On the identification of power-law creep parameters from conical indentation

Load and hold conical indentation responses calculated for materials having creep stress exponents of 1.15, 3.59 and 6.60 are regarded as input ‘experimental’ responses. A Bayesian-type statistical approach (Zhang et al. 2019 J. Appl. Mech. 86 , 011002 ( doi:10.1115/1.4041352 )) is used to infer power-law creep parameters, the creep exponent and the associated pre-exponential factor, from noise-free as well as noise-contaminated indentation data. A database for the Bayesian-type analysis is created using finite-element calculations for a coarse set of parameter values with interpolation used to create the refined database used for parameter identification. Uniaxial creep and stress relaxation responses using the identified creep parameters provide a very good approximation to those of the ‘experimental’ materials with stress exponents of 1.15 and 3.59. The sensitivity to noise increases with increasing stress exponent. The uniaxial creep response is more sensitive to the accuracy of the predictions than the uniaxial stress relaxation response. Good agreement with the indentation response does not guarantee good agreement with the uniaxial response. If the noise level is sufficiently small, the model of Bower et al. (1993 Proc. R. Soc. Lond. A 441 , 97–124 ()) provides a good fit to the ‘experimental’ data for all values of creep stress exponent considered, while the model of Ginder et al. (2018 J. Mech. Phys. Solids 112 , 552–562 ()) provides a good fit for a creep stress exponent of 1.15.

Influence of Assumed Strain Hardening Relation on Plastic Stress-Strain Response Identification From Conical Indentation

Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different uniaxial stress-strain curves can give essentially identical curves of indentation force versus indentation depth. Zhang et al. (2019, “Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach,” ASME J. Appl. Mech., 86, p. 011002) numerically generated “experimental” conical indentation data and showed that using surface profile data and indentation force versus indentation depth data together with a Bayesian-type statistical analysis permitted the uniaxial plastic stress-strain response to be identified even for materials with indistinguishable indentation force versus indentation depth curves. The same form of hardening relation was used in the identification process as was used to generate the “experimental” data. Generally, a variety of power law expressions have been used to characterize the uniaxial plastic stress-strain response of engineering materials, and, of course, the form that gives the best fit for a material is not known a priori. Here, we use the same Bayesian statistics-based analysis but consider four characterizations of the plastic uniaxial stress-strain response and show that the identification of the hardening relation parameters and the associated uniaxial stress-strain response is not very sensitive to the form of the power law strain hardening relation chosen even with data that have significant noise.