Multiscale Simulation of Plasticity in bcc Metals

Literature Cited

1. Taylor GI, Elam CF. 1.  1926. The distortion of iron crystals. Proc. R. Soc. A 112:761337–61 [Google Scholar]
2. Christian JW. 2.  1983. Some surprising features of the plastic deformation of body-centered cubic metals and alloys. Metall. Trans. A 14:71237–56 [Google Scholar]
3. Schmid E, Boas W. 3.  1935. Kristallplastizität unter besonderer Berücksichtigung der Metalle Berlin: Julius Springer
4. Duesbery MS, Foxall RA. 4.  1969. A detailed study of the deformation of high purity niobium single crystals. Philos. Mag. 20:166719–51 [Google Scholar]
5. Bolton CJ, Taylor G. 5.  1972. Anomalous slip in high-purity niobium single crystals deformed at 77°K in tension. Philos. Mag. 26:61359–76 [Google Scholar]
6. Matsui H, Kimura H. 6.  1976. Anomalous {110} slip in high-purity molybdenum single crystals and its comparison with that in V(a) metals. Mater. Sci. Eng. 24:2247–56 [Google Scholar]
7. Duesbery MS, Vitek V. 7.  1998. Plastic anisotropy in b.c.c. transition metals. Acta Mater. 46:51481–92 [Google Scholar]
8. Hsiung LL. 8.  2010. On the mechanism of anomalous slip in bcc metals. Mater. Sci. Eng. A 528:1329–37 [Google Scholar]
9. Vítek V, Perrin RC, Bowen DK. 9.  1970. The core structure of 1/2〈111〉 screw dislocations in b.c.c. crystals. Philos. Mag. 21:1731049–73 [Google Scholar]
10. Vitek V. 10.  1992. Structure of dislocation cores in metallic materials and its impact on their plastic behaviour. Prog. Mater. Sci. 36:1–27 [Google Scholar]
11. Vitek V, Paidar V. 11.  2008. Non-planar dislocation cores: a ubiquitous phenomenon affecting mechanical properties of crystalline materials. Dislocations Solids 14:441 [Google Scholar]
12. Cai W, Bulatov VV, Chang J, Li J, Yip S. 12.  2004. Dislocation core effects on mobility. Dislocations in Solids FRN Nabarro, JP Hirth 1–80 Amsterdam: Elsevier [Google Scholar]
13. Seeger A. 13.  1956. On the theory of the low-temperature internal friction peak observed in metals. Philos. Mag. 1:7651–62 [Google Scholar]
14. Dorn E, Rajnak S. 14.  1964. Nucleation of kink pairs and the Peierls' mechanism of plastic deformation. Trans. AIME 230:1052–64 [Google Scholar]
15. Kubin LP. 15.  2013. Dislocations, Mesoscale Simulations and Plastic Flow Oxford, UK: Oxford Univ. Press
16. Moriarty JA, Vitek V, Bulatov VV, Yip S. 16.  2002. Atomistic simulations of dislocations and defects. J. Comput. Mater. Des. 9:99–132 [Google Scholar]
17. Pettifor DG. 17.  1995. Bonding and Structure of Molecules and Solids Oxford, UK: Oxford Univ. Press
18. Ismail-Beigi S, Arias T. 18.  2000. Ab initio study of screw dislocations in Mo and Ta: a new picture of plasticity in bcc transition metals. Phys. Rev. Lett. 84:71499–502 [Google Scholar]
19. Woodward C, Rao S. 19.  2002. Flexible ab initio boundary conditions: simulating isolated dislocations in bcc Mo and Ta. Phys. Rev. Lett. 88:21216402 [Google Scholar]
20. Trinkle DR, Woodward C. 20.  2005. The chemistry of deformation: how solutes soften pure metals. Science 310:57541665–67 [Google Scholar]
21. Shimizu F, Ogata S, Kimizuka H, Kano T, Li J, Kaburaki H. 21.  2007. First-principles calculation on screw dislocation core properties in bcc molybdenum. J. Earth Simulator 7:March17–21 [Google Scholar]
22. Itakura M, Kaburaki H, Yamaguchi M. 22.  2012. First-principles study on the mobility of screw dislocations in bcc iron. Acta Mater. 60:93698–710 [Google Scholar]
23. Romaner L, Ambrosch-Draxl C, Pippan R. 23.  2010. The effect of rhenium on the dislocation core structure in tungsten. Phys. Rev. Lett. 104:195503 [Google Scholar]
24. Samolyuk GD, Osetsky YN, Stoller RE. 24.  2013. The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten. J. Phys. Condens. Matter. 25:2025403 [Google Scholar]
25. Ventelon L, Willaime F, Clouet E, Rodney D. 25.  2013. Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W. Acta Mater. 61:113973–85 [Google Scholar]
26. Dezerald L, Ventelon L, Clouet E, Denoual C, Rodney D, Willaime F. 26.  2014. Ab initio modeling of the two-dimensional energy landscape of screw dislocations in bcc transition metals. Phys. Rev. B 89:2024104 [Google Scholar]
27. Weinberger C, Tucker G, Foiles S. 27.  2013. Peierls potential of screw dislocations in bcc transition metals: predictions from density functional theory. Phys. Rev. B 87:5054114 [Google Scholar]
28. Frederiksen SL, Jacobsen KW. 28.  2003. Density functional theory studies of screw dislocation core structures in bcc metals. Philos. Mag. 83:3365–75 [Google Scholar]
29. Mrovec M, Nguyen-Manh D, Pettifor D, Vitek V. 29.  2004. Bond-order potential for molybdenum: application to dislocation behavior. Phys. Rev. B 69:9094115 [Google Scholar]
30. Mrovec M, Gröger R, Bailey AG, Nguyen-Manh D, Elsässer C, Vitek V. 30.  2007. Bond-order potential for simulations of extended defects in tungsten. Phys. Rev. B 75:10104119 [Google Scholar]
31. Mrovec M, Nguyen-Manh D, Elsässer C, Gumbsch P. 31.  2011. Magnetic bond-order potential for iron. Phys. Rev. Lett. 106:24246402 [Google Scholar]
32. Lin Y, Mrovec M, Vitek V. 32.  2014. A new method for development of bond-order potentials for transition bcc metals. Model. Simul. Mater. Sci. Eng. 22:034002 [Google Scholar]
33. Moriarty JA, Benedicta LX, Gloslia JN, Hooda RQ, Orlikowskia DA. 33.  et al. 2006. Robust quantum-based interatomic potentials for multiscale modeling in transition metals. J. Mater. Res. 21:3563–73 [Google Scholar]
34. Rao SI, Woodward C. 34.  2001. Atomistic simulations of (a/2)〈111〉 screw dislocations in bcc Mo using a modified generalized pseudopotential theory potential. Philos. Mag. A 81:51317–27 [Google Scholar]
35. Li H, Wurster S, Motz C, Romaner L, Ambrosch-Draxl C, Pippan R. 35.  2012. Dislocation-core symmetry and slip planes in tungsten alloys: ab initio calculations and microcantilever bending experiments. Acta Mater. 60:2748–58 [Google Scholar]
36. Ventelon L, Willaime F. 36.  2010. Generalized stacking-faults and screw-dislocation core-structure in bcc iron: a comparison between ab initio calculations and empirical potentials. Philos. Mag. 90:7–81063–74 [Google Scholar]
37. Mrovec M, Elsässer C, Gumbsch P. 37.  2010. Atomistic simulations of lattice defects in tungsten. Int. J. Refract. Met. Hard Mater. 28:6698–702 [Google Scholar]
38. Li J, Wang C-Z, Chang J-P, Cai W, Bulatov V. 38.  et al. 2004. Core energy and Peierls stress of a screw dislocation in bcc molybdenum: a periodic-cell tight-binding study. Phys. Rev. B 70:10104113 [Google Scholar]
39. Cai W, Bulatov VV, Chang J, Li J, Yip S. 39.  2003. Periodic image effects in dislocation modelling. Philos. Mag. 83:5539–67 [Google Scholar]
40. Ventelon L, Willaime F. 40.  2008. Core structure and Peierls potential of screw dislocations in α-Fe from first principles: cluster versus dipole approaches. J. Comput. Mater. Des. 14:Suppl. 185–94 [Google Scholar]
41. Clouet E, Ventelon L, Willaime F. 41.  2009. Dislocation core energies and core fields from first principles. Phys. Rev. Lett. 102:5055502 [Google Scholar]
42. Clouet E. 42.  2011. Dislocation core field. I. Modeling in anisotropic linear elasticity theory. Phys. Rev. B 84:22224111 [Google Scholar]
43. Clouet E, Ventelon L, Willaime F. 43.  2011. Dislocation core field. II. Screw dislocation in iron. Phys. Rev. B 84:22224107 [Google Scholar]
44. Rodney D, Proville L. 44.  2009. Stress-dependent Peierls potential: influence on kink-pair activation. Phys. Rev. B 79:9094108 [Google Scholar]
45. Gröger R, Vitek V. 45.  2012. Constrained nudged elastic band calculation of the Peierls barrier with atomic relaxations. Model. Simul. Mater. Sci. Eng. 20:3035019 [Google Scholar]
46. Ventelon L, Willaime F, Clouet E, Rodney D. 46.  2013. Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W. Acta Mater. 61:113973–85 [Google Scholar]
47. Weinberger C, Tucker G, Foiles S. 47.  2013. Peierls potential of screw dislocations in bcc transition metals: predictions from density functional theory. Phys. Rev. B 87:5054114 [Google Scholar]
48. Vitek V, Mrovec M, Gröger R, Bassani JL, Racherla V, Yin L. 48.  2004. Effects of non-glide stresses on the plastic flow of single and polycrystals of molybdenum. Mater. Sci. Eng. A 387–389:1–2138–42 [Google Scholar]
49. Chen ZM, Mrovec M, Gumbsch P. 49.  2013. Atomistic aspects of 1/2〈111〉 screw dislocation behavior in α-iron and the derivation of microscopic yield criterion. Model. Simul. Mater. Sci. Eng. 21:5055023 [Google Scholar]
50. Gröger R, Bailey AG, Vitek V. 50.  2008. Multiscale modeling of plastic deformation of molybdenum and tungsten. I. Atomistic studies of the core structure and glide of 1/2〈111〉 screw dislocations at 0 K. Acta Mater. 56:195401–11 [Google Scholar]
51. Vitek V, Mrovec M, Bassani JL. 51.  2004. Influence of non-glide stresses on plastic flow: from atomistic to continuum modeling. Mater. Sci. Eng. A 365:1–231–37 [Google Scholar]
52. Gröger R, Racherla V, Bassani JL, Vitek V. 52.  2008. Multiscale modeling of plastic deformation of molybdenum and tungsten. II. Yield criterion for single crystals based on atomistic studies of glide of 1/2〈111〉 screw dislocations. Acta Mater. 56:195412–25 [Google Scholar]
53. Koester A, Ma A, Hartmaier A. 53.  2012. Atomistically informed crystal plasticity model for body-centered cubic iron. Acta Mater. 60:93894–901 [Google Scholar]
54. Gröger R. 54.  2014. Which stresses affect the glide of screw dislocations in bcc metals?. Philos. Mag. 94:182021–30 [Google Scholar]
55. Domain C, Monnet G. 55.  2005. Simulation of screw dislocation motion in iron by molecular dynamics simulations. Phys. Rev. Lett. 95:21215506 [Google Scholar]
56. Marian J, Cai W, Bulatov VV. 56.  2004. Dynamic transitions from smooth to rough to twinning in dislocation motion. Nat. Mater. 3:3158–63 [Google Scholar]
57. Chaussidon J, Fivel M, Rodney D. 57.  2006. The glide of screw dislocations in bcc Fe: atomistic static and dynamic simulations. Acta Mater. 54:133407–16 [Google Scholar]
58. Gröger R, Vitek V. 58.  2008. Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate. Acta Mater. 56:195426–39 [Google Scholar]
59. Proville L, Ventelon L, Rodney D. 59.  2013. Prediction of the kink-pair formation enthalpy on screw dislocations in α-iron by a line tension model parametrized on empirical potentials and first-principles calculations. Phys. Rev. B 87:14144106 [Google Scholar]
60. Monnet G, Terentyev D. 60.  2009. Structure and mobility of the 1/2 〈111〉 {112} edge dislocation in bcc iron studied by molecular dynamics. Acta Mater. 57:51416–26 [Google Scholar]
61. Kang K, Bulatov VV, Cai W. 61.  2012. Singular orientations and faceted motion of dislocations in body-centered cubic crystals. PNAS 109:3815174–78 [Google Scholar]
62. Weinberger CR. 62.  2010. Dislocation drag at the nanoscale. Acta Mater. 58:196535–41 [Google Scholar]
63. Bulatov V, Cai W. 63.  2002. Nodal effects in dislocation mobility. Phys. Rev. Lett. 89:11115501 [Google Scholar]
64. Bulatov VV, Hsiung LL, Tang M, Arsenlis A, Bartelt MC. 64.  et al. 2006. Dislocation multi-junctions and strain hardening. Nature 440:70881174–78 [Google Scholar]
65. Chen ZM, Mrovec M, Gumbsch P. 65.  2011. Dislocation–vacancy interactions in tungsten. Model. Simul. Mater. Sci. Eng. 19:7074002 [Google Scholar]
66. Cheng Y, Mrovec M, Gumbsch P. 66.  2008. Atomistic simulations of interactions between the 1/2〈111〉 edge dislocation and symmetric tilt grain boundaries in tungsten. Philos. Mag. 88:4547–60 [Google Scholar]
67. Mrovec M, Elsässer C, Gumbsch P. 67.  2009. Interactions between lattice dislocations and twin boundaries in tungsten: a comparative atomistic simulation study. Philos. Mag. 89:34–363179–94 [Google Scholar]
68. Tang M, Kubin LP, Canova GR. 68.  1998. Dislocation mobility and the mechanical response of b.c.c. single crystals: a mesoscopic approach. Acta Mater. 46:93221–35 [Google Scholar]
69. Kocks UF, Argon AS, Ashby MF. 69.  1975. Thermodynamics and Kinetics of Slip (Progress in Materials Science 19 New York: Pergamon
70. Kocks UF. 70.  1976. Laws for work-hardening and low-temperature creep. J. Eng. Mater. Technol. 98:176–85 [Google Scholar]
71. Naamane S, Monnet G, Devincre B. 71.  2010. Low temperature deformation in iron studied with dislocation dynamics simulations. Int. J. Plast. 26:184–92 [Google Scholar]
72. Chaussidon J, Robertson C, Rodney D, Fivel M. 72.  2008. Dislocation dynamics simulations of plasticity in Fe laths at low temperature. Acta Mater. 56:195466–76 [Google Scholar]
73. Srivastava K, Gröger R, Weygand D, Gumbsch P. 73.  2013. Dislocation motion in tungsten: atomistic input to discrete dislocation simulations. Int. J. Plast. 47:126–42 [Google Scholar]
74. Louchet F, Kubin LP. 74.  1975. Dislocation substructures in the anomalous slip plane of single crystal niobium strained at 50 K. Acta Metall. 23:117–21 [Google Scholar]
75. Argon AS. 75.  2008. Strengthening Mechanisms in Crystal Plasticity Oxford, UK: Oxford Univ. Press
76. Caillard D. 76.  2010. Kinetics of dislocations in pure Fe. I. In situ straining experiments at room temperature. Acta Mater. 58:93493–503 [Google Scholar]
77. Caillard D. 77.  2010. Kinetics of dislocations in pure Fe. II. In situ straining experiments at low temperature. Acta Mater. 58:93504–15 [Google Scholar]
78. Srivastava K. 78.  2014. Atomistically-informed discrete dislocation dynamics modeling of plastic flow in body-centered cubic metals PhD Thesis, Karlsruhe Inst. Technol.
79. Gröger R, Vitek V. 79.  2007. Explanation of the discrepancy between the measured and atomistically calculated yield stresses in body-centered cubic metals. Philos. Mag. Lett. 87:2113–20 [Google Scholar]
80. Mott NF. 80.  1956. Creep in metal crystals at very low temperatures. Philos. Mag. 1:6568–72 [Google Scholar]
81. Proville L, Rodney D, Marinica M-C. 81.  2012. Quantum effect on thermally activated glide of dislocations. Nat. Mater. 11:10845–49 [Google Scholar]
82. Barvinschi B, Proville L, Rodney D. 82.  2014. Quantum Peierls stress of straight and kinked dislocations and effect of non-glide stresses. Model. Simul. Mater. Sci. Eng. 22:225006 [Google Scholar]
83. Gilbert MR, Schuck P, Sadigh B, Marian J. 83.  2013. Free energy generalization of the Peierls potential in iron. Phys. Rev. Lett. 111:9095502 [Google Scholar]
84. LeSar R. 84.  2014. Simulations of dislocation structure and response. Annu. Rev. Condens. Matter Phys. 5:1375–407 [Google Scholar]
85. Queyreau S, Monnet G, Devincre B. 85.  2009. Slip systems interactions in α-iron determined by dislocation dynamics simulations. Int. J. Plast. 25:2361–77 [Google Scholar]
86. Monnet G, Vincent L, Devincre B. 86.  2013. Dislocation-dynamics based crystal plasticity law for the low- and high-temperature deformation regimes of bcc crystal. Acta Mater. 61:166178–90 [Google Scholar]
87. Marichal C, Srivastava K, Weygand D, Van Petegem S, Grolimund D. 87.  et al. 2014. Origin of anomalous slip in tungsten. Phys. Rev. Lett. 113:2025501 [Google Scholar]
88. Aono Y, Kuramoto E, Kitajima K. 88.  1981. Plastic deformation of high-purity iron single crystals. Rep. Res. Inst. Appl. Mech. 29:127–93 [Google Scholar]
89. Matsui H, Kimura H. 89.  1973. A mechanism of the “unexpected {110} slip” observed in bcc metals deformed at low temperatures. Scr. Metall. 7:9905–13 [Google Scholar]
90. Weinberger CR, Cai W. 90.  2008. Surface-controlled dislocation multiplication in metal micropillars. PNAS 105:3814304–7 [Google Scholar]
91. Matsui H, Kimura H. 91.  1975. Anomalous {110} slip and the role of co-planar double slip in bcc metals. Scr. Metall. 9:9971–78 [Google Scholar]
92. Barabash RI, Ice GE, Walker FJ. 92.  2003. Quantitative microdiffraction from deformed crystals with unpaired dislocations and dislocation walls. J. Appl. Phys. 93:31457 [Google Scholar]
93. Van Swygenhoven H, Van Petegem S. 93.  2010. The use of Laue microdiffraction to study small-scale plasticity. JOM 62:1236–43 [Google Scholar]
94. Uchic MD, Shade PA, Dimiduk DM. 94.  2009. Plasticity of micrometer-scale single crystals in compression. Annu. Rev. Mater. Res. 39:1361–86 [Google Scholar]
95. Kraft O, Gruber PA, Mönig R, Weygand D. 95.  2010. Plasticity in confined dimensions. Annu. Rev. Mater. Res. 40:1293–317 [Google Scholar]
96. Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA. 96.  et al. 2009. Correlation between critical temperature and strength of small-scale bcc pillars. Phys. Rev. Lett. 103:10105501 [Google Scholar]
97. Schneider AS, Frick CP, Clark BG, Gruber PA, Arzt E. 97.  2011. Influence of orientation on the size effect in bcc pillars with different critical temperatures. Mater. Sci. Eng. A 528:31540–47 [Google Scholar]
98. Schneider AS, Clark BG, Frick CP, Gruber PA, Arzt E. 98.  2010. Effect of pre-straining on the size effect in molybdenum pillars. Philos. Mag. Lett. 90:11841–49 [Google Scholar]
99. Peeters B, Kalidindi SR, Van Houtte P, Aernoudt E. 99.  2000. A crystal plasticity based work-hardening/softening model for b.c.c. metals under changing strain paths. Acta Mater. 48:92123–33 [Google Scholar]
100. Stainier L, Cuitiño AM, Ortiz M. 100.  2002. A micromechanical model of hardening, rate sensitivity and thermal softening in BCC single crystals. J. Mech. Phys. Solids 50:71511–45 [Google Scholar]
101. Ma A, Roters F, Raabe D. 101.  2007. A dislocation density based constitutive law for BCC materials in crystal plasticity FEM. Comput. Mater. Sci. 39:191–95 [Google Scholar]
102. Alankar A, Field DP, Raabe D. 102.  2014. Plastic anisotropy of electro-deposited pure α-iron with sharp crystallographic 〈111〉 texture in normal direction: analysis by an explicitly dislocation-based crystal plasticity model. Int. J. Plast. 52:18–32 [Google Scholar]
103. Knezevic M, Beyerlein IJ, Lovato ML, Tomé CN, Richards AW, McCabe RJ. 103.  2014. A strain-rate and temperature dependent constitutive model for BCC metals incorporating non-Schmid effects: application to tantalum–tungsten alloys. Int. J. Plast. 62:093–104 [Google Scholar]
104. Kröner E. 104.  1969. Initial studies of a plasticity theory based upon statistical mechanics. Inelastic Behavior of Solids MF Kanninen, WF Adler, AR Rosenfield, RI Jaffee 137–47 New York: McGraw-Hill [Google Scholar]
105. Groma I, Csikor FF, Zaiser M. 105.  2003. Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51:1271–81 [Google Scholar]
106. Yefimov S, Groma I, van der Giessen E. 106.  2004. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations. J. Mech. Phys. Solids 52:279–300 [Google Scholar]
107. Bittencourt E, Needleman A, Gurtin ME, van der Giessen E. 107.  2003. A comparison of nonlocal continuum and discrete dislocation plasticity predictions. J. Mech. Phys. Solids 51:281–310 [Google Scholar]
108. Kröner E. 108.  2001. Benefits and shortcomings of the continuous theory of dislocations. Int. J. Solids Struct. 38:6–71115–34 [Google Scholar]
109. Mura T. 109.  1963. Continuous distribution of moving dislocations. Philos. Mag. 8:89843–57 [Google Scholar]
110. Arsenslis A, Parks DM, Becker R, Bulatov VV. 110.  2004. On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals. J. Mech. Phys. Solids 52:1213–46 [Google Scholar]
111. Reuber C, Eisenlohr P, Roters F, Raabe D. 111.  2014. Dislocation density distribution around an indent in single-crystalline nickel: comparing nonlocal crystal plasticity finite-element predictions with experiments. Acta Mater. 71:333–48 [Google Scholar]
112. Zaiser M, Hochrainer T. 112.  2006. Some steps towards a continuum representation of 3D dislocation systems. Scr. Mater. 54:5717–21 [Google Scholar]
113. Kosevich AM. 113.  1979. Crystal dislocations and theory of elasticity. Dislocations in Solids FRN Nabarro 33–142 Amsterdam: North Holland [Google Scholar]
114. El-Azab A. 114.  2000. Statistical mechanics treatment of the evolution of dislocation distributions in single crystals. Phys. Rev. B 61:1811956–66 [Google Scholar]
115. Hochrainer T, Zaiser M, Gumbsch P. 115.  2007. A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation. Philos. Mag. A 87:81261–82 [Google Scholar]
116. Sandfeld S, Hochrainer T, Zaiser M, Gumbsch P. 116.  2010. Numerical implementation of a 3D continuum theory of dislocation dynamics and application to microbending. Philos. Mag. 90:273697–728 [Google Scholar]
117. Hochrainer T, Sandfeld S, Zaiser M, Gumbsch P. 117.  2014. Continuum dislocation dynamics: towards a physical theory of crystal plasticity. J. Mech. Phys. Solids 63:1167–78 [Google Scholar]
118. Ebrahimi A, Monavari M, Hochrainer T. 118.  2014. Numerical implementation of continuum dislocation dynamics with the discontinuous-Galerkin method. MRS Proc. 1651; doi: 10.1557/opl.2014.26
119. Hochrainer T. 119.  2014. Continuum dislocation dynamics based on the second order alignment tensor. MRS Proc. 1651; doi: 10.1557/opl.2014.53
120. Hochrainer T. 120.  2015. Multipole expansion of continuum dislocations dynamics in terms of alignment tensors. Philos. Mag. In press
121. Monavari M, Zaiser M, Sandfeld S. 121.  2014. Comparison of closure approximations for continuous dislocation dynamics. MRS Proc. 1651; doi: 10.1557/opl.2014.62
122. El-Azab A, Deng J, Tang M. 122.  2007. Statistical characterization of dislocation ensembles. Philos. Mag. 87:8–91201–23 [Google Scholar]
123. Deng J, El-Azab A. 123.  2007. Dislocation pair correlations from dislocation dynamics simulations. J. Comput. Mater. Des. 14:1295–307 [Google Scholar]
124. Deng J, El-Azab A. 124.  2007. Mathematical and computational modelling of correlations in dislocation dynamics. Model. Simul. Mater. Sci. Eng. 17:175010 [Google Scholar]
125. Seeger A. 125.  2004. Experimental evidence for the {110}-{112} transformation of the screw-dislocation cores in body-centred cubic metals. Phys. Status Solid. 201:4R21–24 [Google Scholar]
126. Weinberger CR, Boyce BL, Battaile CC. 126.  2013. Slip planes in bcc transition metals. Int. Mater. Rev. 58:5296–314 [Google Scholar]
127. Srivastava K, Weygand D, Gumbsch P. 127.  2014. Dislocation junctions as indicators of elementary slip planes in body-centered cubic metals. J. Mater. Sci. 49:207333–37 [Google Scholar]
128. Groma I, Györgyi G, Ispánovity PD. 128.  2010. Variational approach in dislocation theory. Philos. Mag. 90:27–283679–95 [Google Scholar]
129. Groma I, Vandrus Z, Ispanovity DP. 129.  2015. Scale-free phase field theory of dislocations. Phys. Rev. Lett. 114:1015503 [Google Scholar]
130. Dickel D, Schulz K, Schmitt S, Gumbsch P. 130.  2014. Dipole formation and yielding in a two-dimensional continuum dislocation model. Phys. Rev. B 90:9094118 [Google Scholar]
131. Schulz K, Dickel D, Schmitt S, Sandfeld S, Weygand D, Gumbsch P. 131.  2014. Analysis of dislocation pile-ups using a dislocation-based continuum theory. Model. Simul. Mater. Sci. Eng. 22:2025008 [Google Scholar]
132. LeSar R, Rickman JM. 132.  2002. Multipole expansion of dislocation interactions: application to discrete dislocations. Phys. Rev. B 65:14144110 [Google Scholar]
133. LeSar R, Rickman JM. 133.  2004. Incorporation of local structure in continuous dislocation theory. Phys. Rev. B 69:17172105 [Google Scholar]
134. Zaiser M, Sandfeld S. 134.  2014. Scaling properties of dislocation simulations in the similitude regime. Model. Simul. Mater. Sci. Eng. 22:065012 [Google Scholar]