Interpretations of Indentation Size Effects

[+] Author and Article Information
W. W. Gerberich, N. I. Tymiak, J. C. Grunlan

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue, S.E., Minneapolis, MN 55455

M. F. Horstemeyer

Center for Materials and Engineering Sciences, Sandia National Laboratories, MS 9404, Livermore, CA 94551-0969

M. I. Baskes

Los Alamos National Laboratory, MSG 755, Los Alamos, NM 87545

J. Appl. Mech 69(4), 433-442 (Jun 20, 2002) (10 pages) doi:10.1115/1.1469004 History: Revised January 08, 2001; Received March 15, 2001; Online June 20, 2002
Copyright © 2002 by ASME
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Hardness as a function of contact dimension in 〈100〉 tungsten crystals showing the ISE
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Average strain gradients, χ, versus depth of penetration, δ, into 〈100〉 W (open symbols) and 〈100〉 Al (closed symbols) crystals. Four different diamond tip radii used in each case.
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Schematic of spherical and sharp wedge contacts showing difference in strain gradient dependence on contact shape
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Mises strain as a function of distance, r, from indenter tip for a three-dimensional finite difference numerical analysis
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Ratio of surface to volume works as a function of indentation depth into 〈100〉 Al and 〈100〉 Fe-3wt%Si single crystals
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Surface-to-volume ratio, defined by projected contact area to plastic volume, as a function of indentation depth for (a) 〈100〉 W and 〈100〉 Fe-3wt%Si; (b) 〈100〉 Au and 〈100〉 Al single crystals. Solid and dashed curves represent the mean S/V values for each material. Note the different scales for the two materials in (b).
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Fit of the proposed model (Eq. (19)) for four 〈100〉 oriented single crystals. Single tips of 205 nm and 70 nm radii used in (a) and (c), respectively; multiple spherical tips with radii noted used in (b) and (d)
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Master plot of Eq. (19) for all materials
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Incorporation of the Baskes and Horstemeyer definition of volume to surface ratio, (V/S)B, for comparison of atomistic simulations to the present data: solid line is a power-law fit with −0.38 slope similar to Eq. (21b)




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