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Identification of viscoplastic material parameters from spherical indentation data: Part I. Neural networks

Published online by Cambridge University Press:  01 March 2006

E. Tyulyukovskiy  and
N. Huber
E. Tyulyukovskiy
Affiliation:
Forschungszentrum Karlsruhe, Institut für Materialforschung II, D-76344 Eggenstein-Leopoldshafen, Germany
N. Huber*
Affiliation:
Forschungszentrum Karlsruhe, Institut für Materialforschung II, D-76344 Eggenstein-Leopoldshafen, Germany
*
a) Address all correspondence to this author. e-mail: norbert.huber@imf.fzk.de
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Abstract

In this paper, a new method for the identification of material parameters is presented. Neural networks, which are trained on the basis of finite element simulations, are used to solve the inverse problem. The material parameters to be identified are part of a viscoplasticity model that has been formulated for finite deformations and implemented in the finite element code ABAQUS. A proper multi-creep loading history was developed in a previous paper using a phenomenological model for viscoplastic spherical indentation. Now, this phenomenological model is replaced by a more realistic finite element model, which provides fast computation and numerical solutions of high accuracy at the same time. As a consequence, existing neural networks developed for the phenomenological model have been extended from a power law hardening with two material parameters to an Armstrong–Frederick hardening rule with three parameters. These are the yield stress, the initial slope of work hardening, and maximum hardening stress of the equilibrium response. In addition, elastic deformation is taken into account. The viscous part is based on a Chaboche-like overstress model, consisting of two material parameters determining velocity dependence and overstress as a function of the strain rate. The method has been verified by additional finite element simulations. Its application for various metals will be presented in Part II, [J. Mater. Res.21, 677 (2006)].

Keywords

Elastic propertiesHardnessStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 21 , Issue 3 , March 2006 , pp. 664 - 676
Copyright
Copyright © Materials Research Society 2006

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References

REFERENCES

1.Field, J., Swain, M.: A simple predictive model for spherical indentation. J. Mater. Res. 8, 297 (1993).Google Scholar
2.Jayaraman, S., Hahn, G., Oliver, W., Rubin, C.: Determination of monotonic stress strain curve of hard materials from ultra-low-load indentation tests. Int. J. Solids Struct. 35, 365 (1998).CrossRefGoogle Scholar
3.Kucharski, S., Mroz, Z.: Identification of hardening parameters of metals from spherical indentation tests. Trans. ASME H, J. Eng. Mater. Technol. 135, 245 (2001).CrossRefGoogle Scholar
4.Ahn, J-H., Kwon, D.: Derivation of plastic stress-strain relationship from ball indentations. J. Mater. Res. 16, 3170 (2001).CrossRefGoogle Scholar
5.Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).CrossRefGoogle Scholar
6.Huber, N., Nix, W., Gao, H.: Identification of elastic-plastic material parameters from pyramidal indentation of thin films. Proc. R. Soc. London, Ser. A 458, 1593 (2002).CrossRefGoogle Scholar
7.Atkins, A., Tabor, D.: Plastic indentation in metals with cones. J. Mech. Phys. Solids 13, 149 (1965).CrossRefGoogle Scholar
8.Tabor, D.: Hardness of Metals (Cambridge University Press, Cambridge, 1951).Google Scholar
9.Doerner, M., Nix, W.: A method for interpreting the data from depth-sensing indentation. J. Mater. Res. 1, 601 (1986).CrossRefGoogle Scholar
10.Oliver, W., Pharr, G.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
11.Huber, N., Munz, D., Tsakmakis, C.: Determination of Young’s modulus by spherical indentation. J. Mater. Res. 12, 2459 (1997).Google Scholar
12.Hertz, H.: Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92, 156 (1882).CrossRefGoogle Scholar
13.Love, A.: Boussinesq’s problem for a rigid cone. Quart. J. Math. 10, 161 (1939).CrossRefGoogle Scholar
14.Harding, J., Sneddon, I.: The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. Proc. Cambridge Philos. Soc. 43, 16 (1945).CrossRefGoogle Scholar
15. ISO 14577, Metallic materials—Instrumented indentation test for hardness and materials parameters—Part 1: Test method;—Part 2: Verification and calibration of the testing machine;—Part 3: Calibration of reference test pieces, October 2003.Google Scholar
16.Ullner, Ch.: Requirement of a robust method for the precise determination of the contact point in depth sensing hardness test. Measurement 27, 43 (2000).CrossRefGoogle Scholar
17.Ullner, Ch.: Development of the instrumented indentation test. J. Metrology Soc. India 20, 43 (2005).Google Scholar
18.Jennett, N.M., Maxwell, A.S., Lawrence, K., McCartney, L.N., Hunt, R., Koskinen, J., Muukkonen, T., Rossi, F., Meneve, J., Wegener, W., Gibson, N., Zhihui, Xu, Bushby, A.J., Brookes, S., Cavaleiro, A., Herrmann, K., Bellaton, B., Consiglio, R., Augereau, F., Kolosov, O., Schneider, D., Chudoba, T.European project INDICOAT SMT-CT98-2249, Final Report, Determination of Hardness and Modulus of Thin Films and Coatings by Nanoindentation, NPL Report MATC (A) 24 (2001).Google Scholar
19.DIS, ISO 14577, Metallic materials—Instrumented indentation test for hardness and materials parameters—Part 4: Test method for metallic and non-metallic coatings, October 2005.Google Scholar
20.Diegele, E., Jansohn, W., Tsakmakis, C.: Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules Part I: Constitutive theory and numerical integration. Comp. Mech. 25, 1 (2000).CrossRefGoogle Scholar
21.Diegele, E., Hartmann, S., Tsakmakis, C.: Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules Part II: Representative examples. Comp. Mech. 25, 13 (2000).CrossRefGoogle Scholar
22.Bouzakis, K-D., Michailidis, N., Hadjiyiannis, S., Skordaris, G., Erkens, G.: The effect of specimen roughness and indenter tip geometry on the determination accuracy of thin hard coatings stress-strain laws by nanoindentation. Mater. Charact. 49, 149 (2003).CrossRefGoogle Scholar
23.Huber, N., 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
24.Huber, N., Tsakmakis, C.: Determination of constitutive properties from spherical indentation data using neural networks, Part II: Plasticity with nonlinear isotropic and kinematic hardening. J. Mech. Phys. Solids 47, 1589 (1999).CrossRefGoogle Scholar
25.Mayo, M., Nix, W.: A micro-indentation study of superplasticity in Pb, Sn and Sn-38 wt% Pb. Acta Metall. 36, 2183 (1988).CrossRefGoogle Scholar
26.Raman, V., Berriche, R.: An investigation of the creep process in tin and aluminium using a depth-sensing indentation technique. J. Mater. Res. 7, 627 (1992).CrossRefGoogle Scholar
27.Huber, N., Tioulioukovski, E.: A new loading history for identification of viscoplastic properties by spherical indentation. J. Mater. Res. 19, 101 (2004).CrossRefGoogle Scholar
28.Huber, N., Tsakmakis, C.: A neural network tool for identifying the material parameters of a finite deformation viscoplasticity model with static recovery. Comp. Meth. Appl. Mech. Eng. 191, 353 (2001).CrossRefGoogle Scholar
29.Yagawa, G., Okuda, H.: Neural networks in computational mechanics. Modell. Simul. Mater. Sci. Eng. 3, 435 (1996).Google Scholar
30.Cheng, Y-T., Cheng, C-M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91 (2004).CrossRefGoogle Scholar
31.Haykin, S.: Neural Networks: A Comprehensive Foundation (Macmillan, New York, 1994).Google Scholar
32.Huber, N. Application of neural networks on nonlinear problems of mechanics. Habilitation Thesis, FZKA-Bericht 6504, Forschungszentrum Karlsruhe, Germany (2000, in German).Google Scholar
33.Riedmiller, M. and Braun, H.: A direct adaptive method for faster backpropagation learning: The RPROP algorithm, in Proceedings of the IEEE International Conference on Neural Networks, ICNN 93 (1993).CrossRefGoogle Scholar