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Effect of Hydrostatic Pressure on Indentation Modulus

Published online by Cambridge University Press:  01 February 2011

William M. Mook  and
W. W. Gerberich
William M. Mook
Affiliation:
[email protected], University of Minnesota, Chemical Engineering and Materials Science, 421 Washington Ave. SE, Minneapolis, MN, 55455, United States
W. W. Gerberich
Affiliation:
[email protected], University of Minnesota, Minneapolis, MN, 55455, United States
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Abstract

The high pressures generated at a contact during nanoindentation have a quantifiable effect on the measured indentation modulus. This effect can be accounted for by invoking a Murnaghan equation of state-based analysis where the measured indentation modulus is a function of the hydrostatic component of the stress state which is generated beneath the indenter tip. This approach has implications pertinent to a range of mechanical characterization techniques that include instrumented indentation and quantitative atomic force microscopy (AFM) since these techniques traditionally consider only zero-pressure modulus values during data interpretation. To demonstrate the validity of this approach, the indentation modulus of four materials (fused quartz, sapphire, rutile and silicon) is evaluated using a 1 μm radius conospherical diamond tip to maximum contact depths of 30 nm. The tip area function is independently determined via AFM while the unloading stiffness from the load-displacement data is determined using standard Oliver-Pharr analysis.

Keywords

elastic propertiesnanoscalescanning probe microscopy (SPM)
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1049: Symposium AA – Fundamentals of Nanoindentation and Nanotribology IV , 2007 , 1049-AA02-09
Copyright
Copyright © Materials Research Society 2008

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References

1 Gerberich, W.W., Mook, W.M., Cordill, M.J., Jungk, J.M., Boyce, B., Friedmann, T., Moody, N.R. and Yang, D., Int. J. Fracture, 2006, 138, 75–100.Google Scholar
2 Mook, W.M., Nowak, J.D., Perrey, C.R., Carter, C.B., Mukherjee, R., Girshick, S.L., McMurry, P.H. and Gerberich, W.W., Phys. Rev. B, 2007, 75, 214112–214111.Google Scholar
3 Oliver, W.C. and Pharr, G.M., J. Mater. Res., 1992, 7, 1564–1583.Google Scholar
4 Oliver, W.C. and Pharr, G.M., J. Mater. Res., 2004, 19, 3–20.Google Scholar
5 Strader, J.H., Shim, S., Bei, H., Oliver, W.C., Pharr, G.M., Philos. Mag., 2006, 86, 5285–98.Google Scholar
6 Read, D., Keller, R., Barbosa, N. and Geiss, R., Metall. Mater. Trans. A, 2007, 38, 2242–2248.Google Scholar
7 Murnaghan, F.D., Finite deformation of an elastic solid, John Wiley and Sons, Chapman and Hall, 1951.Google Scholar
8 Anderson, O.L., Equations of State for Solids in Geophysics and Ceramic Science, Oxford U. Press, Oxford, 1995.Google Scholar
9 Stacey, F.D. and Davis, P.M., Phys. Earth Planet. Inter., 2004, 142, 137–184.Google Scholar
10 Christensen, N.E., Ruoff, A.L. and Rodriguez, C.O., Phys. Rev. B, 1995, 52, 9121–9124.Google Scholar
11 Speziale, S., Chang-Sheng, Z., Duffy, T.S., Hemley, R.J. and Ho-Kwang, M., J. Geophys. Res., 2001, 106, 515–528.Google Scholar
12 Poirier, J.P., Introduction to the physics of the Earth's interior, 2nd ed., Cambridge University Press, Cambridge, New York, 2000.Google Scholar
13 Veprek, R.G., Parks, D.M., Argon, A.S. and Veprek, S., Mater. Sci. Eng., A, 2007, 448, 366–378.Google Scholar
14 Wolf, B. and Goken, M., MetaIlkd, Z.., 2005, 96, 1247–1251.Google Scholar
15 Fischer-Cripps, A.C., Nanoindentation, New York: Springer, 2004.Google Scholar
16 Gerward, L. and Olsen, J.S., Mater. Sci. Forum, 1996, 228–231, 383–386.Google Scholar
17 Hazen, R.M. and Finger, L.W., J. Phys. Chem. Solids, 1981, 42, 143–151.Google Scholar
18 Gerward, L. and Olsen, J.S., J. Appl. Crystallogr., 1997, 30, 259.Google Scholar