Application of Probability to Mechanical Design
93
plied laminates
FS
0.30 < -- < 0.60.
(2.98)
-TSSurface endurance strengths [2.32] such as in gear teeth with contact stresses
are generally 2.5-5.0 times flexural endurance limits.
3. Low Cycle Fatigue Using Strain
The a~-N curve may also be presented as t, strain, versus N, cycles. Since
the yield is exceeded at 104 cycles the dimensionless value of strain, t, is
used. Fig. 2.32 a data curve by S. S. Manson et al. [2.67] shows various
metals and condition on one e versus N curve. Boiler and Seegar [2.3] uses
the same data but separate plots of each material are presented. Individual
curves for each material may be constructed from handbook data Fatigue
Curves With Testing by Peter Weihsmann, [2.59].
Note some authors [2.6, 2.35] present total strain amplitude versus 2N
or a form of
~71
Ate Aep
-- ~ (2n) b + t)(2n)
e
(2.99)
2-2 +~
-
The curve Fig. 2.33 is constructed as follows
Point A At = (a,~/E) plotted at N = 1/4(0.25)
Point B Ae = (ae,/E) at stated cycles 106,108,5 x 108 but obtain N greater
also include km Eqs. (2.89) and (2.90).
Point C Ae = tf = lne[100/(100 - Ra)] Ra - % reduction of area plotted
at N = 1/4(0.25)
Point D Ae = ee = (ayt/E) Plotted at N = 104 cycles the boundary between
plastic and elastic strain
This method was used on the curve by Manson et al. [2.67] in Fig. 2.32 for A
356 aluminum casting and 17-4pH (H900) where both materials are
different. The method showed good agreement in Fig. 2.34.
Manson [2.35] simplified the previous Eq. 2.99 to yield
At = 3.5 a.t 1
/~.6 1
-~- j~0.1~
+ ~ = Ate -’lm/3p
(2.100)
where
E- is Youngs Module
aul t - ultimate tensile strength
ef - true strain at fracture in tension