Biomedical Engineering Reference
In-Depth Information
(A)
(B)
FIGURE 17.7
Radial cracks in imprints made by Vickers indenter: (A) central
cracks, (B) Palmqvist's cracks.
17.6
RESISTANCE AGAINST CRACK PROPAGATION
Fracture of brittle materials, such as enamel, proceeds by crack propagation. The material resistance
against propagation of an existing crack can be characterized by fracture toughness
K
IC
, defined as
the value of stress intensity factor at the onset of fast crack growth.
K
IC
is usually determined by
breaking a standard specimen with a preformed crack, but it can also be calculated from the length of
cracks created by an indenter (
Figure 17.7
). This is advantageous for very small specimens, such as
teeth. A semiempirical formula
[37]
is (see also Section 16.3.3):
1 2
/
3 2
/
K
IC
(
k E H
/
)
P c
/
(17.22)
P
is the indenter load, leading to the formation of cracks,
c
is the crack half-length, measured from
the imprint center,
E
is elastic modulus,
H
is Vickers hardness, and
k
is an empirical constant.
Equation (17.22) was proposed for central cracks of semielliptical shape (
Figure 17.7A
), with
[7]
k
0.016 for Vickers and Berkovich indenter. Also cube-corner indenters are used, as they are
sharper than Vickers or Berkovich and nucleate cracks at lower forces. For these indenters
[38]
,
k
0.032
0.040, or even
[7]
0.054. Sometimes, shallow Palmqvist's cracks appear (
Figure 17.7B
),
for which
[39,40]
)
2 5
/
1 2
/
(
(17.23)
K
k E H
/
P ac
/(
)
IC
a
is the half-length of the imprint diagonal and
c
is the crack length measured from the imprint cor-
ner. The constant
k
was recommended
[8]
as
k
0.0084.
The length of the cracks are measured on the specimen surface after the test. With an unknown
material, it can be difficult to decide from this observation whether the cracks are central or
Palmqvist. In such case, it is possible to color the crack surfaces using a dye penetrant and look at
them after breaking the specimen.
