Page 255 - Handbook of Materials Failure Analysis

3 Structural Dynamics Analysis Method of Shovel Front-End Mechanism 251

The damage summation from each cycle needs to be performed to obtain the total
amount of fatigue damage due to all cycles. Palmgren-Miner’s rule is proposed to
calculate the structural fatigue damage for the mining excavators [19]. This theory
is described by the S-N curve as given in Figure 10.9. If there are k different SRs or
levels and n i cycles are applied at SR (where the fatigue life is N i cycles), then
Palmgren-Miner [20] gives the cumulative damage amount D as Equation 10.2.

k
X
(10.2)
n i
¼ D
i¼1 N i
In this study, D at an equivalent constant amplitude SR σ v is linearly proportional to
the ratio of the experienced number of cycles n v to the number of cycles to failure N v
at this stress level. The above equation can be expressed as Equation 10.3.
k m m
X
σ n i
¼
i σ n v (10.3)
v
m m
i¼1 σ N i σ N v
v
i
where m is the crack growth rate constant. From Equation 10.4:
σ N i ¼ Constant (10.4)
m
i
The Equation 10.3 can be written as Equation 10.5.
k
X
(10.5)
m m
σ n i ¼ σ n v
i v
i¼1
A variable amplitude stress spectrum is replaced by an equivalent constant amplitude
SR by Equation 10.6. Using this SR, the fatigue life for this hot spot is determined
from the S-N diagram for the given structure material.
!
1=m
n

X
σ v ¼ m (10.6)
σ n i =n v
i
i¼1
Stress range s i n
s

n N n n i N i
n
Cycles to failure
FIGURE 10.9
S-N curve diagram described by Palmgren-Miner rule.