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Double kink mechanisms for discrete dislocations in BCC crystals

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Abstract

We present an application of the discrete dislocation theory to the characterization of the energetics of kinks in Mo, Ta and W body-centered cubic (BCC) crystals. The discrete dislocation calculations supply detailed predictions of formation and interaction energies for various double-kink formation and spreading mechanisms as a function of the geometry of the double kinks, including: the dependence of the formation energy of a double kink on its width; the energy of formation of a double kink on a screw dislocation containing a pre-existing double kink; and energy of formation of a double kink on a screw dislocation containing a pre-existing single kink. The computed interaction energies are expected to facilitates the nucleation of double kinks in close proximity to each other and to pre-existing kinks, thus promoting clustering of double kinks on screw segments and of ‘daughter’ double kinks ahead of ‘mother’ kinks. The predictions of the discrete dislocation theory are found to be in good agreement with the full atomistic calculations based on empirical interatomic potentials available in the literature.

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References

  • Ariza MP, Ortiz M (2005) Discrete crystal elasticity and discrete dislocations in crystals. Arch Ration Mech Anal 178: 149–226

    Article  Google Scholar 

  • Ariza MP, Ortiz M (2010) Discrete dislocations in graphene. J Mech Phys Solids 58: 710–734

    Article  CAS  Google Scholar 

  • Babuska I, Vitasek E, Kroupa F (1960) Some applications of the discrete fourier transform to problems of crystal lattice deformation, parts i and ii. Czechoslovak J Phys 10:419–427; 488–504

    Google Scholar 

  • Cai W, Bulatov V, Justo JF, Argon AS, Yip S (2000) Intrinsic mobility of a dissociated Dislocation in silicon. Phys Rev Lett 84(15): 3346–3349

    Article  CAS  Google Scholar 

  • Cai W, Bulatov V, Yip S, Argon AS (2001) Kinetic Monte Carlo modeling of dislocation motion in BCC metals. Mater Sci Eng A 309(SI): 270–273

    Google Scholar 

  • Dai X, Kong Y, Li J, Liu B (2006) Extended Finnis–Sinclair potential for bcc and fcc metals and alloys. J Phys Condens Matter 18: 4527–4542

    Article  CAS  Google Scholar 

  • Duesbery M (1983) On kinked screw dislocations in the bcc lattice. II. Kink energies and double kinks. Acta metallurgica 31(10): 1759–1770

    Article  CAS  Google Scholar 

  • Ericksen JL (1979) On the symmetry of deformable crystrals. Arch Ration Mech Anal 72: 1–13

    Article  Google Scholar 

  • Finnis M, Sinclair J (1984) A simple empirical n-body potential for transition-metals. Philos Mag A Phys Condens Matter Struct Defects Mech Prop 50(1): 45–55

    CAS  Google Scholar 

  • Ghoniem NM, Tong SH, Sun LZ (2000) Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys Rev B 61(2): 913–927

    Article  CAS  Google Scholar 

  • Hirth JP, Lothe J (1968) Theory of dislocations. McGraw-Hill, New York

    Google Scholar 

  • Koslowski M, Cuitiño A, Ortiz M (2002) A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals. J Mech Phys Solids 50(12): 2597–2635

    Article  Google Scholar 

  • Madec R, Devincre B, Kubin LP (2002) Simulation of dislocation patterns in multislip. Scripta Materialia 47(10): 689–695

    Article  CAS  Google Scholar 

  • Munkres JR (1984) Elements of algebraic topology. Perseus Publishing, Cambridde, MA

    Google Scholar 

  • Mura T (1987) Micromechanics of defects in solids. Kluwer, Boston

    Book  Google Scholar 

  • Nye JF (1953) Some geometrical relations in dislocated crystals. Acta Metallurgica 1: 153–162

    Article  CAS  Google Scholar 

  • Ramasubramaniam A, Ariza MP, Ortiz M (2007) A discrete mechanics approach to dislocation dynamics in bcc crystals. J Mech Phys Solids 55(3): 615–647

    Article  CAS  Google Scholar 

  • Seeger A (1981) The kink picture of dislocation mobility and dislocation-point-defect interactions. Journal de Physique 42(NC5): 201–228

    Google Scholar 

  • Shenoy VB, Ortiz M, Phillips R (1999) The atomistic structure and energy of nascent dislocation loops. Model Simul Mater Sci Eng 7(4): 603–619

    Article  CAS  Google Scholar 

  • Tang M, Kubin LP, Canova GR (1998) Dislocation mobility and the mechanical response of BCC single crystals: a mesoscopic approach. Acta Materialia 46(9): 3221–3235

    Article  CAS  Google Scholar 

  • Vitek V (1976) Computer-simulation of screw dislocation-motion in bcc metals under effect of external shear and uniaxial stresses. Proc R Soc Lond Ser A 352(1668): 109–124

    Article  CAS  Google Scholar 

  • Wang YU, Jin YM, Cuitino AM, Khatachuryan AG (2001) Nanoscale phase field microelasticity theory of dislocations: model and 3d simulations. Acta Materialia 49(10): 1847–1857

    Article  CAS  Google Scholar 

  • Wang YU, Jin YM, Cuitino AM, Khatachuryan AG (2004) Phase field microelasticity theory and modeling of multiple dislocation dynamics. Appl Phys Lett 78(16): 2324–2326

    Article  Google Scholar 

  • Xu W, Moriarty J (1998) Accurate atomistic simulations of the Peierls barrier and kink-pair formation energy for 〈111〉 screw dislocations in bcc Mo. Comput Mater Sci 9: 348–356

    Article  CAS  Google Scholar 

  • Yang L, Soderlind P, Moriarty J (2001) Accurate atomistic simulation of a/2 〈111〉 screw dislocations and other defects in bcc tantalum. Philosoph Mag A 1(5): 1355–1385

    Article  Google Scholar 

  • Yang LH, Moriarty JA (2001) Kink-pair mechanisms for a/2 〈111〉 screw dislocation motion in bcc tantalum. Mater Sci Eng A 319(SI): 124–129

    Google Scholar 

  • Zbib HM, de la Rubia TD, Bulatov VV (2002) A multiscale model of plasticity based on discrete dislocation dynamics. Int J Mech Sci 124(1): 78–87

    Google Scholar 

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Correspondence to M. P. Ariza.

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Ariza, M.P., Tellechea, E., Menguiano, A.S. et al. Double kink mechanisms for discrete dislocations in BCC crystals. Int J Fract 174, 29–40 (2012). https://doi.org/10.1007/s10704-012-9681-7

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  • DOI: https://doi.org/10.1007/s10704-012-9681-7

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