Biomedical Engineering Reference
In-Depth Information
4.5
Flexure test of strength: (a) three-point bending; (b) four-point
bending.
preparation and which are statistically distributed throughout the micro-
structure. The strength cannot therefore be characterised by one value but
must be statistically treated and described by the appropriate distribution.
Weibull (1951) proposed a distribution that expresses the cumulative
probability of failure P
f
as a function of maximum applied tensile stress,
,
acting in an effective volume of sample V, using three independent variables:
σ
2
4
3
5
m
Z
s s
u
s
0
P
f
¼
exp
½
:
1
dV
4
11
V
where m is the Weibull modulus, which characterises the scatter of strength
values,
σ
u
is
the threshold stress (i.e. stress under which the failure probability is zero).
Weibull's analysis assumes a normal distribution of defect size, that only
one population of critical defects is present and that existing defects do not
interact among themselves.
σ
0
is a normalising parameter called characteristic strength and
