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Some problems related to the metallic fatigue under random loading are studied in the present dissertation. The content of the dissertation is divided into two major parts. The first part focuses on the derivation of mathematical formulas that can be used for the prediction of fatigue damage and fatigue life of a component under random loading. The second part investigates the randomness of the parameters, which result in the scatter of the fatigue crack growth curves. In the first part of the dissertation, a key mathematical formula is derived based on random vibration theory in which Morrow*s nonlinear damage rule and the traditional S-N curve concept are both taken into consideration. Lambert*s empirical assumption or Gumbel*s asymptotic theory of statistical extremes is used to determine the maximum stress needed in applying the key mathematical formula. Computational algorithms for the prediction of fatigue damage and fatigue life under random for the prediction of fatigue damage and fatigue life under random loading are proposed and their accuracy is verified by the experimental data of 7075-T651 aluminum alloy. The following conclusions are made after the study. (1) The aforementioned key formula is general enough to cover other formulas derived by other researchers. (2) The key formula combined with Lambert*s assumption predicts the low-cycle fatigue damage and fatigue life very well. (3) A new derived formula can be used to predict the high-cycle fatigue damage and fatigue life. In the second part of the dissertation, Elber*s law is adopted for the cycle-by-cycle fatigue crack growth simulation. For each run of the simulation, various factors such as the applied load and the material constants are considered random factors. For each random factor, either a random variable or a random process is assumed, and its effect on the scatter of the crack growth curves is investigated. Experimental crack growth data of Type 4340 steel alloy are used for comparison. It is found that if one considers a certain material constant a random variable, the simulation result agrees rather well with the experimental result. It is also found that if one considers any one of the considered parameters as a random process, the scatter among different growth curves is smaller than the real experimental result. A random process with certain correlation length may be appropriate to account for the scatter of the real crack growth curves.
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