PSI - Issue 42

1754 Paulo Mendes et al. / Procedia Structural Integrity 42 (2022) 1752–1761 Paulo Mendes, Rita Dantas, José A.F.O Correia, Nicholas Fantuzzi, Abílio M.P. Jesus / Structural Integrity Procedia 00 (2019) 000 – 000 3 recommending that the two parameter Weibull distribution does correlate with fatigue data. Bayesian analysis has been applied for establishing design S-N curves from small data sets to solve underlying statistical uncertainties (Edwards & Pacheco, 1984). Even though, a number of manuscripts have emerged using Bayesian inference in the analysis of crack growth and crack propagation, not many attempts have been made in the past to use the Bayesian approach in the context of S-N fatigue tests (Guida & Penta, 2010). The fatigue life evaluation of structural connections can be performed using several S-N approaches based on different stress definitions, such as: nominal stresses; local notch stresses and hot spot stresses. For welded structural connections, the hot spot stress approaches are becoming very frequent (Correia et al., 2018). In this study, design S-N curves for a double side welded connection of S355 structural steel considering the nominal and hot spot stresses are formulated based on recommendations. Different statistical methods were implemented to analyze the studied data and to elaborate reliable design S-N curves. The statistical analysis proposed in the standards to define design curves was implemented, and a comparison was established with the implementation of the two-parameter Weibull distribution and a Bayesian inference. 2. Standards and probabilistic approaches Usually, the fatigue experimental data is plotted in a logarithmic scale and for different levels of stress as function of the number of cycles until failure. From the experimental points is obtained a curve usually named S-N curve, and which can be defined as an exponential relation or as a linear relation of logarithms. The exponential function or also known as the Basquin’s law is given by the following equation: = ′ (2 ) (1) where d is a material constant, ′ is the fatigue limit and the stress amplitude (Y. Lee et al., 2012). The second formulation mentioned to define the S-N curve is obtained by applying the logarithmic function to the Basquin law, resulting in the linear relation between number of cycles and stress level summarized in equation below: X = b − aY (2) where Y=log , X=log , and a and b are constants determined by the following equations: a = ∑ (X i − X̅ )(Y i − Y̅ ) n i=1 ∑ (Y i − Y̅ ) 2 n i=1 (3) = ̅ + ̅ (4) where: X̅ = 1 n ∑X i n i (5) Y̅ = 1 n ∑Y n i i (6) In this work for the statistical assessment of the P-S-N curves of the double side welded connection, different statistical procedures presented in ISO 12107, ASTM E739, Eurocode 3, DNVGL-RP-C203, IIW recommendations, probability distributions such as Weibull distribution of two-parameters, and a Bayesian inference were used and compared. The statistical analysis presented in ISO 120107 standard adopts a linear model for the mean S-N curve, which is defined by the Equation (7: ̂ = − (7) where the fatigue life (N) at a given stress level (S) is defined as a random variable which logarithm, X= log N , follows a normal distribution characterized by a mean value, ̂ , and a standard deviation, ̂ . The lower limit to the S-N curve corresponding to a probability of failure at a confidence level of 1 − and for a certain number of degrees of freedom = − 2 is estimated by applying the following equation. Instead of defining tolerance intervals, the methodology presented by ASTM standard defines confidence intervals and suggests a statistical approach very similar to the one described by the IS O’s standard .