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Research Papers

Probing the Relation Between Dislocation Substructure and Indentation Characteristics Using Quantized Crystal Plasticity

[+] Author and Article Information
Lin Li1

Department of Materials Science and Engineering,  The Ohio State University, Columbus, OH 43210 e-mail: linli85@mit.edu

Myoung-Gyu Lee

Graduate Institute of Ferrous Technology,  Pohang University of Science and Technology, Pohang, Gyeongbuk 790-784, Korea e-mail: mglee@postech.ac.kr

Peter M. Anderson

Department of Materials Science and Engineering,  The Ohio State University, Columbus, OH 43210 e-mail: anderson.1@osu.edu

1

Present address: Department of Materials Science and Engineering, MIT, 77 Massachusetts Ave. 8-402, Cambridge, MA, 02139.

J. Appl. Mech 79(3), 031009 (Apr 05, 2012) (9 pages) doi:10.1115/1.4005894 History: Received July 06, 2011; Revised January 17, 2012; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

Novel indentation studies combined with in situ transmission electron microscopy correlate large load drops with instabilities involving dislocation substructure. These instabilities are captured in finite element simulations of indentation that employ quantized crystal plasticity (QCP) in the vicinity of a nanoindenter tip. The indentation load-displacement traces, slip patterns, and creation of gaps are correlated with the scale, strength, and shear strain burst imparted by slip events within microstructural cells. Large load drops (ΔP/P ∼ 25%) are captured provided these cellular slip events produce shear strain bursts ∼ 8%, comparable to 8 dislocations propagating across a 25 nm microstructural cell. The results suggest that plasticity at the submicron, intragranular scale involves violent stress redistributions, triggering multi-cell instabilities that dramatically affect the early stages of a nanoindentation test.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

3D finite element model of indentation of a 10 x 10 x 10 array of cells comprising a [001] oriented grain

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Figure 3

Local (a) shear stress and (b) shear strain on an active slip system α = [1–11][011] in a subsurface cell (see shaded cells, Fig. 5a), for the quantized Q(800 MPa, 4%) and continuum C(800 MPa) cases, with R = 20 s and W = T = H = 10 s

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Figure 4

Normalized indentation load versus displacement for the Q(800 MPa, 4%) and elastic cases, with indentation geometry (R = 20 s, W = T = H = 10 s). Points a, b indicate the first, second load drops, and c, d indicate the start, end of the largest load drop.

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Figure 5

The spatial distribution of the total number of slip events q (Eq. 2) for quantized case Q(800 MPa, 4%), at points (a)–(d) in Fig. 4 (R = 20 s, W = T = H = 10 s)

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Figure 8

(a) Normalized gap opening (g/s) directly under the indenter tip versus normalized indentation depth (δ/R), for the Q(800 MPa, 6%) case; insets show contour plots of g/s at (b) δ/R ∼ 0.017 and (c) δ/R ∼ 0.02, where the largest gaps are created. The indentation geometry is (R = 20 s, W = T = H = 10 s).

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Figure 9

(a) Normalized indentation load versus displacement for the elastic and Q(800 MPa, 4%) cases with a smaller versus larger substructural scale s (s/R = 1/40 versus 1/20, W = T = H = 20 s versus10 s); the spatial distribution of the total number of slip events q at δ/R = 0.015 (point p) for the (b) smaller versus (c) larger substructural scale cases

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Figure 10

(a) Normalized indentation load versus displacement for experiments of Minor [2] versus elastic and quantized cases Q(800 MPa, 4%), Q(1000 MPa, 6%), and Q(1200 MPa, 8%); the spatial distribution of the total number of slip events q at δ/R = 0.2 (point p), for (b) Q(800, 4%); (c) Q(1000, 6%); and (d) Q(1200, 8%). The indenter radius R = 5 s and a smaller sample size (W = T = H = 10 s) is used.

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Figure 11

The same indentation analysis and notation as in Fig. 1, except that a sample of greater in-plane dimensions (W = T = 20 s, H = 10 s) is used

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Figure 12

Discrete points showing simulation data from Table 2 and the line showing the fitted function ΔP/P = B f, where f is defined in Eq. 12 and B = 0.4

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Figure 1

Experimental Berkovich indentation load-displacement trace from an Al grain (size 300 nm). Insets are bright field transmission electron microscope images acquired at points a, b in the indentation trace. After Figs. 1 and 2 of Ref. [2] (Reprinted with permission from Nature Materials).

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Figure 6

Normalized indentation load versus displacement for the continuum C(800 MPa), quantized Q(800 MPa, 2%), Q(800 MPa, 4%), Q(800 MPa, 6%), and elastic cases. The indentation geometry is (R = 20 s, W = T = H = 10 s).

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Figure 7

Spatial distribution of the accumulated slip activity γp (Eq. 2) at indentation depth δ/R = 0.02, for the (a) C(800 MPa), (b) Q(800 MPa, 2%), (c) Q(800 MPa, 4%) and (d) Q(800 MPa, 6%) cases. The indentation geometry is (R = 20 s, W = T = H = 10 s). See Fig. 6.

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Figure 13

Predictions from Eq. 12 of the relative load drop ΔP/P versus indentation depth δ/R for (a) s/R = (a) 1/20 and (b) 1/5. Values of critical strength (τc ) and quantized strain jump (Δγp ) are shown next to each curve.

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