Methods for Randomization of Parameters in the Fatigue Crack Propagation Law da/dN=C(ΔK)^m

Abstract

This paper is concerned with the problem of how to take account of the variability of the fatigue crack propagation rate da/dN in the structural reliability analysis. Specifically, various methods for randomization of the parameters in the crack propagation law da/dN=C(ΔK)^m or da/dN=C₀(ΔK/K₀)^m were examined. These methods were divided into two classes. In the first class, randomization was made based on the inter-specimen variability of the parameters, whereas in the second class randomization was made based on the intra-specimen variability of the parameters. With respect to the first class, the following three methods were examined for da/dN=C₀(ΔK/K₀)^m: (a) m and log C₀ are treated as normal random variables independent of each other, (b) only m is treated as a normal random variable, and (c) only log C is treated as a normal random variable. By using each of the three methods, the variability of the crack propagation life N was analysed, where N was defined as the number of repeated cycles for crack growth from a=a₁ to a=a₂. In this calculation, a₁ was fixed and a₂ was varied. The results of the calculation as a function of a₂ were compared with the authors' experimental result. It was shown that the method (a) was the most reasonable among the three methods. With respect to randomization based on the intra-specimen variability of the parameters, the method was examined in which only C₀ was treated as a spatial random variable in da/dN=C₀(ΔK/K₀)^m. It was shown that this method could also predict the experimental tendency of the variability of the crack propagation life as a function of a₂.