Application of Probability to Mechanical Design
85
perature increased appreciably. For speeds over 7000 cycles per minute
there is some evidence that the fatigue life increases a small amount.
For viscoelastic materials (polymers), considerably more caution must
be exercised in interpreting fatigue data. Normally, fatigue tests are conducted at as rapid a frequency of stressing as possible, with due consideration for temperature rise. However, polymers will exhibit different
fatigue characteristics depending on the stress frequency, which, depending
on the material, will yield different results in ranges of high and low loss
factors. In general, in applications involving fatigue loading it is best to
use materials that exhibit low loss factor under the conditions expected
to persist in the application; if the part is used as a damper or energy
absorber, it should be used at a frequency characterized by a high loss factor.
For example, a vibrating part made of polymethyl methacrylate at room
temperature should not be used at a frequency of 600 cycles per minute
since this is where the loss factor is maximum (Fig. 2.21). Thus, in evaluating
fatigue data for polymers curves such as shown in Fig. 2.21 should be
available.
14. Mean Stress
A structure stress-cycled about some mean stress other than zero has different fatigue characteristics
than one cycled about zero mean stress.
The precise reason for this is unknown, but it is believed due to hysteresis
effects caused by plastic flow that changes the fatigue characteristics on each
cycle. The effect of mean stress has been included empirically in the design
examples discussed later in this section.
The mean stress, Eq. (2.48), for brittle metals requires the application
of Kf values as shown in Eq. (2.68). For some steels, for example, the criterion for brittleness can be found approximately from Charpy or Izod test
data shown in Fig. 2.22. Above the transition temperature the metal acts
in a ductile manner while below the transition temperature the metal acts
in a brittle fashion.
The combined mean stress Fig. 2.23 using distortion energy or Von
Mises energy criterion is Eq. (2.48)
1 ~/
2
2 q_ 3.C2xym
(2.84)
~m ~ ff xm -- ~xm~y m "]- rYym
~¢~m the standard deviation needs to be calculated or a distribution function
developed.
The reversal Fig. 2.24 or amplitude stress Eq. (2.49)
1_/2
-"]- ly2y a "q- 3"C2xya
(2.85)
fir = yffxa ffxaffya
85
perature increased appreciably. For speeds over 7000 cycles per minute
there is some evidence that the fatigue life increases a small amount.
For viscoelastic materials (polymers), considerably more caution must
be exercised in interpreting fatigue data. Normally, fatigue tests are conducted at as rapid a frequency of stressing as possible, with due consideration for temperature rise. However, polymers will exhibit different
fatigue characteristics depending on the stress frequency, which, depending
on the material, will yield different results in ranges of high and low loss
factors. In general, in applications involving fatigue loading it is best to
use materials that exhibit low loss factor under the conditions expected
to persist in the application; if the part is used as a damper or energy
absorber, it should be used at a frequency characterized by a high loss factor.
For example, a vibrating part made of polymethyl methacrylate at room
temperature should not be used at a frequency of 600 cycles per minute
since this is where the loss factor is maximum (Fig. 2.21). Thus, in evaluating
fatigue data for polymers curves such as shown in Fig. 2.21 should be
available.
14. Mean Stress
A structure stress-cycled about some mean stress other than zero has different fatigue characteristics
than one cycled about zero mean stress.
The precise reason for this is unknown, but it is believed due to hysteresis
effects caused by plastic flow that changes the fatigue characteristics on each
cycle. The effect of mean stress has been included empirically in the design
examples discussed later in this section.
The mean stress, Eq. (2.48), for brittle metals requires the application
of Kf values as shown in Eq. (2.68). For some steels, for example, the criterion for brittleness can be found approximately from Charpy or Izod test
data shown in Fig. 2.22. Above the transition temperature the metal acts
in a ductile manner while below the transition temperature the metal acts
in a brittle fashion.
The combined mean stress Fig. 2.23 using distortion energy or Von
Mises energy criterion is Eq. (2.48)
1 ~/
2
2 q_ 3.C2xym
(2.84)
~m ~ ff xm -- ~xm~y m "]- rYym
~¢~m the standard deviation needs to be calculated or a distribution function
developed.
The reversal Fig. 2.24 or amplitude stress Eq. (2.49)
1_/2
-"]- ly2y a "q- 3"C2xya
(2.85)
fir = yffxa ffxaffya