Comparison of two equivalent stress methods based on cumulative damage adjustment and on a consistent fatigue strength reduction for transforming of variable into constant amplitude loading

Abstract

Abstract This paper compares two methods for transforming a stress or load spectrum into a damage-equivalent constant amplitude loading, i.e., the required fatigue strength (RFS) and the consistent equivalent strength (CES) concepts. Because of their shared fundamentals, i.e., the modified Palmgren-Miner hypothesis for a given allowable damage sum, the resulting RFS- and CES-amplitudes are comparable to each other, but not equal, when the slopes after the knee-points of the Woehler-lines differ. The RFS-method delivers a damage-equivalent stress as the knee-point of a fictitious bi-linear or linear Woehler-line by positioning of the Woehler-line for a given allowable damage sum. In contrast to this, the CES-method also results in a damage-equivalent stress as the knee-point, which depends on the consistent fatigue strength reduction by increasing cumulating damage until the allowable damage sum is reached. Thus, the main difference to the RFS-method is that the CES-method retains the constant amplitude loading slope after the knee-point. Both methods indicate a lowest necessary strength quality, but, like the calculated fatigue lives, they differ according to the calculation methods, and depend on the slopes of the Woehler-lines after the knee-points.