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Research Papers

Modeling and Analysis of Cylindrical Nanoindentation of Graphite

[+] Author and Article Information
B. Yang, R. M. Rethinam

Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 32901

S. Mall

Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433

J. Appl. Mech 76(1), 011010 (Nov 05, 2008) (7 pages) doi:10.1115/1.2999412 History: Received March 24, 2008; Revised June 24, 2008; Published November 05, 2008

Graphite at the nanoscale is modeled as a material system consisting of a stack of parallel plates buffered by an elastic material. While the plates represent individual graphene sheets, the buffer material models the Van der Waals interaction between the graphene sheets. As such, the loading on graphite at the nanoscale is characterized by the membrane force, the bending moment, and the shear force in the graphene sheets. Cylindrical nanoindentation of graphite is analyzed by applying a special boundary element method that employs Green’s function for multilayers with platelike interfaces. Because Green’s function satisfies the traction-free surface, the interfacial displacement continuity and the interfacial traction discontinuity conditions, only the indentation surface area where the boundary condition is altered, are numerically discretized. Numerical results of cylindrical nanoindentation are presented. It is shown that the bending moment and the shear force in the graphene sheets are concentrated around the edge of contact, consistent with the singularities existing in the second and the third derivatives of the surface displacement in the reduced case of a semi-infinite homogeneous solid under cylindrical contact. Kinks of single, double, and triple joints are related to the bending moment, the shear force, and the concentrated force, respectively.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cylindrical nanoindentation of a graphite sample specimen modeled as a stack of buffered plates on top of a homogeneous graphite substrate

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Figure 2

Variation of transverse displacement on the surface and along the graphene sheets under cylindrical nanoindentation

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Figure 3

Variation of the second derivative of transverse displacement on the surface and along the graphene sheets

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Figure 4

Variation of the third derivative of transverse displacement on the surface and along the graphene sheets

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Figure 5

Traces of maximum w,11 and w,111 in individual graphene sheets across the stack of graphene sheets. The number of graphene sheets is counted from the top surface (0).

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Figure 6

Variation of maximum w,11 in individual graphene sheets across the stack of graphene sheets

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Figure 7

Variation of maximum w,111 in individual graphene sheets across the stack of graphene sheets

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Figure 8

Variation of total indentation force P with contact half width a

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Figure 9

Variation of maximum w,11 at the EOC with contact half width a

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Figure 10

Variation of maximum w,111 at the EOC with contact half width a

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Figure 11

(a) Bending moment-controlled single-joint kink, (b) shear force-controlled double-joint kink, and (c) concentrated load-controlled triple-joint kink

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