Abstract
The solution for a crystalline edge dislocation is presented within a framework of continuum linear elasticity, and is compared with the Peierls–Nabarro solution based on a semi-discrete method. The atomic disregistry and the shear stress across the glide plane are discussed. The Peach–Koehler configurational force is introduced as the gradient of the strain energy with respect to the dislocation position between its two consecutive equilibrium positions. The core radius is assumed to vary periodically between equilibrium positions of the dislocation. The critical force is expressed in terms of the core radii or the energies of the stable and unstable equilibrium configurations. This is used to estimate the Peierls stress for both wide and narrow dislocations.
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Peierls R. (1940) The size of a dislocation. Proc. Phys. Soc. 52, 34–37
Nabarro F.R.N. (1947) Dislocations in a simple cubic lattice. Proc. Phys. Soc. 59, 256–272
Joós B., Duesbery M.S. (1987) The Peierls–Nabarro model and the mobility of the dislocation line. Phil. Mag. A 81, 1329–1340
Nabarro F.R.N. (1989) The Peierls stress for a wide dislocation. Mater. Sci. Eng. A 113, 315–326
Indenbom V.L., Petukhov B.V., Lothe J. (1992) Dislocation motion over the Peierls barrier. In: Indenbom V.L., Petukhov B.V., Lothe J. (eds). Elastic Strain Fields and Dislocation Mobility. North Holland, Amsterdam, pp. 489–516
Bulatov V.V., Kaxiras E. (1997) Semidiscrete variational Peierls framework for dislocation core properties. Phys. Rev. Lett. 78, 4221–4224
Nabarro F.R.N. (1997) Theoretical and experimental estimates of the Peierls stress. Phil. Mag. A 75, 703–711
Schoeck G. (1999) Peierls energy of dislocations: a critical assessment. Phys. Rev. Lett. 82, 2310–2313
Lu G., Kioussis N., Bulatov V.V., Kaxiras E. (2000) The Peierls–Nabarro model revisited. Phil. Mag. Lett. 80, 675–682
Joós B., Zhou J. (2001) The Peierls stress of dislocations: an analytic formula. Phys. Rev. Lett. 78, 266–269
Schoeck G. (2005) The Peierls model: progress and limitations. Mater. Sci. Eng. A 400–401, 7–17
Lubarda, V.A., Markenscoff, X.: A variable core model and the Peierls stress for the mixed (screw-edge) dislocation (2006) (submitted)
Lothe J. (1992) Dislocations in continuous elastic media. In: Indenbom V.J., Lothe J. (eds) Elastic Strain Fields and Dislocation Mobility. North Holland, Amsterdam, pp. 187–235
de Wit R. (1973) Theory of disclinations: II. Continuous and discrete disclinations in anisotropic elasticity. J. Res. Nat. Bureau Standards 77A: 49–100
Eshelby J.D. (1966) A simple derivation of the elastic field of an edge dislocation. Br. J. Appl. Phys. 17, 1131–1135
Lubarda V.A., Blume J.A., Needleman A. (1993) An analysis of equilibrium dislocation distributions. Acta Metall. Mater. 41, 625–642
Lubarda V.A., Kouris D.A. (1966) Stress fields due to dislocation walls in infinite and semi-infinite bodies. Mech. Mater. 23, 169–189
Hirth J.P., Lothe J. (1982) Theory of Dislocations, 2nd ed. Wiley, New York
Leibfried G., Lücke K. (1947) Über das Spannungsfeld einer Versetzung. Z. Phys. 126, 450–464
Nabarro F.R.N. (1967) Theory of Crystal Dislocations. Oxford University Press, Oxford
Lubarda V.A. (2006) Dislocation equilibrium conditions revisited. Int. J. Solids Struct. 43, 3444–3458
Maugin G.A. (1995) Material forces: concepts and applications. Appl. Mech. Rev. 48, 247–285
Kienzler R., Herrmann G. (2001) Mechanics in Material Space. Springer, Berlin Heidelberg New York
Eshelby J.D. (1970) Energy relations and the energy–momentum tensor in continuum mechanics. In: Kanninen M.F., Adler W.F., Rosenfield A.R., Janee R.I. (eds) Inelastic behavior of solids. McGraw–Hill, New York, pp. 77–115
Eshelby J.D. (1980) The energy–momentum tensor of complex continua. In: Kröner E., Anthony K.-H., (eds) Continuum Models of Discrete Systems. University of Waterloo Press, Canada, pp. 651–665
Lubarda V.A. (2003) The effects of couple stresses on dislocation strain energy. Int. J. Solids Struct. 40, 3807–3826
Lazar M. (2005) Peach–Koehler forces within the theory of nonlocal elasticity. In: Steinmann P., Maugin G.A. (eds.) Mechanics of material forces. Springer, Berlin Heidelberg New York, pp. 149–158
Indenbom V.L., Orlov A.N. (1962) Physical theory of plasticity and strength. Usp. Fiz. Nauk. 76, 557–591
Hobart R. (1965) Peierls stress dependence on dislocation width. J. Appl. Phys. 36, 1944–1948
Foreman A.J., Jaswon W.A., Wood J.K. (1951) Factors controlling dislocation widths. Proc. Phys. Soc. A 64, 156–163
Huntington H.B. (1955) Modification of the Peierls–Nabarro model for edge dislocation core. Proc. Phys. Soc. Lond. B 68, 1043–1048
Lee M.S., Dundurs J. (1972) On the Peierls force. Phil. Mag. 26, 929–933
Kelly A., Macmillan N.H. (1986) Strong Solids, 3rd ed. Clarendon, Oxford
Estrada R., Kanwal R.P. (2000) Singular Integral Equations. Birkhäuser, Boston
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Lubarda, V.A., Markenscoff, X. Configurational force on a lattice dislocation and the Peierls stress. Arch Appl Mech 77, 147–154 (2007). https://doi.org/10.1007/s00419-006-0068-y
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DOI: https://doi.org/10.1007/s00419-006-0068-y