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Mark R. VanLandingham Weapons and Materials Research Directorate—Materials and Manufacturing Sciences Division, U.S. Army Research Laboratory, ATTN: RDRL-WMM-B, Aberdeen Proving Ground, Maryland 21005-5069

An instrumented indentation method is established to accurately measure the local elastic-plastic material properties of a single fiber by accounting for the additional sources of compliance associated with fiber indentation. The Oliver-Pharr instrumented indentation data analysis method is compared for indentation of a standard, planar fused silica sample and in the radial direction of homogeneous, isotropic E-glass fibers of two different diameters. Compliance contributions from substrate deflection and other nonindentation-related fiber deflections are quantified and shown to be negligible. The added compliance observed is attributed to the lack of constraint due to the finite geometry of a curved fiber surface. This compliance contribution is accounted for by using a proposed area correction to capture the geometry of the curved fiber-probe contact combined with a structural compliance correction. Implementation of these corrections to experimental indentation curves results in accurate measurements of the fiber elastic modulus and hardness.

I. INTRODUCTION

High performance filament (e.g. fiber glass, carbon fiber, aramid etc.) properties are of considerable interest for their use as reinforcement in composite materials. Prior characterization has primarily considered the macroscale (i.e. entire filament) properties of fibers through various microtensile testing and compression techniques.1–11 In this study, the focus will be on material deformation under indentation and measuring the local properties of isotropic, homogeneous E-glass fibers in the radial direction. A. Traditional indentation theory: the Oliver-Pharr method

The Oliver-Pharr method12 is the universally accepted data reduction technique for instrumented indentation, or nanoindentation. Elastic modulus, E, and hardness, H can be extracted from a nanoindentation experimental load (P) versus displacement (h) curve (Fig. 1). The total elastic compliance of the contact, Ct, is defined by the reciprocal of the slope of the unloading curve fit at maximum indendh tation depth, dP at hmax. When all of the assumptions of the Oliver-Pharr method are satisfied, a reduced modulus (E*), or effective probematerial indentation modulus, can then be determined from bulk indentation measurements using Eq. (1). Equation (2) models the indentation “system” of two bodies (i.e., sample a)

Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.336 J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012

http://journals.cambridge.org

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and indenter) as two springs in series, where the effective modulus is the plane strain modulus, E/(1
m2); and the material hardness is given by Eq. (3). E ¼

p1=2 Ct 2bA1=2

;

1 1
m2s 1
m2i ¼ þ E Es Ei H¼

Pmax Amax

ð1Þ

;

:

ð2Þ ð3Þ

In Eq. (2), the subscripts “s” and “i” represent the sample