The Effect of Stress Amplitudes below Endurance Limit on the Cumulative Fatigue Life

In the design of machines the fatigue life of a member under service load is usually calculated on the assumption that Miner's rule can be applied. However according to the results of many program fatigue tests, the linear calculative cycle ratio is not always equal to 1, and the Miner's rule does not take into account the stress cycles under fatigue limit. But the results of fatigue tests, including the stress amplitudes below fatigue limit, obviously show that they influence the cumulative life. This fact is particulary important in the ordinary mechanical structure, because the load spectrum mostly consists of stress amplitude less than the fatigue limit, and the stress amplitude over the fatigue limit is smaller in number. Therefore simple application of Miner's rule is somewhat questionable.The authors have performed the program fatigue tests of carbon steel S35C under the load spectra which have the same pattern of distribution as the frequency diagram measured on the axles of railways. The load spectra are with or without stress amplitude less than fatigue limit to investigate the influence of the stress below the fatigue limit to the cumulative life. From the experimental results a new equation is proposed to estimate the cumulative fatigue life with the effect of the stress amplitude less than the fatigue limit. The total number of cycles of stresses to failure for fluctuating stress can be shown as follows:Ng=N1/{σmi=1[αi(σi/σ1)c]+σrp=m+1[αp(σp/σ1)b×c]}in which n1, n2, ……, nk are the numbers of cycles at stress amplitudeσ1, σ2, ……, σk in each program cycle.If n1+n2+……+nk=ng, then α1=n1/ng, α2=n2/ng, ……, αk=nk/ngthe value c is decided by the equation Nσc=K, K and b is a constant.