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Research Papers

A Discrete Dislocation Plasticity Analysis of a Single-Crystal Half-Space Indented by a Rigid Cylinder

[+] Author and Article Information
X. Yin

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

K. Komvopoulos1

Department of Mechanical Engineering, University of California, Berkeley, CA 94720kyriakos@me.berkeley.edu

1

Corresponding author.

J. Appl. Mech 78(4), 041019 (Apr 15, 2011) (10 pages) doi:10.1115/1.4003431 History: Received November 28, 2010; Revised December 23, 2010; Posted January 12, 2011; Published April 15, 2011; Online April 15, 2011

Elastic-plastic indentation of a single-crystal half-space by a rigid cylinder was analyzed by discrete dislocation plasticity. Short-range dislocation interactions were modeled by a set of constitutive rules of dislocation emission, glide, pinning (by obstacles), and annihilation. The occurrence of the first dislocation dipole, multiplication of dislocations, and evolution of subsurface stress field were examined in terms of contact load, dislocation source density, slip-plane distance and orientation angle, and indenter radius. In the presence of defects (dislocation sources), the critical load for dislocation initiation is less than that of a defect-free medium and depends on dislocation source density, slip-plane distance, and indenter radius. The critical indenter radius resulting in deformation under the theoretical material strength is determined from numerical results, and the role of dislocation obstacles is interpreted in terms of their spatial density. Simulations provide insight into yielding and plastic deformation of indented single-crystal materials, and establish a basis for developing coarse-grained plasticity models of localized contact deformation in polycrystalline solids.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 6

Dimensionless dislocation density ρd/ρs versus dimensionless contact load P/bE and dimensionless indenter radius R/b for slip-plane orientation angles (a) θ=45 deg and (b) θ=0 deg

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Figure 7

Dislocation maps for different contact widths 2r (loads) and slip-plane orientation angle θ=45 deg (Positive and negative dislocations are shown by red and blue symbols, respectively.)

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Figure 8

Dimensionless shear band width w/b versus dimensionless contact load P/PY

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Figure 9

Contours of dimensionless total resolved shear stress τ/τe for different contact widths 2r corresponding to the dislocation maps shown in Fig. 7

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Figure 10

Dimensionless total and mobile dislocation densities ρd/ρs versus dimensionless load P/PY and dislocation obstacle density ρo for slip-plane orientation angles (a) θ=45 deg and (b) θ=0 deg

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Figure 11

Effect of (a) dislocation source density ρs and (b) dislocation obstacle density ρo on the variation of dimensionless mean contact pressure pm/Y with representative macroscopic strain ε

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Figure 12

Ratio of threshold radius of rigid indenter to slip-plane distance Rth/d versus dimensionless slip-plane distance d/b for slip-plane orientation angles θ=0 deg and 45 deg

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Figure 5

Dislocation density ρd versus dimensionless contact load P/PY and dislocation source density ρs for slip-plane orientation angles (a) θ=45 deg and (b) θ=0 deg

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Figure 4

Dimensionless dislocation density ρd/ρs versus dimensionless contact load P/PY and slip-plane orientation angle θ

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Figure 3

Dimensionless dislocation density ρd/ρs versus slip-plane orientation angle θ for contact load P=12 N/m corresponding to the onset of yielding in the least favorable slip-plane direction (θ=90 deg)

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Figure 2

Damage parameter DY defined at the onset of yielding (emission of first dislocation dipole) versus (a) dimensionless slip-plane distance d/b, (b) dislocation source density ρs, and (c) dimensionless indenter radius R/b

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Figure 1

Schematic of a single-crystal half-space with parallel and equally spaced slip-planes of fixed orientation indented by a rigid cylinder

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