Micromorphic crystal plasticity versus discrete dislocation dynamics analysis of multilayer pile-up hardening in a narrow channel
详细信息    查看全文
  • 作者:Hyung-Jun Chang ; Nicolas M. Cordero ; Christophe Déprés…
  • 关键词:Dislocation dynamics ; Strain gradient plasticity ; Crystal plasticity ; Micromorphic continuum ; Dislocation pile ; up ; Field dislocation mechanics ; Kinematic hardening
  • 刊名:Archive of Applied Mechanics (Ingenieur Archiv)
  • 出版年:2016
  • 出版时间:January 2016
  • 年:2016
  • 卷:86
  • 期:1-2
  • 页码:21-38
  • 全文大小:2,614 KB
  • 参考文献:1.Acharya, A., Bassani, J.: Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48, 1565–1595 (2000)CrossRef MathSciNet MATH
    2.Aifantis, E.: On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106, 326–330 (1984)CrossRef
    3.Arsenlis, A., Parks, D.M.: Crystallographic aspects of geometrically-necessary and statistically stored dislocation density. Acta Mater. 47, 1597–1611 (1999)CrossRef
    4.Aslan, O., Cordero, N.M., Gaubert, A., Forest, S.: Micromorphic approach to single crystal plasticity and damage. Int. J. Eng. Sci. 49, 1311–1325 (2011)CrossRef MathSciNet
    5.Bardella, L., Panteghini, A.: Modelling the torsion of thin metal wires by distortion gradient plasticity. J. Mech. Phys. Solids 78, 467–492 (2015)CrossRef MathSciNet
    6.Bardella, L., Segurado, J., Panteghini, A., Llorca, J.: Latent hardening size effects in small-scale plasticity. Modell. Simul. Mater. Sci. Eng. 21(055), 009 (2013)
    7.Baskaran, R., Akarapu, S., Mesarovic, S., Zbib, H.: Energies and distributions of dislocations in stacked pile-ups. Int. J. Solids Struct. 47, 1144–1153 (2010a)CrossRef MATH
    8.Baskaran, R., Akarapu, S., Mesarovic, S.D., Zbib, H.M.: Energies and distributions of dislocations in stacked pile-ups. Int. J. Solids Struct. 47, 1144–1153 (2010b)CrossRef MATH
    9.Bassani, J., Needleman, A., Van der Giessen, E.: Plastic flow in a composite: a comparison of nonlocal continuum and discrete dislocation predictions. Int. J. Solids Struct. 38, 833–853 (2001)CrossRef MATH
    10.Berbenni, S., Berveiller, M., Richeton, T.: Intra-granular plastic slip heterogeneities: discrete vs. mean field approaches. Int. J. Solids Struct. 45, 4147–4172 (2008)CrossRef MATH
    11.Bittencourt, E., Needleman, A., ME, G., Van der Giessen, E.: A comparison of nonlocal continuum and discrete dislocation plasticity predictions. J. Mech. Phys. Solids 51, 281–310 (2003)CrossRef MathSciNet MATH
    12.Busso, E., Meissonnier, F., O’Dowd, N.: Gradient-dependent deformation of two-phase single crystals. J. Mech. Phys. Solids 48, 2333–2361 (2000)CrossRef MATH
    13.Chang, H.J., Gaubert, A., Fivel, M., Berbenni, S., Bouaziz, O., Forest, S.: Analysis of particle induced dislocation structures using three-dimensional dislocation dynamics and strain gradient plasticity. Comput. Mater. Sci. 52, 33–39 (2012)CrossRef
    14.Chokshi, A., Rosen, A., Karch, J., Gleiter, H.: On the validity of the Hall–Petch relationship in nanocrystalline materials. Scr. Metall. 23, 1679–1683 (1989)CrossRef
    15.Chou, Y., Li, J.: Theory of dislocation pile-ups. In: Mura, T. (ed.) Mathematical Theory of Dislocations, pp. 116–177. ASME, New York (1969)
    16.Cleveringa, H., Van der Giessen, E., Needleman, A.: Comparison of discrete dislocation and continuum plasticity predictions for a composite material. Acta Mater. 45, 3163–3179 (1997)CrossRef
    17.Cleveringa, H., Van der Giessen, E., Needleman, A.: Discrete dislocation simulations and size dependent hardening in single slip. J. Phys. IV 8, Pr4-83–Pr4-92 (1998)
    18.Cleveringa, H., Van der Giessen, E., Needleman, A.: A discrete dislocation analysis of residual stresses in a composite material. Philos. Mag. A 79, 863–920 (1999)CrossRef
    19.Collard, C., Favier, V., Berbenni, S., Berveiller, M.: Role of discrete intra-granular slip bands on the strain-hardening of polycrystals. Int. J. Plast. 26, 310–328 (2010)CrossRef MATH
    20.Cordero, N.M., Gaubert, A., Forest, S., Busso, E., Gallerneau, F., Kruch, S.: Size effects in generalised continuum crystal plasticity for two-phase laminates. J. Mech. Phys. Solids 58, 1963–1994 (2010)CrossRef MathSciNet MATH
    21.Cordero, N.M., Forest, S., Busso, E.P.: Generalised continuum modelling of grain size effects in polycrystals. C. R. Mec. 340, 261–274 (2012a)CrossRef
    22.Cordero, N.M., Forest, S., Busso, E.P., Berbenni, S., Cherkaoui, M.: Grain size effects on plastic strain and dislocation density tensor fields in metal polycrystals. Comput. Mater. Sci. 52, 7–13 (2012b)CrossRef
    23.Déprés, C.: Modélisation physique des stades précurseurs de l’endommagement en fatigue dans l’acier inoxydable 316L. Ph.D. thesis, Grenoble INP, France (2004)
    24.Déprés, C., Robertson, C., Fivel, M.: Low-strain fatigue in 316l steel surface grains: a three-dimensional discrete dislocation dynamics modeling of the early cycles. Philos. Mag. 84, 2257–2275 (2004)CrossRef
    25.Déprés, C., Reddy, G., Robertson, C., Fivel, M.: An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation. Philos. Mag. 94, 4115–4137 (2014)CrossRef
    26.Eshelby, J., Frank, F., Nabarro, F.: The equilibrium of linear arrays of dislocations. Philos. Mag. 7, 351–364 (1951)CrossRef MathSciNet
    27.Déprés, C., Fivel, M.: An easy implementation of displacement calculations in 3D discrete dislocation dynamics codes. Philos. Mag. 94, 3206–3214 (2014)CrossRef
    28.Fivel, M., Tabourot, L., Rauch, E., Canova, G.: Identification through mesoscopic simulations of macroscopic parameters of physically based constitutive equations for the plastic behaviour of fcc single crystals. J. Phys. IV 8, 151–158 (1998)
    29.Fleck, N., Hutchinson, J.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825–1857 (1993)CrossRef MathSciNet MATH
    30.Fleck, N., Hutchinson, J.: Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361 (1997)CrossRef
    31.Forest, S.: Questioning size effects as predicted by strain gradient plasticity. J. Mech. Behav. Mater. 22, 101–110 (2013)CrossRef
    32.Forest, S., Guéninchault, N.: Inspection of free energy functions in gradient crystal plasticity. Acta. Mech. Sin. 29, 763–772 (2013)CrossRef MathSciNet
    33.Forest, S., Sedláček, R.: Plastic slip distribution in two-phase laminate microstructures: dislocation-based vs. generalized-continuum approaches. Philos. Mag. A 83, 245–276 (2003)CrossRef
    34.Gao, H., Huang, Y., Nix, W., Hutchinson, J.: Mechanism-based strain gradient plasticity—I. theory. J. Mech. Phys. Solids 47, 1239–1263 (1999)CrossRef MathSciNet MATH
    35.Geers, M., Peerlings, R., Peletier, M., Scardia, L.: Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Ration. Mech. Anal. 209, 495–539 (2013)CrossRef MathSciNet MATH
    36.Ghoniem, N., Sun, L.: Fast-sum method for the elastic field of three-dimensional dislocation ensembles. Phys. Rev. B 60, 128–140 (1999)CrossRef
    37.Gurtin, M.: On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989–1036 (2000)CrossRef MathSciNet MATH
    38.Gurtin, M.: A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5–32 (2002)CrossRef MathSciNet MATH
    39.Hall, E.: The deformation and ageing of mild steel: III discussion of results. Proc. Phys. Soc. B 64, 747–753 (1951)CrossRef
    40.Herzer, G.: Nanocrystalline soft-magnetic materials. Phys. Scr. T49A, 307–314 (1993)CrossRef
    41.Kim, G., Fivel, M., Lee, H.J., Shin, C., Han, H., Chang, H., Oh, K.: A discrete dislocation dynamics modeling for thermal fatigue of preferred oriented copper via patterns. Scr. Mater. 63, 788–791 (2010)CrossRef
    42.Kochmann, D., Le, K.: Dislocation pile-ups in bicrystals within continuum dislocation theory. Int. J. Plast. 24, 2125–2147 (2008)CrossRef MATH
    43.Kooiman, M., Hütter, M., Geers, M.: Microscopically derived free energy of dislocations. J. Mech. Phys. Solids 78, 186–209 (2015)CrossRef MathSciNet
    44.Kubin, L., Canova, G., Condat, M., Devincre, B., Pontikis, V., Bréchet, Y.: Dislocation microstructures and plastic flow: a 3D simulation. Solid State Phenom. 23 & 24, 455–472 (1992)CrossRef
    45.Lefebvre, S., Devincre, B., Hoc, T.: Yield stress strengthening in ultrafine-grained metals: a two-dimensional simulation of dislocation dynamics. J. Mech. Phys. Solids 55, 788–802 (2007)CrossRef MATH
    46.Madec, R., Devincre, B., Kubin, L., Hoc, T., Rodney, D.: The role of collinear interaction in dislocation-induced hardening. Science 301, 1879–1882 (2003)CrossRef
    47.Mesarovic, S., Baskaran, R., Panchenko, A.: Thermodynamic coarsening of dislocation mechanics and the size-dependent continuum crystal plasticity. J. Mech. Phys. Solids 58, 311–329 (2010)CrossRef MathSciNet MATH
    48.Mesarovic, S., Forest, S., Jaric, J.: Size-dependent energy in crystal plasticity and continuum dislocation models. Proc. R. Soc. A 471(20140), 868 (2015)MathSciNet
    49.Mughrabi, H.: Dislocation wall and cell structures and long-rang internal stresses in deformed metal crystals. Acta Metall. 31, 1367–1379 (1983)CrossRef
    50.Nye, J.: Some geometrical relations in dislocated crystals. Acta Metall. 1, 153–162 (1953)CrossRef
    51.Ohno, N., Okumura, D.: Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations. J. Mech. Phys. Solids 55, 1879–1898 (2007)CrossRef MathSciNet MATH
    52.Ortiz, M., Repetto, E., Stainier, L.: A theory of subgrain dislocation structures. J. Mech. Phys. Solids 48, 2077–2114 (2000)CrossRef MathSciNet MATH
    53.Petch, N.: The cleavage strength of polycrystals. J. Iron Steel Inst. 174, 25–28 (1953)
    54.Richeton, T., Berbenni, S.: Effect of heterogeneous elasticity coupled to plasticity on stresses and lattice rotation in bicrystals: a Field Dislocation Mechanics viewpoint. Eur. J. Mech. A Solids 37, 231–247 (2013)CrossRef MathSciNet
    55.Roy, A., Acharya, A.: Finite element approximation of field dislocation mechanics. J. Mech. Phys. Solids 53, 143–170 (2005)CrossRef MATH
    56.Scardia, L., Peerlings, R., Peletier, M., Geers, M.: Mechanics of dislocation pile-ups: a unification of scaling regimes. J. Mech. Phys. Solids 70, 42–61 (2014)CrossRef MathSciNet
    57.Schwartz, K.: Simulation of dislocations on the mesoscale: I. Methods and example. J. Appl. Phys. 85, 108–119 (1999)CrossRef
    58.Scouwenaars, R., Seefeldt, M., Houtte, P.: The stress field of an array of parallel dislocation pile-ups: implications for grain boundary hardening and excess dislocation distributions. Acta Mater. 58, 4344–4353 (2010)CrossRef
    59.Shin, C.S., Fivel, M.C., Verdier, M., Oh, K.H.: Dislocation-impenetrable precipitate interaction: a three-dimensional discrete dislocation dynamics analysis. Philos. Mag. 83, 3691–3704 (2003)CrossRef
    60.Shu, J., Fleck, N., Van der Giessen, E., Needleman, A.: Boundary layers in constrained plastic flow: comparison of non local and discrete dislocation plasticity. J. Mech. Phys. Solids 49, 1361–1395 (2001)CrossRef MATH
    61.Šiška, F., Weygand, D., Forest, S., Gumbsch, P.: Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity. Comput. Mater. Sci. 45, 793–799 (2009)CrossRef
    62.Svendsen, B.: Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations. J. Mech. Phys. Solids 50, 1297–1329 (2002)CrossRef MathSciNet MATH
    63.Taupin, V., Berbenni, S., Fressengeas, C., Bouaziz, O.: On particle size effects: an internal length mean field approach using field dislocation mechanics. Acta Mater. 58, 5532–5544 (2010)CrossRef
    64.Taupin, V., Berbenni, S., Fressengeas, C.: Size effects on the hardening of channel-type microstructures: a field dislocation mechanics-based approach. Acta Mater. 60, 664–673 (2012)CrossRef
    65.Upadhyay, M., Capolungo, L., Taupin, V., Fressengeas, C.: Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations, disclinations and G-disclinations. Philos. Mag. 93, 794–832 (2012)CrossRef
    66.Weygand, D., Friedman, L., Van der Giessen, E., Needleman, A.: Discrete dislocation modeling in three-dimensional confined volumes. Mater. Sci. Eng. A 309–310, 420–424 (2001)CrossRef
    67.Wulfinghoff, S., Böhlke, T.: Equivalent plastic strain gradient enhancement of single crystal plasticity: theory and numerics. Proc. R. Soc. A 468, 2682–2703 (2012)CrossRef
    68.Wulfinghoff, S., Bayerschen, E., Böhlke, T.: A gradient plasticity grain boundary yield theory. Int. J. Plast. 51, 33–46 (2013)CrossRef
    69.Wulfinghoff, S., Forest, S., Böhlke, T.: Logarithmic and rank-one defect energies in gradient crystal plasticity analytical and numerical 1D solutions. J. Mech. Phys. Solids 79, 1–20 (2015)CrossRef MathSciNet
    70.Yefimov, S., Van der Giessen, E.: Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations. Int. J. Solids Struct. 42, 3375–3394 (2005)CrossRef MATH
    71.Yefimov, S., Groma, I., Van der Giessen, E.: A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations. J. Mech. Phys. Solids 52, 279–300 (2004)CrossRef MathSciNet MATH
    72.Zbib, H., Rhee, M., Hirth, J.: On plastic deformation and the dynamics of 3D dislocations. Int. J. Mech. Sci. 40, 113–127 (1998)CrossRef MATH
  • 作者单位:Hyung-Jun Chang (1)
    Nicolas M. Cordero (1)
    Christophe Déprés (2)
    Marc Fivel (3)
    Samuel Forest (1)

    1. MINES ParisTech, Centre des Matériaux, UMR CNRS 7633, BP 87, 91003, Evry, France
    2. SYMME, Univ. Savoie Mt Blanc, 74000, Annecy, France
    3. SIMAP GPM2, CNRS, Univ Grenoble Alpes, 38000, Grenoble, France
  • 刊物类别:Engineering
  • 刊物主题:Theoretical and Applied Mechanics
    Mechanics
    Complexity
    Fluids
    Thermodynamics
    Systems and Information Theory in Engineering
  • 出版者:Springer Berlin / Heidelberg
  • ISSN:1432-0681
文摘
Size effects in the mechanical behavior of multilayer pile-ups embedded in channel microstructures are investigated in terms of work-hardening, plastic slip and geometrically necessary dislocations (GND) distributions. The mechanical responses with various channel sizes are computed by three-dimensional discrete dislocation dynamics (DDD), micromorphic crystal plasticity (Microcurl) and field dislocation mechanics (FDM). The analysis is first limited to single slip with a slip plane perpendicular to the channel walls. In DDD simulations, it is found that the overall work-hardening is strongly dependent on distance between neighbor slip layers. The size dependence disappears when the neighbor layers are close enough to interact with each other. It is confirmed by direct comparison between DDD simulations and two analytical expressions derived from simplified model of multilayer pile-ups. Distributions of slip and GNDs are presented and analyzed for various channel sizes. The cases of inclined slip plane and of double slip systems in a channel are also considered and investigated. The two alternative crystal plasticity theories, Microcurl and FDM, are then found to reproduce the results of DDD. In particular, quantitative correspondence is found between the Microcurl and DDD results.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700