High Frequency Fatigue and Using Frequency Domain Techniques

Abstract In recent years API 579 has provided the analyst with a detailed outline of the Wang-Brown algorithm (WBCC) for the cycle counting. The WBCC algorithm has become the generally accepted core of cycle counting implementations whenever multi-axial non-proportional fatigue stress histories are encountered. However, for vibration based fatigue, in the absence of any time history at all; it is common in industry to assess fatigue using frequency domain techniques. This paper presents special considerations for determination of the spectral stress fatigue in the spirit of API 579. In the frequency domain the stress cycles are counted a priori as a set of complex vectors. These complex stress vectors may represent the full stress tensor of a reduced set in an appropriate sub-space. The phase relationship between the vectors represents the time delay between the stress components of the stress field. This paper presents some of the actions that are necessary in order to accurately capture the phase relationships. It is often the case that the physics of the driving loads are either unknown or too complex to practically model. This is the case for complex fluid and particle interactions with vessel shells, piping or other wetted surfaces. This paper presents some tools and techniques that can be applied in order to characterize the loading spectrum in a manner which is specifically designed to capture the important fatigue characteristics. Any fatigue estimation technique must convert the stress vector set into a singularly dimensioned scalar metric that represents the stress amplitude of a cycle. However, the maximum stress amplitude from the cycle is not immediately accessible from the complex stress vectors. While a number of papers present techniques that are intended to calculate the maximum stress amplitude in the case where the stress metric is the equivalent stress this paper provides a slightly more general relation for the phase of the maximum amplitude. Finally the analyst must compare their calculated fatigue stress amplitudes to the API 579 fatigue curves. Closed form expressions for mono-linear spectral fatigue have been extensively investigated in the literature but more complex fatigue curves do not have such simple solutions. To this end this paper investigates the smooth bar carbon steel fatigue curves of ASME VIII-2.