A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics

Modelling and Simulation in Materials Science and Engineering

Volumn 14, Issue 7, 2006, Pages 1139-1151

  Tang, Meijie ^a   Cai, Wei ^b   Xu, Guanshui ^c   Bulatov, Vasily V ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b Stanford University   (United States)

^c University of California Riverside   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; NUMERICAL METHODS; STRESS ANALYSIS;

DISLOCATION DYNAMICS; IMAGE STRESSES; STRESS FIELDS;

DISLOCATIONS (CRYSTALS);

EID: 33749420415     PISSN: 09650393     EISSN: 1361651X     Source Type: Journal    
DOI: 10.1088/0965-0393/14/7/003     Document Type: Article

References (39)

1. Brown L M 1964 The self-stress of dislocations and the shape of extended nodes Phil. Mag. 10 441
2. Bulatov V V, Cai W, Fier J, Hiratani M, Pierce T, Tang M, Rhee M, Yates K and Arsenlis A 2004 Scalable line dynamics of ParaDiS SuperComputing p 19 online at http://www.sc-conference.org/sc2004/schedule/pdfs/pap206.pdf
3. Bulatov V V, Tang M and Zbib H M 2001 Dislocation plasticity from dislocation dynamics MRS Bull. 26 191
4. Cai W 2001 Atomistic and mesoscale modeling of dislocation mobility PhD Thesis Massachusetts Institute of Technology
5. Cai W, Arsenlis A, Weinberger C R and Bulatov V V 2005 A non-singular continuum theory of dislocations J. Mech. Phys. Solids 54 561
6. Cai W and Bulatov V V 2004 Mobility laws in dislocation dynamics simulations Mater. Sci. Eng. A 387-389 277
7. Cai W, Bulatov V V, Chang J, Li J and Yip S 2004a Dislocation core effects on mobility Dislocations in Solids vol 12 ed F R N Nabarro and J P Hirth (Amsterdam: Elsevier) p1
8. Cai W, Bulatov V V, Pierce T G, Hiratani M, Rhee M, Bartelt M and Tang M 2004b Massively-parallel dislocation dynamics simulations Solid Mechanics and Its Applications vol 115 ed H Kitagawa and Y Shibutani (Dorchet: Kluwer) p 1
9. Devincre B 1995 Three dimensional stress field expressions for straight dislocation segments Solid State. Commun. 93 875
10. Devincre B 1996 Meso-scale simulation of the dislocation dynamics Computer Simulation in Materials Science (NATO ASI Series E) vol 308 ed H O Kirchner et al (Dordrecht: Kluwer) p 309
11. Eshelby J D 1979 Boundary problems Dislocations in Solids vol 1 ed F R N Nabarro (New York: North-Holland) p 167
12. Eshelby J D and Stroh A N 1951 Dislocations in thin plates Phil. Mag. 42 1401
13. Fivel M C, Gosling T J and Canova G R 1996 Implementing image stresses in a 3D dislocation simulation Modelling Simul. Mater. Sci. Eng. 4 581
14. Gavazza S D and Barnett D M 1976 The self-force on a planar dislocation loop in an anisotropic linear-elastic medium J. Mech. Phys. Solids 24 171
15. Ghoniem N M, Tong S-H and Sun L Z 2000 Parametric dislocation dynamics: A thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys. Rev. B 61 913
16. Hazzledine P M and Shaibani S J 1982 The behaviour of dislocations near a free surface ICSMA ed R C Gifkins (Oxford: Pergamon) p 45
17. Hirth J P and Lothe J 1982 Theory of Dislocations 2nd edn (New York: Wiley)
18. Honda K 1979 Dislocation walls consisting of double arrays in white tin single crystals Japan. J. Appl. Phys. 18 215
19. Hughes T J R 2000 The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (New York: Dover)
20. Khraishi T A and Zbib H M 2002 Free-surface effects in 3D dislocation dynamics: formulation and modeling J. Eng. Mater. Tech. 124 342
21. Kubin L P and Canova G R 1992 The modelling of dislocation patterns Scr. Metall. Mater. 27 957
22. Kukta R V 1998 PhD Thesis Brown University
23. Lemchand C, Devincre B and Kubin L P 2001 Homogenization method for a discrete-continuum simulation of dislocation dynamics J. Mech. Phys. Solids 49 1969
24. Liu X H, Ross F M and Schwarz K W 2000 dislocated epitaxial islands Phys. Rev. Lett. 85 4088
25. Liu X H and Schwarz K W 2005 Modelling of dislocations intersecting a free surface, Modelling Simul. Mater. Sci. Eng. 13 1233
26. Lothe J 1992 Dislocations in continuous elastic media Elastic Strain Fields And Dislocation Mobility ed V L Indenbom and J Lothe (Amsterdam: North-Holland) p 175
27. Martinez R and Ghoniem N M 2002 The Influence of crystal surfaces on dislocation interactions in mesoscopic plasticity: a combined dislocation dynamics- finite element approach J. Comp. Meth. Eng. Sci. 3 229
28. Shaibani S J and Hazzledine P M 1981 The displacement and stress fields of a general dislocation close to a free surface of an isotropic solid Phil. Mag. 44 657
29. Schwarz K W 1999 Simulation of dislocations on the mesoscopic scale. I. Methods and examples J. Appl. Phys. 85 108
30. Smith I M and Griffiths D V 1998 Programming the Finite Element Method 3rd edn (NewYork: Wiley)
31. Tang M, Kubin L P and Canova G R 1998 Dislocation mobility and the mechanical response of B.C.C. single crystals: a mesoscopic approach Acta Mater. 46 3221
32. Tang M, Xu G, Cai W and Bulatov V V 2003 Dislocation image stresses at free surfaces by the finite element method Thin Film Stresses and Mechanical Properties 795 ed S G Corcoran et al (Warrendale, PA: Materials Research Society) U2.4
33. Van der Geissen E and Needleman A 1995 Discrete dislocation plasticity: a simple planar model Modelling Simul. Mater. Sci. Eng. 3 689
34. Wang Z, McCabe R J, Ghoniem N M, LeSar R, Misra A and Mitchell T E 2004 Dislocation motion in thin Cu foils: comparison between computer simulations and experiment Acta Mater. 52 1535
35. Weygand D, Friedman L H, Van der Geissen E and Needleman A 2002 Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics Modelling Simul. Mater. Sci. Eng. 10 437
36. Yan L, Khraishi T A, Shen Y L and Horstemeyer M F 2004 A distributed dislocation method for treating free-surface image stresses in three dimensional dislocation dynamics simulations Modelling Simul. Mater. Sci. Eng. 12 289
37. Yasin H, Zbib H M and Khaleel M A 2001 Size and boundary effects in discrete dislocation dynamics: coupling with continuum finite element Mater. Sci. Eng. A 309-310 294
38. Yoffe E H 1961 A dislocation at a free surface Phil. Mag. 6 1147
39. Zbib H M, Rhee M and Hirth J P 1998 On plastic deformation and the dynamcis of 3D dislocations Int. J. Mech. Sci. 40 113