An analysis of exhaustion hardening in micron-scale plasticity. (English) Zbl 1138.74010

Summary: The rate-dependent behavior of micron-scale model planar crystals is investigated using the framework of mechanism-based discrete dislocation plasticity. Long-range interactions between dislocations are accounted for through elasticity. Mechanism-based constitutive rules are used to represent the short-range interactions between dislocations, including dislocation multiplication and dislocation escape at free surfaces. Emphasis is laid on circumstances where the deformed samples are not statistically homogeneous. The calculations show that dimensional constraints selectively set the operating dislocation mechanisms, thus giving rise to the phenomenon of exhaustion hardening whereby the applied strain rate is predominantly accommodated by elastic deformation. When conditions are met for this type of hardening to take place, the calculations reproduce some interesting qualitative features of plastic deformation in microcrystals, such as flow intermittency over coarse time-scales and large values of the flow stress with no significant accumulation of dislocation density. In addition, the applied strain rate is varied down to 0.1 s\(^{ - 1}\) and is found to affect the rate of exhaustion hardening.


74C20 Large-strain, rate-dependent theories of plasticity
74E15 Crystalline structure
74A60 Micromechanical theories
Full Text: DOI


[1] Amodeo, R. J.; Ghoniem, N. M.: Dislocation dynamics. I. A proposed methodology for deformation micromechanics, Phys. rev. B 41, 6958-6967 (1990)
[2] Balint, D.S., Deshpande, V.S., Needleman, A., Van der Giessen, E., in press. Discrete dislocation plasticity analysis of the Hall – Petch effect. Int. J. Plasticity, doi:10.1016/j.ijplas.2007.08.005. · Zbl 1120.74615
[3] Benzerga, A. A.; Shaver, N. F.: Scale dependence of mechanical properties of single crystals under uniform deformation, Scripta mater. 54, 1937-1941 (2006)
[4] Benzerga, A. A.; Bréchet, Y.; Needleman, A.; Van Der Giessen, E.: Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics, Model. simul. Mater. sci. Eng. 12, 159-196 (2004)
[5] Biner, S. B.; Morris, J. R.: The effects of grain size and dislocation source density on the strengthening behaviour of polycrystals: a two-dimensional discrete dislocation simulation, Philos. mag. 83, 3677-3690 (2003)
[6] Cleveringa, H. H. M.; Van Der Giessen, E.; Needleman, A.: Comparison of discrete dislocation and continuum plasticity predictions for a composite material, Acta mater. 45, No. 8, 3163-3179 (1997)
[7] Cleveringa, H. H. M.; Van Der Giessen, E.; Needleman, A.: A discrete dislocation analysis of bending, Int. J. Plasticity 15, 837-868 (1999) · Zbl 0976.74048
[8] Deshpande, V. S.; Needleman, A.; Van Der Giessen, E.: A discrete dislocation analysis of near-threshold fatigue crack growth, Acta mater. 49, 3189 (2001) · Zbl 1093.74559
[9] Deshpande, V. S.; Needleman, A.; Van Der Giessen, E.: Finite strain discrete dislocation plasticity, J. mech. Phys. solid 51, 2057-2083 (2003) · Zbl 1041.74504
[10] De Wit, G.; Koehler, J. S.: Interaction of dislocations with an applied stress in anisotropic crystals, Phys. rev. 116, 1113-1120 (1959) · Zbl 0090.39601
[11] Dimiduk, D. M.; Uchic, M. D.; Parthasarathy, T. A.: Size-affected single-slip behavior of pure nickel microcrystals, Acta mater. 53, 4065-4077 (2005)
[12] Foreman, A. J. E.: The bowing of a dislocation segment, Philos. mag. 15, 1011-1021 (1967)
[13] Frank, F. C.; Read, W. T.: Multiplication processes for slow moving dislocations, Phys. rev. 79, 722-723 (1950)
[14] Friedel, J.: LES dislocations, (1956) · Zbl 0123.45205
[15] Sevillano, J. Gil: Flow stress and work hardening, Materials science and technology 6, 19-88 (1993)
[16] Gómez-Garcia, D., Devincre, B., Kubin, L.P., 2000. Forest hardening and boundary conditions in 2D simulations of dislocation dynamics. In: Robertson, I.M., Lassila, D.H., Devincre, B., Phillips, R. (Eds.), Mater. Res. Soc. Symp. Proc. MRS, Warrendale, Pennsylvania.
[17] 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)
[18] Greer, J. R.; Oliver, W. C.; Nix, W. D.: Corrigendum to ”size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients”, Acta mater. 54, 1705 (2006)
[19] Guruprasad, P. J.; Benzerga, A. A.: Size effects under homogeneous deformation of single crystals: a discrete dislocation analysis, J. mech. Phys. solid. 56, 132-156 (2008) · Zbl 1162.74336
[20] Hirth, J. P.; Lothe, J.: Theory of dislocations, (1968)
[21] Kocks, U. F.; Mecking, H.: Physics and phenomenology of strain hardening: the FCC case, Prog. mater. Sci. 48, 171-273 (2003)
[22] Kreuzer, H. G. M.; Pippan, R.: Discrete dislocation simulation of nanoindentation: indentation size effect and the influence of slip band orientation, Acta mater. 55, 3229-3235 (2007)
[23] Kubin, L.P., Canova, G., Condat, M., Devincre, B., Pontikis, V., Bréchet, Y., 1992. Dislocation microstructures and plastic flow: a 3D simulation. In: Martin, J., Kubin, L.P. (Eds.), Nonlinear Phenomena in Materials Science. Sci-Tech, Vaduz, pp. 455 – 472.
[24] Lefebvre, S.; Devincre, B.; Hoc, T.: Yield stress strengthening in ultrafine-grained metals: a two-dimensional simulation of dislocation dynamics, J. mech. Phys. solid 55, 788-802 (2007) · Zbl 1162.74421
[25] Moulin, A.; Condat, M.; Kubin, L. P.: Simulation of franck – Read sources in silicon, Acta mater. 45, 2339-2348 (1997)
[26] Nicola, L.; Van Der Giessen, E.; Needleman, A.: Discrete dislocation analysis of size effects in thin films, J. appl. Phys. 93, 5920-5928 (2003)
[27] Nicola, L.; Van Der Giessen, E.; Needleman, A.: Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity, Philos. mag. 85, 1507-1518 (2005)
[28] O’day, M. P.; Curtin, W. A.: Bimaterial interface fracture: a discrete dislocation model, J. mech. Phys. solid 53, 359-382 (2005) · Zbl 1162.74449
[29] Ohashi, T.; Kawamukai, M.; Zbib, H. M.: A eultiscale approach for modeling scale-dependent yield stress in polycrystalline metals, Int. J. Plasticity 23, 897-914 (2007) · Zbl 1115.74013
[30] Parthasarathy, T. A.; Rao, S. I.; Dimiduk, D. M.; Uchic, M. D.; Trinkle, D. R.: Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples, Scripta mater. 56, 313-316 (2007)
[31] Rhee, M.; Zbib, H. M.; Hirth, J. P.; Huang, H.; De La Rubia, T. D.: Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals, Model. simul. Mater. sci. Eng. 6, 467-492 (1998)
[32] Uchic, M. D.; Dimiduk, D. M.; Florando, J. N.; Nix, W. D.: Sample dimensions influence strength and crystal plasticity, Science 305, 986-989 (2004)
[33] Van Der Giessen, E.; Needleman, A.: Discrete dislocation plasticity: a simple planar model, Model. simul. Mater. sci. Eng. 3, 689-735 (1995)
[34] Volkert, C. A.; Lilleodden, E. T.: Size effects in the deformation of sub-micron au columns, Philos. mag. 86, 5567-5579 (2006)
[35] Weygand, D., Poignant, M., Gumbsch, P., Kraft, O., in press. 3D dislocation dynamics simulation of the influence of sample size on the stress – strain behavior of FCC single-crystalline pillars. Mater. Sci. Eng.
[36] Wu, B.; Heidelberg, A.; Boland, J. J.: Nat. mater., Nat. mater. 4, 525-529 (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.