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Research Papers

Effect of Plastic Flattening on the Shearing Response of Metal Asperities: A Dislocation Dynamics Analysis

[+] Author and Article Information
Fengwei Sun

Department of Materials Science and Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: f.sun@tudelft.nl

Erik Van der Giessen

Zernike Institute for Advanced Materials,
University of Groningen,
Groningen 9747 AG, The Netherlands
e-mail: E.van.der.Giessen@rug.nl

Lucia Nicola

Department of Materials Science and Engineering,
Delft University of Technology,
Delft 2628 CD, The Netherlands
e-mail: l.nicola@tudelft.nl

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 12, 2014; final manuscript received February 26, 2015; published online June 3, 2015. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 82(7), 071009 (Jul 01, 2015) (9 pages) Paper No: JAM-14-1578; doi: 10.1115/1.4030321 History: Received December 12, 2014; Revised February 26, 2015; Online June 03, 2015

Discrete dislocation (DD) plasticity simulations are carried out to investigate the effect of flattening and shearing of surface asperities. The asperities are chosen to have a rectangular shape to keep the contact area constant. Plasticity is simulated by nucleation, motion, and annihilation of edge dislocations. The results show that plastic flattening of large asperities facilitates subsequent plastic shearing, since it provides dislocations available to glide at lower shear stress than the nucleation strength. The effect of plastic flattening disappears for small asperities, which are harder to be sheared than the large ones, independently of preloading. An effect of asperity spacing is observed with closely spaced asperities being easier to plastically shear than isolated asperities. This effect fades when asperities are very protruding, and therefore plasticity is confined inside the asperities.

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References

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Figures

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Fig. 1

Two-dimensional model of an asperity on a larger crystal flattened and sheared by a rigid platen (the dimensions are not to scale). The rigid platen is drawn only as illustration and its influence on the asperity is simply accounted for by means of boundary conditions.

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Fig. 2

(a) The mean contact pressure and total dislocation density during flattening under different contact conditions for the asperity with w = 4 μm and hp = 2 μm. The letters A, B, and C represent the points on the loading curve when the shearing starts. (b) The contact shear stress as a function of tangential displacement during shearing.

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Fig. 3

The stress state σ12 and dislocation distribution for frictionless contact at flattening depths: (a) u2 = 0.0012 μm (corresponding to point A in Fig. 2(a)), (b) u2 = 0.02 μm (corresponding to point C), after shearing to u1 = 0.01 μm starting from a flattening depth, (c) u2 = 0.0012 μm (corresponding to point A), (d) u2 = 0.02 μm, and after shearing to u1 = 0.03 μm starting from a flattening depth, (e) u2 = 0.0012 μm and (f) u2 = 0.02 μm

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Fig. 4

The shear traction profiles σ12 after (a) only flattening (u2 = 0.02 μm and u1 = 0 μm) and (b) flattening and subsequent shearing (u2 = 0.02 μm and u1 = 0.03 μm)

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Fig. 5

(a) The mean contact pressure during flattening and unloading under sticking contact conditions for the asperity with w = 4 μm and hp = 2 μm. The letters B and C represent the points on the curves when unloading starts; M and N represent the points when the normal pressure disappears. (b) The contact shear traction at the contact as a function of tangential displacement during shearing from different dislocation distributions.

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Fig. 6

The stress state σ22 and dislocation distribution for sticking contact when the asperity is totally unloaded from flattening depths: (a) u2 = 0.012 μm and (b) u2 = 0.02 μm

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Fig. 7

(a) The normal mean contact pressure and total dislocation density during flattening under sticking contact conditions for a pillar with w = 0.8 μm and hp = 0.4 μm. The letters A, B, and C represent when the shearing starts. (b) The shear stress as a function of tangential displacement at different flattening depths.

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Fig. 8

The stress state σ12 and dislocation distribution for the asperity with w = 0.8 μm and hp = 0.4 μm, on the left column is for the flattening depth u2 = 0.0012 μm and on the right column is for the flattening depth u2 = 0.02 μm

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Fig. 9

(a) The mean contact pressure versus flattening depth and (b) the contact shear stress versus tangential displacement starting from different flattening depths u2 with impenetrable obstacles which are placed at 0.02 μm and 0.4 μm underneath the contact

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Fig. 10

Two-dimensional model of three asperities on a larger crystal flattened and sheared by a rigid platen

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Fig. 11

(a) The elastic shear response of the middle pillar and a sketch that illustrates the definition of strain. (b) The shear traction of the middle pillar as a function of shear strain for different spacings.

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Fig. 12

Stress state σ12 and dislocation structure of three asperities with w = 0.8 μm at shear strain γ = 0.008 for different spacings. (a) sp = 8.0 μm and (b) sp = 0.4 μm.

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Fig. 13

The elastic stress state σ12 for (a) a single asperity and (b) three asperities with spacing sp = 0.4 μm at the strain γ = 0.02

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Fig. 14

The shear traction as a function of shear strain for pillars with width w = 0.8 μm and height hp = 0.4 μm with different spacings

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Fig. 15

Stress state σ12 and dislocation structure of pillars with hp/w = 0.5 and w = 0.8 μm at strain 0.03 for different spacings. (a) sp = 8.0 μm and (b) sp = 0.4 μm.

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Fig. 16

The shear stress as a function of shear strain at the flattening depth u2 = 0.02 μm for the asperity size: (a) w = 0.8 μm, hp = 0.08 μm and (b) w = 0.8 μm, hp = 0.4 μm

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