COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 153

indentation responses, material properties, and indenter geometries. The
strain gradient effect 47 is usually ignored by assuming that the
indentation depth is sufficiently deep so that the continuum mechanics
still applies to the bulk specimen. The rigid contact surface option can be
used to simulate the rigid indenter, and the Coulomb's friction law can
be easily embedded. In fact, friction is a minor factor for indentation 1,48
as long as this value is relatively small - when the Coulomb's friction
coefficient is less than about 0.15 the contact solution is close to that of
frictionless indent. This has been verified by the studies by Bucaille
et al . 49 and Wang et al . 50,51
In order to reduce computational cost, most researchers reduce the
indentation problem to axisymmetric. Previous numerical work has
shown that the loading and unloading P - h curves are almost same for
pyramidal and conical indentations, as long as the ratios of cross-
sectional area to depth are the same for these two types of indenters. 1,52
To simplify the analysis, the sharp pyramidal indenter is usually modeled
as a rigid cone with half apex angle , so that the ratio of cross-

sectional area to depth is the same as for a widely used Berkovich or
Vickers indenter. 1,3 Other variants of α

α =° 70.3

are also commonly used in the

indentation analyses, 5,49,53-56 such as (Rockwell tip), α =° 60 α = 63.14 °

(the cross-sectional area is half of that of the Berkovich indenter),
75.79 α = ° (the cross-section area is twice of that of the Berkovich tip),

and

α =° , etc. For other common shapes such as spherical or conical,
the indentation analyses are naturally axisymmetric. The axisymmetric
assumption can also be employed when an indenter penetrates normally
to thin films and multilayers.
However, in many other cases axisymmetry does not hold, such as in
particle reinforced composites, anisotropic and inhomogeneous materials,
and special indentation cases where indenter is close to specimen
boundary, indentation induced surface radial fracture, 57 or when uniaxial
in-plane residual stress present, 58 among others. In those cases three-
dimensional mesh must be used.
Typical meshes for the axisymmetric indentation model and three-
dimensional indentation model are shown in Fig. 6-3 . Several key issues
should be noted during computation: First, the effect of boundary

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