Experimental method to account for structural compliance in nanoindentation measurements
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C.R. Frihart, J.F. Beecher, and R.J. Moon United States Department of Agriculture (USDA) Forest Products Laboratory, Madison, Wisconsin 53726
D.S. Stone Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706; and Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706 (Received 10 October 2007; accepted 10 January 2008)
The standard Oliver–Pharr nanoindentation analysis tacitly assumes that the specimen is structurally rigid and that it is both semi-infinite and homogeneous. Many specimens violate these assumptions. We show that when the specimen flexes or possesses heterogeneities, such as free edges or interfaces between regions of different properties, artifacts arise in the standard analysis that affect the measurement of hardness and modulus. The origin of these artifacts is a structural compliance (Cs), which adds to the machine compliance (Cm), but unlike the latter, Cs can vary as a function of position within the specimen. We have developed an experimental approach to isolate and remove Cs. The utility of the method is demonstrated using specimens including (i) a silicon beam, which flexes because it is supported only at the ends, (ii) sites near the free edge of a fused silica calibration standard, (iii) the tracheid walls in unembedded loblolly pine (Pinus taeda), and (iv) the polypropylene matrix in a polypropylene–wood composite. I. INTRODUCTION 1
When Oliver and Pharr originally derived what has now become the most commonly applied method for analysis of nanoindentation data, they constructed it based on a study of bulk, homogeneous materials. This “standard” method implicitly relies on the assumptions that the specimen be homogeneous, that it fill a halfspace, and that it be rigidly supported in the testing machine. Notably, though, the greatest potential of nanoindentation is reached when it is used to study specimens that violate these assumptions: specimens that are themselves extremely small, or specimens that possess heterogeneities with length scales comparable to the nanoindents themselves. Our interest in the applicability of nanoindentation stems from our investigations of the mechanical properties of wood. In recent years, scientists have used nanoindentation to study tracheid walls in softwood trees2–6 and to investigate the effects of chemical additions7–9 and heat treatments10 on the mechanical properties of the a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0131 J. Mater. Res., Vol. 23, No. 4, Apr 2008
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walls. The tracheid is the predominant type of cell found in softwood, and a transverse cross section of a tracheid is illustrated in Fig. 1. A tracheid is basically a hollow cylindrical tube with a wall composed of several concentric laminations. Individual tracheids are held together by the middle lamella. Although the standard nanoindentation analyses have proven to be a useful tool for wood science res
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