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.

A study on robust indentation techniques to evaluate elastic–plastic properties of metals

“…The sensitivity issues on the indentation tests are quite important and critical, and many studies have performed to examine the robustness of the developed methods (Capehart and Cheng, 2003;Prchlik, 2004;Lee et al, 2005;Lan and Venkatesh, 2007;Ge et al, 2009). We found that for our shallow spherical indentation tests (Lee et al, 2005), the sensitivity of estimated properties to variations in the load was negligible, however, as shown in Fig.…”

“…If we could not solve the each problem one by one, we could not get the proper results. For example, Lan and Venkatesh (2007) have studied the uniqueness and sensitivity issues for power law hardening materials. However, it can be another problem if we consider actual material properties not obeying powerlaw hardening relation well, and use actual experimental indentation data containing lots of uncertainties.…”

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

“…The reasons for such significant errors in the yield stress and strain hardening exponent values are linked to the high sensitivity of these parameters to the uncertainties in the indentation response parameters. 23,24 We thus study how the inverse method can improve the identification of these parameters.…”

“…[15][16][17][18][19][20] Reviews of the existing models have been published by Capehart and Cheng 21 and by Gouldstone et al 22 To increase the robustness of the semi-analytical approach presented here, multiple input data sets have been coupled, 10,11 and recently in-depth sensitivity analysis has been performed to determine the sensitivity and robustness of the results. [23][24] The inverse method developed consists of fitting a constitutive law to a set of input data (see Fig. 1).…”

Mechanism of Damage of Ferritic Ductile Iron, Influence of Matrix Heterogeneity

“…the same load (P) vs penetration (h) curve. In consequence, several aspects related to the uniqueness of the solution provided by inverse methods were discussed by different authors [7][8][9][10][11][12]. For example, Mata et al [14] developed mathematical formulations to relate the hardness and pile-up or sinking-in phenomenon around sharp indentations with the elastic-plastic mechanical properties by using the results retrieved from instrumented indentation test and atomic force microscopy (from now on "methodology A").…”