Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T17:14:37.106Z Has data issue: false hasContentIssue false

Modeling microbending of thin films through discrete dislocation dynamics, continuum dislocation theory, and gradient plasticity

Published online by Cambridge University Press:  14 December 2011

Katerina E. Aifantis*
Affiliation:
Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Daniel Weygand
Affiliation:
Karlsruher Institut für Technologie, Institute for Applied Materials, 76131 Karlsruhe, Germany
Christian Motz
Affiliation:
Karlsruher Institut für Technologie, Institute for Applied Materials, 76131 Karlsruhe, Germany
Nikolaos Nikitas
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, United Kingdom
Michael Zaiser
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, United Kingdom
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Constitutive models that describe crystal microplasticity in a continuum framework can be envisaged as average representations of the dynamics of dislocation systems. Thus, their performance needs to be assessed not only by their ability to correctly represent stress–strain characteristics on the specimen scale but also by their ability to correctly represent the evolution of internal stress and strain patterns. Three-dimensional discrete dislocation dynamics (3D DDD) simulations provide complete knowledge of this evolution, and averages over ensembles of statistically equivalent simulations can therefore be used to assess the performance of continuum models. In this study, we consider the bending of a free-standing thin film. From a continuum mechanics point of view, this is a one-dimensional (1D) problem as stress and strain fields vary only in one dimension. From a dislocation plasticity point of view, on the other hand, the spatial degrees of freedom associated with the bending and piling up of dislocations are essential. We compare the results of 3D DDD simulations with those obtained from a simple 1D gradient plasticity model and a more complex dislocation-based continuum model. Both models correctly reproduce the nontrivial strain patterns predicted by 3D DDD for the microbending problem.

Type
Articles
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Hoffmann, S., Utke, I., Moser, B., Michler, J., Christiansen, S.H., Schmidt, V., Senz, S., Werner, P., Gösele, U., and Ballif, C.: Measurement of the bending strength of vapor−liquid−solid grown silicon nanowires. Nano Lett. 6, 622 (2006).CrossRefGoogle ScholarPubMed
2.Jämting, Å.K., Bell, J.M., Swain, M.V., and Schwarzer, N.: Investigation of the elastic modulus of thin films using simple biaxial bending techniques. Thin Solid Films 308309, 304 (1997).Google Scholar
3.Cleveringa, H.H.M., van der Giessen, E., and Needleman, A.: Comparison of discrete dislocation and continuum plasticity predictions for a composite material. Acta Mater. 45, 3163 (1997).CrossRefGoogle Scholar
4.Needleman, A. and van der Giessen, E.: 2D dislocation dynamics in thin metal layers. Mater. Sci. Eng. A309, 274 (2001).Google Scholar
5.Yefimov, S., Groma, I., and van der Giessen, E.: A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations. J. Mech. Phys. Solids 52, 279 (2004).Google Scholar
6.Sauzay, M. and Kubin, L.P.: Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals. Prog. Mater. Sci. 56, 725 (2011).CrossRefGoogle Scholar
7.Ghoniem, N.M., Busso, E., Kioussis, N., and Huang, H.: Multiscale modeling of nanomechanics and micromechanics: An overview. Philos. Mag. A 83, 3475 (2003).Google Scholar
8.Aifantis, E.C.: Dislocation kinetics and the formation of deformation bands, in Defects, Fracture and Fatigue, edited by Sih, G.C. and Provan, J.W. (Martinus-Nijhoff, The Hague, 1983), pp. 7584.CrossRefGoogle Scholar
9.Aifantis, E.C.: On the dynamical origin of dislocation patterning. Mater. Sci. Eng. 81, 563 (1986).Google Scholar
10.Walgraef, D. and Aifantis, E.C.: Dislocation patterning in fatigued metals as a result of dynamical instabilities. J. Appl. Phys. 58, 688 (1985).CrossRefGoogle Scholar
11.El-Azab, A., Zaiser, M., and Busso, E.P. (eds): Density-based modelling of dislocations. Philos. Mag. 87(8–9), (2007) (special issue).Google Scholar
12.Aifantis, E.C.: On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 106, 326 (1984).Google Scholar
13.Aifantis, E.C.: Deformation and failure of bulk nanograined and ultrafine-grained materials. Mater. Sci. Eng., A 503, 190 (2009).CrossRefGoogle Scholar
14.Fleck, N.A. and Hutchinson, J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245 (2001).CrossRefGoogle Scholar
15.Gurtin, M.E. and Anand, L.: Thermodynamics applied to gradient theories involving the accumulated plastic strain: The theories of Aifantis and Fleck and Hutchinson and their generalization. J. Mech. Phys. Solids 57, 405 (2009).Google Scholar
16.Aifantis, K.E. and Willis, J.R.: The role of interfaces in enhancing the yield strength of composites and polycrystals. J. Mech. Phys. Solids 53, 1505 (2005).Google Scholar
17.El-Azab, A.: Statistical mechanics treatment of the evolution of dislocation distributions in single crystals. Phys. Rev. B 61, 11956 (2000).Google Scholar
18.Sedlacek, R., Kratochvil, J., and Werner, E.: The importance of being curved: Bowing dislocations in a continuum description. Philos. Mag. 83, 3735 (2003).CrossRefGoogle Scholar
19.Hochrainer, T., Zaiser, M., and Gumbsch, P.: A three-dimensional continuum theory of dislocation systems: Kinematics and mean-field formulation. Philos. Mag. 87, 1261 (2007).CrossRefGoogle Scholar
20.Sandfeld, S., Hochrainer, T., Zaiser, M., and Gumbsch, P.: Continuum modeling of dislocation plasticity: Theory, numerical implementation and validation by discrete dislocation simulations. J. Mater. Res. 26, 623 (2011).Google Scholar
21.Aifantis, K.E., Senger, J., Weygand, D., and Zaiser, M.: Discrete dislocation dynamics simulation and continuum modeling of plastic boundary layers in tricrystal micropillars. IOP Conf. Ser. Mat. Sci. Eng. 3, 012025 (2009).CrossRefGoogle Scholar
22.Weygand, D., Friedman, L.H., van der Giessen, E., and Needleman, A.: Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Modell. Simul. Mater. Sci. Eng. 10, 437 (2002).CrossRefGoogle Scholar
23.Motz, C., Weygand, D., Senger, J., and Gumbsch, P.: Micro-bending tests: A comparison between three-dimensional discrete dislocation dynamics simulations and experiments. Acta Mater. 56, 1942 (2008).Google Scholar
24.Sedlacek, R.: Orowan-type size effect in plastic bending of free-standing thin crystalline strips. Mater. Sci. Eng., A 393, 387 (2005).Google Scholar
25.Zaiser, M. and Hochrainer, T.: Some steps towards a continuum representation of dislocation systems. Scr. Mater. 54, 717 (2006).Google Scholar
26.Schwarz, C., Sedlacek, R., and Werner, E.: Refined short-range interactions in the continuum dislocation-based model of plasticity at the microscale. Acta Mater. 56, 341 (2008).Google Scholar
27.Zaiser, M., Nikitas, N., Hochrainer, T., and Aifantis, E.C.: Modelling size effects using 3D density-based dislocation dynamics. Philos. Mag. 87, 1283 (2007).Google Scholar
28.Aifantis, K.E. and Ngan, A.H.W.: Modeling dislocation-grain boundary interactions through gradient plasticity and nanoindentation. Mater. Sci. Eng., A 459, 251 (2007).Google Scholar
29.Zaiser, M. and Aifantis, E.C.: Geometrically necessary dislocations and strain gradient plasticity––a dislocation dynamics point of view. Scr. Mater. 48, 133 (2002).Google Scholar