Biomedical Engineering Reference
In-Depth Information
calculated:
K
IC
s
f
¼
½
4
:
5
1
=
2
Y
ðp
a
c
Þ
1
p
Y
2
K
IC
s
f
a
c
¼
½
4
:
6
Equations 4.5 and 4.6 describe the close relation between fracture strength
and size of the critical defects. It may clearly be seen that given a particular
value of K
IC
, the size of microstructural features (whether macro-, micro- or
nano-cracks) determines the failure or survival of the stressed material.
4.2.3 Measurement of fracture toughness
The measurement of fracture toughness in ceramics is based on the methods
developed for metals. However, in newly developed brittle materials, the
choice is restricted as only a limited number of small specimens are available
and of practical use. The most common methods are as follows.
Single edge notched beam (SENB) and single edge pre-cracked beam
(SEPB)
Both are simple to use. In a rectangular beam, the sharpest possible notch is
made on one side (Fig. 4.4(a)). In a SEPB, a crack is created at the tip of the
notch, i.e. a situation close to an ideally sharp controlled flaw is created. The
beam is loaded in four-point bending mode and the fracture toughness is
calculated from the fracture load:
!
;
where M
3
1
=
2
F
max
S
1
S
2
ðaÞ
K
IC
¼
M
¼
f
ða ¼
a
=
W
Þ½
4
:
7
1
=
2
W
3
=
2
B
ð
W
Þ
2
ð
1
aÞ
Double torsion (DT)
The double torsion test (Fig. 4.4(b)) is convenient because the stress
intensity K
I
does not depend on the length of the crack for 0.25 L
0.75
L. The crack can therefore be propagated in a stable and controllable
manner. The fracture toughness is given by:
<
a
<
1
=
2
3
ð
þ nÞ
Wt
3
t
1
1
K
I
¼
FW
m
½
4
:
8
