The Fatigue Damage Spectrum
GlyphWorks' Accelerated Testing uses the fatigue damage spectrum (FDS), a very useful analysis technique to quantitatively assess the potential for a fatigue failure mode in components or systems operating in a mechanical vibration environment. The mathematical theory used to calculate the FDS is presented in AECTP-240 Environmental Test Methods (Edition 4) Leaflet 2410, and is referenced by standards NATO STANAG 4370, UK DEF STAN 00-35 and USA MIL-STD- 810G.
The FDS (and MRS) examples illustrated in The Fatigue Damage Spectrum: Explained utilize the previous edition of Leaflet 2410, and follow references back to the withdrawn French standard, GAM-EG-13 and the Lalanne books from which it is based.
FDS should be used as a relative comparison method between two or more time history waveforms or vibration test environments. Used in this way the fatigue properties of the material are the same for each case and the relative similarity or difference of the time history waveforms or vibration test environments are revealed. For such relative analyses the only fatigue property required is the Basquin exponent ‘b’, the gradient of the stress-life curve in log space. The other primary assumption, and limitation, is the unknown damping factor Q. In practice this is usually defaulted to 10, and again for a relative analysis reveals the similarities and differences between the vibration environments.
This means that the FDS can be used to compare the potential cumulative fatigue damage for the duration of various vibration environments, such as within:
- Test Tailoring: Def Stan 00-35 , AECTP-240  and Mil Std 810  all recommend test tailoring of laboratory vibration test schedules. The vibration chapter of Mil Std 810 begins with the words “Tailoring is essential”, and AECTP-240  Leaflet 2410/1 Annex C describes the FDS as “an attractive technique in development of a laboratory vibration test schedule”.
- Vibration Qualification by Read Across Evidence: In many cases existing vibration qualification test evidence is available for equipment to be used in a specific aircraft vibration environment or to an environment defined by one the Def Stan 00-35, AECTP-240 or Mil Std 810 standards. In such cases FDS comparison of existing test evidence with the manufacturer’s vibration requirements may prove sufficient for the new aircraft enabling full type approval to be awarded without recourse to additional testing. This offers huge cost savings because vibration tests are very expensive on account of the direct testing costs and the cost of the test component which is life expired at the end of the test. If the existing test evidence is insufficient for full type approval, it is often sufficient to justify experimental flight approval subject to a limited flight envelope or number of flight hours.
- Health Usage Monitoring: The FDS is an analysis method that can increase the capability of on-board health usage monitoring systems (HUMS). For many years aircraft have used fatigue meters and counting accelerometers to monitor their inflight acceleration levels in order to estimate their structural life consumed during flight. This FDS approach is very suitable for assessment of vibration life consumed, with respect to the vibration qualification test evidence, for sensitive materiel (e.g. electronic equipment and missile structures, ref AECTP-200  Leaflet 2410/1) and localised complex systems such as hydraulics, fuel systems, etc.
Complete references are listed on The Fatigue Damage Spectrum: Explained poster available for download.
Example Application of FDS
All three of the FDS applications were used during the successful integration of external fuel tanks to a helicopter.
- Existing vibration qualification test evidence was insufficient for full type approval, but was sufficient to justify a limited number of hours of experimental flight by read across evidence.
- The health of this system was monitored during experimental flight testing by comparing the cumulative FDS with the FDS of the existing vibration qualification test evidence.
- This showed that the cumulative FDS from experimental flight testing increased rapidly at certain frequencies and would exceed those from the qualification test evidence.
- Identification of this led the supplier to a successful redesign of their system to pass a new vibration qualification test tailored to this specific helicopter vibration environment.
- The qualification of the redesign was confirmed by further experimental flight monitoring and FDS analysis of the measured accelerations.