Experimental assessment of the representative strains in instrumented sharp indentation N. Chollacoop a , U. Ramamurty b, * a National Metal and Materials Technology Center (MTEC), 114 Paholyothin Road, Pathumthani 12120, Thailand b Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India Received 21 September 2004; received in revised form 2 December 2004; accepted 17 March 2005 Available online 8 April 2005 Abstract Experimental assessment of the reverse algorithms that enable the extraction of plastic properties from the load–depth of pen- etration curves was conducted. Results show that they predict the stresses at 3.3% and 5.7% representative strains for Berkovich and 60° cone-equivalent three-sided pyramidal indenters, respectively, with good accuracy. It was shown that the uniaxial stress–strain curves could be reconstructed from the indentation data. Ó 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Microindentation; Plastic deformation; Tension test; Hardness; Representative strain 1. Introduction Instrumented indentation is a widely-used technique to evaluate the elastic modulus, E, and the hardness, H, from the load, P, vs. depth of penetration, h, data. However, extraction of the yield strength, r y and the work hardening exponent, n, from the P–h curves of sharp indenters is not done as routinely, due to the lack of reliable and simple-to-implement methodologies. Re- cently, Dao et al. [1] and Chollacoop et al. [2] have con- ducted computational studies within the framework of large-strain finite element analysis (LFEA) for sharp indentation on power-law hardening elastic–plastic sol- ids and identified a set of analytical functions that take the pile-up/sink-in effects into account. Further, they identified a representative plastic strain, e r for each in- denter geometry as a strain level that allows for the description of the indentation loading response indepen- dent of n. Estimated values of e r are 3.3% and 5.7% for Berkovich and 60° cone-equivalent pyramidal indenters, respectively. On this basis, they developed algorithms to assess properties of materials within the context of single and dual indentations. These algorithms promise an opportunity to extract r y and n from the P–h curves with similar ease to E and H measurement. However, a critical experimental assessment of them is necessary before they can be fully deployed. This is particularly important since the reported values of e r in the literature are significantly different. Tabor [3] proposed that it is 8% within the plastically deformed region of a Vickers indent. JohnsonÕs expanding cavity model shows that e r = 0.2cot(70.3°) for Vickers indenter [4]. Small-strain finite element simulations of Giannakopoulos et al. [5] suggest that the e r for Vickers and Berkovich indenters is 29%, which is in agreement with the maximum sub- surface strain observed in the region adjacent to the tip of Vickers indentation of Cu by Chaudhri [6]. Atkins and Tabor [7] estimated e r values as a function of the cone angle through hardness measurements on copper and mild-steel samples that are work hardened to differ- ent levels prior to indentation. These are plotted, along with those estimated by Chollacoop et al. [2], as a 1359-6462/$ - see front matter Ó 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2005.03.030 * Corresponding author. Tel.: +91 802 2933241; fax: +91 802 3600472. E-mail address: ramu@met.iisc.ernet.in (U. Ramamurty). www.actamat-journals.com Scripta Materialia 53 (2005) 247–251