Application of Probability to Mechanical Design
75
1.0
0.8
o.6
0.4
0.2
~
Quenched and tempered steel
/ ~ Annealed and normalized steels
For t/r < 3
0
1/32
1/16
3/32
I/8
5/32
3/].6
Notch radius r (in.)
Figure 2.16 Typical notch sensitivity data for steel (data by Peterson [2.49]).
and an axial load.
M,~c Kf, ff_~
(2.68)
where Kj,~ and Kf~ stand for the stress concentration factors for bending and
tension.
In general Kf is from Eq. (2.65) where
Kf = 1 + q(Kt - 1)
If q = 1 then Kf = ~ which is the first iteration of a part size then Kf is
calculated when the notch radii and part across sections dimensions are
known. The variations are in K~ and q. Haugen [2.18] has plotted and calculated K~ for some shapes. The C~s are ~10.9% with R(0.99) and 95% confidence for the smaller radii and higher K~s but the 10.9% becomes smaller as
the Kt curve flattens out.
The q average values are published in most texts but in [2.52] and [2.36]
the coefficient of variation for q, and C~,, Table 2.7, may be developed and
the estimates are as follows
EXAMPLE 2.17. The card sort may be used to find ~f for the maximum or minimum variables where a symmetric distribution is used, such
as tolerance on a part size