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Strain rate effect of strength is a crucial factor for material characterization. Attempts have been made to evaluate strain rate effect by indentation tests. An indentation causes a non-uniform stress and strain field inside a specimen. This must induce a non-uniform strain rate field. However, little has been reported about strain rate distribution beneath the indenter. So far, various indenter control methods have been used. In previous studies, no direct comparisons were available as to how strain rate distribution was affected by different control methods. In this study, we report on the strain rate effect of indentation with two indenter control methods: constant loading rate (CLR) and constant indentation strain rate (CISR). The finite element method was designed to reproduce deformation caused by a conical indenter of a half apex angle of 70.3°. Pure aluminum (99.999 mass% purity), which showed high strain rate dependence of strength, was chosen as a specimen. Material properties were obtained from low strain rate (10−4, 10−2/s) to high strain rate (102/s) tests, and results were incorporated into a FEM analysis using the Cowper–Symonds equation. Four constant loading rates (from 0.7 to 350 mN/s) and constant indentation strain rates (from 0.006 to 6/s) were used, and both results were compared. Differences between both indenter control methods were displacement-dependent. Loading curvature, which has been defined as a material constant in the indentation, was calculated from load divided by square of displacement. Although loading curvatures were decreased with increasing displacement for CLR, they were constant for CISR. Results also showed that values of strain rate decreased as displacement increased for CLR, whereas they were the same for CISR. Similarities of both indenter control methods were found as follows. The highest strain rate regions were observed at the edge of the indenter. In addition, higher strain rate region was distributed hemispherically from the edge of the indenter.
finite element analysis, indentation, indentation strain rate, pure aluminum, strain rate, strain rate sensitivity
[1] Fischer-Cripps, A.C., Nanoindentation Third Edition, Springer New York, 2011. https://doi.org/10.1016/B978-0-12-387667-6.00013-0
[2] Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A. & Suresh, A., Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Materialia, 49(19), pp. 3899–3918, 2001.https://doi.org/10.1016/S1359-6454(01)00295-6
[3] Tabor, D., The physical meaning of indentation and scratch hardness. British Journal of Applied Physics, 7, pp. 159–166, 1956.https://doi.org/10.1088/0508-3443/7/5/301
[4] Johnson, K.L., The correlation of indentation experiments. Journal of the Mechanics Physics of Solids, 18(1), pp. 115–126, 1970.https://doi.org/10.1016/0022-5096(70)90029-3
[5] Mulhearn, T.O., The deformation of metals by vickers-type pyramidal indenters. Journal of Mechanics and Physics of Solids, 7(2), pp. 85–88, 1959. https://doi.org/10.1016/0022-5096(59)90013-4
[6] Chaudhri, M.M., Subsurface strain distribution around vickers hardness indentations in annealed polycrystalline copper. Acta Materialia, 46(9), pp. 3047–3056, 1998. https://doi.org/10.1016/S1359-6454(98)00010-X
[7] Branch, N.A., Arakere, N.K., Subhash, G. & Klecka, M.A., Determination of constitutive response of plastically graded materials. International Journal of Plasticity, 27(5), pp. 728–738, 2011.https://doi.org/10.1016/j.ijplas.2010.09.001
[8] Kese, K.O., Li, Z.C. & Bergman, B., Influence of residual stress on elastic modulus and hardness of soda-lime glass measured by nanoindentation. Journal of Materials Research, 19(10), pp. 3109–3119, 2011.https://doi.org/10.1557/JMR.2004.0404
[9] Cabibbo, M., Ciccarelli, D. & Spigarelli, S., Nanoindentation hardness measurement in piling up SiO2 coating. Physics Procedia, 40, pp. 100–112, 2013. https://doi.org/10.1016/j.phpro.2012.12.014
[10] Ogasawara, N., Chiba, N. & Chen, X., Representative strain of indentation analysis. Journal of Materials Research, 20(08), pp. 2225–2234, 2005. https://doi.org/10.1557/JMR.2005.0280
[11] Cheng, Y. & Li, Z., Hardness obtained from conical indentations with various cone angles. Journal of Materials Research, 15(12), pp. 2830–2835, 2000. https://doi.org/10.1557/JMR.2000.0404
[12] Mesarovic, S.D. & Fleck, N.A., Spherical indentation of elastic-plastic solids. Proceeding of the Royal Society London A, 455, pp. 2707–2728, 1999. https://doi.org/10.1098/rspa.1999.0423
[13] Ma, X., Yoshida, F. & Shinbata, K., On the loading curve in microindentation of viscoplastic solder alloy. Materials Science and Engineering: A, 344, pp. 296–299, 2003. https://doi.org/10.1016/S0921-5093(02)00442-2
[14] Yamada, H., Ogasawara, N., Shimizu, Y., Horikawa, K., Kobayashi, K. & Chen, X., Effect of high strain rate on indentation in pure aluminum. Journal of Engineering Materials and Technology, 135(2), p. 021010, 2013. https://doi.org/10.1115/1.4023778
[15] Bowden, F.P. & Tabor, D., The Friction and Lubrication of Solids, Clarendon Press, Walton Street, Oxford OX2 6DP, UK, 1986.
[16] Bucaille, J.L., Stauss, S., Felder, E. & Michler, J., Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Materialia, 51(6), pp. 1663–1678, 2003.https://doi.org/10.1016/S1359-6454(02)00568-2
[17] Cowper, G.R. & Symonds, P.S., Strain hardening and strain-rate effects in the impact loading of cantiliver beams. Brown Univ., Div. Appl. Mech., Report,. 28, 1957.
[18] Yamada, H., Midori, H., Kami, T., Ogasawra, N. & Chen, X., Effect of dynamic strain rate on micro-indentation properties of pure aluminum. EPJ Web Conferences, 94, 04034, 2015.https://doi.org/10.1051/epjconf/20159404034
[19] Doerner, M.F. & Nix, W.D., A method for interpreting the data from depth-sensing indentation instruments. Journal of Materials Research, 1(4), pp. 601–609, 1986. https://doi.org/10.1557/JMR.1986.0601
[20] Mayo, M.J. & Nix, W.D., A micro-indentation study of superplasticity in Pb, Sn, and Sn-38 wt% Pb. Acta Metall, 36(8), pp. 2183–2192, 1988.https://doi.org/10.1016/0001-6160(88)90319-7
[21] Andrews, E.W., Giannakopoulos, A.E., Plisson, E. & Suresh, S., Analysis of the impact of a sharp indenter. International Journal of Solids and Structures, 39, pp. 281–295, 2002.https://doi.org/10.1016/S0020-7683(01)00215-3
[22] Guo, Y.Z., Behm, N.A., Ligda, J.P., Li, Y.L., Pan, Z., Horita, Z. & Wei, Q., Critical issues related to instrumented indentation on non-uniform materials: application to niobium subjected to high pressure torsion. Materials Science and Engineering: A, 586, pp. 149–159, 2013.https://doi.org/10.1016/j.msea.2013.08.015
[23] Lucas, B.N. & Oliver, W.C., Indentation power-law creep of high-purity indium. Metallurgical and Materials Transaction A, 30A, pp. 601–610, 1999. https://doi.org/10.1007/s11661-999-0051-7
[24] Alkorta, J., Manuel, M.E.J. & Sevillano, J.G., On the elastic effects in power-law indentation creep with sharp conical indenters. Journla of Materials, Research, 23(1), pp. 182–188, 2008.https://doi.org/10.1557/JMR.2008.0011
[25] Poisl, W.H., Oliver, W.C. & Fabes, B.C., The relationship between indentation and uniaxial creep in amorphous selenium. Journal of Materials Research, 10(08), pp. 2024– 2032, 1994.https://doi.org/10.1557/JMR.1995.2024