Page 309 - Shigley's Mechanical Engineering Design

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284 Mechanical Engineering Design
for both high-cycle and low-cycle regions, requiring the parameters of the Manson-
Coffin equation plus the strain-strengthening exponent m. Engineers often have to work
with less information.
3
Figure 6–10 indicates that the high-cycle fatigue domain extends from 10 cycles
6
7
for steels to the endurance limit life N e , which is about 10 to 10 cycles. The purpose
of this section is to develop methods of approximation of the S-N diagram in the high-
cycle region, when information may be as sparse as the results of a simple tension test.
Experience has shown high-cycle fatigue data are rectified by a logarithmic transform
to both stress and cycles-to-failure. Equation (6–2) can be used to determine the fatigue
3
strength at 10 cycles. Defining the specimen fatigue strength at a specific number of
cycles as (S ) N = E ε e /2, write Eq. (6–2) as

f

(S ) N = σ (2N) b (6–9)

f F
3
At 10 cycles,
3 b
3
(S ) 10 = σ (2 · 10 ) = fS ut
f F
where f is the fraction of S ut represented by (S ) 10 cycles. Solving for f gives

3
f
σ F 3 b
f = (2 · 10 ) (6–10)
S ut
m

Now, from Eq. (2–15), σ = σ 0 ε , with ε = ε . If this true-stress–true-strain equation
F F
11
is not known, the SAE approximation for steels with H B ≤ 500 may be used:
σ = S ut + 50 kpsi or σ = S ut + 345 MPa (6–11)

F
F

To find b, substitute the endurance strength and corresponding cycles, S and N e ,
e
respectively into Eq. (6–9) and solving for b

log σ /S e

F
b =− (6–12)
log (2N e )
b
Thus, the equation S = σ (2N) is known. For example, if S ut = 105 kpsi and

f F
6
S = 52.5 kpsi with N e = 10 cycles,

e

Eq. (6–11) σ = 105 + 50 = 155 kpsi
F
log(155/52.5)
Eq. (6–12) b =− =−0.0746
log 2 · 10 6
155 3 −0.0746

Eq. (6–10) f = 2 · 10 = 0.837
105

and for Eq. (6–9), with S = (S ) N ,

f f
S = 155(2N) −0.0746 = 147 N −0.0746 (a)

f
11 Fatigue Design Handbook, vol. 4, Society of Automotive Engineers, New York, 1958, p. 27.