Estimation of the Hall–Petch strengthening coefficient of steels through nanoindentation Moo-Young Seok, a In-Chul Choi, a Joonoh Moon, b Sungju Kim, c Upadrasta Ramamurty d,e and Jae-il Jang a,⇑ a Division of Materials Science and Engineering, Hanyang University, Seoul 133-791, Republic of Korea b Ferrous Alloys Research Group, Korea Institute of Materials Science, Changwon 641-831, Republic of Korea c R&D Center, Sheet Products Design Team, Hyundai Steel Company, Dangjin 343-823, Republic of Korea d Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India e Center of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia Received 22 March 2014; revised 13 May 2014; accepted 13 May 2014 Available online 20 May 2014 A method to estimate the Hall–Petch coefficient k for yield strength and flow stress of steels through nanoindentation experi- ments is proposed. While determination of k f for flow stress is on the basis of grain boundary strengthening evaluated by sharp indentation, k y for yield strength was computed with pop-in data from spherical indentations. Good agreement between estimated and literature data, obtained from the tensile tests, validates the proposed methodology. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Steel; Hall–Petch relation; Nanoindentation; Grain boundary strengthening One of the most important microstructural parameters that control the yield strength, r y , of poly- crystalline metals and alloys is the grain size, d [1]. At the beginning of 1950s, Hall [2] and Petch [3] indepen- dently observed that r y scales with d 0.5 in a number of metals and alloys. On this basis, the widely known Hall–Petch (HP) relation is derived: r y ¼ðr y Þ 0 þ k y d  1 2 ð1Þ where (r y ) 0 is the friction stress free from grain bound- ary (GB) contributions (and thus is approximately the r y of an extremely coarse-grained, untextured polycrys- tal) and k y is a material constant, which is often referred to as the “HP coefficient” or the “locking parameter”. Note that in alloys with different microstructural con- stituents, such as a/b Ti alloy with grains, colonies and laths, d can be replaced by the deformation-controlling microstructural length scale; the functional form of Eq. (1) is still obeyed [4]. Later, it was suggested that the flow stress at any given strain r(e) also obeys the HP relation [1,5]: rðeÞ¼ r 0 ðeÞþ k f d  1 2 ð2Þ where r 0 (e) corresponds to the flow stress of single crys- tal at that strain and k f is the HP coefficient for flow stress. Similarly, it was reported that the HP equation can successfully describe the grain size effect on hard- ness, H, albeit with a different k [5]. The HP coefficient is an important indicator of the relative contribution of GBs to the strength of the material. If k is small – as in Ti alloys, for example – the strength enhancement that one can obtain through grain refinement may not be much and other alloy design principles may have to be invoked for strength- ening the alloy. Usually, the experimental evaluation of k of a material is performed through a series of stan- dard tensile tests on samples with varying d, and some values of k for r y are listed in Table 1 [2,6–13]. How- ever, this procedure requires a large amount of mate- rial as several tests on many standard-sized samples with different grain sizes are essential for a complete study. http://dx.doi.org/10.1016/j.scriptamat.2014.05.004 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +82 222200402; fax: +82 222202294; e-mail: jijang@hanyang.ac.kr Available online at www.sciencedirect.com ScienceDirect Scripta Materialia 87 (2014) 49–52 www.elsevier.com/locate/scriptamat