A reliability-based design method has been proposed for fatigue under service loads. The method is a practical one because it does not require to conduct fatigue tests on a large number of specimens under the relevant loading condition. In order to develop such a practical method, literature survey was carried out concerning the statistical nature of the cumulative cycle ratio
D≅∑
ni/
Ñi where
Ñi was the fatigue life under constant amplitude loading as given by the
S-
N curve. The survey revealed the following common tendencies: (i)
D follows a log-normal distribution approximately, and (ii) η
D, the coefficient of variation of
D, is roughly equal to η
N, the coefficient of variation of the fatigue life
N under constant amplitude loading. Based on (i) and (ii) above, a reliability based design method was proposed. In this method,
S-
Ñ/
k curve is used as the design fatigue curve, and ∑
ni/(
Ñi/
k)≤1 is used as a design criterion. The factor
k is determined from ln 1/
k=ln(μ
D/√1+η
N2)+[Φ
-1(
Pa)+
n-1/2Φ
-1(γ)]√ln(1+η
N2) where, μ
D is the estimate of the mean value of
D≅∑
ni/
Ñi,
n is the number of specimens tested to obtain μ
D, 1-
Pa is the reliability goal, 1-γ is the confidence coefficient, and Φ
-1 is the inverse function of the standard normal distribution function. The above equation was derived from the condition that the reliability of 1-
Pa is attained with the confidence of 1-γ. The most remarkable point in employing this design method is that fatigue tests to be conducted under the relevant loading condition is simply for obtaining μ
D, hence a large number of samples are not required. A simple design diagram for obtaining
k easily was also proposed.
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