COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 171

If the substrate is stiffer than the film, when h is normalized by the
specimen thickness t f , the dimensionless variable h / t f of film indentation
would play a somewhat opposite role as h / R of spherical indentation.
That is, when the indenter is approaching the coating/substrate interface,
the increasing “hard” substrate effect (which is directly related with h / t f )
offers a new independent geometrical factor, just like continuously
increasing the sharp indenter angle α in the plural indenter method.
Therefore, the substrate effect could be utilized to determine the
elastoplastic properties from one indentation test, and it complements the
spherical indentation in terms of the trend of variation of . Zhao et al . α

have proposed a framework of measuring ( E , ) based

on the normalized indentation loading curvatures taken at h / t f = 1/3 and
2/3, and the normalized unloading work taken at h m / t f = 2/3. This
theoretical formulation, which is similar to the spherical indentation
introduced above, is proven to work well for soft metal coatings on
elastic and stiff substrates 89,90 ; an example is given in Fig. 6-9a for a
copper film and it is expected that such technique could work well in
general for other thin films on substrates, including the biological
membranes. It is further shown that this technique works well to
distinguish the mystical materials. 65
When the specimen is porous as many biological materials do,
including bones and tissues, indentation induces densification effect
beneath the indenter which must be taken into account. Once again, by
comparing the indentation characteristics of a porous specimen with that
of a reference specimen, the effect of porosity can be deduced and the
existing indentation approach can be modified. 19 An example is given in
Fig. 6-9b where a modified factor is proposed: using such factor, the
hardness can be easily converted to the intrinsic yield strength of the
porous material, depending on different porosity and elastic stiffness of
the specimen.
For composite materials or material with other types of
micro-structure, the same principle can be applied. More refinements
can be incorporated to include time-dependent viscoelastic behavior,
nonlinear elastic behavior, anisotropic behavior, and inhomogeneous
properties. Many of such properties are important for biological materials
where computational modeling of indentation is an indispensable tool

, n ) (with σ ν = 0.3

y