A preliminary study on dispersions of fatigue properties of materials
  Static mechanical properties (e.g. elastic modulus) and fatigue properties of a material all have dispersions. Material inhomogeneity (it can be characterized well by the dispersion of elastic modulus) is the internal factor of dispersions of fatigue properties and the dispersion of the load is the external factor. In this paper, according to theoretical derivation and preliminary experiments verification, the following relationships between dispersions of fatigue properties and dispersions of static mechanical properties of a material are obtained: the dispersion of fatigue life is n (the fatigue index) times of the sum of the dispersion of elastic modulus and the dispersion of the load. The corresponding dispersion of fatigue life is a decreasing function of the given fatigue strength in the stage of high cycle fatigue; P-S curve (the probability statistical distribution of fatigue strength) under the given fatigue life cannot be directly by test, but P-S curve can be obtained on the bias of P-N curve (the probability statistical distribution of fatigue life), and the corresponding dispersion of fatigue strength is a decreasing function of the given fatigue life. On bias of conclusions above, not only the inhomogeneity of material but also the dispersion of the load needs to be considered in the fatigue design, especially in high cycle fatigue design. 
L Zhou, H M Qu
cond-mat.mtrl-sci