Skip to main content Accessibility help
  • Print publication year: 2021
  • Online publication date: May 2021

8 - Indentation Plastometry


Indentation plastometry is now emerging as a potentially valuable addition to the range of testing techniques in widespread use. In many ways, it incorporates an amalgamation of the convenience and ease of usage offered by hardness testing with the more rigorous and meaningful outcomes expected of tensile testing. The indentation procedure itself is very similar to that of hardness testing, except that the loads required are higher than those used in most types of hardness test. The major difference is that the experimental data extracted are much more comprehensive, either in the form of a load–displacement plot or as a residual indent profile (with the latter offering several advantages). However, these experimental data only become useful if they can be processed so as to obtain a (true) stress–strain relationship, which can in turn be used to predict the (nominal) stress–strain curve of a conventional tensile test, including the strength (UTS) and the post-necking and rupture characteristics. This can only be done in a reliable way via iterative FEM simulation of the indentation process, but commercial packages in which this capability is integrated with a test facility are now becoming available.

Related content

Powered by UNSILO
1.Pelletier, H, Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation. Tribology International, 2006. 39: 593606.
2.Heinrich, C, Waas, AM and Wineman, AS, Determination of material properties using nanoindentation and multiple indenter tips. International Journal of Solids and Structures, 2009. 46: 364376.
3.Dean, J, Wheeler, JM and Clyne, TW, Use of quasi-static nanoindentation data to obtain stress–strain characteristics for metallic materials. Acta Materialia, 2010. 58: 36133623.
4.Guelorget, B, Francois, M, Liu, C and Lu, J, Extracting the plastic properties of metal materials from microindentation tests: experimental comparison of recently published methods. Journal of Materials Research, 2007. 22: 15121519.
5.Dao, M, Chollacoop, N, Van Vliet, KJ, Venkatesh, TA and Suresh, S, Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Materialia, 2001. 49: 38993918.
6.Bouzakis, K and Michailidis, N, Coating elastic–plastic properties determined by means of nanoindentations and FEM-supported evaluation algorithms. Thin Solid Films, 2004. 469: 227232.
7.Bouzakis, K and Michailidis, N, An accurate and fast approach for determining materials stress–strain curves by nanoindentation and its FEM-based simulation. Materials Characterisation, 2006. 56: 147157.
8.Bolzon, G, Maier, G and Panico, M, Material model calibration by indentation, imprint mapping and inverse analysis. International Journal of Solids and Structures, 2004. 41(11–12): 29572975.
9.Bobzin, K, Bagcivan, N, Theiss, S, Brugnara, R and Perne, J, Approach to determine stress strain curves by FEM supported nanoindentation. Materialwissenschaft Und Werkstofftechnik, 2013. 44(6): 571576.
10.Patel, DK and Kalidindi, SR, Correlation of spherical nanoindentation stress–strain curves to simple compression stress–strain curves for elastic–plastic isotropic materials using finite element models. Acta Materialia, 2016. 112: 295302.
11.Dean, J and Clyne, TW, Extraction of plasticity parameters from a single test using a spherical indenter and FEM modelling. Mechanics of Materials, 2017. 105: 112122.
12.Campbell, JE, Thompson, RP, Dean, J and Clyne, TW, Experimental and computational issues for automated extraction of plasticity parameters from spherical indentation. Mechanics of Materials, 2018. 124: 118131.
13.Campbell, JE, Thompson, RP, Dean, J and Clyne, TW, Comparison between stress–strain plots obtained from indentation plastometry, based on residual indent profiles, and from uniaxial testing. Acta Materialia, 2019. 168: 8799.
14.Taljat, B, Zacharia, T and Kosel, F, New analytical procedure to determine stress–strain curve from spherical indentation data. International Journal of Solids and Structures, 1998. 35(33): 44114426.
15.Herbert, EG, Pharr, GM, Oliver, WC, Lucas, BN and Hay, JL, On the measurement of stress–strain curves by spherical indentation. Thin Solid Films, 2001. 398: 331335.
16.Pelletier, H, Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation. Tribology International, 2006. 39(7): 593606.
17.Kang, BSJ, Yao, Z and Barbero, EJ, Post-yielding stress–strain determination using spherical indentation. Mechanics of Advanced Materials and Structures, 2006. 13(2): 129138.
18.Basu, SM, Moseson, A and Barsoum, MW, On the determination of spherical nanoindentation stress–strain curves. Journal of Materials Research, 2006. 21(10): 26282637.
19.Hausild, P, Materna, A and Nohava, J, On the identification of stress–strain relation by instrumented indentation with spherical indenter. Materials & Design, 2012. 37: 373378.
20.Hamada, AS, Haggag, FM and Porter, DA, Non-destructive determination of the yield strength and flow properties of high-manganese twinning-induced plasticity steel. Materials Science and Engineering A: Structural Materials Properties Microstructure and Processing, 2012. 558: 766770.
21.Xu, BX and Chen, X, Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test. Journal of Materials Research, 2010. 25(12): 22972307.
22.Pathak, S and Kalidindi, SR, Spherical nanoindentation stress–strain curves. Materials Science & Engineering R: Reports, 2015. 91: 136.
23.Pintaude, G and Hoechele, AR, Experimental analysis of indentation morphologies after spherical indentation. Materials Research, 2014. 17: 5660.
24.Futakawa, M, Wakui, T, Tanabe, Y and Ioka, I, Identification of the constitutive equation by the indentation technique using plural indenters with different apex angles. Journal of Materials Research, 2001. 16: 22832292.
25.Chollacoop, N, Dao, M and Suresh, S, Depth-sensing instrumented indentation with dual sharp indenters. Acta Materialia, 2003. 51(13): 37133729.
26.Cheng, Y-T and Cheng, C-M, Scaling, dimensional analysis, and indentation measurements. Materials Science and Engineering: R: Reports, 2004. 44(4–5): 91149.
27.Capehart, TW and Cheng, YT, Determining constitutive models from conical indentation: sensitivity analysis. Journal of Materials Research, 2003. 18(4): 827832.
28.Bucaille, JL, Stauss, S, Felder, E and Michler, J, Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Materialia, 2003. 51(6): 16631678.
29.Ma, ZS, Zhou, YC, Long, SG, Zhong, XL and Lu, C, Characterization of stress–strain relationships of elastoplastic materials: an improved method with conical and pyramidal indenters. Mechanics of Materials, 2012. 54: 113123.
30.Sun, Y, Zheng, S, Bell, T and Smith, J, Indenter tip radius and load frame compliance calibration using nanoindentation loading curves. Philosophical Magazine Letters, 1999. 79(9): 649658.
31.Ullner, C, Reimann, E, Kohlhoff, H and Subaric-Leitis, A, Effect and measurement of the machine compliance in the macro range of instrumented indentation test. Measurement, 2010. 43(2): 216222.
32.Van Vliet, KJ, Prchlik, L and Smith, JF, Direct measurement of indentation frame compliance. Journal of Materials Research, 2011. 19(1): 325331.
33.Campbell, JE, Kalfhaus, T, Vassen, R, Thompson, RP, Dean, J and Clyne, TW, Mechanical properties of sprayed overlayers on superalloy substrates, obtained via indentation testing. Acta Materialia, 2018. 154: 237245.
34.Lee, J, Lee, C and Kim, B, Reverse analysis of nano-indentation using different representative strains and residual indentation profiles. Materials & Design, 2009. 30(9): 33953404.
35.Yao, WZ, Krill, CE, Albinski, B, Schneider, HC, and You, JH, Plastic material parameters and plastic anisotropy of tungsten single crystal: a spherical micro-indentation study. Journal of Materials Science, 2014. 49(10): 37053715.
36.Wang, MZ, Wu, JJ, Hui, Y, Zhang, ZK, Zhan, XP and Guo, RC, Identification of elastic–plastic properties of metal materials by using the residual imprint of spherical indentation. Materials Science and Engineering A: Structural Materials Properties Microstructure and Processing, 2017. 679: 143154.
37.Richmond, JC and Francisco, AC, Use of plastic replicas in evaluating surface texture of enamels. Journal of Research of the National Bureau of Standards, 1949. 42(5): 449460.
38.Skelton, RP, Maier, HJ and Christ, HJ, The Bauschinger effect, Masing model and the Ramberg–Osgood relation for cyclic deformation in metals. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 1997. 238(2): 377390.
39.Samuel, KG and Rodriguez, P, On power-law type relationships and the Ludwigson explanation for the stress–strain behaviour of AISI 316 stainless steel. Journal of Materials Science, 2005. 40(21): 57275731.
40.Belytschko, T, Gracie, R and Ventura, G, A review of extended/generalized finite element methods for material modeling. Modelling and Simulation in Materials Science and Engineering, 2009. 17(4).
41.Roters, F, Eisenlohr, P, Hantcherli, L, Tjahjanto, DD, Bieler, TR and Raabe, D, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Materialia, 2010. 58(4): 11521211.
42.Giannakopoulos, AE and Suresh, S, Determination of elastoplastic properties by instrumented sharp indentation. Scripta Materialia, 1999. 40(10): 11911198.
43.Taljat, B and Pharr, GM, Development of pile-up during spherical indentation of elastic–plastic solids. International Journal of Solids and Structures, 2004. 41(14): 38913904.
44.Karthik, V, Visweswaran, P, Bhushan, A, Pawaskar, DN, Kasiviswanathan, KV, Jayakumar, T and Raj, B, Finite element analysis of spherical indentation to study pile-up/sink-in phenomena in steels and experimental validation. International Journal of Mechanical Sciences, 2012. 54(1): 7483.
45.Klein, CA, Anisotropy of Young modulus and Poisson ratio in diamond. Materials Research Bulletin, 1992. 27(12): 14071414.
46.Isselin, J, Iost, A, Golek, J, Najjar, D, and Bigerelle, M, Assessment of the constitutive law by inverse methodology: small punch test and hardness. Journal of Nuclear Materials, 2006. 352(1–3): 97106.
47.Swaddiwudhipong, S, Hua, J, Harsono, E, Liu, ZS and Ooi, NSB, Improved algorithm for material characterization by simulated indentation tests. Modelling and Simulation in Materials Science and Engineering, 2006. 14(8): 13471362.
48.Peyrot, I, Bouchard, PO, Ghisleni, R and Michler, J, Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm. Journal of Materials Research, 2009. 24(3): 936947.
49.Chen, J, Chen, HN and Chen, J, Evaluation of mechanical properties of structural materials by a spherical indentation based on the representative strain – an improved algorithm at great depth ratio. Acta Metallurgica Sinica – English Letters, 2011. 24(5): 405414.
50.Meng, L, Breitkopf, P, Raghavan, B, Mauvoisin, G, Bartier, O and Hernot, X, On the study of mystical materials identified by indentation on power law and Voce hardening solids. International Journal of Material Forming, 2019. 12: 587602.
51.Nelder, JA and Mead, R, A simplex method for function minimization. The Computer Journal, 1965. 7(4): 308313.
52.Gao, FC and Han, LX, Implementing the Nelder–Mead simplex algorithm with adaptive parameters. Computational Optimization and Applications, 2012. 51(1): 259277.
53.Oliphant, TE, Python for scientific computing. Computing in Science & Engineering, 2007. 9(3): 1020.
54.van der Walt, S, Colbert, SC and Varoquaux, G, The Numpy array: a structure for efficient numerical computation. Computing in Science & Engineering, 2011. 13(2): 2230.
55.Bunge, HJ, Texture Analysis in Materials Science: Mathematical Methods. London: Butterworth, 1982.
56.Wenk, HR and Van Houtte, P, Texture and anisotropy. Reports on Progress in Physics, 2004. 67(8): 13671428.
57.Zhao, Z, Mao, W, Roters, F and Raabe, D, A texture optimization study for minimum earing in aluminium by use of a texture component crystal plasticity finite element method. Acta Materialia, 2004. 52(4): 10031012.
58.Raabe, D, Wang, Y and Roters, F, Crystal plasticity simulation study on the influence of texture on earing in steel. Computational Materials Science, 2005. 34(3): 221234.
59.Clyne, TW and Withers, PJ, An Introduction to Metal Matrix Composites. Cambridge Solid State Science Series, Davis, E and Ward, I, eds. Cambridge: Cambridge University Press, 1993.
60.Taljat, B and Pharr, GM. Measurement of residual stresses by load and depth sensing spherical indentation, in Thin Films: Stresses and Mechanical Properties VIII. Warrendale, PA: Materials Research Society, 2000, pp. 519524.
61.Swadener, JG, Taljat, B and Pharr, GM, Measurement of residual stress by load and depth sensing indentation with spherical indenters. Journal of Materials Research, 2001. 16(7): 20912102.
62.Jang, JI, Estimation of residual stress by instrumented indentation: a review. Journal of Ceramic Processing Research, 2009. 10(3): 391400.
63.Sakharova, NA, Prates, PA, Oliveira, MC, Fernandes, JV and Antunes, JM, A simple method for estimation of residual stresses by depth-sensing indentation. Strain, 2012. 48(1): 7587.
64.Cao, YP and Lu, J, A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve. Acta Materialia, 2004. 52: 40234032.
65.Xu, ZH and Li, XD, Influence of equi-biaxial residual stress on unloading behaviour of nanoindentation. Acta Materialia, 2005. 53(7): 19131919.
66.Larsson, PL, On the influence of elastic deformation for residual stress determination by sharp indentation testing. Journal of Materials Engineering and Performance, 2017. 26(8): 38543860.
67.Zhang, TH, Yu, C, Peng, GJ and Feng, YH, Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test. MRS Communications, 2017. 7(2): 221228.
68.Wang, ZY, Deng, LX and Zhao, JP, A novel method to extract the equi-biaxial residual stress and mechanical properties of metal materials by continuous spherical indentation test. Materials Research Express, 2019. 6(3).
69.Zhang, TH, Cheng, WQ, Peng, GJ, Ma, Y, Jiang, WF, Hu, JJ and Chen, H, Numerical investigation of spherical indentation on elastic-power-law strain-hardening solids with non-equibiaxial residual stresses. MRS Communications, 2019. 9(1): 360369.
70.Pham, TH and Kim, SE, Determination of equi-biaxial residual stress and plastic properties in structural steel using instrumented indentation. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2017. 688: 352363.
71.Peng, GJ, Lu, ZK, Ma, Y, Feng, YH, Huan, Y and Zhang, TH, Spherical indentation method for estimating equibiaxial residual stress and elastic–plastic properties of metals simultaneously. Journal of Materials Research, 2018. 33(8): 884897.
72.Peng, GJ, Xu, FG, Chen, JF, Wang, HD, Hu, JJ and Zhang, TH, Evaluation of non-equibiaxial residual stresses in metallic materials via instrumented spherical indentation. Metals, 2020. 10.
73.Dean, J, Aldrich-Smith, G and Clyne, TW, Use of nanoindentation to measure residual stresses in surface layers. Acta Materialia, 2011. 59(7): 27492761.
74.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.
75.Takagi, H, Dao, M and Fujiwara, M, Analysis on pseudo-steady indentation creep. Acta Mechanica Solida Sinica, 2008. 21: 283288.
76.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.
77.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.
78.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.
79.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.
80.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.
81.Ma, Y, Peng, GJ, Wen, DH and Zhang, TH, 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.
82.Ginder, RS, Nix, WD and Pharr, GM, A simple model for indentation creep. Journal of the Mechanics and Physics of Solids, 2018. 112: 552562.
83.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.
84.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 Technoology, 2009. 203(12): 16091617.
85.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.
86.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.
87.Liu, YJ, Zhao, B, Xu, BX and Yue, ZF, Experimental and numerical study of the method to determine the creep parameters from the indentation creep testing. Materials Science and Engineering: A Structural Materials: Properties, Microstructure and Processing, 2007. 456(1–2): 103108.
88.Galli, M and Oyen, ML, Spherical indentation of a finite poroelastic coating. Applied Physics Letters, 2008. 93(3).
89.Wu, JL, Pan, Y and Pi, JH, On indentation creep of two Cu-based bulk metallic glasses via nanoindentation. Physica B: Condensed Matter, 2013. 421: 5762.
90.Dean, J, Bradbury, A, Aldrich-Smith, G and Clyne, TW, A procedure for extracting primary and secondary creep parameters from nanoindentation data. Mechanics of Materials, 2013. 65: 124134.
91.Su, CJ, Herbert, EG, Sohn, S, LaManna, JA, Oliver, WC and Pharr, GM, Measurement of power-law creep parameters by instrumented indentation methods. Journal of the Mechanics and Physics of Solids, 2013. 61(2): 517536.
92.Cordova, ME and Shen, YL, Indentation versus uniaxial power-law creep: a numerical assessment. Journal of Materials Science, 2015. 50(3): 13941400.
93.Rickhey, F, Lee, JH and Lee, H, An efficient way of extracting creep properties from short-time spherical indentation tests. Journal of Materials Research, 2015. 30(22): 35423552.
94.Burley, M, Campbell, JE, Dean, J and Clyne, TW, A methodology for obtaining primary and secondary creep characteristics from indentation experiments, using a recess. International Journal of Mechanical Sciences, 2020. 176: 105577
95.Muir Wood, AJ and Clyne, TW, Measurement and modelling of the nanoindentation response of shape memory alloys. Acta Materialia, 2006. 54(20): 56075615.
96.Neupane, R and Farhat, Z, Prediction of indentation behavior of superelastic TiNi. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2014. 45A(10): 43504360.
97.Frost, M, Kruisova, A, Shanel, V, Sedlak, P, Hausild, P, Kabla, M, Shilo, D and Landa, M, Characterization of superelastic NiTi alloys by nanoindentation: experiments and simulations. Acta Physica Polonica A, 2015. 128(4): 664669.
98.Roberto-Pereira, FF, Campbell, JE, Dean, J and Clyne, TW, Extraction of superelasticity parameter values from instrumented indentation via iterative FEM modelling. Mechanics of Materials, 2019. 134: 143152.