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A new scheme for computational modeling of conical indentation in plastically graded materials

Published online by Cambridge University Press:  03 March 2011

Yan Ping Cao  and
Jian Lu
Yan Ping Cao
Affiliation:
LASMIS, Universite de Technologie de Troyes, 10010 Troyes, France
Jian Lu*
Affiliation:
LASMIS, Universite de Technologie de Troyes, 10010 Troyes, France
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

In this paper, a new scheme has been proposed for the computational modeling of conical indentation in plastically graded materials. Based on the new scheme and the work of Dao et al. [Acta Mater.49, 3899 (2001)], and taking the example of conical indentation with an indenter whose tip apex angle is θ = 70.3°, an analytical expression to predict the loading P - h curve for the indentation of plastically graded materials has been presented. A reverse algorithm has further been established to determine the plastic properties of a plastically graded surface. The existence, uniqueness, and stability of the solution to the inverse problem have been systematically investigated. The current work can be applied to the evaluation or optimization of various plastically graded surfaces.

Keywords

MicroindentationNanoindentationStress/strain relationship
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 6 , June 2004 , pp. 1703 - 1716
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1Suresh, S., Graded materials for resistance to contact deformation and damage, Science 292, 2447 (2001).CrossRefGoogle ScholarPubMed
2Giannakopoulos, A.E., Indentation of plastically graded substrates by sharp indenters, Int. J. Solids Structures 39, 2495 (2002).CrossRefGoogle Scholar
3Oliver, 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
4Cheng, Y.T. and Cheng, C.M., Scaling approach to conical indentation in elastic-plastic solids with work hardening, J. App. Phys. 84, 1284 (1998).Google Scholar
5 Y.T. Cheng and C.M. Cheng, Scaling relationships in conical indentation of elastic-perfectly plastic solids, Int. J. Solids Structures 36, 1231 (1999).CrossRefGoogle Scholar
6 A.E. Giannakopoulos and S. Suresh, Determination of elastoplastic properties by instrumented sharp indentation, Scripta Mater. 40, 1191 (1999).CrossRefGoogle Scholar
7Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., and Suresh, S.: Computational modelling of the forward and reverse problems in instrumented sharp indentation. Acta. Mater. 49, 3899 (2001).CrossRefGoogle Scholar
8Cheng, Y.T. and Cheng, C.M., Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493 (1999).Google Scholar
9Tunvisut, K., O’Dowd, N.P., and Busso, E.P., Use of scaling functions to determine mechanical properties of thin coatings from microindentation tests, Int. J. Solids Structures 38, 335 (2001).CrossRefGoogle Scholar
10Capehart, T.W., Cheng, Y.T. and indentation, Determining constitutive models from conical: Sensitivity analysis, J. Mater. Res. 18, 827 (2003).Google Scholar
11Futakawa, M., Wakui, T., Tanabe, Y.J., and Ioka, I., Identification of the constitutive equation by the indentation technique using plural indenters with different apex angles, J. Mater. Res. 16, 2283 (2001).Google Scholar
12DiCarlo, A. and Yang, H.T.Y., Semi-inverse method for predicting stress-strain relationship from cone indentations, J. Mater. Res. 18, 2068 (2003).CrossRefGoogle Scholar
13Bucaille, 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
14 N. Chollacoop, M. Dao, and S. Suresh, Depth-sensing instrumented indentation with dual sharp indenters, Acta Mater. 51, 3713 (2003).Google Scholar
15Cao, Y.P., Lu, J. and indenters, Depth-sensing instrumented indentation with dual: Stability analysis and corresponding regularization schemes, Acta Mater. 52, 1143 (2004).CrossRefGoogle Scholar
16Suresh, S. and Giannakopoulos, A.E.: Report No: 99-1-IND (Laboratory for Experimental and Computational Micromechanics, Massachusetts Institute of Technology, Cambridge, MA, 1999),p. 3.Google Scholar
17 P.P. Castaneda and P. Suquet, Nonlinear composites, Adv. Appl. Mech. 34, 171 (1998).Google Scholar
18Elghazal, H., Lormand, G., Hamel, A., Girodin, D., Vincent, A. and measurements, Microplasticity characteristics obtained through nanoindentation: application to surface hardened steels, Mater. Sci. Eng. A 303, 110 (2001).CrossRefGoogle Scholar
19 K. Lu and J. Lu, Surface nanocrystallization (SNC) of metallic materials-presentation of the concept behind a new approach, Mater. Sci. Technol. 15, 193 (1999).Google Scholar
20Lu, J. and Lu, K.: Encyclopedia of Comprehensive Structural Integrity , 8, 495 (2003).Google Scholar
21Jia, D., Ramesh, K.T., and Ma, E., Effects of nanocrystalline and ultrafine grain sizes on constitutive behavior and shear bands in iron, Acta Mater. 51, 3495 (2003).Google Scholar
22 W.P. Tong, N.R. Tao, Z.B. Wang, J. Lu, and K. Lu, Nitriding iron qt low-temperatures, Science 299, 686 (2003).CrossRefGoogle Scholar
23ABAQUS, : Theory Manual Version 6.2 (Hibbitt, Karlsson and Sorensen Inc., Pawtucket, 2001).Google Scholar
24Hadamard, J., Lectures on Cauchy’s Problems in Linear Partial Differential Equations (Yale University Press, New Haven, CT, 1923).Google Scholar
25Kirsch, A., An Introduction to the Mathematical Theory of Inverse Problems (Springer, New York, 1996), p. 10.CrossRefGoogle Scholar
26Cheng, Y.T., Cheng, C.M. and curves, Further analysis of indentation loading: Effects of tip rounding on mechanical property measurements, J. Mater. Res. 13, 1059 (1998).CrossRefGoogle Scholar
27 S. Suresh and A.E. Giannakopoulos, A new method for estimating residual stresses by instrumented sharp indentation, Acta Mater. 46, 5755 (1998).Google Scholar
28Carlsson, S., Larsson, P.L., stress, On the determination of residual and I, strain fields by sharp indentation testing. Part: theoretical and numerical analysis. Acta Mater. 49, 2179 (2001).Google Scholar
29 S. Carlsson and P.L. Larsson, On the determination of residual stress and strain fields by sharp indentation testing. Part II. Acta Mater. 49, 2193 (2001).Google Scholar
30 J. Malzbender and G. de With, Indentation load-displacement curve, plastic deformation, and energy. J. Mater. Res. 17, 502 (2002).Google Scholar
31Arzt, E., microstructural, Size effect in materials due to and constraints, dimensional: a comparative review. Acta Mater. 46, 5611 (1998).CrossRefGoogle Scholar
32 M.R. Begley and J.W. Hutchinson, The mechanics of size-dependent indentation. J. Mech. Phys. Solids 46, 2049 (1998).Google Scholar
33Nix, W.D., Gao, H. and materials, Indentation size effects in crystalline: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).CrossRefGoogle Scholar
34 N.A. Fleck and W.J. Hutchinson, A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825 (1993).CrossRefGoogle Scholar
35 H. Gao, Y. Huang, W.D. Nix, and J.W. Hutchinson, Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 47, 1239 (1999).Google Scholar
36 Y. Huang, H. Gao, W.D. Nix, and J.W. Hutchinson, Mechanism-based strain gradient plasticity-II. J. Mech. Phys. Solids 48, 99 (2000).Google Scholar