Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T12:11:57.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal length scale and grain boundary yield strength in gradientmodels of polycrystal plasticity: How do they relate to the dislocationmicrostructure?

Published online by Cambridge University Press:  12 September 2014

Xu Zhang ,
Katerina E. Aifantis ,
Jochen Senger ,
Daniel Weygand  and
Michael Zaiser
Xu Zhang
Affiliation:
School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China; Lab of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; and University of Erlangen, Institute for Materials Simulation WW8, Fürth 90762, Germany
Katerina E. Aifantis
Affiliation:
Lab of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; and Department of Civil Engineering-Engineering Mechanics, University of Arizona, Tucson, AZ 85721, USA
Jochen Senger
Affiliation:
Institute for Applied Materials IAM, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany
Daniel Weygand
Affiliation:
Institute for Applied Materials IAM, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany
Michael Zaiser*
Affiliation:
University of Erlangen, Department of Materials Science and Engineering, Institute for Materials Simulation WW8, Fürth 90762, Germany
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Gradient plasticity provides an effective theoretical framework to interpretheterogeneous and irreversible deformation processes on micron and submicronscales. By incorporating internal length scales into a plasticity framework,gradient plasticity gives access to size effects, strain heterogeneities atinterfaces, and characteristic lengths of strain localization. To relate themagnitude of the internal length scale to parameters of the dislocationmicrostructure of the material, 3D discrete dislocation dynamics (DDD)simulations were performed for tricrystals of different dislocation sourcelengths (100, 200, and 300 nm). Comparing the strain profiles deduced from DDDwith gradient plasticity predictions demonstrated that the internal length scaledepends on the flow-stress-controlling mechanism. Different dislocationmechanisms produce different internal lengths. Furthermore, by comparing agradient plasticity framework with interfacial yielding to the simulations itwas found that, even though in the DDD simulations grain boundaries (GBs) werephysically impenetrable to dislocations, on the continuum scale the assumptionof plastically deformable GBs produces a better match of the DDD data than theassumption of rigid GBs. The associated effective GB strength again depends onthe dislocation microstructure in the grain interior.

Type
Invited Feature Paper
Information
Journal of Materials Research , Volume 29 , Issue 18 , 28 September 2014 , pp. 2116 - 2128
Copyright
Copyright © Materials Research Society 2014 

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

Fleck, N.A., Muller, G.M., Ashby, M.F., and Hutchinson, J.W.: Strain gradient plasticity: Theory and experiment. Acta Metall. Mater. 42(2), 475 (1994).CrossRefGoogle Scholar
Dunstan, D.J., Ehrler, B., Bossis, R., Joly, S., P’ng, K.M.Y., and Bushby, A.J.: Elastic limit and strain hardening of thin wires in torsion. Phys. Rev. Lett. 103(15), 155501 (2009).CrossRefGoogle ScholarPubMed
Liu, D., He, Y., Tang, X., Ding, H., Hu, P., and Cao, P.: Size effects in the torsion of microscale copper wires: Experiment and analysis. Scr. Mater. 66(6), 406 (2012).CrossRefGoogle Scholar
Stölken, J.S. and Evans, A.G.: A microbend test method for measuring the plasticity length scale. Acta Mater. 46(14), 5109 (1998).CrossRefGoogle Scholar
Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46(3), 411 (1998).CrossRefGoogle Scholar
Uchic, M.D., Dimiduk, D.M., Florando, J.N., and Nix, W.D.: Sample dimensions influence strength and crystal plasticity. Science 305(5686), 986 (2004).CrossRefGoogle ScholarPubMed
Volkert, C.A. and Lilleodden, E.T.: Size effects in the deformation of sub-micron Au columns. Philos. Mag. 86(33–35), 5567 (2006).CrossRefGoogle Scholar
Aifantis, E.C.: On the microstructural origin of certain inelastic models. Trans. ASME, J. Eng. Mater. Technol. 106(4), 326 (1984).CrossRefGoogle Scholar
Aifantis, E.C.: The physics of plastic deformation. Int. J. Plast. 3(3), 211 (1987).CrossRefGoogle Scholar
Gao, H., Huang, Y., Nix, W.D., and Hutchinson, J.W.: Mechanism-based strain gradient plasticity—I. Theory. J. Mech. Phys. Solids 47(6), 1239 (1999).CrossRefGoogle Scholar
Fleck, N.A. and Hutchinson, J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49(10), 2245 (2001).CrossRefGoogle Scholar
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(5), 1047 (2005).CrossRefGoogle Scholar
Fleck, N.A. and Willis, J.R.: A mathematical basis for strain-gradient plasticity theory—Part I: Scalar plastic multiplier. J. Mech. Phys. Solids 57(1), 161 (2009).CrossRefGoogle Scholar
Fleck, N.A. and Willis, J.R.: A mathematical basis for strain-gradient plasticity theory. Part II: Tensorial plastic multiplier. J. Mech. Phys. Solids 57(7), 1045 (2009).CrossRefGoogle Scholar
Polizzotto, C.: A unified residual-based thermodynamic framework for strain gradient theories of plasticity. Int. J. Plast. 27(3), 388 (2011).CrossRefGoogle Scholar
Gurtin, M.E. and Ohno, N.: A gradient theory of small-deformation, single-crystal plasticity that accounts for GND-induced interactions between slip systems. J. Mech. Phys. Solids 59(2), 320 (2011).CrossRefGoogle Scholar
Voyiadjis, G.Z. and Faghihi, D.: Thermo-mechanical strain gradient plasticity with energetic and dissipative length scales. Int. J. Plast. 30–31, 218 (2012).CrossRefGoogle Scholar
Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95(1–4), 299 (1999).CrossRefGoogle Scholar
Zhang, X. and Aifantis, K.E.: Interpreting strain bursts and size effects in micropillars using gradient plasticity. Mater. Sci. Eng., A 528(15), 5036 (2011).CrossRefGoogle Scholar
Konstantinidis, A.A., Aifantis, K.E., and De Hosson, J.T.M.: Capturing the stochastic mechanical behavior of micro and nanopillars. Mater. Sci. Eng., A 597(0), 89 (2014).CrossRefGoogle Scholar
Aifantis, E.C.: Update on a class of gradient theories. Mech. Mater. 35(3–6), 259 (2003).CrossRefGoogle Scholar
Zaiser, M. and Aifantis, E.C.: Geometrically necessary dislocations and strain gradient plasticity - A dislocation dynamics point of view. Scr. Mater. 48(2), 133 (2003).CrossRefGoogle Scholar
Gurtin, M.E. and Anand, L.: A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. J. Mech. Phys. Solids 53(7), 1624 (2005).CrossRefGoogle Scholar
Gao, H. and Huang, Y.: Geometrically necessary dislocation and size-dependent plasticity. Scr. Mater. 48(2), 113 (2003).CrossRefGoogle Scholar
Groma, I., Csikor, F.F., and Zaiser, M.: Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51(5), 1271 (2003).CrossRefGoogle Scholar
Aifantis, K.E. and Ngan, A.H.W.: Modeling dislocation-grain boundary interactions through gradient plasticity and nanoindentation. Mater. Sci. Eng., A 459(1–2), 251 (2007).CrossRefGoogle Scholar
Van der Giessen, E. and Needleman, A.: Discrete dislocation plasticity: A simple planar model. Modell. Simul. Mater. Sci. Eng. 3(5), 689 (1995).CrossRefGoogle Scholar
Zbib, H.M. and Diaz de la Rubia, T.: A multiscale model of plasticity. Int. J. Plast. 18(9), 1133 (2002).CrossRefGoogle Scholar
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(4), 437 (2002).CrossRefGoogle Scholar
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.: Mater. Sci. Eng. 3, 012025 (2009).CrossRefGoogle Scholar
Weygand, D. and Gumbsch, P.: Study of dislocation reactions and rearrangements under different loading conditions. Mater. Sci. Eng., A 400–401(1–2 Suppl.), 158 (2005).CrossRefGoogle Scholar
Foreman, A.J.E.: The bowing of a dislocation segment. Philos. Mag. 15, 1011 (1967).CrossRefGoogle Scholar
Aifantis, K.E. and Konstantinidis, A.A.: Hall-Petch revisited at the nanoscale. Mater. Sci. Eng., B 163(3), 139 (2009).CrossRefGoogle Scholar
Zhang, X. and Aifantis, K.E.: Interpreting the softening of nanomaterials through gradient plasticity. J. Mater. Res. 26(11), 1399 (2011).CrossRefGoogle Scholar
Hochrainer, T., Sandfeld, S., Zaiser, M., and Gumbsch, P.: Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids 63, 167 (2014).CrossRefGoogle Scholar
Zaiser, M. and Sandfeld, S.: Scaling properties of dislocation simulations in the similitude regime. Modell. Simul. Mater. Sci. Eng. 22, 065012 (2014).CrossRefGoogle Scholar