Page 356 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 331
Figure 6–36 Class No.
1 All metals 380
The lognormal probability 2 Nonferrous 152
density PDF of the fatigue ratio 3 3 Iron and carbon steels 111
4 4 Low-alloy steels 78
φ b of Gough.
5 Special alloy steels 39
Probability density 1 5
2
5

0
0.3 0.4 0.5 0.6 0.7
Rotary bending fatigue ratio b

Also, 25 plain carbon and low-alloy steels with S ut > 212 kpsi are described by

S = 107LN(1, 0.139) kpsi
e
In summary, for the rotating-beam specimen,

⎧
⎪ 0.506S ut LN(1, 0.138) kpsi or MPa S ut ≤ 212 kpsi (1460 MPa)
¯
¯
⎨
¯ (6–70)
S = 107LN(1, 0.139) kpsi S ut > 212 kpsi
e
⎪
740LN(1, 0.139) MPa S ut > 1460 MPa
⎩ ¯
where S ut is the mean ultimate tensile strength.
¯
Equations (6–70) represent the state of information before an engineer has chosen
a material. In choosing, the designer has made a random choice from the ensemble of
possibilities, and the statistics can give the odds of disappointment. If the testing is lim-
ited to finding an estimate of the ultimate tensile strength mean S ut with the chosen
¯
material, Eqs. (6–70) are directly helpful. If there is to be rotary-beam fatigue testing,
then statistical information on the endurance limit is gathered and there is no need for
the correlation above.
¯
Table 6–9 compares approximate mean values of the fatigue ratio φ 0.30 for several
classes of ferrous materials.
Endurance Limit Modifying Factors
A Marin equation can be written as

S e = k a k b k c k d k f S (6–71)
e
where the size factor k b is deterministic and remains unchanged from that given in
Sec. 6–9. Also, since we are performing a stochastic analysis, the “reliability factor” k e
is unnecessary here.
The surface factor k a cited earlier in deterministic form as Eq. (6–20), p. 288, is
now given in stochastic form by
b
¯
k a = aS LN(1, C) (S ut in kpsi or MPa) (6–72)
¯
ut
where Table 6–10 gives values of a, b, and C for various surface conditions.