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  • Print publication year: 2021
  • Online publication date: May 2021

9 - Nanoindentation and Micropillar Compression


Mechanical testing on a very fine scale, particularly indentation, has become extremely popular. Sophisticated equipment has been developed, often with accompanying software that facilitates the extraction of properties such as stiffness, hardness and other plasticity parameters. The region being tested can be very small – down to sub-micron dimensions. However, strong caveats should be noted concerning such measurements, particularly relating to plasticity. Some of these concern various potential sources of error, such as the effects of surface roughness, oxide films, uncertainty about the precise geometry of the indenter tip etc. Moreover, even if these can be largely eliminated, extraneous effects tend to arise when (plastically) deforming a small region that is constrained by surrounding (elastic) material. They are often grouped together under the heading of “size effects,” with a clear tendency observed for material to appear harder as the scale of the testing is reduced. Various explanations for this have been put forward, some based on dislocation characteristics, but understanding is incomplete and compensating for them in a systematic way does not appear to be viable. A similar level of uncertainty surrounds the outcome of fine scale uniaxial compression testing, although the conditions, and the sources of error, are rather different from those during nanoindentation. Despite the attractions of these techniques, and the extensive work done with them, they are thus of limited use for the extraction of meaningful mechanical properties (related to plasticity).

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1.Oliver, WC and Pharr, GM, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 1992. 7(6): 15641583.
2.Wei, YG, Wang, XZ and Zhao, MH, Size effect measurement and characterization in nanoindentation test. Journal of Materials Research, 2004. 19(1): 208217.
3.Fischer-Cripps, AC, Critical review of analysis and interpretation of nanoindentation test data. Surface and Coatings Technology, 2006. 200: 41534165.
4.Golovin, Y, Nanoindentation and mechanical properties of solids in submicrovolumes, thin near-surface layers, and films: a review. Physics of the Solid State, 2008. 50(12): 22052236.
5.Oliver, WC and Pharr, GM, Nanoindentation in materials research: past, present, and future. MRS Bulletin, 2010. 35(11): 897907.
6.Morris, JR, Bei, H, Pharr, GM and George, EP, Size effects and stochastic behavior of nanoindentation pop in. Physical Review Letters, 2011. 106(16).
7.Voyiadjis, GZ and Yaghoobi, M, Review of nanoindentation size effect: experiments and atomistic simulation. Crystals, 2017. 7(10).
8.Shahbeyk, S, Voyiadjis, GZ, Habibi, V, Astaneh, SH and Yaghoobi, M, Review of size effects during micropillar compression test: experiments and atomistic simulations. Crystals, 2019. 9(11).
9.Fischer-Cripps, AC, Nanoindentation. Mechanical Engineering Series, Ling, FF, ed. New York: Springer-Verlag, 2004.
10.Chen, L, ed. Micro-Nanoindentation in Materials Science. ML Books International, 2015.
11.Tiwari, A and Natarajan, S, eds. Applied Nanoindentation in Advanced Materials. Hoboken, NJ: Wiley, 2017.
12.Tsui, T and Volinsky, AA, eds. Small Scale Deformation Using Advanced Nanoindentation Techniques. MDPI, 2019.
13.Soler, R, Wheeler, JM, Chang, HJ, Segurado, J, Michler, J, Llorca, J and Molina-Aldareguia, JM, Understanding size effects on the strength of single crystals through high-temperature micropillar compression. Acta Materialia, 2014. 81: 5057.
14.Bittencourt, E, Interpretation of the size effects in micropillar compression by a strain gradient crystal plasticity theory. International Journal of Plasticity, 2019. 116: 280296.
15.Takata, N, Takeyasu, S, Li, HM, Suzuki, A and Kobashi, M, Anomalous size-dependent strength in micropillar compression deformation of commercial-purity aluminum single-crystals. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2020. 772.
16.Li, WD, Bei, HB, Qu, J and Gao, YF, Effects of machine stiffness on the loading–displacement curve during spherical nano-indentation. Journal of Materials Research, 2013. 28(14): 19031911.
17.Dargenton, JC and Woirgard, J, Description of an electrostatic force nanoindenter. Journal de Physique III, 1996. 6(9): 12471260.
18.Woirgard, J and Dargenton, JC, A new proposal for design of high accuracy nanoindenters. Measurement Science and Technology, 1995. 6(1): 1621.
19.Yu, N, Bonin, WA and Polycarpou, AA, High-resolution capacitive load-displacement transducer and its application in nanoindentation and adhesion force measurements. Review of Scientific Instruments, 2005. 76(4).
20.Bobji, MS, Ramanujan, CS, Pethica, JB and Inkson, BJ, A miniaturized TEM nanoindenter for studying material deformation in situ. Measurement Science and Technology, 2006. 17(6): 13241329.
21.Elhebeary, M and Saif, MTA, A micromechanical bending stage for studying mechanical properties of materials using nanoindenter. Journal of Applied Mechanics: Transactions of the ASME, 2015. 82(12).
22.Wheeler, JM and Michler, J, Invited article: indenter materials for high temperature nanoindentation. Review of Scientific Instruments, 2013. 84(10): 101301.
23.Monclus, MA, Lotfian, S and Molina-Aldareguia, JM, Tip shape effect on hot nanoindentation hardness and modulus measurements. International Journal of Precision Engineering and Manufacturing, 2014. 15(8): 15131519.
24.Nohava, J, Randall, NX and Conte, N, Novel ultra nanoindentation method with extremely low thermal drift: principle and experimental results. Journal of Materials Research, 2009. 24(3): 873882.
25.Wheeler, JM, Armstrong, DEJ, Heinz, W and Schwaiger, R, High temperature nanoindentation: the state of the art and future challenges. Current Opinion in Solid State & Materials Science, 2015. 19(6): 354366.
26.Chen, J, Bell, GA, Dong, HS, Smith, JF and Beake, BD, A study of low temperature mechanical properties and creep behaviour of polypropylene using a new sub-ambient temperature nanoindentation test platform. Journal of Physics D: Applied Physics, 2010. 43(42).
27.Lee, SW, Cheng, YT, Ryu, I and Greer, JR, Cold-temperature deformation of nano-sized tungsten and niobium as revealed by in-situ nano-mechanical experiments. Science China Technological Sciences, 2014. 57(4): 652662.
28.Wheeler, JM, Oliver, RA and Clyne, TW, AFM observation of diamond indenters after oxidation at elevated temperatures. Diamond & Related Materials, 2010. 19: 13481353.
29.Harris, A, Beake, BD, Armstrong, DEJ and Davies, MI, Development of high temperature nanoindentation methodology and its application in the nanoindentation of polycrystalline tungsten in vacuum to 950˚C. Experimental Mechanics, 2017. 57(7): 11151126.
30.Rzepiejewska-Malyska, KA, Buerki, G, Michler, J, Major, RC, Cyrankowski, E, Asif, SAS and Warren, OL, In situ mechanical observations during nanoindentation inside a high-resolution scanning electron microscope. Journal of Materials Research, 2008. 23(7): 19731979.
31.Nowak, JD, Rzepiejewska-Malyska, KA, Major, RC, Warren, OL and Michler, J, In-situ nanoindentation in the SEM. Materials Today, 2010. 12: 4445.
32.Warren, OL, Shan, ZW, Asif, SAS, Stach, EA, Morris, JW and Minor, AM, In situ nanoindentation in the TEM. Materials Today, 2007. 10(4): 5960.
33.Li, XD and Bhushan, B, A review of nanoindentation continuous stiffness measurement technique and its applications. Materials Characterization, 2002. 48(1): 1136.
34.Wang, LG and Rokhlin, SI, Universal scaling functions for continuous stiffness nanoindentation with sharp indenters. International Journal of Solids and Structures, 2005. 42(13): 38073832.
35.Pharr, GM, Strader, JH and Oliver, WC, Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. Journal of Materials Research, 2009. 24(3): 653666.
36.Bolshakov, A and Pharr, GM, Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation. Journal of Material Research, 1998. 13(4): 10491058.
37.Hay, JC, Bolshakov, A and Pharr, GM, A critical examination of the fundamental relations used in the analysis of nanoindentation data. Journal of Materials Research, 1999. 14(6): 22962305.
38.Nye, JF, Physical Properties of Crystals – Their Representation by Tensors and Matrices. Oxford: Clarendon, 1985.
39.Kim, SH, Kim, YC, Lee, S and Kim, JY, Evaluation of tensile stress–strain curve of electroplated copper film by characterizing indentation size effect with a single nanoindentation. Metals and Materials International, 2017. 23(1): 7681.
40.Chen, X, Ashcroft, IA, Wildman, RD and Tuck, CJ, A combined inverse finite element – elastoplastic modelling method to simulate the size-effect in nanoindentation and characterise materials from the nano to micro-scale. International Journal of Solids and Structures, 2017. 104: 2534.
41.Liu, H, Chen, Y, Tang, Y, Wei, S and Nuiu, G, Tensile and indentation creep behaviour of Mg-5%Sn and Mg-5%Sn-2%Di alloys. Materials Science and Engineering A, 2007. 464: 124128.
42.Takagi, H, Dao, M and Fujiwara, M, Analysis on pseudo-steady indentation creep. Acta Mechanica Solida Sinica, 2008. 21: 283288.
43.Marques, VMF, Wunderle, B, Johnston, C and Grant, PS, Nanomechanical characterisation of Sn-Ag-Cu/Cu joints – part 2: nanoindentation creep and its relationship with uniaxial creep as a function of temperature. Acta Materialia, 2013. 61(7): 24712480.
44.Geranmayeh, AR and Mahmudi, R, Indentation creep of a cast Mg-6Al-1Zn-0.7Si alloy. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2014. 614: 311318.
45.Chatterjee, A, Srivastava, M, Sharma, G and Chakravartty, JK, Investigations on plastic flow and creep behaviour in nano and ultrafine grain Ni by nanoindentation. Materials Letters, 2014. 130: 2931.
46.Wang, Y and Zeng, J, Effects of Mn addition on the microstructure and indentation creep behaviour of the hot dip Zn coating. Materials & Design, 2015. 69: 6469.
47.Mahmudi, R, Shalbafi, M, Karami, M and Geranmayeh, AR, Effect of Li content on the indentation creep characteristics of cast Mg-Li-Zn alloys. Materials & Design, 2015. 75: 184190.
48.Ma, Y, GJ Peng, DH Wen, and TH Zhang, Nanoindentation creep behavior in a CoCrFeCuNi high-entropy alloy film with two different structure states. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2015. 621: 111117.
49.Ginder, RS, Nix, WD and Pharr, GM, A simple model for indentation creep. Journal of the Mechanics and Physics of Solids, 2018. 112: 552562.
50.Goodall, R and Clyne, TW, A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Materialia, 2006. 54(20): 54895499.
51.Chen, J and Bull, SJ, The investigation of creep of electroplated Sn and Ni-Sn coating on copper at room temperature by nanoindentation. Surface and Coatings Technology, 2009. 203(12): 16091617.
52.Dean, J, Campbell, J, Aldrich-Smith, G and Clyne, TW, A critical assessment of the “stable indenter velocity” method for obtaining the creep stress exponent from indentation data. Acta Materialia, 2014. 80: 5666.
53.Campbell, J, Dean, J and Clyne, TW, Limit case analysis of the “stable indenter velocity” method for obtaining creep stress exponents from constant load indentation tests. Mechanics of Time-dependent Materials, 2016. 1: 3143.
54.Nix, WD and Gao, H, Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 1998. 46: 411425.
55.Elmustafa, AA and Stone, DS, Nanoindentation and the indentation size effect: kinetics of deformation and strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 2003. 51: 357381.
56.Zhao, MH, Slaughter, WS, Li, M and Mao, SX, Material-length-scale-controlled nanoindentation size effects due to strain-gradient plasticity. Acta Materialia, 2003. 51(15): 44614469.
57.Lee, H, Ko, S, Han, J, Park, H and Hwang, W, Novel analysis for nanoindentation size effect using strain gradient plasticity. Scripta Materialia, 2005. 53(10): 11351139.
58.Gao, H, Huang, H, Nix, WD and Hutchinson, JW, Mechanism-based strain gradient plasticity – I: theory. Journal of Mechanics and Physics of Solids, 1999. 47: 12391263.
59.Fleck, NA and Hutchinson, JW, A reformulation of strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 2001. 49(10): 22452271.
60.Lorenz, D, Zeckzer, A, Hilpert, U, Grau, P, Johansen, H, and Leipner, HS, Pop-in effect as homogeneous nucleation of dislocations during nanoindentation. Physical Review B, 2003. 67(17).
61.Shim, S, Bei, H, George, EP and Pharr, GM, A different type of indentation size effect. Scripta Materialia, 2008. 59(10): 10951098.
62.Barnoush, A, Welsch, MT and Vehoff, H, Correlation between dislocation density and pop-in phenomena in aluminum studied by nanoindentation and electron channeling contrast imaging. Scripta Materialia, 2010. 63(5): 465468.
63.Ahn, TH, Oh, CS, Lee, K, George, EP and Han, HN, Relationship between yield point phenomena and the nanoindentation pop-in behavior of steel. Journal of Materials Research, 2012. 27(1): 3944.
64.Chrobak, D, Nordlund, K and Nowak, R, Nondislocation origin of GaAs nanoindentation pop-in event. Physical Review Letters, 2007. 98(4).
65.Wang, ZG, Bei, H, George, EP and Pharr, GM, Influences of surface preparation on nanoindentation pop-in in single-crystal Mo. Scripta Materialia, 2011. 65(6): 469472.
66.Watson, MC and Clyne, TW, The tensioned push-out test for measurement of fibre/matrix interfacial toughness under mixed mode loading. Materials Science and Engineering, 1993. A160: 15.
67.Eldridge, JI and Ebihara, BT, Fiber push-out testing apparatus for elevated temperatures. Journal of Materials Research, 1994. 9(4): 10351042.
68.Kalton, AF, Howard, SJ, Janczak-Rusch, J and Clyne, TW, Measurement of interfacial fracture energy by single fibre push-out testing and its application to the titanium–silicon carbide system. Acta Materiala, 1998. 46: 31753189.
69.Rebillat, F, Lamon, J, Naslain, R, Lara-Curzio, E, Ferber, MK and Besmann, TM, Interfacial bond strength in SiC/C/SiC composite materials, as studied by single-fiber push-out tests. Journal of the American Ceramic Society, 1998. 81(4): 965978.
70.Uchic, MD and Dimiduk, DA, A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2005. 400: 268278.
71.Burek, MJ and Greer, JR, Fabrication and microstructure control of nanoscale mechanical testing specimens via electron beam lithography and electroplating. Nano Letters, 2010. 10(1): 6976.
72.Chen, M, Wehrs, J, Michler, J and Wheeler, JM, High-temperature in situ deformation of GaAs micro-pillars: lithography versus FIB machining. JOM, 2016. 68(11): 27612767.
73.Hutsch, J and Lilleodden, ET, The influence of focused-ion beam preparation technique on microcompression investigations: lathe vs. annular milling. Scripta Materialia, 2014. 77: 4951.
74.Kiener, D, Motz, C, Rester, M, Jenko, M and Dehm, G, FIB damage of Cu and possible consequences for miniaturized mechanical tests. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2007. 459(1–2): 262272.
75.Soler, R, Molina-Aldareguia, JM, Segurado, J, Llorca, J, Merino, RI and Orera, VM, Micropillar compression of LiF 111 Single crystals: effect of size, ion irradiation and misorientation. International Journal of Plasticity, 2012. 36: 5063.
76.Uchic, MD, Dimiduk, DM, Florando, JN and Nix, WD, Sample dimensions influence strength and crystal plasticity. Science, 2004. 305(5686): 986989.