Expanding upon ANSYS Fatigue Slides
Vibration fatigue calculations are “ballpark” calculations given uncertainties in S-N curves, stress concentration factors, non-linearity, temperature, surface finish, heat treatment, load sequence, multi-axis loading, mean stress, size, geometry and other variables.
Perhaps the best that can be expected is to calculate the accumulated fatigue damage to the correct “order-of-magnitude.”
The ANSYS reference gave an example of a cantilever beam subjected to a PSD base excitation. The fatigue analysis was performed by counting the stress cycles in three bands: 0 to 1σ, 1σ to 2σ, 2σ to 3σ.
The 3-band fatigue method was taken from Steinberg, Vibration Analysis for Electronic Equipment. A deficiency of the three-band method is that higher sigma peaks may occur which make a significant contribution to fatigue damage.
In addition, the maximum expected stress level in the following example is a few percentage points above the ultimate limit which raises a cautionary flag.
The ultimate tensile stress for aluminum 6061-T6 is 310 MPa (45 ksi)
This presentation expands upon the ANSYS example using two methods:
Dirlik in the frequency domain
Rainflow cycle counting in the time domain
The two methods use a Palmgren-Miners equation with the MIL-HDBK-5J S-N curve for aluminum 6061-T6. Note that the ANSYS referenced used a modified Basquin S-N curve with at fatigue exponent of 6.4.
The finite element method is used for modeling the beam’s stress response. The maximum stress occurs at the beam’s fixed end. The Dirlik method is a semi-empirical method for calculating the cumulative damage index from the stress response PSD.
The rainflow cycle method from ASTM E 1049-85 is carried out by using a time domain synthesis. The time domain synthesis for the PSD is non-unique due to uncontrolled phase angles.
The results in the expanded analysis show that failure will occur at a shorter time than that in the ANSYS reference.
The three-band fatigue method served the industry well for many years. But rainflow cycle counting and the Dirlik methods are the current “best practices.” Engineers must also realize that response peaks of 4, 5 and 6σ may occur even for well-behaved, stationary, Gaussian stress response time histories.
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See also:
Dirlik Method
Peak Response to Random Vibration
Beam Bending FEA
– Tom Irvine