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A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales. (English) Zbl 1235.74013

Summary: Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.

MSC:

74C20 Large-strain, rate-dependent theories of plasticity
74E15 Crystalline structure
74A60 Micromechanical theories
74S05 Finite element methods applied to problems in solid mechanics
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[1] Aoyagi, Y.; Shizawa, K.: Multiscale crystal plasticity modeling based on geometrically necessary crystal defects and simulation on fine-graining for polycrystal, Int. J. Plasticity 23, 1022-1040 (2007) · Zbl 1115.74011
[2] Benzerga, A. A.: An analysis of exhaustion hardening in micron-scale plasticity, Int. J. Plasticity 24, 1128-1157 (2008) · Zbl 1138.74010
[3] Bulatov, V. V.; Cai, W.: Computer simulations of dislocations, (2006) · Zbl 1119.74001
[4] Cai, W.; Arsenlis, A.; Weinberger, C. R.; Bulatov, V. V.: A non-singular continuum theory of dislocations, J. mech. Phys. solids 54, 561-587 (2006) · Zbl 1120.74329
[5] Counts, W. A.; Braginsky, M. V.; Battaile, C. C.; Holm, E. A.: Predicting the Hall – petch effect in fcc metals using non-local crystal plasticity, Int. J. Plasticity 24, 1243-1263 (2008) · Zbl 1154.74007
[6] Deshpande, V. S.; Needleman, A.; Van Der Giessen, E.: Discrete dislocation plasticity analysis of static friction, Acta mater. 52, 3135-3149 (2004)
[7] Devincre, B.; Kubin, L. P.: Mesoscopic simulations of plastic deformation, Mater. sci. Eng. A 309 – 310, 211-219 (2001)
[8] Dimiduk, D. M.; Woodward, C.; Lesar, R.; Uchic, M. D.: Scale-free intermittent flow in crystal plasticity, Science 312, 1188-1190 (2006)
[9] Fivel, M. C.; Robertson, C. F.; Canova, G. R.; Boulanger, L.: Three-dimensional modeling of indent-induced plastic zone at a mesoscale, Acta mater. 46, 6183-6194 (1998)
[10] Greer, J. R.; Oliver, W. C.; Nix, W. D.: Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta mater. 53, 1821-1830 (2005)
[11] Guo, Y.; Zhuang, Z.; Li, X. Y.; Chen, Z.: An investigation of the combined size and rate effects on the mechanical responses of fcc metals, Int. J. Solids struct. 44, 1180-1195 (2007) · Zbl 1144.74006
[12] Han, C. -S.; Hartmaier, A.; Gao, H.; Huang, Y.; Nix, W. D.: Discrete dislocation dynamics simulations of surfaces induced size effects in plasticity, Mater. sci. Eng. A 415, 224-233 (2006)
[13] Han, C. -S.; Ma, A.; Roters, F.; Raabe, D.: A finite element approach with patch projection for strain gradient plasticity formulations, Int. J. Plasticity 23, 690-710 (2007) · Zbl 1190.74025
[14] Hemker, K. J.; Nix, W. D.: Seeing is believing, Nat. mater. 7, 97-98 (2008)
[15] Hirth, J. P.; Lothe, J.: Theory of dislocations, (1982)
[16] Kreuzer, H. G. M.; Pippan, R.: Discrete dislocation simulation of nanoindentation: the effect of moving conditions and indenter shape, Mater. sci. Eng. A 387, 254-256 (2004) · Zbl 1067.74549
[17] Kuchnicki, S. N.; Radovitzky, R. A.; Cuitiño, A. M.: An explicit formulation for multi-scale modeling of bcc metals, Int. J. Plasticity 24, 2173-2191 (2008) · Zbl 1421.74024
[18] Lemarchand, C.; Devincre, B.; Kubin, L. P.: Homogenization method for a discrete-continuum simulation of dislocation dynamics, J. mech. Phys. solids 49, 1969-1982 (2001) · Zbl 0998.74063
[19] Liu, X. H.; Schwarz, K. W.: Modeling of dislocations intersecting a free surface, Model. simul. Mater. sci. Eng. 13, 1233-1247 (2005)
[20] Liu, Z. L.; You, X. C.; Zhuang, Z.: A mesoscale investigation of strain rate effect on dynamic deformation of single-crystal copper, Int. J. Solids struct. 45, 3674-3687 (2008) · Zbl 1169.74363
[21] Meyers, M. A.: Dynamic behavior of materials, (1994) · Zbl 0893.73002
[22] Nicola, L.; Bower, A. F.; Kim, K. -S.; Needleman, A.; Van Der Giessen, E.: Surface versus bulk nucleation of dislocations during contact, J. mech. Phys. solids 55, 1120-1144 (2007) · Zbl 1178.74126
[23] Ohashi, T.; Kawamukai, M.; Zbib, H.: A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals, Int. J. Plasticity 23, 897-914 (2007) · Zbl 1115.74013
[24] Peirce, D.; Asaro, R. J.; Needleman, A.: Material rate dependence and localized deformation in crystalline solid, Acta metall. 31, 1951-1976 (1983)
[25] Rabkin, E.; Nam, H. S.; Srolovitz, D. J.: Atomistic simulation of the deformation of gold nanopillars, Acta mater. 55, 2085-2099 (2007)
[26] Rhee, M.; Zbib, H. M.; Hirth, J. P.; Huang, H.; Rubia, T. D. D.L.: Models for long/short range interactions in 3D dislocation simulation, Model. simul. Mater. sci. Eng. 6, 467-492 (1998)
[27] Schwarz, K. W.: Simulation of dislocations on the mesoscopic scale. I. methods and examples, J. appl. Phys. 85, 108-119 (1999)
[28] Shan, Z. W.; Mishra, R.; Asif, S. A. Syed; Warren, O. L.; Minor, A. M.: Mechanical annealing and source-limited deformation in submicrometre-diameter ni crystals, Nat. mater. 7, 115-119 (2008)
[29] Suo, Z.; Hutchinson, J. W.: Steady-state cracking in brittle substrates beneath adherent films, Int. J. Solids struct. 25, 1337-1353 (1989)
[30] Uchic, M. D.; Dimiduk, D. M.; Florando, J. N.; Nix, W. D.: Sample dimensions influence strength and crystal plasticity, Science 305, 986-989 (2004)
[31] Van Der Giessen, E.; Needleman, A.: Discrete dislocation plasticity: a simple planar model, Mater. sci. Eng. 3, 689-735 (1995)
[32] Wang, J.; Shrotriya, P.; Yu, H. H.; Kim, K. -S.: Experimental measurements of surface residual stress caused by nano-scale contact of rough surfaces, Mater. res. Soc. symp. Proc. 795, U9.9 (2004)
[33] Widjaja, A.; Van Der Giessen, E.; Needleman, A.: Discrete dislocation modelling of submicron indentation, Mater. sci. Eng. A 400, 456-459 (2005)
[34] Yu, H. H.; Shrotriya, P.; Gao, Y. F.; Kim, K. -S.: Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation, J. mech. Phys. solids 55, 489-516 (2007) · Zbl 1207.74017
[35] Zaiser, M.; Aifantis, E. C.: Randomness and slip avalanches in gradient plasticity, Int. J. Plasticity 22, 1432-1455 (2006) · Zbl 1331.74035
[36] Zaiser, M.: Scale invariance in plastic flow of crystalline solids, Adv. phys. 55, 185-245 (2006)
[37] Zbib, H. M.; Rhee, M.; Hirth, J. P.: On plastic deformation and the dynamics of 3D dislocations, Int. J. Mech. sci. 40, 113-127 (1998) · Zbl 0909.73074
[38] Zbib, H. M.; De La Rubia, T. Diaz: A multi-scale model of plasticity, Int. J. Plasticity 18, 1133-1163 (2002) · Zbl 1062.74008
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