On the fatigue-life distributions of engineering materials

The applicability of the fatigue-life distribution of Birnbaum-Saunders for modeling the components of partially prestressed concrete girder bridges is argued by the agreement of the calculated distribution with a large data set comprised of many small censored samples, each put into standardized form, of the fatigue-lives of bridge components. Also, the Weibull and lognormal distributions are compared by the appropriateness of the assumptions in their derivation to the cumulative damage to bridge components. The maximum likelihood estimates of the parameters of the fatigue lives of the prestressing steel, mild steel, and concrete are found from randomly censored samples, for several censored data-sets under various stress regimes. The parameters are postulated to be log-linear functions of the maximum stress and stress regimes. Weighted least-square regression is applied to determine the unknown coefficients. To compensate for differences in the precision of the estimates obtained under each stress regime the variances are calculated by the bootstrap statistical method. This procedure gives an estimated distribution of the fatigue life with its parameters functions of the stress regime which is applicable under virtually any realistic condition.