225
Views
0
CrossRef citations to date
0
Altmetric
Part A: Materials Science

Displacement field of doubly periodic array of dislocation dipoles in elastically anisotropic media

&
Pages 230-252 | Received 30 Apr 2015, Accepted 05 Dec 2015, Published online: 13 Jan 2016

References

  • R.J. Amodeo and N.M. Ghoniem, Dislocation dynamics: I. A proposed methodology for deformation micromechanics: Phys. Rev. B 41 (1990), pp. 6958–6967.10.1103/PhysRevB.41.6958
  • L.P. Kubin, G. Canova, M. Condat, B. Devincre, V. Pontikis and Y. Brechet, Dislocation microstructures and plastic flow: A 3D simulation, Solid State Phenomena 23 (1992), pp. 455–472.10.4028/www.scientific.net/SSP.23-24
  • H.M. Zbib, M. Rhee and J.P. Hirth, On plastic deformation and the dynamics of 3D dislocations, Int. J. Mech. Sci. 40 (1998), pp. 113–127.10.1016/S0020-7403(97)00043-X
  • K.W. Schwartz, Simulation of dislocations on the mesoscopic scale. I. Methods and examples, J. Appl. Phys. 85 (1999), pp. 108–119.10.1063/1.369429
  • A.A. Benzerga, Y. Brechet, A. Needleman and E. Van der Giessen, Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics, Model. Simul. Mater. Sci. Eng. 12 (2004), pp. 159–196.10.1088/0965-0393/12/1/014
  • V.V. Bulatov and W. Cai, Computer Simulation of Dislocations, Oxford University Press, New York, 2006.
  • X. Han, N.M. Ghoniem and Z. Wang, Parametric dislocation dynamics of anisotropic crystals, Philos. Mag. 83 (2003), pp. 3705–3721.10.1080/14786430310001599531
  • A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, M. Hiratani, G. Hommes, T.G. Pierce and V.V. Bulatov, Enabling strain hardening simulations with dislocation dynamics, Model. Simul. Mater. Sci. Eng. 15 (2007), pp. 553–595.10.1088/0965-0393/15/6/001
  • J. Yin, D.M. Barnett and W. Cai, Efficient computation of forces on dislocation segments in anisotropic elasticity, Model. Simul. Mater. Sci. Eng. 18 (2010), p.045013.10.1088/0965-0393/18/4/045013
  • S. Aubry, S. Fitzgerald and A. Arsenlis, Methods to compute dislocation line tension energy and force in anisotropic elasticity, Model. Simul. Mater. Sci. Eng. 22 (2014), p. 015001.10.1088/0965-0393/22/1/015001
  • H.H.M. Cleveringa, E. Van Der Giessen and A. Needleman, Comparison of discrete dislocation and continuum plasticity predictions for a composite material, Acta Mater. 45 (1997), pp. 3163–3179.10.1016/S1359-6454(97)00011-6
  • L. Nicola, Y. Xiang, J.J. Vlassak, E. Van der Giessen and A. Needleman, Plastic deformation of freestanding thin films: Experiments and modeling, J. Mech. Phys. Solids 54 (2006), pp. 2089–2110.10.1016/j.jmps.2006.04.005
  • D.S. Balint, V.S. Deshpande, A. Needleman and E. Van der Giessen, Size effects in uniaxial deformation of single and polycrystals: A discrete dislocation plasticity analysis, Model. Simul. Mater. Sci. Eng. 14 (2006), pp. 409–422.10.1088/0965-0393/14/3/005
  • S.S. Chakravarthy and W.A. Curtin, Origin of plasticity length-scale effects in fracture, Phys. Rev. Lett. 105 (2010) p. 115502.10.1103/PhysRevLett.105.115502
  • S.S. Shishvan, L. Nicola and E. Van der Giessen, Bauschinger effect in unpassivated freestanding thin films, J. Appl. Phys. 107 (2010), p. 093529.10.1063/1.3407505
  • E. Van der Giessen and A. Needleman, Discrete dislocation plasticity: a simple planar model, Model. Simul. Mater. Sci. Eng. 3 (1995), pp. 689–735.10.1088/0965-0393/3/5/008
  • W. Cai, V.V. Bulatov, J. Chang, J. Li and S. Yip, Periodic image effects in dislocation modelling, Philos. Mag. 83 (2003), pp. 539–567.10.1080/0141861021000051109
  • W.P. Kuykendall and W. Cai, Conditional convergence in two-dimensional dislocation dynamics, Model. Simul. Mater. Sci. Eng. 21 (2013), p. 055003.10.1088/0965-0393/21/5/055003
  • S.S. Shishvan, S. Mohammadi, M. Rahimian and E. Van der Giessen, Plane-strain discrete dislocation plasticity incorporating anisotropic elasticity, Int. J. Solids Struct. 48 (2011), pp. 374–387.10.1016/j.ijsolstr.2010.10.010
  • D.J. Bacon, D.M. Barnett and R.O. Scattergood, Anisotropic continuum theory of lattice defects, Prog. Mater. Sci. 23 (1980), pp. 51–262.10.1016/0079-6425(80)90007-9
  • J.P. Hirth and J. Lothe, Theory of Dislocations, 2nd ed., Wiley, New York, 1982.
  • S.S. Shishvan and E. Van der Giessen, Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity: I. Formulation and crack growth, Model. Simul. Mater. Sci. Eng. 21 (2013), p. 065006.10.1088/0965-0393/21/6/065006
  • S.S. Shishvan and E. Van der Giessen, Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity: II. Stationary crack tip fields, Model. Simul. Mater. Sci. Eng. 21 (2013), p. 065007.10.1088/0965-0393/21/6/065007
  • N. Hansen, Hall-Petch relation and boundary strengthening, Scrip. Mater. 51 (2004), pp. 801–806.10.1016/j.scriptamat.2004.06.002
  • S.B. Biner and J.R. Morris, A two-dimensional discrete dislocation simulation of the effect of grain size on strengthening behaviour, Model. Simul. Mater. Sci. Eng. 10 (2002), pp. 617–635.10.1088/0965-0393/10/6/303
  • S.B. Biner and J.R. Morris, The effects of grain size and dislocation source density on the strengthening behaviour of polycrystals: A two-dimensional discrete dislocation simulation, Philos. Mag. 83 (2003), pp. 3677–3690.10.1080/14786430310001599414
  • D.S. Balint, V.S. Deshpande, E. Van der Giessen and A. Needleman, A discrete dislocation plasticity analysis of grain-size strengthening, Mater. Sci. Eng.: A 400–401 (2005), pp. 186–190.10.1016/j.msea.2005.02.082
  • D.S. Balint, V.S. Deshpande, E. Van der Giessen and A. Needleman, Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals, Int. J. Plast. 24 (2008), pp. 2149–2172.10.1016/j.ijplas.2007.08.005
  • S. Lefebvre, B. Devincre and T. Hoc, Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics, J. Mech. Phys. Solids 55 (2007), pp. 788–802.10.1016/j.jmps.2006.10.002
  • S.S. Shishvan and E. Van der Giessen, Distribution of dislocation source length and the size dependent yield strength in freestanding thin films, J. Mech. Phys. Solids 58 (2010), pp. 678–695.10.1016/j.jmps.2010.02.011
  • J.R. Rice, Tensile crack tip fields in elastic-ideally plastic crystals, Mech. Mater. 6 (1987), pp. 317–335.10.1016/0167-6636(87)90030-5
  • J.W. Kysar, Y.X. Gan, T.L. Morse, X. Chen and M.E. Jones, High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities, J. Mech. Phys. Solids 55 (2007), pp. 1554–1573.10.1016/j.jmps.2006.09.009
  • Y. Wang, J.W. Kysar, S. Vukelic and Y.L. Yao, Spatially resolved characterization of geometrically necessary dislocation dependent deformation in microscale laser shock peening, J. Manuf. Sci. Eng. 131 (2009), pp. 041014-1–041014-9.
  • M.P. O’Day and W.P. Curtin, A superposition framework for discrete dislocation plasticity, J. Appl. Mech. 71 (2004) pp. 805–815.10.1115/1.1794167
  • R.W. Armstrong, 60 years of Hall-Petch: Past to present nano-scale connections, Mater. Trans. 55 (2014), pp. 2–12.10.2320/matertrans.MA201302
  • J.D. Embury, Strengthening by dislocation substructures, in Strengthening Methods in Crystals, A. Kell, and R.B. Nicholson, eds., Applied Sciences, London, 1971, pp. 331–402.
  • Z. Gan, Y. He, D. Liu, Z. Bo and L. Shen, Hall-Petch effect and strain gradient effect in the torsion of thin gold wires, Scrip. Mater. 87 (2014), pp. 41–44.10.1016/j.scriptamat.2014.05.011
  • L.B.W. Jolley, Summation of Series, 2nd ed., Dover., New York, 1961.
  • M. Abramowitz and I.A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 9th ed., Dover, New York, 1970.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.