PSI - Issue 57

Mehdi Ghanadi et al. / Procedia Structural Integrity 57 (2024) 386–394 Mehdi Ghanadi et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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thicker. However, accordingto Fig. 6(b), the curves show a similar trend when the plate thickness exceeds the reference thickness, but probabilistic stress diverges below that reference value. As it is stated before, unlike the thickness effect, the thinness effect is defined for plates thinner than the reference thickness. In view of this, it can be stated that probabilistic stress deviates from the ENS and corrected nominal stress in the region where the thinness effect defines.

Figure 6. Stress range versus plate thickness (a) actual values (b) normalized values at reference thickness.

7. Discussion The current study gives some insight into the probability analysis of size effect with focus on the weakest link theory. The study has been carried out on non-load-carrying cruciform joints, Fig. 1, for various plate thicknesses. The fatigue failure in these types of joints usually initiates at the weld toe region due to the local stress-raising effect in the sharp notch transition. Thus, it is essential to accurately capture the stress gradients surrounding this point, especially through the thickness of the joint. Detailed FE simulations are then used to capture these gradient fields from which the equivalent stress range for the complete joint is determined and the results are statistically evaluated by means of the weakest link theory. It should be noted that different notch radii (r=1 mm, r=0.3 mm and r=0.05 mm), and their corresponding FAT-values, have been recommended to be used dependingon the thickness of welded sheets. However, FE modelling should be carried out in such a way that the stress results for all FE models are comparable with each other. To this aim, a fictitious radius of 1mm, regardless of plate thickness, has been applied in FE models. This ensures that FAT-value, in relation to a 1mm notch radius, remains the same for all models. Distribution of surface stress through joint cross-section, illustrated in Fig. 2, reveals that as the size of plates enhances, the ENS, and thereby stress concentration factor also increase, which in fact is the negative side of the size effect (Pedersen, 2019) as it decreases fatigue life of the components (Yamamoto et al., 2014). This is also apparent in Fig. 3 where maximum stress is increasing as plates become thicker and that becomes more pronounced at localized area of stress concentration, weld toe in this case. Of importance is the variation of standard deviation of probabilistic stress against Weibull shape parameter, . By increasing the standard deviation decreases considerably until it reaches its minimum point, for = 12 , which can be stated as the most fitted value of the shape parameter, Fig. 4. Increasing above this value will not give further obvious changes in probabilistic stress variation and the graph will almost level off. In this view, the most fitted Weibull shape parameterhas been utilized to calculate the equivalent stress value; reference is made to Fig. 5, where the degree of scatter has been reduced for equivalent stress compared with the case for nominal stress. Overall, the probabilistic stress, calculated for most fitted Weibull shape parameter, together with effective notch stress tends to arise when plates become thicker, Fig. 6, however, their variation deviates from each other as plates become thinner than the reference value. This could be more noticeable by looking at the normalized plot, Fig. 6(b) which shows for plates thicker than the reference thickness, the variation of probabilistic stress together with effective notch stress and corrected nominal stress, Eq.(4), are converging towards each other. It is the region where fatigue strength decreases as a result of the thickness effect. This shows that the 1 mm ENS method is well suited for thicker plates as the extent of the highly stressed volume is small in comparison to the maximum stress (the gradient through the thickness is shallow in Fig. 2). Fig. 6 shows this through the coinciding curves for the ENS method and the probabilistic evaluation presented within the present study for the 1 mm radius. In contrast, joints in thinner plates show that the 1mm ENS method does not capture the fatigue behaviour accurately. The results from Fig. 6(b) have shown that the probabilistic evaluation of the 1 mm radius deviates from the ENS method as plates become thinner, with increasing prediction accuracy. Thus, according to Eq.(2), the larger highly stressed region in the cross-section area influences the fatigue response (the gradient through the thickness for thinner plates is steeper in Fig. 2). This is a direct response of the incomplete geometry scaling, as previously shown by Pedersen, 2019. It is in this thickness region where beneficialeffects on fatigue life are observed due to decreasing thickness, and thinness effects.