Some fatigue damage measures for longitudinal elements based on the Wohler field

In this paper, the problem of selecting damage measures and ways of accumulating damage due to a fatigue load history is dealt with. First, a statistical model and a normalization procedure, that allow using a reference stress level or a reference random variable for analysing the fatigue data coming from tests at different stress ranges, are presented. Next, some desirable properties for a damage measure are discussed and several alternative damage measures are investigated based on these properties. It is shown how several damage measures, such as the Palmgren–Miner number, do not satisfy these properties. On the contrary, the standardized logarithm of the number of cycles, which coincides with the standardized Palmgren–Miner number, a Weibull reference variable and a probability based damage measure are demonstrated to satisfy these properties and to be good alternatives for a damage measure. It is shown that the most convenient damage measures are obtained by assuming that two pieces subjected to different stress level tests suffer the same damage if, at the end of the corresponding tests, they have the same probability of failure. The problem of extending the damage measure below the zero‐percentile area (where fatigue failure does not occur) is also analysed. Finally, the damage accumulation problem for non‐constant stress range load histories is discussed, and formulae for calculating the associated damage are given. For the sake of illustration, several examples of different load types are also given.