Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T23:25:33.458Z Has data issue: false hasContentIssue false
  • English
  • Français

Contact area and size effects in discrete dislocation modeling of wedge indentation

Published online by Cambridge University Press:  03 March 2011

Andreas Widjaja ,
Erik Van der Giessen ,
Vikram S. Deshpande  and
Alan Needleman
Andreas Widjaja
Affiliation:
University of Groningen, Department of Applied Physics, Nijenborgh 4, 9747 AG, Groningen, The Netherlands
Erik Van der Giessen*
Affiliation:
University of Groningen, Department of Applied Physics, Nijenborgh 4, 9747 AG, Groningen, The Netherlands
Vikram S. Deshpande
Affiliation:
University of Cambridge, Engineering Department, Cambridge CB2 1PZ, United Kingdom
Alan Needleman
Affiliation:
Brown University, Division of Engineering, Providence, Rhode Island 02912
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Plane strain indentation of a single crystal by a rigid wedge is analyzed using discrete dislocation plasticity. We consider two wedge geometries having different sharpness, as specified by the half-angle of the indenter: α = 70° and 85°. The dislocations are all of edge character and modeled as line singularities in a linear elastic material. The crystal has initial sources and obstacles randomly distributed over three slip systems. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles, and dislocation annihilation are incorporated through a set of constitutive rules. Several definitions of the contact area (contact length in plane strain) are used to illustrate the sensitivity of the hardness value in the submicron indentation regime to the definition of contact area. The size dependence of the indentation hardness is found to be sensitive to the definition of contact area used and to depend on the wedge half-angle. For a relatively sharp indenter, with a half-angle of 70°, an indentation size effect is not obtained when the contact area is small and when the hardness is based on the actual contact length, while there does appear to be a size effect for some hardness values based on other measures of contact length.

Keywords

DislocationsHardnessSimulation
Type
Articles
Information
Journal of Materials Research , Volume 22 , Issue 3 , March 2007 , pp. 655 - 663
Copyright
Copyright © Materials Research Society 2007

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

1Ma, Q. and Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853 (1995).Google Scholar
2Swadener, J.G., George, E.P., and Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681 (2002).Google Scholar
3Wei, Y. and Hutchinson, J.W.: Hardness trends in micron scale indentation. J. Mech. Phys. Solids 51, 2037 (2003).CrossRefGoogle Scholar
4Lou, J., Shrotriya, P., Buchheit, T., Yang, D., and Soboyejo, W.O.: Nanoindentation study of plasticity length scale effects in LIGA Ni microelectromechanical systems structures. J. Mater. Res. 18, 719 (2003).Google Scholar
5Zhu, T., Li, J., Van Vliet, K.J., Yip, S., and Suresh, S.: Simulation of nanoindentation via interatomic potential finite element method. Comp. Fluid Solid Mech. 1–2, 795 (2003).Google Scholar
6Nix, W.D. and Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 43, 411 (1998).CrossRefGoogle Scholar
7Begley, M.R. and Hutchinson, J.W.: The mechanics of size-dependent indentation. J. Mech. Phys. Solids 46, 2049 (1998).Google Scholar
8Abu Al-Rub, R.K. and Voyiadjis, G.Z.: Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments. Int. J. Plast. 20, 1139 (2004).CrossRefGoogle Scholar
9Qu, S., Huang, Y., Pharr, G.M., and Hwang, K.C.: The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 22, 1265 (2006).CrossRefGoogle Scholar
10Fivel, M.C., Robertson, C.F., Canova, G.R., and Boulanger, L.: Three-dimensional modeling of indent-induced plastic zone at a mesoscale. Acta Mater. 46, 6183 (1998).Google Scholar
11Kreuzer, H.G.M. and Pippan, R.: Discrete dislocation simulation of nanoindentation. Comp. Mech. 33, 292 (2004).Google Scholar
12Kreuzer, H.G.M. and Pippan, R.: Discrete dislocation simulation of nanoindentation: The effect of statistically distributed dislocations. Mater. Sci. Eng., A 400–401, 460 (2005).Google Scholar
13Widjaja, A., Van der Giessen, E., and Needleman, A.: Discrete dislocation modelling of submicron indentation. Mater. Sci. Eng., A 400–401, 456 (2005).Google Scholar
14Balint, D.S., Deshpande, V.S., Needleman, A., and Van der Giessen, E.: Discrete dislocation plasticity analysis of the wedge indentation of films. J. Mech. Phys. Solids (2006, in press).Google Scholar
15Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar
16Oliver, W.C. and Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, 3 (2004).Google Scholar
17Van der Giessen, E. and Needleman, A.: Discrete dislocation plasticity, Handbook of Materials Modeling. Volume I: Methods and Models edited by Yip, S. (Springer, Dordrecht, The Netherlands, 2005), pp.1115–1131.Google Scholar
18Van der Giessen, E. and Needleman, A.: Discrete dislocation plasticity: A simple planar model. Model. Simul. Mater. Sci. Eng. 3, 689 (1995).CrossRefGoogle Scholar