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Dislocation Mediated Continuum Plasticity: Case Studies on Modeling Scale Dependence, Scale-Invariance, and Directionality of Sharp Yield-Point

  • Claude Fressengeas
  • A. Acharya
  • A. J. Beaudoin
Chapter

Abstract

Plasticity of crystalline solids is a dynamic phenomenon resulting from the motion under stress of linear crystal defects known as dislocations. Such a statement is grounded on numerous convincing observations, and it is widely accepted by the scientific community. Nevertheless, the conventional plasticity theories use macroscopic variables whose definition does not involve the notion of dislocation. This paradoxical situation arises from the enormous range covered by the length scales involved in the description of plasticity, from materials science to engineering. Itmay have seemed impossible to account for the astounding complexity of the (microscopic) dynamics of dislocation ensembles at the (macroscopic) scale of the mechanical properties of materials. Justifications offered for such a simplification usually reside in perfect disorder assumptions. Namely, plastic strain is regarded as resulting from a large number of randomly distributed elementary dislocation glide events, showing no order whatsoever at intermediate length scales. Hence, deriving the mechanical properties from the interactions of dislocations with defects simply requires averaging on any space and time domain. The existence of grain boundaries in polycrystals is of course affecting this averaging procedure, but it does not change it fundamentally.

Keywords

Screw Dislocation Dislocation Dynamic Dislocation Velocity Plastic Activity Internal Stress Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

AA gratefully acknowledges the support from the National Science Foundation through the CMU MRSEC, grant no. DMR-0520425, the LMA-CNRS, Marseille and the Dept. of Civil and Env. Engineering at CMU. AB received support under US Dept. of Energy grant DEFG03-02-NA00072 and the Center for Simulation of Advanced Rockets at the University of Illinois at Urbana-Champaign (UIUC), US DOE subcontract B341494. AB and CF benefited from exchanges under a joint agreement between Centre National de la Recherche Scientifique and UIUC. We thank Juliette Chevy for providing Figs.4, 8 and Russell J. McDonald for his help in carrying out the experiments in Fig.18.

References

  1. L.P. Kubin, C. Fressengeas and G. Ananthakrishna, Collective Behaviour of Dislocations in Plasticity, in Dislocations in Solids, vol 11, Eds. F.R.N. Nabarro and M.S. Duesbery, Elsevier Science B.V., 100–192 (2002).Google Scholar
  2. M. Legros, A. Jacques and A. George, Mat. Sci. Eng. A 387–389, 495 (2004).CrossRefGoogle Scholar
  3. M. Neubert and P. Rudolph, Prog. Cryst. Growth Charact. Matr. 43, 119 (2001).CrossRefGoogle Scholar
  4. M. Zaiser, Adv. Phys. 55, 185 (2006).CrossRefGoogle Scholar
  5. E.C. Aifantis, Mat. Sci. Eng. 81, 563 (1986).CrossRefGoogle Scholar
  6. N.A. Fleck, G.M. Muller, M.F. Ashby and J.W. Hutchinson, Acta Metall. Mater. 42, 475 (1994).CrossRefGoogle Scholar
  7. W.D. Nix and H. Gao, J. Mech. Phys. Solids, 46, 411 (1998).MATHCrossRefGoogle Scholar
  8. F. Forest, G. Cailletaud and R. Sievert, Arch. Mech. 49, 705 (1997).MATHMathSciNetGoogle Scholar
  9. A. Acharya, J. Mech. Phys. Solids 49, 761 (2001).MATHCrossRefGoogle Scholar
  10. J.F. Nye, Acta Metall. 1, 153 (1953).CrossRefGoogle Scholar
  11. E. Kröner, Erg. Angew. Math. 5, 1–179 (1958).Google Scholar
  12. T. Mura, Phil. Mag. 89, 843 (1963).CrossRefGoogle Scholar
  13. A.M. Kosevich, Crystal dislocations and the theory of elasticity, in Dislocations in Solids, Ed. F.R.N. Nabarro, North-Holland, Amsterdam, 33–141 (1979).Google Scholar
  14. E. Kröner, Continuum theory of defects, in Physics of Defects, Ed. R. Balian et al., North-Holland, Amsterdam, 218–314 (1980).Google Scholar
  15. A. Acharya and A. Roy, J. Mech. Phys. Sol. 54, 1687 (2006).MATHCrossRefMathSciNetGoogle Scholar
  16. A. Roy and A. Acharya, J. Mech. Phys. Sol. 53, 43–170 (2005).Google Scholar
  17. A. Roy and A. Acharya, J. Mech. Phys. Sol. 54, 1711–1743 (2006).MATHCrossRefGoogle Scholar
  18. S. Varadhan, A.J. Beaudoin, A. Acharya and C. Fressengeas, Modelling Simul. Mater. Sci. Eng. 14, 1 (2006).CrossRefGoogle Scholar
  19. V. Taupin, S. Varadhan, J. Chevy, C. Fressengeas, A.J. Beaudoin, M. Montagnat and P. Duval, Phys. Rev. Lett. 99, 155507 (2007).CrossRefGoogle Scholar
  20. R. Becker and E. Orowan, Z. Phys. 79, 566 (1932).CrossRefGoogle Scholar
  21. J. Weiss and J.R. Grasso, J. Phys. Chem. 101, 6113 (1997).Google Scholar
  22. M.C. Miguel, A. Vespignani, S. Zapperi, J. Weiss and J.R. Grasso, Nature (London) 410, 667 (2001).Google Scholar
  23. D.M. Dimiduk, C. Woodward, R. LeSar and M.D. Uchic, Science 312, 1188 (2006).CrossRefGoogle Scholar
  24. S. Brinckmann, J.Y. Kim and J.R. Greer, Phys. Rev. Lett. 100, 155502 (2008).CrossRefGoogle Scholar
  25. J. Weiss, T. Richeton, F. Louchet, F. Chmelik, P. Dobron, D. Entemeyer, M. Lebyodkin, T. Lebedkina, C. Fressengeas and R.J. McDonald, Phys. Rev. B. 76, 224110 (2007).CrossRefGoogle Scholar
  26. C. Fressengeas, A.J. Beaudoin, D. Entemeyer, T.Lebedkina, M. Lebyodkin, and V. Taupin, Phys. Rev. B, 79, 014108 (2009).CrossRefGoogle Scholar
  27. V. Taupin, S. Varadhan, C. Fressengeas and A.J. Beaudoin, Acta Mater. 56, 3002 (2008).CrossRefGoogle Scholar
  28. M. Koslowski, R. LeSar and R. Thomson, Phys. Rev. Lett. 93, 125502 (2004).CrossRefGoogle Scholar
  29. F.F. Csikor, C. Motz, D. Weygand, M. Zaiser and S. Zapperi, Science 318, 251 (2007).CrossRefGoogle Scholar
  30. B. Devincre, T. Hoc and L.P. Kubin, Science 320, 1745 (2008).CrossRefGoogle Scholar
  31. M. Babic, Int. J. Eng. Sci. 35, 523–548 (1997).MATHCrossRefMathSciNetGoogle Scholar
  32. A. Acharya, Proc. Roy. Soc. A 459, 1343 (2003).Google Scholar
  33. M.J. Marcinkowsky, Phys. Stat. Sol. B 152, 9 (1989).CrossRefGoogle Scholar
  34. C. Meneveau and J. O’Neil, Phys. Rev. E 49, 2866 (1994).CrossRefMathSciNetGoogle Scholar
  35. P. Duval, M.F. Ashby and I. Anderman, J. Phys. Chem. 87, 4066 (1983).CrossRefGoogle Scholar
  36. C. Shearwood and R.W. Whitworth, Phil. Mag. 64, 289 (1991).CrossRefGoogle Scholar
  37. J. Chevy, Ph. D. Thesis, Institut Polytechnique de Grenoble (2008).Google Scholar
  38. M. Montagnat, P. Duval, P. Bastie and B. Hamelin, Scripta Mater. 49, 411 (2003).CrossRefGoogle Scholar
  39. J. Chevy, C. Fressengeas, M. Lebyodkin, V. Taupin, P. Bastie, P. Duval, Acta Mater. 58, 1837 (2010).CrossRefGoogle Scholar
  40. M. Montagnat, J. Weiss, J. Chevy, P. Duval, H. Brunjail, P. Bastie and J. Gil Sevillano, Phil. Mag. 86, 4259 (2006).CrossRefGoogle Scholar
  41. P.J. Armstrong and C.O. Frederick, A mathematical representation of the multiaxial Bauschinger effect, Technical Report RD/B/N/731, Central Electricity Generating Board (1966).Google Scholar
  42. F. Louchet, C.R. Physique, 5, 687 (2004).Google Scholar
  43. S.J. Basinski, Z.S. Basinski, Plastic deformation and work hardening, in Dislocations in Solids, Ed. F.R.N. Nabarro, Vol 4, 261–362, North-Holland, Amsterdam (1979).Google Scholar
  44. J. Diehl, 47, 331–343 (1956).Google Scholar
  45. H. Suzuki, S. Ikeda and S. Takeuchi, J. Phys. Soc. Jpn. 11, 382 (1956).CrossRefGoogle Scholar
  46. J. Garstone, R.W.K. Honeycombe and G. Greetham, Acta Met. 4, 485 (1956).CrossRefGoogle Scholar
  47. J.T. Fourie, Phil. Mag. 15, 187 (1967).CrossRefGoogle Scholar
  48. J. Weertman, Acta Mater. 50, 673 (2002).CrossRefGoogle Scholar
  49. L.B. Zuev, Ann. Phys. 16, 286–310 (2007).CrossRefGoogle Scholar
  50. A. Acharya, A.J. Beaudoin and R. Miller, Math. Mech. Solids 13, 292 (2008).MATHCrossRefMathSciNetGoogle Scholar
  51. S. Varadhan, A.J. Beaudoin and C. Fressengeas, Proc. of Science, SMPRI2005, 004 (2006).Google Scholar
  52. O. Nittono, Jap. J. Appl. Phys. 10, 188 (1971).CrossRefGoogle Scholar
  53. S.S. Brenner, J. Appl. Phys. 28, 1023 (1957).CrossRefGoogle Scholar
  54. Y. Gotoh, Phys. Stat. Sol. A 24, 305 (1974).CrossRefGoogle Scholar
  55. A. Piobert, Mémoires de l’artillerie 5, 502 (1842).Google Scholar
  56. W. Lüders, Dinglers Polytech. J. 155, 18 (1860).Google Scholar
  57. A.H. Cottrell, Dislocations and Plastic Flow in Crystals, University Press, Oxford, (1953).MATHGoogle Scholar
  58. L.P. Kubin, Y. Estrin and C. Perrier, Acta Metall. Mater. 40, 1037 (1992).CrossRefGoogle Scholar
  59. C.F. Tipper, J. Iron Steel Inst. 2, 143 (1952).Google Scholar
  60. D.V. Wilson and G.R. Ogram, J. Iron Steel Inst. 911–920 (1968).Google Scholar
  61. R.A. Elliott, E. Orowan, T. Udoguchi, A.S. Argon, Mech. Mat. 36, 1143 (2004).CrossRefGoogle Scholar
  62. L.P. Kubin and Y. Estrin, Acta Metall. Mater. 38, 697 (1990).CrossRefGoogle Scholar
  63. A. Acharya and A.J. Beaudoin, J. Mech. Phys. Sol. 48, 2213 (2000).MATHCrossRefGoogle Scholar
  64. N. Louat, Scripta Metall. 15, 1167 (1981).CrossRefGoogle Scholar
  65. P.G. McCormick, Acta Metall. 36, 3061 (1988).CrossRefGoogle Scholar
  66. A. Ziegenbein, Ch. Achmus, J. Plessing and H. Neuhäuser, in Plastic and Fracture Instabilities in Materials, 200, 101, ASME-AMD (1995).Google Scholar
  67. T. Hasegawa, T. Yakou and S. Karashima, Mat. Sci. Eng. 20, 267 (1975).CrossRefGoogle Scholar
  68. B. Peeters, S.R. Kalidindi, P. Van Houtte, E. Aernoudt, Acta Mater. 48, 2123 (2000).CrossRefGoogle Scholar
  69. B. Peeters, S.R. Kalidindi, C. Teodosiu, P. Van Houtte, E. Aernoudt, J. Mech. Phys. Sol. 50, 783 (2002).MATHCrossRefGoogle Scholar
  70. S. Kok, M.S. Bharathi, A.J. Beaudoin, C. Fressengeas, G. Ananthakrishna, L.P. Kubin, M. Lebyodkin, Acta Mater. 51 3651–3662 (2003).CrossRefGoogle Scholar
  71. J.W. Hutchinson and K. Neale, J. Mech. Phys. Sol. 31, 405–426 (1983).MATHCrossRefGoogle Scholar
  72. S. Varadhan, A.J. Beaudoin and C. Fressengeas, J. Mech. Phys. Sol. 57, 1733–1748 (2009).MATHCrossRefGoogle Scholar
  73. S. Limkumnerd and J.P. Sethna, J. Mech. Phys. Sol. 56, 1450 (2008).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.LPMMUniversite Paul Verlaine-Metz/CNRS Ile du SaulcyMetz Cedex 01France

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