Strength Analysis - Finite Element Analysis for Satellite Structures - page 156

aluminum alloy plates with 0.25 - 2 inch thickness. Figure 4.55 shows the
typical constant life diagram for fatigue behavior of 6061-T6 aluminum alloy.
The fatigue data of this alloy are presented for unnotched various wrought
products under room temperature without specification for surface finish. The
stresses in the fatigue diagram are presented in (Ksi), so all stress values in (MPa)
from harmonic and mean static analyses must be converted into (Ksi) values.
Using the formula:

r ks ðÞ¼ r MPa

ð Þ

6 : 89

The following empirical stress equation provides an appropriate approximation
for the fatigue behavior data of wrought products made of 6061-T6 aluminum
alloy at room temperature [9]:

log N j ¼ a 1 a 2 log ½ r Max ð 1 R Þ n a 3

where:

• N j : life time cycles
• r Max : maximum value of stress in the stress cycle (ksi)
• R: stress ratio R = r Min = r Max
• a 1 , a 2 , a 3 , and n are empirical constants having the following values:
• a 1 = 20.68, a 2 = 9.84, a 3 = 0, n = 0.63
For accurate results, the previous equation is used to calculate the life time
cycles N j corresponding to each dynamic loading phase and resonance frequency
at the most critical points of Small Sat structure.
Calculate cumulative fatigue damage at the critical points by the relation:
X D j ¼ X n j
N j
If fatigue damage accumulation is more than one P D j [ 1 ; proper changes
have to be made either for the section dimensions or the type of material used in
design.

4.12.4 Fatigue Damage Calculation Results

The cumulative fatigue damage is calculated for the most critical points located in
the satellite structure. These points are specified during performing the harmonic
response analysis of Small Sat structure. By reviewing Sect. 4.9.4 , there are 29
critical points distributed on the whole satellite structure. The cyclic stress loading
acting on each critical point is specified from the harmonic response analysis for
all dynamic loading phases. Table 4.19 lists the cumulative fatigue damage values
for each critical point calculated according to the criterion mentioned before.