A new mathematical theory is proposed to analyze the propagation of fatigue crack based on the concepts of fracture mechanics and random processes. The time-dependent crack size is approximated by a Markov process. Analytical expressions are obtained for the probability distribution of crack size at any given time and the probability distribution of the random time at which a given crack size is reached, conditional on the knowledge of the initial crack size. Examples are given to illustrate the application of the theory, and the results are compared with available experimental data.
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Ye et al. (1985) studied this question.
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