Biomedical Engineering Reference
In-Depth Information
A notch is cut in the brittle material. A crack occurs during loading and
grows with F. This method requires only small specimens.
Indentation methods
Indentations can generate cracks in brittle materials and the equilibrium
length, c, of these cracks is related to the indentation load and fracture
toughness. However, the relationship is not simple and many authors have
proposed different formulas. One of the most widely used, which is suitable
for very brittle materials, was developed by Anstis et al. (1981):
1
=
2
E
H
F
c
3
=
2
K
IC
¼ Z
½
4
:
9
where
is a shape factor (0.016 for a Vickers indentation), E and H are
Young's modulus and hardness respectively, F is the indentation load and c
is the crack length (Fig. 4.4(c)). These tests are easy to carry out and may be
done with very small specimens. Their disadvantages are high scatter and
subjective errors. This technique is therefore used mostly for comparative
purposes and to obtain preliminary results for new materials.
η
4.2.4 Measurement of strength
It is difficult to prepare and perform a standard tensile strength test for new
brittle materials. The most widely used methods for measuring strength are
three- and four-point bending of rectangular bars (Fig. 4.5). The stress
across the specimen changes in a linear manner from compression to
tension. For this reason, the fracture usually originates either close to, or
directly at, the tensile surface. In an elastic beam bent at four points, the
bending moment is constant in the inner span (Fig. 4.5(b)). After the
fracture load F is reached, the strength can be calculated as:
3
2
F
ð
S
1
S
2
Þ
W
2
B
s
c
¼
½
4
:
10
For three-point bending, S
2
=0.
4.2.5 Critical flaw, statistical character of strength in
ceramics, Weibull distribution
As shown by equation 4.5, there is a direct relationship between the size of
the critical flaw and the resultant measured fracture strength. The measured
strength is therefore not a fixed value but depends on the size (and shape) of
defects and flaws that result from the technological process of material
