Continuum theory of evolving dislocation fields

Philosophical Magazine

Volumn 87, Issue 8-9, 2007, Pages 1225-1260

  Sedlaek R ^a   Schwarz, C ^a   Kratochvil J ^b   Werner, E ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALS; DISLOCATIONS (CRYSTALS); LAGRANGE MULTIPLIERS; PLASTICITY; PROBLEM SOLVING;

CONTINUUM THEORY; CRYSTAL PLASTICITY; DISLOCATION FIELDS;

CONTINUUM MECHANICS;

EID: 33847158341     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786430600972921     Document Type: Conference Paper

References (47)

1. N.A. Fleck, G.M. Muller, M.F. Ashby et al. Acta Metall. Mater. 42 475 (1994).
2. E. Arzt, Acta Mater. 46 5611 (1998).
3. J.S. Stölken and A.G. Evans, Acta Mater. 46 5109 (1998).
4. J.W. Hutchinson, Int. J. Solids Struct. 37 225 (2000).
5. A. Needleman, Acta Mater. 48 105 (2000).
6. L.P. Kubin and G. Canova, Scripta Metall. Mater. 27 957 (1992).
7. B. Devincre and L.P. Kubin, Mater. Sci. Eng. A 234-236 8 (1997).
8. E. Van der Giessen and A. Needleman, Model. Simul. Mater. Sci. Eng. 3 689 (1995).
9. M.C. Fivel and A. El-Azab, J. de Phys. IV Pr9 261 (1999).
10. C. Lemarchand, B. Devincre and L.P. Kubin, J. Mech. Phys. Solids 49 1969 (2001).
11. V. Bulatov, J. Comput. Mater. Design 9 133 (2002).
12. E. Kröner, in Inelastic Behavior of Solids, edited by M. F. Kanninen, W. F. Adler, A. R. Rosenfeld and R. I. Jaffee (McGraw-Hill, New York, 1969), p. 137.
13. I. Groma, Phys. Rev. B 56 5807 (1997).
14. I. Groma, F.F. Csikor and M. Zaiser, Acta Mater. 51 1271 (2003).
15. S. Yefimov, I. Groma and E. van der Giessen, J. Mech. Phys. Solids 52 279 (2002).
16. E. Kröner, Kontinuumstheorie der Versetzungen und Eigenspannungen (Springer, Berlin, 1958).
17. E. Kröner, in Physics of Defects, edited by R. Balian, M. Kléman and J.P. Poirier (NATO ASI, North Holland, Amsterdam, 1981).
18. A.M. Kosevich, Sov. Phys. Usp. 7 837 (1965).
19. A.M. Kosevich, in Dislocations in Solids, Volume 1, The Elastic Theory, edited by F.R.N. Nabarro (North-Holland, Amsterdam, 1979), p. 33.
20. T. Mura, Int. J. Eng. Sci. 1 371 (1963).
21. T. Mura, Phil. Mag. 8 843 (1963).
22. R. Sedláček and S. Forest, Phys. Stat. Sol. (b) 221 583 (2000).
23. R. Sedláček, J. Kratochvíl and E. Werner, Phil. Mag. 83 3735 (2003).
24. J. Kratochvíl and R. Sedláček, Phys. Rev. B 67 094105 (2003).
25. R. Sedláček and E. Werner, Phys. Rev. B 69 134114 (2004).
26. V. John and P. Knobloch, Comp. Meth. Appl. Mech. Eng., submitted (Preprint Nr. 156, FR 6.1 - Mathematik, Universität des Saarlandes, Saarbrücken, 2005).
27. A. Smolianski, O. Shipilova and H. Haario, Research report 98, Laboratory of Applied Mathematics, Lappeenranta University of Technology, 2005.
28. A. Arsenlis, D.M. Parks, R. Becker et al., J. Mech. Phys. Solids 52 1213 (2004).
29. A. Roy and A. Acharya, J. Mech. Phys. Solids 53 143 (2005).
30. Y. Xiang, L. Cheng, D.J. Srolovitz et al., Acta Mater. 51 5499 (2003).
31. E. Kröner, Int. J. Solids Struct. 38 1115 (2001).
32. R.W. Ogden, Non-linear Elastic Deformation (John Wiley, Horwood, 1984).
33. J.P. Hirth and J. Lothe, Theory of Dislocations (John Wiley, New York, 1982).
34. J. Kratochvíl and M. Saxlová, Scripta Metall. Mater. 26 113 (1992).
35. R. Sedláček, Scripta Metall. Mater. 33 283 (1995).
36. A. El-Azab, Phys. Rev. B 61 11956 (2000).
37. R. Sedláček, Mater. Sci. Eng. A 393 387 (2005).
38. C. Schwarz, R. Sedláček and E. Werner, Model. Simul. Mater. Sci. Eng. (accepted).
39. G. de Wit and J.S. Koehler, Phys. Rev. 116 1113 (1959).
40. J. Kratochvil and R. Sedláček, Proceedings of the Second International Conference on Multiscale Materials Modeling, edited by N.M. Ghoniem, UCLA, 2004, p. 221.
41. L.P. Kubin, C. Fressengeas and G. Anantakrishna, in Dislocations in Solids, Volume 11, edited by F.R.N. Nabarro and M.S. Duesbery (Elsevier Science, Amsterdam, 2002), p. 101.
42. R.J. Asaro, Acta Metall. 27 445 (1979).
43. R.J. Asaro, J. Appl. Mechanics 50 921 (1983).
44. M. Zaiser and A. El-Azab, Mat. Res. Soc. Symp. Proc. 779 W5.7.1 (2003).
45. W.D. Nix, Metall. Trans. A 20A 2217 (1989).
46. C. Schwarz, R. Sedláček and E. Werner, Mater. Sci. Eng. A 400-401 443 (2005).
47. H. Mughrabi, Acta Metall. 31 1367 (1983).