68
Chapter 2
Time
Figure 2.12 Typical sinusoidal fatigue loading with a mean stress.
maximum (or minimum) stress. The average or mean stress am and the alternating component ar are Fig. 2.12.
O’ma x q- O’mi
n
O’ma x -- O-mi n
am2
and at2
(2.51)
where a compressive stress is a negative number. For a complete reversal,
am = 0; that is,
O-mi n ~--- --O’ma x and tr r = O-ma x. In every case,
(2.52)
O’ma x ~ O" m -]- O"
r
A parameter used to locate the curves of Fig. 2.11 is a stress ratio R defined
as
R -- O’mi~n , O" m -- ar
(2.53)
O’ma x
O" m --]- O"
r
with stresses used algebraically; R = - 1 for completely reversed stress, Fig.
2.11.
The curve Fig. 2.11 represents an average for O’e, O’u, fir, and a,t. Hence
when N-- 1 the Pf ---- 50% which should be avoided. The trr-am curve from
extensive testing as per [2.27] will show with the average and spread about
the average or mean. The unfortunate case is that only O’y, flu, and oe
are generally known as estimates of Cz from much test data. The Cv
can be derived from class A and B materials in [2.1,2.18,2.63,2.65] for metallic materials.
C~,~ = +0.08
~’e’
Z~y~
Cw, = +0.07
tTyt
C .... = ±0.05 z~,,_ tYut
(2.54)