Application of the Paris formula with m=2 and the variable load spectrum to a simplified method for evaluation of reliability and fatigue life demonstrated by aircraft components

The presented paper is the follow-up to the study, where the method for assessment of the fatigue life of a structural component was outlined with consideration of the variable spectrum of loads and with use of the Paris formula for m ≠ 2. Due to the different nature inherent to analytic forms of solutions for the Paris equations with their exponential parameter m = 2, that special case is the subject of a separate analysis. This paper also uses the transformation of a real spectrum with variable values of fatigue cycles into a homogenous spectrum with weighted cycles. The method was developed that uses the transformed spectrum to evaluate fatigue life for a selected component of the aircraft structure when the component suffers from an initial crack. The method for modeling of the crack length expansion uses a differential equation that is then subjected to transformations to obtain a partial differential equation of the Fokker-Planck type, which has a particular solution, explicitly the length density function for the crack of the component in question. That length density function served subsequently to determine reliability and fatigue life of a structural component where the crack length expanded from the permissible value ld to the critical threshold lkr..