Biomedical Engineering Reference
In-Depth Information
Similar to the Berkovich tip, the cube corner tip is a kind of three-sided pyramidal sharp tip. The
cube corner tip has a face angle of 35.3° and, therefore, is sharper than the Berkovich tip. The main
advantage of this sharper tip is that it will create plastic deformation even at shallow indentation
depths and ensures that accurate hardness measurements can still be made even when the indent size
is small. The cube corner tip is often used for measuring fracture toughness, K IC , of materials since
the stress field created by the tip geometry has more cutting action in comparison to the Berkovich
tip. Radian and median cracks, therefore, are more readily developed around the indents made by
the cube corner tip. The crack length, c , is measured from the center of the indent to the tip of the
crack on the specimen surface. The fracture toughness, K IC , of the material is then calculated using
the empirical relation
1 2
/
IC α
E
H
P
(16.6)
K
3 2
/
c
For a cube corner tip, the value for α is known to range from 0.032 to 0.040 [31] .
The sharp tips described above will create plastic deformation in the specimen even at small pen-
etration depths and can only produce a constant nominal strain value during indentation. In contrast,
the cono-spherical tip is blunt and produces almost no plastic deformation on the specimen during the
initial part of loading. The strain induced by the tip geometry also varies with indentation depth. These
characteristics allow the cono-spherical tips to capture the smooth transition from elastic to plastic
contact during indentation. The mean contact stress during indentation for h max R is calculated as
4
3 π
E a
R
r
(16.7)
P
m
and the corresponding indentation strain is calculated as
a
R
(16.8)
ε 0 .
In the above, R refers to the radius of the cono-spherical tip and a the radius of the indentation
area [32] ( Figure 16.4 ).
For the flat-end tips, only the flat surface at the end of the tip remains in contact with the specimen
surface throughout the experiment such that A c is always a constant value. However, during an actual
indentation, there is often difficulty in aligning the sample perfectly parallel to the tip surface, leading
to deviation from the ideal condition. It is worth noting that the elastic deformation of a flat-end tip
cannot be described by the term [(1 v 2 )/ E ] tip in Eq. (16.4), but if the specimen is much softer than
the tip, the deformation of the latter can be ignored anyway so that E r [ E /(1 v 2 )] sample , i.e., Eq.
(16.4) is still applicable in the limit E tip . Both the cono-spherical and flat-end tips are useful for
soft materials such as demineralized dentin, since their stress field is much milder than the sharp tips.
16.3.4 Load Function and Data Analysis
It is sometimes desirable to have a constant strain-rate condition when investigating the deformation
behavior of viscoelastic materials since their mechanical properties are strain-rate dependent. The
 
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