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Computational mechanical property determination of viscoelastic/plastic materials from nanoindentation creep test data

Published online by Cambridge University Press:  31 January 2011

Jianjun Wang  and
Timothy C. Ovaert
Jianjun Wang
Affiliation:
ABB Robotics, Windsor, Connecticut 06095
Timothy C. Ovaert*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
*
a) Address all correspondence to this author. e-mail: tovaert@nd.edu
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Abstract

Nanoindentation is a widely accepted test method for materials characterization. On account of the complexity of contact deformation behavior, design of parametric constitutive models and determination of the unknown parameters is challenging. To address the need for identification of mechanical properties of viscoelastic/plastic materials from nanoindentation data, a combined numerical finite element/optimization-based indentation modeling tool was developed, fully self-contained, and capable of running on a PC as a stand-alone executable program. The approach uses inverse engineering and formulates the material characterization task as an optimization problem. The model development consists of finite element formulation, viscoelastic/plastic material models, heuristic estimation to obtain initial solution boundaries, and a gradient-based optimization algorithm for fast convergence to extract mechanical properties from the test data. A four-parameter viscoelastic/plastic model is presented, then a simplified three-parameter model with more rapid convergence. The end result is a versatile tool for indentation simulation and mechanical property analysis.

Keywords

NanoindentationSimulationViscoelasticity
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 1245 - 1257
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.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
2.Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
3.Cheng, L.L., Xia, X., Scriven, L.E., and Gerberich, W.W.: Spherical tip indentation of a viscoelastic material. Mech. Mater. 37, 213 (2005).CrossRefGoogle Scholar
4.Zhang, C.Y., Zhang, Y.W., Zeng, K.Y., and Shen, L.: Nanoindentation of polymers with a sharp indenter. J. Mater. Res. 20, 1597 (2005).CrossRefGoogle Scholar
5.Cheng, L.L., Xia, X., Yu, W., Scriven, L.E., and Gerberich, W.W.: Flat-punch indentation of viscoelastic material. J. Polym. Sci., Part B: Polvrn. Phys. 38, 10 (2000).3.0.CO;2-6>CrossRefGoogle Scholar
6.Oyen, M.L. and Cook, R.F.: Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
7.Huber, N. and Tyulyukovskiy, E.: A new loading history for identification of viscoplastic properties by spherical indentation. J. Mater. Res. 19, 101 (2004).CrossRefGoogle Scholar
8.Weia, P.J. and Lin, J.F.: Determination for elasticity and plasticity from time-dependent nanoindentations. Mater. Sci. Eng., A 496, 90 (2008).CrossRefGoogle Scholar
9.Menèík, J., Rauchs, G., Bardon, J., and Riche, A.: Determination of elastic modulus and hardness of viscoelastic-plastic materials by instrumented indentation under harmonic load. J. Mater. Res. 20, 2660 (2005).Google Scholar
10.Zhang, C.Y., Zhang, Y.W., Zeng, K., and Shen, L.: Characterization of mechanical properties of polymers by nanoindentation tests. Philos. Mag. 86, 4487 (2006).CrossRefGoogle Scholar
11.Giannakopoulos, A.E. and Suresh, S.: Determination of elastoplas-tic properties by instrumented sharp indentation. Scr. Mater. 40, 1191 (1999).CrossRefGoogle Scholar
12.Cailletaud, C. and Pilvin, P.: Identification and inverse problems related to material behavior, in Inverse Problems in Engineering Mechanics (Balkema, Rotterdam, 1994).Google Scholar
13.Gavrus, A., Massoni, E., and Chenot, J.L.: Computer aided rheolo-gy for nonlinear large strain thermo-viscoplastic behaviour formulated as an inverse problem, in Inverse Problems in Engineering Mechanics (Balkema, Rotterdam, 1994).Google Scholar
14.Mahnken, R. and Stein, E.: A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput. Methods Appl. Mech. Eng. 136, 225 (1996).CrossRefGoogle Scholar
15. ABAQUS Theory Manual, V6.5, ABAQUS Inc., Providence, RI, 2004.Google Scholar
16.Laursen, T.A. and Simo, J.C.: A continuum-based finite element formulation for the implicit solution of multi-body, large deformation frictional contact problems. Int. J. Numer. Methods Eng. 36, 3451 (1993).CrossRefGoogle Scholar
17.Kleiber, M., Antunez, H., Hien, T.D., and Kowalczyk, P.: Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations (Wiley, New York, 1997).Google Scholar
18.Bonet, J. and Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis (Cambridge University Press, Cambridge, UK, 1997).Google Scholar
19.Bathe, K-J.: Finite Element Procedures in Engineering Analysis (Prentice Hall, Upper Saddle River, NJ, 1982).Google Scholar
20.Hughes, T.J.R.: The Finite Element Method (Prentice Hall, Upper Saddle River, NJ, 1985).Google Scholar
21.Simo, J.C., Armero, F., and Taylor, R.L.: Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Comput. Methods Appl. Mech. Eng. 110, 359 (1993).CrossRefGoogle Scholar
22.Ovaert, T.C., Kim, B.R., and Wang, J.: Multi-parameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modeling. Prog. Org. Coat. 47, 312 (2003).CrossRefGoogle Scholar
23.Zhang, J., Niebur, G.L., and Ovaert, T.C.: Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation. J. Biomech. 41, 267 (2008).CrossRefGoogle ScholarPubMed
24.Simo, J.C. and Hughes, T.J.R.: Computational Inelasticity (Springer Verlag, New York, 1998).Google Scholar
25.Kikuchi, N. and Oden, J.T.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Method (SIAM, Philadelphia, 1988).CrossRefGoogle Scholar
26. CSpivey, O. and Tortorelli, D.A.: Tangent operators, sensitivity expressions, and optimal design of non-linear elastica with applications to beams. Int. J. Numer. Methods Eng. 37, 49 (1994).CrossRefGoogle Scholar
27.Antunez, H.J. and Kleiber, M.: Sensitivity analysis of metal forming process involving frictional contact in steady state. J. Mater. Process. Technol. 60, 485 (1996).CrossRefGoogle Scholar
28.Pollock, G.D. and Noor, A.K.: Sensitivity analysis of the contact/impact response of composite structures. Compos. Struct. 61, 251 (1996).CrossRefGoogle Scholar
29.Karaoglan, L. and Noor, A.K.: Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures. Comput. Methods Appl. Mech. Eng. 128, 169 (1995).CrossRefGoogle Scholar
30.Huber, N. and Tsakmakis, Ch.: 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
31.Huber, N. and Tsakmakis, Ch.: 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
32.Dennis, J.E. Jr, and Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Upper Saddle River, NJ, 1983).Google Scholar
33.Byrd, R.H., Lu, P., Nocedal, J., and Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190 (1995).CrossRefGoogle Scholar
34.More, J.J. and Thuente, D.J.: Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Softw. 20, 286 (1994).CrossRefGoogle Scholar
35.Ahmad, M.: Flexible vinyl resiliency property enhancement with hollow thermoplastic microspheres. J. Vinyl Additive Tech. 7, 156 (2001).CrossRefGoogle Scholar
36.Kobayashi, H., Kodama, I., and Nashima, T.: New apparatus for measuring ultrahigh viscosity of plastics. Jpn. J. Appl. Phys. 46, 7959 (2007).CrossRefGoogle Scholar
37.Kobayashi, H., Takahashi, H., and Hiki, Y.: A new apparatus for measuring high viscosity of solids. Int. J. Thermophys. 16, 577 (1995).CrossRefGoogle Scholar
38.Yamaguchi, M.: Rheological properties of linear and crosslinked polymer blends: Relation between crosslink density and enhancement of elongational viscosity. J. Polym. Sci. B: Polym. Phys. 39, 228 (2001).3.0.CO;2-Z>CrossRefGoogle Scholar