Fatigue Damage Spectrum

The Fatigue Damage Spectrum (FDS) Project type creates accelerated life-cycle testing profiles for vibrations tests. The FDS function helps reduce testing time by calculating the quickest path to destruction or damage. Testing time is accelerated by concentrating the random or swept sine energy, depending on the FDS calculation, to where it will induce the most fatigue damage. The FDS function can be used to determine the amount of damage on the object being tested. The information gleaned from the FDS function can be combined with other parameters, to reduce testing time.

 
 

The damage caused by vibration can be caused in one of the following conditions:

  1. Damage caused by an extreme instantaneous stress on an object

  2. Damage caused by fatigue when a high amount of a certain stress is applied to the object

FDS represents a spectrum with regard to the fatigue damage on an object. The FDS function makes use of the S-N curve to construct the spectrum. The S-N curve represents the stress applied to a material (S) versus the number of cycles of applied stress. The S-N curve of aluminum is shown below:

S-N Curve of Aluminum
After the number of fatigue cycles has been extracted from the S-N curve, we can move on to the analytical model for the FDS. To do so, we must start with an understanding of how the system under investigation responds to a shock.

The Shock Response Spectrum (SRS) is a Frequency Response Function (FRF) that describes the frequency response of a system to a shock or a transient event.  Its analog in the time domain is the Extreme Response Spectrum (ERS), but the ERS predicts system response due to a lengthier loading duration. The equation for the ERS for the acceleration response of a system is:

Where:

The FDS builds on the assumptions of the SRS and ERS. The FDS is an FRF that describes the cyclic fatigue damage of a system. The equation for the FDS is:

Where:

The FDS can also be calculated using a time-dependent input. Like the SRS, the FDS for a range of frequencies can be summed together to obtain the lifetime fatigue damage of the system. Once the FDS is obtained, it can be inverted into a test PSD. This PSD can be used for accelerated vibration testing, and a whole lifecycle of damage can be imparted to a system with a single test.