Continuum modeling of dislocation plasticity: Theory, numerical implementation, and validation by discrete dislocation simulations

Journal of Materials Research

Volumn 26, Issue 5, 2011, Pages 623-632

  Sandfeld, Stefan ^a   Hochrainer, Thomas ^b   Zaiser, Michael ^c   Gumbsch, Peter ^a,d  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b FLORIDA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

^d FRAUNHOFER INSTITUTE FOR MECHANICS OF MATERIALS IWM   (Germany)

Author keywords

Crystal; Defects; Dislocations

Indexed keywords

CONTINUUM DESCRIPTION; CONTINUUM MODELING; CONTINUUM PLASTICITY; CONTINUUM THEORY; DISCRETE DISLOCATION DYNAMICS; DISCRETE DISLOCATIONS; DISLOCATION DYNAMICS; DISLOCATION MICROSTRUCTURES; DISLOCATION PLASTICITY; DISLOCATION SYSTEMS; LENGTH SCALE; NUMERICAL EXAMPLE; NUMERICAL IMPLEMENTATION;

CONTINUUM MECHANICS; CRYSTAL MICROSTRUCTURE; PLASTICITY;

DISLOCATIONS (CRYSTALS);

EID: 80054932769     PISSN: 08842914     EISSN: 20445326     Source Type: Journal    
DOI: 10.1557/jmr.2010.92     Document Type: Article

References (51)

1. A. Acharya: A model of crystal plasticity based on the theory of continuously distributed dislocation. J. Mech. Phys. Solids 49(4), 761 (2001).
2. A. Acharya: Driving forces and boundary conditions in continuum dislocation mechanics. Proc. R. Soc. London, Ser. A 459(2034), 1343 (2003).
3. E. C. Aifantis: The physics of plastic deformation. Int. J. Plast. 3, 211 (1987).
4. K. E. Aifantis, J. Senger, D. Weygand, and M. Zaiser: Discrete dislocation dynamics simulation and continuum modeling of plastic boundary layers in tricrystal micropillars. IOP Conf. Ser.: Mat. Sci. Eng. 3, 012025 (2009).
5. A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G. Pierce, and V. V. Bulatov: Enabling strain hardening simulations with dislocation dynamics. Modell. Simul. Mater. Sci. Eng. 15, 553 (2007).
6. A. Arsenslis, D. Parks, R. Becker, and V. Bulatov: On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals. J. Mech. Phys. Solids 52, 1213 (2004).
7. E. Arzt, G. Dehm, P. Gumbsch, O. Kraft, and D. Weiss: Interface controlled plasticity in metals: Dispersion hardening and thin film deformation. Prog. Mater. Sci. 46(3-4), 283 (2001).
8. B. A. Bilby, R. Bullough, and E. Smith: Continuous distributions of dislocations: A new application of the methods of non-Riemannian geometry. Proc. R. Soc. London, Ser. A 231, 263 (1955).
9. E. Bittencourt, A. Needleman, M. E. Gurtin, and E. van der Giessen: A comparison of nonlocal continuum and discrete dislocation plasticity predictions. J. Mech. Phys. Solids 51, 281 (2003).
10. V. V. Bulatov and W. Cai: Nodal effects in dislocation mobility. Phys. Rev. Lett. 89(11), 115501 (2002).
11. E. Cosserat and F. Cosserat: Theorie des corps deformables (Libraire scientifique, A. Hermann & Fils, Paris, France, 1909).
12. B. Devincre, L. Kubin, C. Lemarchand, and R. Madec: Mesoscopic simulations of plastic deformation. Mater. Sci. Eng., A 309-310, 211 (2001).
13. A. El-Azab: Statistical mechanics treatment of the evolution of dislocation distributions in single crystals. Phys. Rev. B 61(18), 11, 956 (2000).
14. A. G. Evans and J. W. Hutchinson: A critical assessment of theories of strain gradient plasticity. Acta Mater. 57(5), 1675 (2009).
15. M. Fivel, M. Verdier, and G. Ganova: 3D simulation of a nanoindentation test at a mesoscopic scale. Mater. Sci. Eng., A 234-236, 923 (1997).
16. N. A. Fleck and J. W. Hutchinson: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41(12), 1825 (1993).
17. S. Forest: Generalized continuum modeling of single and polycrystal plasticity, Continuum Scale Simulation of Engineering Materials, edited by D. Raabe, F. Roters, F. Barlat, and L. Chen (Wiley-VCH Verlag GmbH & Co., KGaA, Weinhem, Germany, 2005).
18. N. M. Ghoniem and L. Z. Sun: Fast-sum method for the elastic field of three-dimensional dislocation ensembles. Phys. Rev. B 60(1), 128 (1999).
19. I. Groma: Link between the microscopic and mesoscopic lengthscale description of the collective behavior of dislocations. Phys. Rev. B 56, 5807 (1997).
20. I. Groma, F. F. Csikor, and M. Zaiser: Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51, 1271 (2003).
21. M. E. Gurtin: A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50(1), 5 (2002).
22. M. E. Gurtin: A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. J. Mech. Phys. Solids 56(2), 640 (2008).
23. T. Hochrainer: Evolving systems of curved dislocations: Mathematical foundations of a statistical theory. Ph. D. Thesis, Universität Karlsruhe (TH), Shaker Verlag, Aachen, Germany, 2006.
24. T. Hochrainer, P. Gumbsch, and M. Zaiser: A non-linear multiple slip theory in continuum dislocation dynamics, in Proc. of the 4th Int. Conf. on Multiscale Materials Modeling, pp. 115-118 (2008).
25. T. Hochrainer, M. Zaiser, and P. Gumbsch: A three-dimensional continuum theory of dislocations: Kinematics and mean field formulation. Philos. Mag. 87, 1261 (2007).
26. T. Hochrainer, M. Zaiser, and P. Gumbsch: Dislocation transport and line length increase in averaged descriptions of dislocations. AIP Conf. Proc. 1168(1), 1133 (2009).
27. K. Kondo: On the geometrical and physical foundations of the theory of yielding, in Proc. 2nd Japan Nat. Congress of Appl. Mech., pp. 41-47 (1952).
28. A. Kosevich: Crystal dislocations and the theory of elasticity, Dislocations in Solids, Vol. 1: The elastic theory, edited by F. R. N. Nabarro, (North-Holland, Amsterdam, 1979).
29. J. Kratochvíl and R. Sedlácek: Statistical foundation of continuum dislocation plasticity. Phys. Rev., B 77, 134102/1 (2008).
30. E. Kröner: Kontinuumstheorie der Versetzungen und Eigenspannungen (Springer-Verlag, Berlin, 1958).
31. E. Kröner: Benefits and shortcomings of the continuous theory of dislocations. Int. J. Solids Struct. 38(6-7), 1115 (2001).
32. L. Kubin and G. Canova: The modeling of dislocation patterns. Scr. Metall. Mater. 27(8), 957 (1992).
33. H. Mecking and U. Kocks: Kinetics of flow and strain-hardening. Acta Metall. 29(11), 1865 (1981).
34. C. Motz, D. Weygand, J. Senger, and P. Gumbsch: Micro-bending tests: A comparison between three-dimensional discrete dislocation dynamics simulations and experiments. Acta Mater. 56, 1942 (2008).
35. C. Motz, D. Weygand, J. Senger, and P. Gumbsch: Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity. Acta Mater. 57(6), 1744 (2009).
36. W. D. Nix and H. Gao: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46(3), 411 (1998).
37. J. F. Nye: Some geometrical relations in dislocated crystals. Acta Metall. 1, 153 (1953).
38. R. D. Mindlin: Microstructure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51 (1964).
39. S. Reese and B. Svendsen: Continuum thermodynamic modeling and simulation of additional hardening due to deformation incompatibility, Kluwer Series on Solid Mechanics and Its Application, Vol. 108, edited by C. Miehe, (Dordrecht, The Netherlands, 2003), pp. 141-150.
40. F. Roters and D. Raabe: A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater. 54, 2169 (2006).
41. S. Sandfeld: The evolution of dislocation density in a higher-order continuum theory of dislocation plasticity. Ph. D. Thesis, Shaker Verlag, Aachen, Germany, 2010.
42. S. Sandfeld, T. Hochrainer, M. Zaiser, and P. Gumbsch: Numerical implementation of a 3D continuum theory of dislocation dynamics and application to microbending. Philos. Mag. 90(27-28), 3697-3728 (2010).
43. S. Sandfeld, T. Hochrainer, and M. Zaiser: Application of a 3D-continuum theory of dislocations to problems of constrained plastic flow: Microbending of a thin film, in Mechanical Behavior at Small Scales-Experiments and Modeling, edited by J. Lou, E. Lilleodden, B. L. Boyce, L. Lu, P. M. Derlet, D. Weygand, J. Li, M. Uchic, and E. Le Bourhis, (Mater. Res. Soc. Symp. Proc, 1224, Warrendale, PA, 2010), p. 143.
44. S. Sandfeld, M. Zaiser, and T. Hochrainer: Expansion of quasidiscrete dislocation loops in the context of a 3D continuum theory of curved dislocations. AIP Conf. Proc. 1168(1), 1148 (2009).
45. R. Sedlácek, J. Kratochvíl, and E. Werner: The importance of being curved: Bowing dislocations in a continuum description. Philos. Mag. 83(31-34), 3735 (2003).
46. J. Senger, D. Weygand, P. Gumbsch, and O. Kraft: Discrete dislocation simulations of the plasticity of micro-pillars under uniaxial loading. Scr. Mater. 58(7), 587 (2008).
47. D. Weygand, L. H. Friedman, E. van der Giessen, and A. Needleman: Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Modell. Simul. Mater. Sci. Eng. 10, 437 (2002).
48. D. Weygand and P. Gumbsch: Study of dislocation reactions and rearrangements under different loading conditions. Mater. Sci. Eng., A 400-401, 158 (2005).
49. D. Weygand, J. Senger, C. Motz, W. Augustin, V. Heuveline, and P. Gumbsch: High performance computing and discrete dislocation dynamics: Plasticity of micrometer sized specimens, High Performance Computing in Science and Engineering'08, edited by W. E. Nagel (Springer, Berlin, Germany 2009), pp. 507-523.
50. S. Yefimov and E. van der Giessen: Size effects in single crystal thin films: Nonlocal crystal plasticity simulations. Eur. J. Mech. A Solids 24(2), 183 (2005).
51. M. Zaiser, N. Nikitas, T. Hochrainer, and E. Aifantis: Modeling size effects using 3D density-based dislocation dynamics. Philos. Mag. 87, 1283 (2007).