Extreme Maximum Model And Application For The Probabilistic Fatigue S-N Relations

It's one of the bases of the probabilistic S-N model for the fatigue reliability design. Three advanced issues are studied. They are the statistical distributions for the errors of the average S-N relation fitting into the test data, the maximum value model for the probabilistic model, and the material probabilistic fatigue strength under spectrum-loads.(1) From the considering of the probabilistic model being actually established by randomness of the average relations fitting into the test data, the appropriated statistical distributions for the fatigue lives are explored by the errors, which is different from the commonsense. By the features of the errors, it's first deduced that there are four possible models for the errors. There models are the three-parameter Weibull, the normal, the extreme maximum value, and the extreme minimum value. Three previous rules are taken into account to determine the appropriate models. These rules consist of the total fit, the mathematics and fatigue physics, and the safety in tail predictions. An analysis of the test S-N data of 16Mn steel weld joints reveals that the four models are reasonable if only considering the total fit as the conventional method did. But if by the present three rules, the appropriate models should be the normal or the extreme maximum value.(2) The maximum value model for the probabilistic S-N relations is first proposed. The relations consist of the survival probability (P)-S-N curves, the confidence(C)-S-N curves, and the P-C-S-N curves. The effects are on the probabilistic assessment of both scattering regularity and sampling size of the test S-N data. P-S-N curves are characterized by the scale and location parameters related S-N relations for the maximum value model. The materials constants of in the scale relations are given by the average S-N relations and the locations. The materials constants in the average relations are estimated by the least square method in the linear regression. Then the material constants in the locationrelations are determined by the maximum likelihood function for the maximum value model. In addition, the C-S-N curves are estimated by the rank distribution with concurrent principle of confidence bounds. The P-C-S-N curves are given by the composed of the P-S-N curves and the C-S-N curves. Availability and feasibility have indicated by an analysis of the test S-N data of 16Mn steel-welded joint.(3) The equivalent stress, which is from the coefficients for the spectrum-loads and Miner linear accumulated damage rule, an approach for material probabilistic fatigue strength for spectrum loads is suggested. This approach are established by the composed of P-C-S-N curves for extreme maximum model. It's employed effectively for evaluation of the probabilistic fatigue strength of 16Mn steel welded joints under spectrum-loads.