Enhanced B-PFEM model for fatigue life prediction of metals during crack propagation

In a previous paper [Eng. Fract. Mech. 63 (1999) 675] a new model to predict the cumulative distribution function of fatigue life during the crack propagation stage was described. This problem was there considered as a cumulative damage process following the probabilistic approach of Bogdanoff and Kozin [Probabilistic Models of Cumulative Damage, Wiley, New York, 1985], assuming a linear approximation for the random variable “fatigue life” and a truncated uniform distribution for the crack length. In a second work [Computational Mechanics of Probabilistic an Reliability Analysis, Elme Press, Lausanne, Switzerland, 1989], two corrections to this initial model were discussed: a second order approximation of the fatigue life and an analytical expression for the probability density distribution of the crack length derived from the ones of the initial and final crack lengths. The obtained results showed a much better performance, especially for high standard deviations. Finally, a different possibility is studied in this paper: the correction of the initial linear model by a correction of the Wu’s type [2nd Annual Report NASA, Contract NAS3-24389, Appendix F, 1987]. This is based on the correction of the abscise of the probability distribution function of the fatigue life, by computing its “exact” value for the estimated values of the state random variables at the most probable point of the initial linear approximation. This approach implies a much lower computational cost than the second order approach cited above, but demonstrates unfortunately not to be adequate when applied to our case. This is due to the strong non-linearity induced by the exponential function that appears in the Paris law, that defines the fatigue life of metals. This effect is clearly shown in the different examples, especially in those with not very small variances.