Assessment of elastic anisotropy and incipient plasticity in Fe 3 C by nanoindentation
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The elastic anisotropy of cementite (Fe3C) is still under discussion. Recent theoretical (ab initio) calculations predict a very high elastic anisotropy for this iron carbide, and a few published experiments suggest that prediction could be true. This work presents a first attempt of using nanoindentation for assessing the elastic anisotropy of such an important component of steels. Our nanoindentation results show that the elastic anisotropy of Fe3C is high but smaller than predicted by ab initio calculations. The elastic modulus is obtained from the load–penetration curves before the first pop-in indicative of plasticity nucleation is detected. The tests thus provide information on the plastic anisotropy of cementite. Surprisingly, the mean indentation pressure or the maximum shear stress under the indenter at the onset of plasticity has been observed to be nearly independent of the crystalline orientation of the indented surface. I. INTRODUCTION
Instrumented indentation and specially nanoindentation has provided us with a high-resolution tool for characterizing the mechanical properties in very small specimens or in very localized volumes. The well-known work by Oliver and Pharr1 set the conditions for a standard procedure to measure both hardness and Young’s modulus of materials by means of this technique. Based on Sneddon’s2 work on purely isotropic elastic contact, Oliver and Pharr showed that the elastic unloading could be related to the indentationreduced elastic modulus (Mr) as follows: pffiffiffiffiffi 2 S ¼ pffiffiffi Mr Ac ; ð1Þ p where S is the unloading stiffness at maximum load and Ac is the projected contact area between the surface of the sample and the indenter. The stiffness contribution of the indenter can be corrected as follows: 1 1 Mr1 ¼ Msam þ Mind
;
ð2Þ
where Msam and Mind are, respectively, the indentation modulus of the sample and the indenter. In the case of elastically isotropic materials, the indentation modulus reduces to the well-known expression: M¼
E 1 m2
;
ð3Þ
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.284 J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012
http://journals.cambridge.org
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where E is the Young’s modulus and m is the Poisson’s ratio. The work by Oliver and Pharr has two main limitations: (i) the contact area is not obvious since sink-in and pile-up phenomena may occur in the neighborhood of the indentation depending on both the elastic and plastic properties of the sample3,4 and (ii) the indentation modulus may vary with the crystal orientation as a consequence of the elastic anisotropy of the crystal. The first limitation can be circumvented if the indentation modulus is calculated from the initial elastic loading segment of the indentation. This can be done from the analysis of very shallow indentations if the transition from elastic to elastic–plastic regime can be detected (pop-in phenomenon indicative of early plasticity) and provided no surface layer or film disturbs the accurate measurement of the in
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