Corrections to B-models for fatigue life prediction of metals during crack propagation

In this paper a new model for the prediction of the Cumulative Distribution Function (CDF) of fatigue life of structural elements during the crack propagation stage is described. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdano! and Kozin [1] (B-models). The initial and "nal crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads may be considered as random variables. In this initial approach, a linear approximation of the random variable &fatigue lifeʹ and a truncated uniform distribution for the crack length variable are considered. Two corrections to this model are discussed: a second-order approximation of the fatigue life to compute its variance, and a modi"cation of the Probability Density Distribution (PDD) of the crack length, which is now derived from the truncated uniform distributions of the initial and "nal crack lengths. Some examples for mode I are compared to the ones obtained using a Monte Carlo scheme with 400 000 samples, showing a good agreement and a much better performance of the corrected version of the model, specially for big standard deviations