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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: e.van.der.giessen@rug.nl
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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

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