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Semi-inverse method for predicting stress–strain relationship from cone indentations

Published online by Cambridge University Press:  31 January 2011

A. DiCarlo ,
H. T. Y. Yang  and
S. Chandrasekar
A. DiCarlo
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, California 93106
H. T. Y. Yang
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, California 93106
S. Chandrasekar
Affiliation:
School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907
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Abstract

A method for determining the stress–strain relationship of a material from hardness values H obtained from cone indentation tests with various apical angles is presented. The materials studied were assumed to exhibit power-law hardening. As a result, the properties of importance are the Young's modulus E, yield strength Y, and the work-hardening exponent n. Previous work [W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992)] showed that E can be determined from initial force–displacement data collected while unloading the indenter from the material. Consequently, the properties that need to be determined are Y and n. Dimensional analysis was used to generalize H/E so that it was a function of Y/E and n [Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1999); Philos. Mag. Lett. 77, 39 (1998)]. A parametric study of Y/E and n was conducted using the finite element method to model material behavior. Regression analysis was used to correlate the H/E findings from the simulations to Y/E and n. With the a priori knowledge of E, this correlation was used to estimate Y and n.

Type
Articles
Information
Journal of Materials Research , Volume 18 , Issue 9 , September 2003 , pp. 2068 - 2078
Copyright
Copyright © Materials Research Society 2003

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References

REFERENCES

1.Ludwik, P., Die Kegelprobe (Springer, Berlin, Germany 1908).CrossRefGoogle Scholar
2.Sneddon, I.N., Int. J. Eng. Sci. 3, 47 (1965).CrossRefGoogle Scholar
3.Doerner, M.F. and Nix, W.D., J. Mater. Res. 1, 601 (1986)CrossRefGoogle Scholar
4.Oliver, W.C. and Pharr, G.M., J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
5.Tabor, D., Philos. Mag. A 74, 1207 (1996).CrossRefGoogle Scholar
6.Bhattacharya, K.A. and Nix, W.D., Int. J. Solids Struct. 24, 881 (1988).CrossRefGoogle Scholar
7.Cheng, Y-T. and Cheng, C-M., J. Mater. Res. 14, 3493 (1999).CrossRefGoogle Scholar
8.Atkins, A.G. and Tabor, D., J. Mech. Phys. Solids 13, 149 (1965).CrossRefGoogle Scholar
9.Hill, R., The Mathematical Theory of Plasticity (Clarendon Press, Oxford, U.K., 1950).Google Scholar
10.Lockett, F.J., J. Mech. Phys. Solids 11, 345 (1963).CrossRefGoogle Scholar
11.Johnson, K.L., J. Mech. Phys. Solids 18, 115 (1969).CrossRefGoogle Scholar
12.Rawlings, J.O., Pantula, S.G., and Dickey, D.A., Applied Regression Analysis: A Research Tool (Springer, New York, 1998).CrossRefGoogle Scholar
13.Munson, B.R., Young, D.F., and Okiishi, T.H., Fundamentals of Fluid Mechanics (John Wiley & Sons, New York, 1994).Google Scholar
14.Cheng, Y-T. and Cheng, C-M., J. Appl. Phys. 84, 1284 (1999).CrossRefGoogle Scholar
15.Cheng, Y-T. and Cheng, C-M., Philos. Mag. Lett. 77, 39 (1998).CrossRefGoogle Scholar
16.Dieter, G.E., Materials Science and Engineering Series: Mechanical Metallurgy (McGraw-Hill, New York, 1976).Google Scholar
17.ABAQUS, version 5.8 (Hibbitt, Karlsson & Sorensen, Pawtucket, RI, 1996).Google Scholar
18.Callahan, J. and Hoffman, K., Calculus in Context: Five College Calculus Project (Freeman, New York, 1995).Google Scholar
19.Krishnamurthy, V., Master Thesis, Purdue University, West Lafayette, IN (2001).Google Scholar