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Research Papers

Modeling Nanowire Indentation Test With Adhesion Effect

[+] Author and Article Information
Yin Zhang, Ya-pu Zhao

State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

J. Appl. Mech 78(1), 011007 (Oct 12, 2010) (12 pages) doi:10.1115/1.4002305 History: Received November 02, 2009; Revised February 07, 2010; Posted August 03, 2010; Published October 12, 2010; Online October 12, 2010

Because of the large aspect ratio of its length to radius and the large surface area to volume ratio, the nanowire is highly flexural and susceptible to the adhesion influence. The bending deflection of nanowire and its adhesion effect make the previous indentation models inappropriate for the nanowire indentation test. In this paper, a new model incorporating the nanowire bending deflection, loading symmetry/asymmetry, and adhesion effect is presented and compared with the previous models. Because of the bending deflection of the flexural nanowire, the nanowire may lift-off/separate from its contacting elastic medium and the localized contact effects may thus be induced. The localized contact effects as predicted by this new model can cause the relatively large deflection difference of the nanowire in test as compared with those obtained by the previous models, which impacts directly and significantly on the interpretation of the indentation experimental data. The nanowire is modeled as a cylinder/beam and the indentation force is modeled as a concentrated force. The elastic medium is modeled as an elastic foundation. The elastic foundation behaves as a linear spring in nonadhesive Hertz contact and as a nonlinear softening spring in adhesive contact. In the Hertz contact, due to lift-off, the contact length is independent of the load. However, in adhesive contact, larger load results in smaller contact length. Unlike the Hertz contact in which lift-off always occurs when adhesion force is too large for bending cylinder to overcome, there is no lift-off for cylinder and the full contact scenario is thus formed.

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Figures

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Figure 1

(a) The schematic diagram of a cylinder with Young’s modulus E1, Poisson ratio ν1, radius R and length L in contact with an elastic medium with E2 and ν2. J is the concentrated load and P is the uniformly distributed line load. (b) The contact profile in x−z plane. For the rigid contact scenario, the whole cylinder sinks into the elastic medium with a constant δ. For the flexible contact scenario, the cylinder lifts-off and δ varies with x. x1 and x2 are the left-side and right-side contact lengths. (c) The contact area in x−y plane. For the rigid contact scenario, the contact area is a rectangle and the contact width 2a is constant. For the flexible contact scenario, the contact is an ellipselike zone and the contact width 2a varies with x.

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Figure 2

(a) Geometric relations of R, δ, and a in a cylinder contact and (b) the discontinuous contact scenario in which the cylinder has multiple separated contact zones

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Figure 3

(a) The displacement comparison of flexible contact and rigid contact when l=4 and F=0.1, 0.2, respectively. The concentrated load F is at center, i.e., l1=l2=2. (b) The comparison of contact zones.

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Figure 4

(a) The displacement comparison of flexible contact and rigid contact when l=8 and F=0.1, 0.2, respectively. The concentrated load F is at center, i.e., l1=l2=4. (b) The comparison of contact zones.

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Figure 5

The asymmetric contact scenario. The cylinder length is l=8 and the concentrated force F is located at l1=2.4 and l2=5.6. The comparison of (a) the displacement and (b) the contact zone.

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Figure 8

The comparison of the cylinder displacements of l=4 and α=1×10−3 for F=0.1 and 0.2, respectively

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Figure 9

(a) The cylinder center displacement (W(0)) of l=4 as a function of α for F=0.1 and 0.2, respectively. (b) The right-side contact length (ξ2) as a function of α for F=0.1 and 0.2, respectively.

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Figure 10

The cylinder displacements of l=8 and F=0.1 for α=0, 4×10−3, and 8×10−3, respectively

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Figure 11

The comparison of the cylinder displacements of l=8 and α=4×10−3 for F=0.1 and 0.2, respectively

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Figure 12

(a) The cylinder center displacement (W(0)) of l=8 as a function of α for F=0.1 and 0.2, respectively. (b) The right-side contact length (ξ2) as a function of α for F=0.1 and 0.2, respectively.

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Figure 13

Comparison of the cylinder contact scenarios under tension and compression

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Figure 7

The cylinder displacements of l=4 and F=0.1 for α=0, 1×10−3, and 3×10−3, respectively

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Figure 6

(a) The comparison of A/2Rβ of the rigid and flexible contact scenarios as a function of F for l=4 and 8, respectively. For the flexible contact, A is taken at ξ=0. (b) The comparison of A/2Rβ of the rigid and flexible contact scenarios as a function of l for F=0.1 and 0.5, respectively.

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