The estimation of guaranteed fatigue life under random loading

One of the pressing problems of mechanical reliability still requiring a satisfactory solution is that of ensuring the guaranteed fatigue life of a component or structure subject to random dynamic loading. In the past, this problem has generally been solved in technical practice by the choice of a sufficiently large “safety factor” when dimensioning critically stressed parts of a complex structure. Application of probability and statistical methods now offers the possibility of developing a theory of reliability of mechanical systems, where the risk of failure can be expressed as a probability, taking into account effects of random loading processes, which characterize either the functioning of the system itself or external environmental operating conditions. In the following paper we describe one method of approach to the solution of this problem. The solution consists of a combination of the Weibull‐Freudenthal‐Gumbel theory of fatigue estimation using (s̀, N, P) relations, the Palmgren‐Miner hypothesis of linear accumulation of damage and the theory of stationary random processes having a given autocorrelation function or spectral density. Several other stochastic models are discussed in [1]. The subject of this paper was chosen in acknowledgement of the fact that H. C. Hamaker in his applied theoretical work also dealt with a related problem concerning the breaking strength of glass [2].