A weakest-link theory is proposed for analyzing the rate of fatigue crack growth. The joint probability density of a fatigue crack growing an amount X between x and x+dx, and in time η between N and N+dN cycles is derived from an initial probability function. The rate of crack growth is then obtained as the expectation of the random variable (X/η). It is shown that the average rate of crack growth obeys the power law for small ΔK, and that the power is a function of the shape parameter in the Weibull distribution.

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