Constant amplitude fatigue strength and P-S_a-S_m-N camber family

Functions of the P - S_a - S_m - N camber family in constant amplitude cyclic loading are established by combining the P - S - N curve family and constant life diagrams, which is feasible in engineering application. Meanwhile, the preconditions of mechanics and probability-statistics are clearly presented. According to Weibull's assumptions i.e., monotone decreasing and nonintersecting about individual S - N curves, the relation of isostructural measure preserving transformation (IMPT) between the probability spaces of constant amplitude fatigue life and constant amplitude fatigue strength is proved based on the measure theory. Therefore, an individual specimen possesses the same percentile value in different probability spaces of fatigue life and fatigue strength under constant amplitude loading. The P - S_a - S_m - N cambers of individual, population and sample are also distinguished.