Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T23:36:40.411Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

Published online by Cambridge University Press:  31 January 2011

I. Peyrot ,
P-O. Bouchard ,
R. Ghisleni  and
J. Michler
I. Peyrot
Affiliation:
Laboratory for Mechanics of Materials and Nanostructures, EMPA—Swiss Federal Laboratories for Materials Testing and Research, Feuerwerkerstrasse 39, 3602 Thun, Switzerland
P-O. Bouchard
Affiliation:
Mines ParisTech, CEMEF, Centre de Mise en Forme des Matériaux, UMR CNRS 7635, BP 207, 06904 Sophia-Antipolis Cedex, France
R. Ghisleni
Affiliation:
Laboratory for Mechanics of Materials and Nanostructures, EMPA—Swiss Federal Laboratories for Materials Testing and Research, Feuerwerkerstrasse 39, 3602 Thun, Switzerland
J. Michler*
Affiliation:
Laboratory for Mechanics of Materials and Nanostructures, EMPA—Swiss Federal Laboratories for Materials Testing and Research, Feuerwerkerstrasse 39, 3602 Thun, Switzerland
*
a) Address all correspondence to this author. e-mail: Johann.Michler@empa.ch
Get access

Abstract

A novel optimization approach, capable of extracting the mechanical properties of an elasto-plastic material from indentation data, is proposed. Theoretical verification is performed on two simulated configurations. The first is based on the analysis of the load–displacement data and the topography of the residual imprint of a single conical indenter. The second is based on the load–displacement data obtained from two conical indenters with different semi-angles. In both cases, a semi-analytical approach [e.g., Dao et al., Acta Mater.49, 3899 (2001) and Bucaille et al., Acta Mater.51, 1663 (2003)] is used to estimate Young’s modulus, yield stress, and strain hardening coefficient from the load–displacement data. An inverse finite element model, based on a commercial solver and a newly developed optimization algorithm based on a robust stochastic methodology, uses these approximate values as starting values to identify parameters with high accuracy. Both configurations use multiple data sets to extract the elastic-plastic material properties; this allows the mechanical properties of materials to be determined in a robust way.

Keywords

NanoindentationSimulationStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 936 - 947
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Loubet, J.L., Georges, J.M., Marchesini, O., and Meille, G.: Vickers indentation curves of magnesium-oxide (MgO). J. Tribol. 106, 43 (1984).CrossRefGoogle Scholar
2.Pethica, J.B., Hutchings, R., and Oliver, W.C.: Hardness measurement at penetration depths as small as 20 nm. Philos. Mag. A 48, 593 (1983).CrossRefGoogle Scholar
3.Stauss, S., Schwaller, P., Bucaille, J-L., Rabe, R., Rohr, L., Michler, J., and Blank, E.: Determining the stress–strain behaviour of small devices by nanoindentation in combination with inverse methods. Microelectron. Eng. 67–68, 818 (2003).CrossRefGoogle Scholar
4.Doerner, M.F. and Nix, W.D.: A method for interpreting the data from depth-sensing indentation. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
5.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
6.Tabor, D.: The Hardness of Metals (Clarendon Press, Oxford, UK, 1951).Google Scholar
7.Cheng, Y.T. and Cheng, C.M.: Scaling approach to conical indentation in elastic-plastic solids with work hardening., J. Appl. Phys. 84, 1284 (1998).Google Scholar
8.Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).CrossRefGoogle Scholar
9.Bouzakis, K.D., Michailidis, N., and Erkens, G.: Thin hard coatings stress-strain curve determination through a FEM supported evaluation of nanoindentation test results. Surf. Coat. Technol. 142, 102 (2001).CrossRefGoogle Scholar
10.Bucaille, J.L., Stauss, S., Felder, E., and Michler, J.: Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663 (2003).CrossRefGoogle Scholar
11.Chollacoop, N., Dao, M., and Suresh, S.: Depth-sensing instrumented indentation with dual sharp indenters. Acta Mater. 51, 3713 (2003).CrossRefGoogle Scholar
12.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
13.Giannakopoulos, A.E. and Suresh, S.: Determination of elastoplastic properties by instrumented sharp indentation. Scr. Mater. 40, 1191 (1999).Google Scholar
14.Huber, N. and Tsakmakis, C.: Determination of constitutive properties from spherical indentation data using neural networks. Part I: The case of pure kinematic hardening in plasticity laws. J. Mech. Phys. Solids 47, 1569 (1999).CrossRefGoogle Scholar
15.Backes, B., Durst, K., and Goken, M.: Determination of plastic properties of polycrystalline metallic materials by nanoindentation: Experiments and finite element simulations. Philos. Mag. 86, 5541 (2006).CrossRefGoogle Scholar
16.Cao, Y.P. and Huber, N.: Further investigation on the definition of the representative strain in conical indentation. J. Mater. Res. 21, 1810 (2006).CrossRefGoogle Scholar
17.Choi, I.S., Dao, M., and Suresh, S.: Mechanics of indentation of plastically graded materials. I: Analysis. J. Mech. Phys. Solids 56, 157 (2008).CrossRefGoogle Scholar
18.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. J. Mater. Res. 22, 1512 (2007).Google Scholar
19.Qian, X.Q., Cao, Y.P., and Lu, J.: Dependence of the representative strain on the hardening functions of metallic materials in indentation. Scr. Mater. 57, 57 (2007).CrossRefGoogle Scholar
20.Swaddiwudhipong, S., Harsono, E., Hua, J., and Liu, Z.S.: Reverse analysis via efficient artificial neural networks based on simulated Berkovich indentation considering effects of friction. Eng. Comput. 24, 127 (2008).Google Scholar
21.Capehart, T.W. and Cheng, Y.T.: Determining constitutive models from conical indentation: Sensitivity analysis. J. Mater. Res. 18, 827 (2003 ).CrossRefGoogle Scholar
22.Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A.M., and Shen, Y.L.: Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, 4015 (2007).Google Scholar
23.Lan, H. and Venkatesh, T.A.: Determination of the elastic and plastic properties of materials through instrumented indentation with reduced sensitivity. Acta Mater. 55, 2025 (2007).CrossRefGoogle Scholar
24.Lan, H. and Venkatesh, T.A.: On the uniqueness and sensitivity issues in determining the elastic and plastic properties of powerlaw hardening materials through sharp and spherical indentation. Philos. Mag. 87, 4671 (2007).CrossRefGoogle Scholar
25.Cohon, J.L.: MultiObjective Programming and Planning (Academic Press, New York, 1978).Google Scholar
26.Gilbert, J.C.: Differentiable Optimization: Theory and Algorithms (INRIA, Roquencourt, France, 1999).Google Scholar
27.Pilvin, P.: Multiscale approach for the prediction of the materials andastic component, Ph.D. Thesis, Universite de Paris VI, France (1983).Google Scholar
28.Bocciarelli, M. and Maier, G.: Indentation and imprint mapping method for indentation of residual stresses. Comp. Mater. Sci. 39, 381 (2007).CrossRefGoogle Scholar
29.Stauss-Ueno, S.N.: Assessment of mechanical properties using instrumented indentation and inverse methods, Ph.D. Thesis, EPF Lausanne, Switzerland, (2006).Google Scholar
30.Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, MA, 1989).Google Scholar
31.Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin, Germany, 1992).Google Scholar
32.Rechenberg, I.: Evolutionsstrategie: Technical System Optimization from Biological Evolution Principle (Frommann-Holzboog, Stuttgart, Germany, 1973).Google Scholar
33.Zeng, K. and Chiu, C.H.: An analysis of laod-penetration curves from instrumented indentation. Acta Mater. 49, 3539 (2001).Google Scholar
34.Emmerich, M., Giotis, A., Özdemir, M., Bäck, T., and Giannakoglou, K.: Metamodel-assisted evolution strategies, in Parallel Problem Solving from Nature VII, edited by Merelo Guervss, J.J., Adamidis, P., Bever, H.G., Fernández-Villacañas, J-L., and Schwefel, H-P. (Springer, Secaucus, NJ, 2002).Google Scholar
35.ABAQUS—Standard User's manual version 6.4 (Hibbit, Karlsson and Sorensen Inc., 2002).Google Scholar
36.Bucaille, J.L., Rossoll, A., Moser, B., Stauss, S., and Michler, J.: Determination of the matrix in situ flow stress of a continuous fibre reinforced metal matrix composite using instrumented indentation. Mater. Sci. Eng., A 369, 82 (2004).CrossRefGoogle Scholar
37.Gronostajski, Z.: The constitutive equations for FEM analysis. J. Mater. Process. Technol. 106, 40 (2000).CrossRefGoogle Scholar
38.Hollomon, J.H.: Tensile deformation. Trans. Am. Inst. Mining Metall. Eng. 162, 268 (1945).Google Scholar
39.Dieter, G.: Mechanical Metallurgy, 2nd ed. (Mc Graw-Hill, New York, 1976).Google Scholar
40.Lubliner, J.: Plasticity Theory (Macmillan, New York, 1990).Google Scholar
41.Swift, H.W.: Plastic instability under plane stress. J. Mech. Phys. Solids 1, 1 (1952).Google Scholar
42.Ramberg, W. and Osgood, W.R.: Description of stress-strain curves by three parameters. National Advisory Committee for Aeronautics, Technical Note 902 (1943).Google Scholar
43. Python Software Foundation (www.python.org, 2005).Google Scholar
44.Holland, J.H.: Outline for a logical theory of adaptive systems. J. Assoc. Computing Machinery 9, 297 (1962).CrossRefGoogle Scholar
45.Schwefel, H-P.: Numerical Optimization of Computer Models, 2nd ed. (JohnWiley and Sons, New York, 1995).Google Scholar
46.Fogel, L.J.: On the organization of intellect, Ph.D. Dissertation, UCLA, CA, (1964).Google Scholar
47.Cramer, N.: A representation for the adaptive generation of simple sequential programs, in Genetic Algorithms and the Applications, edited by Grefenstette, J. (Lawrence Erlbaum Associates, Mahwah, NJ, 1985), p. 183.Google Scholar
48.Bäck, T., Fogel, D., and Michalewicz, Z.: Handbook of Evolutionary Computation (Oxford University Press, Oxford, UK, 1997).Google Scholar
49.Sakata, S., Ashida, F., and Zako, M.: Structural optimization using Kriging approximation. Comput. Methods Appl. Mech. Eng. 192, 923 (2003).Google Scholar
50.Ghouati, O. and Gelin, J.C.: Gradient based methods, genetic algorithms and the finite element method for the identification of material parameters, in Simulation of Materials Processing: Theory, Methods and Applications, edited by Huétink, J. and Baaijens, F.P.T. (A.A. Balkema, Rotterdam, The Netherlands, 1998), p. 157.Google Scholar
51.Alcalá, J., Barone, A.C., and Anglada, M.: The influence of plastic hardening on surface deformation modes around Vickers and spherical indents. Acta Mater. 48, 3451 (2000).Google Scholar
52.Chaudhri, M.M. and Winter, M.: The load-bearing area of a hardness indentation. J. Phys. D 21, 370 (1988).CrossRefGoogle Scholar
53.Hill, R., Storakers, B., and Zdunek, A.: A theoretical study of the Brinell hardness test. Proc. R. Soc. London A 423, 301 (1989).Google Scholar
54.Feng, X.Y. and Wang, T.C.: Scaling functions in conical indentation of elastic-plastic solids. Acta Mech. 196, 245 (2008).CrossRefGoogle Scholar
55.Gao, X-L., Jing, X.N., and Subhash, G.: Two new expanding cavity models for indentation deformations of elastic strain-hardening materials. Int. J. Solids Struct. 43, 2193 (2006).Google Scholar
56.Zielinski, W., Huang, H., and Gerberich, W.W.: Microscopy and microindentation mechanics of single crystal Fe–3 wt.% Si: Part II. TEM of the indentation plastic zone. J. Mater. Res. 8, 1300 (1993).Google Scholar
57.Harding, J.W. and Sneddon, I.N.: The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. Proc. Camb. Philol. Soc. 41, 16 (1945).Google Scholar
58.Love, A.E.H.: Boussinesq's problem for a rigid cone. Q. J. Math. 10, 161 (1939).Google Scholar
59.Sneddon, I.N.: The relation between load and penetration in the axisymmetric Bossinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).Google Scholar
60.Tho, K.K., Swaddiwudhipong, S., Liu, Z.S., Zheng, K., and Hua, J.: Uniqueness of reverse analysis from conical indentation tests. J. Mater. Res. 19, 2498 (2004).Google Scholar
61.Bucaille, J.L., Stauss, S., Schwaller, P., and Michler, J.: A new technique to determine the elastic properties of thin metallic films using sharp indenters. Thin Solid Films 447–448, 239 (2004).CrossRefGoogle Scholar
62.Swaddiwudhipong, S., Tho, K.K., Liu, Z.S., and Zeng, K.: Material characterization based on dual indenters. Int. J. Solids Struct. 42, 69 (2005).CrossRefGoogle Scholar