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Research Papers

Scratching of Elastic∕Plastic Materials With Hard Spherical Indenters

[+] Author and Article Information
Shane E. Flores, Michael G. Pontin, Frank W. Zok

Materials Department, University of California, Santa Barbara, CA 93106

J. Appl. Mech 75(6), 061021 (Aug 22, 2008) (7 pages) doi:10.1115/1.2966268 History: Received January 22, 2008; Revised June 30, 2008; Published August 22, 2008

A mechanistic framework has been developed for interpreting scratch tests performed with spherical indenters on elastic∕plastic materials. The pertinent scaling relations have been identified through a plastic analysis and the model has been subsequently calibrated by finite element calculations. The results show that the ratio of scratch force to normal force (or apparent friction coefficient) can be partitioned into two additive components: one due to interfacial friction and another associated with plastic deformation. The plastic component scales parabolically with the normal force and depends only weakly on the true (elastic) friction coefficient. A simple formula for the scratch force, based on the plastic analysis and the numerical results, has been derived. Finally, experimental measurements on two material standards commonly used for nanoindenter calibration have been used to verify the theoretical results.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 8

Indentation hardness of PMMA, measured over a wide force range using both spheroconical and cube-corner indenters

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Figure 9

Experimental measurements of scratch force and normal displacement for (a) and (b) PMMA and (c) and (d) Al. The open circles in (b) and (d) denote approximate points at which steady state is attained.

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Figure 10

SPM images of scratches in PMMA (top) and Al (bottom) at various levels of normal force

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Figure 11

Summary of scratch force measurements. Tests performed with (a) 1μm and (b) 50μm tip radius indenters. The error bars represent standard deviations. The values of FL∕FN at FN∕R2σy=0 in (a) were obtained from the plateau values in (b). The dashed line in (b) represents the predicted dependence on FN∕R2σy through Eqs. 4,11 for μ=0.2.

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Figure 1

Overview of the scratch configuration, the dominant behavioral domains, and the trends in scratch force with normal force and friction coefficient

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Figure 2

Schematic of virtual cutting, indenting, and pasting operations used to model steady-state scratching

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Figure 3

Finite element mesh used for scratch and indentation simulations

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Figure 4

Indentation of elastic-plastic materials with a rigid spherical indenter. Analytical solutions: Eq. 8 for elastic contact, Eq. 9 for plastic contact, and Eq. 10 for elastic∕plastic contact. Data for steel adapted from Johnson (20). Finite element results and experimental measurements on PMMA are from the present study.

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Figure 5

Results of finite element calculations, showing the effects of normal force and friction coefficient on scratch force and scratch depth. The open circles in (b) denote the approximate points at which steady state is attained.

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Figure 6

Development of plastic strain beneath the indenter during a typical scratch simulation for scratch displacements, w∕R, of (a) 0, (b) 0.25, and (c) 2.5 for ((FN∕R2σy)1∕2=0.76, μ=0.125)

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Figure 7

Effects of normal force and friction coefficient on scratch force. The solid lines calculated using the formula shown with k1=0.184 and k2=1.75. Filled symbols: E=3GPa. Open symbols: E=300GPa.

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