 43: 519–528

    Article  Google Scholar 

  19. Fougere GE, Weertman JR, Siegel RW, Kim S. Grain size dependent hardening and softening of nonocrystalline Cu and Pd.Scr Metll Meter, 1992, 26: 1879–1883

    Article  Google Scholar 

  20. Kutumba Rao V, Taplin DMR, Rama Rao P. The grain size dependence of flow and fracture in a Cr−Mn−N austenitic steel from 300 to 1300 K.Met Trans, 1975, 6A: 77–94

    Google Scholar 

  21. El-Sherik AM, Erb U, Palumbo G, Aust KT. Deviation from Hall-Petch behavior in as-prepared nanocrystalline nickel.Scr Metall Mater, 1992, 27: 1185–1188

    Article  Google Scholar 

  22. Lian J, Baudelet B, Nazarov AA. Model for prediction of the mechanical behavior of nanocrystalline materials.Mater Sci and Engng, 1993, A172: 23–29

    Article  Google Scholar 

  23. Yang Q, Yang W. Scale dependence of submicron polycrystal based on configurational entropy.Appl Phys Lett, 1998, 73: 3384–3386

    Article  Google Scholar 

  24. Weiner JH. Statistical Mechanics of Elasticity, New York: Wiley-Interscience, 1983

    MATH  Google Scholar 

  25. Thompson AW, Baskes ML, Flanagan WF. The dependence of work hardening on grain size.Acta Metall, 1973, 21: 1017–1028

    Article  Google Scholar 

  26. Meyers MA, Chawla KK. Mechanical Metallurgy, New Jersey: Prentice-Hall, Englewood Cliffs, 1992

    Google Scholar 

  27. Hirth JP, Lothe J. Theory of Dislocations, 2nd ed., New York: Wiley, 1982

    Google Scholar 

  28. Blin J. Energie mutuelle de deux dislocations.Acta Metall, 1955, 3: 199–200

    Article  Google Scholar 

  29. Stroh AN. The deformation of a tilt boundary under applied forces.Acta Metall, 1961, 9: 315–319

    Article  Google Scholar 

  30. Hanson N, Kuhlmann-Wilsdorf D. Low energy dislocation structures due to unidirectional deformation at low temperature.Mater Sci and Engng, 1986, 81: 141–161

    Article  Google Scholar 

  31. Conrad H. Work-hardening model for the effect of grain size on the flow stress of metals, in Ultrafine-Grain Metals, ed. Burke, J. J. and Weiss, V., 1970. 213–229

  32. Gleiter H. Nanocrystalline materials.Prog Mater Sci, 1989, 33: 223–315

    Article  Google Scholar 

  33. Lasalmonie A, Strudel JL. Influence of grain size on the mechanical behaviour of some high strength materials.J Mater Sci, 1986, 21: 1837–1852

    Article  Google Scholar 

  34. Shen TD, Koch CC, Tsui TY, Pharr GM. On the elastic moduli of nanocrystalline Fe, Cu, Ni and Cu−Ni alloys prepared by mechanical milling/alloying.J Mater Res, 1995, 10: 2892–2896

    Google Scholar 

  35. Schiotz J, Tolla FDD, Jacobsen KW. Softening of nanocrystalline metals at very small grain size.Nature, 1998, 391: 561–563

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Yang Qiang & Yang Wei

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  1. Yang Qiang
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  2. Yang Wei
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Correspondence to Yang Wei.

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The project supported by the National Natural Science Foundation of China (19891180-01)

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Qiang, Y., Wei, Y. Three-dimensional analysis of scale dependence of sub-micron polycrystals due to configuration entropy. Acta Mech Sinica 17, 172–182 (2001). https://doi.org/10.1007/BF02487605

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  • DOI: https://doi.org/10.1007/BF02487605

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