تأثیر چگالی نابجایی‌ها بر نمودار حد شکل‌دهی پیش‌بینی‌شده به روش پلاستیسیته‌ بلوره‌ای

[1]    W. Lee, Y. Chen, Simulation of microindentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity, International Journal of Plasticity, 26(10) (2010) 1527-1540.

[2]    G.I. Taylor, The mechanism of plastic deformation of crystals. Part I-Theoretical, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 145(855) (1934) 326.783

[3]    K.S. Havner, A.H. Shalaby, A simple mathematical theory of finite distortional latent hardening in single crystals, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 358(1692) (1977) 47-70.

[4]    R. Peirce, R.J. Asaro, A. Needleman, An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metallurgica, 30(6) (1982) 1087-1119.

[5]    R.J. Asaro, Micromechanics of crystals and polycrystals, in:  Advances In Applied Mechanics, Elsevier, 1983, pp. 1-115.

[6]    T.Y. Wu, J.L. Bassani, C. Laird, Latent hardening in single crystals-I. Theory and experiments, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 435 (1991) 1-19.

[7]    J.L. Bassani, T.Y. Wu, Latent hardening in single crystals. II. Analytical characterization and predictions, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 435(1893) (1991) 2141.

[8]    S.R. Kalidindi, C.A. Bronkhorst, L. Anand, Crystallographic texture evolution in bulk deformation processing of FCC metals, Journal of the Mechanics and Physics of Solids, 40(3) (1992) 537-569.

[9]    J. Friedel, CXXX.On the linear work hardening mate of face-centred cubic single crystals, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 46(382) (1955) 1169-1186.

[10]A. Seeger, CXXXII. The generation of lattice defects by moving dislocations, and its application to the temperature dependence of the flow-stress of FCC crystals, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 46(382) (1955) 11941217.

[11]A. Seeger, J. Diehl, S. Mader, H. Rebstock, Work-hardening and work-softening of facecentred cubic metal crystals Philosophical Magazine, 2(5) (1957) 323-350.

[12]P. Hirsch, T. Mitchell, Stage II work hardening in crystals, Canadian Journal of Physics, 45(2) (1967) 663-706.

[13]F.R.N. Nabarro, Work hardening and dynamical recovery of FCC metals in multiple glide, Acta metallurgica, 37(6) (1989) 1521-1546.

[14]D.K. Wilsdorf, The theory of dislocation-based crystal plasticity, Philosophical Magazine A, 79(4) (1999) 955-1008.

[15]K.M. Davoudi, J.J. Vlassak, Dislocation evolution during plastic deformation: Equations vs. discrete dislocation dynamics study, Journal of Applied Physics 123(8) (2018).

[16]H. Mecking, U.F. Kocks, Kinetics of flow and strain-hardening, Acta Metallurgica 29(11) (1981) 1865-1875.

[17]Y. Estrin, H. Mecking, A unified phenomenological description of work hardening and creep based on one-parameter models, Acta metallurgica, 32(1) (1984) 57-70.

[18]Y. Estrin, Dislocation-density-related constitutive modeling, Unified constitutive laws of plastic deformation, 1 (1996) 69-106.

[19]P.D. Ispánovity, I. Groma, G. Györgyi, F.F. Csikor, D. Weygand, Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution, Physical review letters, 105(8) (2010) 085503.

[20]P.D. Ispánovity, Á. Hegyi, I. Groma, G. Györgyi, K. Ratter, D. Weygand, Average yielding and weakest link statistics in micronscale plasticity, Acta Materialia, 61(16) (2013) 6234-6245.

[21]K.M. Davoudi, L. Nicola, J.J. Vlassak, Dislocation climb in two-dimensional discrete dislocation dynamics, Journal of Applied Physics 111(10) (2012).

[22]S.S. Shishvan, L. Nicola, E. Van der Giessen, Bauschinger effect in unpassivated freestanding thin films, Journal of Applied Physics, 107(9) (2010) 093529.

[23]K. Danas, V.S. Deshpande, Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations, Modelling Simul. Mater.Science and Engineering, 21(4) (2013).

[24]D. Li, H. Zbib, X. Sun, M. Khaleel, Predicting plastic flow and irradiation hardening of iron single crystal with mechanism-based continuum dislocation dynamics, International Journal of Plasticity, 52 (2014) 3-17.

[25]K.M. Davoudi, L. Nicola, J.J. Vlassak, Bauschinger effect in thin metal films: Discrete dislocation dynamics study, Journal of Applied Physics 115(1) (2014).

[26]A. Roos, J.T.D. Hosson, E.V.d. Giessen, High-speed dislocations in high strain-rate deformations, Computational Materials Science 20(1) (2001) 19-27.

[27]D. Gómez-García, B. Devincre, L.P. Kubin, Dislocation patterns and the similitude principle: 2.5 D mesoscale simulations, Physical review letters, 96(12) (2006).

[28]P.J. Guruprasad, A.A. Benzerga, Size effects under homogeneous deformation of single crystals: a discrete dislocation analysis, Journal of the Mechanics and Physics of Solids, 56(1) (2008) 132-156.

[29]R. Madec, B. Devincre, L.P. Kubin, From dislocation junctions to forest hardening, Physical review letters, 89(25) (2002) 255508.

[30]R. Kumar, L. Nicola, E.V.d. Giessen, Density of grain boundaries and plasticity size effects: A discrete dislocation dynamics study, Materials Science and Engineering, 527(1-2) (2009) 7-15.

[31]E. Van der Giessen, Discrete Dislocation Plasticity Analysis of Cracks and Fracture, in: Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics, Springer, 2010, pp. 185-212.

[32]A. Vattré, B. Devincre, F. Feyel, R. Gatti, S. Groh, O. Jamond, A. Roos, Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: the discrete-continuous model revisited, Journal of the Mechanics and Physics of Solids 63 (2014) 491–505.

[33]L. P. Kubin and G. Canova, The modelling of dislocation patterns, Scr. Metall. Mater. 27(8) (1992) 957–962

[34]M. Sauzay and L. P. Kubin, Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals, Progress in Materials Science56(6), (2011(725–784.

[35]M. Hillert and J. Ågren, Extremum principles for irreversible processes, Acta Mater. 54(8), (2006(2063–2066.

[36]U. F. Kocks, A. S. Argon, and M. F. Ashby, Thermodynamics and Kinetics of Slip ( Pergamon Press Ltd., 1975(

[37]H. Mecking and U. F. Kocks, Kinetics of flow and strain-hardening, Acta Metall. 29, (1981( 1865–1875.

[38]Y. Estrin and H. Mecking, A unified phenomenological description of work hardening and creep based on one-parameter models, Acta Metall. 32(I), (1984(57–70.

[39]D. Walgraef and E. C. Aifantis, On the formation and stability of dislocation patterns -I: One-dimensional considerations, International Journal of Engineering Science. 23, (1985( 1351–1358.

[40]H.A. Askari, A continuum dislocation dynamics framework for plasticity of polycrystalline materials, 2014.

[41]A. Acharya, J.L. Bassani, On non-local flow theories that preserve the classical structure of incremental boundary value problems, in: IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials, Springer, Dordrecht, 1996, pp. 3-9.

[42]C.S.Han, et al., Mechanism-based strain gradient crystal plasticity. II. Analysis. Journal of the Mechanics and Physics of Solids, 53)2005b( 1204–1222

[43]R.T. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 1(1) (1952) 19-30.

[44]S. Stören, J.R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 23(6) (1975) 421-441.

[45]A. Petek, T. Pepelnjak, An improved method for determining a forming limit diagram in the digital environment, Strojniski Vestnik, 51(6) (2005) 330-345.

[46]T. Pepelnjak, A. Petek, K. Kuzman, Analyses of the forming limit diagram in digital environment, Trans Tech Publications, 2005.

[47]A. Zajkani, A. Bandizaki, An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets, International Journal of Mechanical Sciences, 133 (2017) 794-803.

[48]A. Zajkani, A. Bandizaki, A path-dependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects, The International Journal of Advanced Manufacturing Technology, 95(1-4) (2018) 759-774.

[49]M.B. Bettaieb, F. Abed-Meraim, Investigation of localized necking in substrate-supported metal layers: comparison of bifurcation and imperfection analyses, International Journal of Plasticity, 65 (2015) 168-190.

[50]V. Tvergaard, K.L. Nielsen, Relations between a micro-mechanical model and a damage model for ductile failure in shear, Journal of the Mechanics and Physics of Solids, 58(9) (2010) 1243-1252.

[51]Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences, 9(9) (1967) 609-620.

[52]T. Ohashi, M. Kawamukai, H.M. Zbib, A multiscale approach for modeling scaledependent yield stress in polycrystalline metals, International Journal of Plasticity, 23(5) (2007) .419-798

[53]N. Hansen, Hall–Petch relation and boundary strengthening, Scripta Materialia, 51(8) (2004) .608–108

[54]M.J. Serenelli, M.A. Bertinetti, J.W. Signorelli, Study of limit strains for FCC and BCC sheet metal using polycrystal plasticity, International Journal of Solids and Structures, 48(7-8) (2011) 1109–1119.

[55]R.E. Reed-Hill, and W.D. Robertson, Pyramidal slip in magnesium. Transaction of Metallurgical Soc.. AIME, 212(1958).

[56]I. Robertson, , The effect of hydrogen on dislocation dynamics. Engineering fracture mechanics, 68(6) (2001)671-692

[57]B.C. Wonsiewicz, and W.A. Backofen, Independent slip systems and ductility of hexagonal polycrystals. Transaction of Metallurgical Soc. AIME, 239, (1967)14221433.

[58]H.Yoshinaga, and R.Horiuchi, Deformation mechanisms in magnesium single crystals compressed in the direction parallel to hexagonal axis. Transactions of the Japan Institute of Metals, 4(1) (1963)1-8.

[59]T.Obara, H., Yoshinga, and S.Morozumi, Æ-1123æ slip system in magnesium. Acta Metall, .358-548.)3791( 12

[60]F. Lavrentev, Y.A. Pokhil, Effect of „Forest” Dislocations in the {11-22}<11-23>system on hardening in Mg single crystals under basal slip, physica status solidi (a), 32(1) (1975) 227-232.

[61]A. Alankar, L.N. Mastorakos, D.P. Field, H.M. Zbib, Determination of dislocation interaction strengths using discrete dislocation dynamics of curved dislocations, Journal of engineering materials and technology, 134(2) (2012).

[62]F. Lavrentev, The type of dislocation interaction as the factor determining work hardening, Materials Science and Engineering, 46(2) (1980) 191-208.

[63]E. Nes, K. Marthinsen, Y. Brechet, On the mechanisms of dynamic recovery, Scripta Materialia 47(9) (2002) 607–611.

[64]R. Hill, J.R. Rice, Constitutive analysis of elastic-plastic crystals at arbitrary strain, Journal of the Mechanics and Physics of Solids, 20(6) (1972) 401-413.

[65]Y. Huang, A user-material subroutine incroporating single crystal plasticity in the ABAQUS finite element program, Harvard University, Cambridge, 1991.