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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2. Effective notch stress Stress concentration at geometrical discontinuities like notches can yield local damage in the form of initiation and propaga tion of cracks which may lead to fatigue failure of the component. Hence accurate analysis of welded plate joints with respect to fatigue failure requires proper knowledge of how stresses are distributed at notches. In this regard, the effective notch stress (ENS) method, as a local fatigue assessment approach, which is mainly based on peak stress and stress concentration values, has been studied for different weld joints. To avoid singularity challenges when using the ENS method, the weld toe and root are modelled with a fictitious radius (Baumgartner, 2017; Fricke et al., 2017; Ohta et al., 2002; Radaj et al., 2013; Sonsino et al., 2010). Depending on plate thickness, various notch radii (r=1 mm, r=0.3 mm and r=0.05 mm) can be introduced in the notch zone. Different FAT-values are then recommended to be assigned for each radius (Baumgartner, 2017). In the current study, the fictitious radius of r=1mm is utilized for FE modelling, although it is not recommended for plates thinner than 5 mm. This indicates that one FAT-value is considered for all models, making it possible to do a comparative study of the results for a range of sheet thicknesses. 3. Probabilistic method The knowledge about statisticaland probability models of size effect is of great importance since it helps to better underst and the correlation between small-size specimens with large-scale components. The statistical size effect is mainly characterized by two approaches namely the critical defect method and the weakest link approach(Zhu et al., 2022), where the latter is the focus of the underlying study. Hultgren et al. (Hultgren et al., 2023; Hultgren, Mansour, et al., 2021) studied how the variation in weld geometry was related to the fatigue strength of the welded joints. By implementing the weakest link theory and by means of the commerc ial weld quality assurance Winteria® the uncertainty in the fatigue strength of a welded structure as an effect of the weld geometry variations could be addressed. According to the weakest link method, the weakest local sub-volume governs the fatigue strength of the global component. Considering the size effect, it should be noted that a larger specimen increases the probability of weaker zones. The basic concept of this method can be formulated by a chain made up of chain n number of links under tensile load. The chain fails when the weakest part fails. Regarding Weibull distribution, as a tool to evaluate statistical failure in materia ls, the weakest link concept is mathematically explained as (Zhu et al., 2022): ( ) chain 1 exp( ) f ref p n       = − −   (1) Where ( ) f p  represents the probability that the failure stress is smaller than for a chain consisting of chain n links. ref  is a reference stress and  is the Weibull shape parameter. The probability distribution of fatigue strength can be derived based on the weakest link area model, applicable for surface defect, in which the probability of finding a defect is ( ) i ref q s A A  where ( ) q s is the number of critical defects in a specimen with a surface area ref A divided into a sub-area i A  . By using the failure probability, the equivalent stress, as fatigue driving stress of the welded joint, is determined as below (Hultgren et al., 2023): (2) In the above formula, the ∆ is the equivalent stress range, is the first principal stress and Weibull shape parameter. The influence of variation of the Weibull shape parameter, , on the equivalent stress for the weld geometry with toe radius is evaluated in the current study. 4. Finite element modelling Non-load-carrying cruciform joints are considered in the current study. A 2D finite element modelfor a quarterof the joint, which would show similar behaviour to the complete joint, is developed in the software ANSYS classic 2022 R1. Symmetric boundary conditions were utilized in order to reduce element number and computational time. The model is subjected to uniform axial (tension) load of 100 MPa applied at the right boundary side of the model, depicted in Fig. 1. Fatigue assessment has been carried out on the basis of the ENS method. In order to do an effective notch-based fatigue assessment, only the weld toe, as the most critical zone which is prone to fatigue failure in non-load-carrying cruciform joints, is required to be modelled with a fictitious radius. The mesh properties, including the quality and dimension of elements aligned with their type and shape function, are decisive factors. Hence, the accuracy of effective notch stress calculation is highly dependent on the mesh pattern consisting of the density and quality of mesh in the notch area. The mapped meshing technique has been used for modelling and discretization. In this method for adjusting element shape, the user has more control over the mesh quality of hexahedralor quadrilateralelements compared to triangular element types. Analysis was then carried out, and the calculated first principal stress was extracted at the critical point.     1 (    =  ) equ FEM ref dA A  