On the uniqueness and sensitivity issues in determining the elastic and plastic properties of power-law hardening materials through sharp and spherical indentation

Abstract

A systematic study of the uniqueness, reversibility and sensitivity issues associated with seven indentation-based methods of property extraction demonstrates that: (i) The indentation algorithms generally identify the elastic and plastic properties of materials uniquely for most materials. (ii) The indentation forward algorithms (wherein the indention responses are determined from the elastic and plastic properties of the indented materials) and the reverse algorithms (wherein the elastic and the plastic properties of materials are extracted from the indentation responses) are distinct for each indentation method and are internally consistent in that the differences in the elastic and plastic properties determined through the reverse analysis and the ‘true’ material properties are generally small for a large number of materials, for each of the seven methods. (iii) While the differences in the indentation response parameters predicted by each of the seven indentation methods (for a particular material) could be small, there could be considerable dispersion in the elastic and plastic properties predicted by the reverse algorithms of the seven methods (for a particular set of indentation response parameters). (iv) In the forward analysis, small uncertainties in the elasto-plastic properties lead to small uncertainties in the predictions of the indentation response of materials. The sensitivity distribution is generally heterogeneous and symmetric across positive and negative variations in the material elasto-plastic properties. (v) In the reverse analysis, the elastic modulus exhibits low sensitivity, while the yield strength and the strain-hardening exponent generally exhibit high sensitivity to uncertainties in the indentation response parameters. The sensitivity distribution is heterogeneous and asymmetric across positive and negative variations in the indentation response parameters. (vi) The representative stresses are fairly robust to uncertainties in the indentation response parameters. Consequently, dual sharp and spherical indentation methods, which identify multiple representative stresses, exhibit reduced sensitivity in the determination of the plastic properties.

Acknowledgements

The present study was supported in part by National Science Foundation grants DMR-0547903 and CMS-0527779.