Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-29T15:24:10.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining constitutive models from conical indentation: Sensitivity analysis

Published online by Cambridge University Press:  06 January 2012

T. W. Capehart  and
Y-T. Cheng
T. W. Capehart
Affiliation:
Materials and Processes Laboratory, General Motors R&D Center, 30500 Mound Road, Warren, Michigan 48090
Y-T. Cheng
Affiliation:
Materials and Processes Laboratory, General Motors R&D Center, 30500 Mound Road, Warren, Michigan 48090
Get access

Abstract

Several procedures have previously been advanced for extracting constitutive relations from the force–displacement curves obtained from indentation. This work addresses the specific problem of determining the elastic modulus E, yield stress Y, and hardening exponent n, which define the isotropic strain-hardening model from a single force–displacement curve with a sharp conical tip. The sensitivity of the inversion process was tested through a series of finite element calculations using ABAQUS. Different magnitudes of normally distributed noise were superimposed on a calculated force–displacement curve to simulate hypothetical data sets for specific values of E, Y, and n. The sensitivity of the parameter confidence intervals to noise was determined using the χ2-curvature matrix, statistical Monte Carlo simulations, and a conjugate gradient algorithm that explicitly searches the global parameter space. All three approaches demonstrate that 1% noise levels preclude the accurate determination of the strain-hardening parameters based on a single force–displacement curve.

Type
Articles
Information
Journal of Materials Research , Volume 18 , Issue 4 , April 2003 , pp. 827 - 832
Copyright
Copyright © Materials Research Society 2003

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

Tabor, D., The Hardness of Metals (Clarendon Press, Oxford, U.K., 1951).Google Scholar
Hill, R., Storakers, B., and Zudnek, A.B., Proc. R. Soc. London A 423, 301 (1989).Google Scholar
Oliver, W.C. and Pharr, G.M., J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
Field, J.S. and Swain, M.V., J. Mater. Res. 8, 297 (1993).CrossRefGoogle Scholar
Field, J.S. and Swain, M.V., J. Mater. Res. 10, 101 (1995).CrossRefGoogle Scholar
Hainsworth, S.V., Chandler, W.H., and Page, T.F., J. Mater. Res. 11, 1987 (1996).CrossRefGoogle Scholar
Meyers, S.M., Knapp, J.A., Follstaedt, D.M., and Dugger, M.T., J. App. Phys. 83, 1256 (1997).CrossRefGoogle Scholar
Cheng, Y.T. and Cheng, C.M., J. Mater. Res. 14, 3493 (1999).CrossRefGoogle Scholar
Jayaraman, S., Hahn, G.T., Oliver, W.C., Rubin, C.A., and Bastias, P.C., Int. J. Solids Structures 35, 365 (1999).CrossRefGoogle Scholar
Huber, H. and Ch. Tsakmakis, J. Mech. Phys. Solids B, 1569 (1999).Google Scholar
Venkatesh, T.A., K.J. Van Vliet, A.E. Giannakopoulos, and S. Suresh, Scripta Mater. 43, 8333 (2000).Google Scholar
Nakamura, T., Wang, T., and Sampath, S., Acta Mater. 48, 4293 (2000).CrossRefGoogle Scholar
Fatakawa, M., Wakai, T., and Tunabe, Y., J. Mater. Res. 16, 2283 (2001).CrossRefGoogle Scholar
Kurcharski, S. and Mroz, Z., Mater. Sci. Eng. A 318, 65 (2001).CrossRefGoogle Scholar
Tunvisit, K., O’Dowd, N.P., Busso, E.P., Int. J. Solid Struct. 38, 335 (2001).CrossRefGoogle Scholar
Dao, M., Chollacoop, N., Vliet, K.J. Van, Venkatesh, T.A., and Suresh, S., Scripta Mater. 49, 3899 (2001).Google Scholar
Tunvisit, K., Busso, E.P., O’Dowd, N.P., and Brantner, H.P., Philos. Mag. A 82, 2013 (2002).CrossRefGoogle Scholar
Constantinescu, and Tardieu, N., Inv. Prob. Eng. 9, 19 (2001).CrossRefGoogle Scholar
Nayebi, , Bartier, O., Mauvoisin, G., and Abdi, R., Int. J. Mech. Sci. 43, 2679 (2001).CrossRefGoogle Scholar
Timoshenko, S. and Lessells, J.M., Applied Elasticity, 1st ed. (Westinghouse, Pittsburgh, PA, 1925).Google Scholar
Dieter, G., Mechanical Metallurgy, 2nd ed. (McGraw-Hill, New York, 1976).Google Scholar
Taljat, B., Zacharia, T., and Kosel, F., Int. J. Solid Structures 35, 441 (1998).CrossRefGoogle Scholar
Cheng, Y.T. and Cheng, C.M., J. Appl. Phys. 84, 1284 (1998).CrossRefGoogle Scholar
ABAQUS version 6.2, Hibbit, Karlson & Sorensen, Inc. Pawtucket, RI 02860.Google Scholar
Bevington, P.R., Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).Google Scholar
Press, W.H., Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, U.K., 1992).Google Scholar
Lockett, F.J., J. Mech. Phys. Solids 11, 345 (1963).CrossRefGoogle Scholar
Mathematica version 4.1, Wolfram Research Institute.Google Scholar
Gao, H., Huang, Y., and Nix, W.D., Naturwissenschaftern 86, 507 (1999).CrossRefGoogle Scholar