COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 166

pre-determine what kind of Δ needs to be used in an experiment.
Moreover, when extreme indenter angles are used, the measured
hardness would differ by orders of magnitude and new numerical
problems associated with the resolution of the instrument emerge, and
very sharp indenters may cause cracking and alignment problems.
When the Poisson's ratio is allowed to vary, an example is given in
Fig. 6-7b , where the mystical materials can again exist within a wide
range of indenter angles include those used in the literature, and for most
materials their mystical siblings can be readily identified, which
invalidates the uniqueness assumption of the conventional dual (or plural)
sharp indenter method. The most distinct mystical materials can be
obtained when ν is varied between 0 and 0.5.
In essence, the uniqueness problem is similar to error sensitivity.
From a physical point of view, the mystical materials show a feature
related to power-law strain hardening materials and the self-similarity of
cone indenters. It means that by using plural sharp indenter techniques
with experimental uncertainties, it is difficult to accurately obtain the
elastoplastic properties for a wide range of materials. From a
mathematical point of view, mystical materials exhibit low deviations
between their corresponding indentation parameters. Since all
experiments (lab or numerical) are subject to error, a few percent of such
data fluctuation will lead to large perturbation of the determined material
elastoplastic properties, and the mystical materials are especially
sensitive to errors or data uncertainties. Alternative indentation
techniques must be sought to more effectively distinguish these mystical
materials.
5. Spherical Indentation Analysis
There have been several attempts to measure the elastoplastic properties
with spherical indentation 23,80,81 ; these methods, however, require an
accurate determination of the contact radius which is very difficult in
experiments. Once again, the key is to determine the unique elastoplastic
properties solely from the trustworthy P − curves. Based on the contact
stiffness, maximum load and penetration, Lee et al . 82 proposed a
numerical technique which involves quite a few fitting parameters and