where:
a 
= 
N from the inverse power law = material dependent
parameter (slope of the SN curve) 
N_{i} 
= 
the number of cycles to failure under
stress S_{i} 
S_{i} 
= 
stress level associated with
N_{i} cycles 
S_{1} 
= 
stress level required for failure in 1
stress reversal 
where:
n_{i} =
the number of applied stress reversals at a single stress level
i
s_{i} = stress level associated with
ni
An SN diagram is commonly used to present the data from
equation 8.45. The SN diagram plots the number of stress cycles required to
break an item at a given stress level. The power of accelerated fatigue
testing can then be demonstrated by simplifying equation 8.45 and assuming a
material parameter. Since S1
is a constant:

CD µn_{i}(s_{i})^{a} 
(8.46) 
The cumulative fatigue damage then becomes proportional to the
number of stress cycles and their associated stress level. To illustrate,
calculate the increase in cumulative fatigue damage during accelerated testing
when the stress level (si) is doubled, assuming (for the
sake of illustration only that) the material parameter a = 10, then:
DCDµni(2)^{10}=n_{i}(1024)
Thus the fatigue damage accumulates 1024 times
(2^{10}) faster than what it would
at the baseline stress. Hence, a 20second test with the applied stress
doubled becomes the equivalent of a 300minute vibration test at normal stress
level! Properly applied, this technique can be a powerful tool. In this
example (assuming that the yield
strength of the material was not exceeded during the test), identifying design problems quickly could be readily
achieved using an accelerated stress test.