PSI - Issue 42

Paulo Mendes et al. / Procedia Structural Integrity 42 (2022) 1752–1761 1755 Paulo Mendes, Rita Dantas, José A.F.O Correia, Nicholas Fantuzzi, Abílio M.P. Jesus / Structural Integrity Procedia 00 (2019) 000 – 000 Usually, the category’s number is the fatigue strength at a reference number of cycles . The detail category, ∆ , is the numerical designation given to a certain detail for a defined direction of cyclic loading application, in order to indicate the design fatigue curve that should be considered to evaluate the fatigue strength of the detail. Eurocode 3 proposes the evaluation of fatigue curves based on experimental results for a probability of failure of 95%. The detail categories were established based on experimental tests and their reference fatigue strength values correspond to a confidence level of 75% and probability of survival of 95%. The DNVGL-RP-C203 (2016) (DNV GL, 2016) standard applied to offshore structures suggest S-N curves considering a probability of failure of 97.7%. The joint classification and corresponding S-N curves considers the local stress concentrations created by the joints themselves and by the weld profile. For practical fatigue design, welded joints are divided into several classes, each with a corresponding design S-N curve, depending upon: the geometrical arrangement of the detail, the direction of the fluctuating stress relative to the detail and the method of fabrication and inspection of the detail. This standard defines a different S-N curve for thicknesses equal or larger than 16mm for tubular joints and 25mm for another welded connections. The fatigue curves for the IIW recommendations (Hobbacher, 2008) are based on representative experimental investigations and thus include the effects of: structural hot spot stress concentrations due to the detail geometry, local stress concentrations due to the weld geometry, weld imperfections consistent with normal fabrication standards, direction of loading, high residual stresses, metallurgical conditions, welding process, inspection procedure and post weld treatment. Each fatigue strength S-N curve is identified by the characteristic fatigue strength of the detail in MPa at two million of cycles, which is the fatigue class (FAT), but the constant amplitude knee point is defined at ten million of cycles. The slope of the fatigue strength S-N curves for details assessed on the basis of normal stresses is usually three for steel. It also defines a reference thickness as the DNVGL standard. Weibull distribution of two parameters is widely applied to estimate the probability to failure of materials (Freire Júnior & Belísio, 2014; Kawai & Yano, 2016; J. Lee et al., 1997). The determination of scale and shape parameters is a crucial step on the Weibull distribution’s application which can be performed through different methodologies. In this work, four different methods of estimation were selected: Maximum Likelihood Method (MLM), Method of Moments (MOM), Linear Least Square Method (LLSEM) and Weight Linear Least Squares Estimation (WLLSEM). Bayesian analysis allows the introduction of previous knowledge in order to estimate the model parameters and its methods have increased in popularity in recent years (Chen et al., 2020; Prabhu et al., 2019). It involves the use of the Bayes theorem and gives a method for updating the probabilities of unobserved events, given that another related event has occurred. To determine the posterior distribution for the estimators of the linear regression model, the Markov Chain Monte Carlo algorithms were employed. In these methods, Monte Carlo samples are directly generated from the posterior distribution by setting up a Markov Chain that has the posterior distribution as its limiting distribution. The Markov Chain converges to the posterior distribution after a certain number of iterations, named the “burn - in”. The increasing applications and practical implementations of Bayesian models have owed much to the development of MCMC algorithms, such as Gibbs sampling for estimation relatively recently. The Bayesian approach expands the class of models to fit data, enabling one to handle complex correlations, unbalanced or missing data, etc. 3. Experimental fatigue data The experimental tests of a double-side welded specimens, made in S355 steel, were performed on a RUMUL HPF 500 kN servo-hydraulic machine at controlled room temperature conditions, for a stress R -ratio ranging up to 1 , at room temperature conditions. A total of 18 and 11 specimens were tested to evaluate the experimental S-N curves based on nominal and hot-spot stresses, respectively. In some tests the nominal stress in the smaller cross section was measured and controlled. In other tests, strain gauges were placed at 0.5 and 1.5 from the weld toe and stresses were computed from a linear extrapolation to the weld toe location . Since the experimental data was obtained for different stress ratios, it is required to include the effect of mean stress. Thus, the experimental range stresses were normalized by the application of the following equation proposed by Taras and Greiner (Pedrosa et al., 2020; Taras & Greiner, 2018) . = ( ∆ ) (8)