Abstract
In this paper a Weibull methodology to determine the probabilistic percentiles for the S-N curve of the A572 Gr. 50 steel is formulated. The given Weibull/S-N formulation is based on the true stress and true strain values, which are both determined from the stress-strain analysis. For the analysis, the Weibull β and η parameters are both determined directly from the maximum and minimum addressed stresses values. The S-N curve parameters are determined for 103 and 106 cycles. In the application, published experimental data for the CSA G40.21 Gr. 350W steel is used to derive the true stress and true strain parameters of the A572 Gr. 50 steel. Additionally, the application of the S-N curve, its probabilistic percentiles and the Weibull parameters that represent these percentiles are all determined step by step. Since the proposed method is flexible, then it can be applied to determine the probabilistic percentiles of any other material.
Highlights
For the A572 Gr. 50 steel material, a probabilistic S-N curve does not exist
In structural design, two different approaches have been used, and they are: (1) the application of a failure theory to determine if the designed element is safe or not; and (2) the fatigue approach [1,7]. These approaches are not very efficient for predicting the reliability of a structural element. This mainly because, while the failure theory does not consider the time in the analysis, as it is the case of the Goodman, Elliptical and Soderberg failure theories given by Budynas and Nisbett [8], in the fatigue strength analysis, the S-N curve only represents the strength average [9,10]
In this paper based on the A572 Gr. 50 steel true stress-true strain analysis, the method to determine the probabilistic percentiles of the S-N curve is formulated, based on the two parameter Weibull distribution
Summary
For the A572 Gr. 50 steel material, a probabilistic S-N curve does not exist. The main goal of the. In this paper based on the A572 Gr. 50 steel true stress-true strain analysis, the method to determine the probabilistic percentiles of the S-N curve is formulated, based on the two parameter Weibull distribution. The efficiency of the proposed method to determine the probabilistic percentiles is based on the fact that the Weibull shape β and scale η parameters are both directly determined from the maximum and minimum material strength (σ1 , σ2 ) values, which are given from the true stress-true strain analysis [13]. Since the objective is to determine the maximum σ1 and minimum σ2 material strength values of the A572 Gr. 50 steel to perform the corresponding probabilistic analysis, the fatigue strain-life method approach is used to define the nature of the fatigue behavior [1,2,6,8,20].
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