Issue 41

F. Chebat et alii, Frattura ed Integrità Strutturale, 41 (2017) 447-455; DOI: 10.3221/IGF-ESIS.41.56 448 radius ρ f =1.0 mm if the weld toe and root radius be considered as zero [8]. Fatigue failure is generally characterized by the nucleation and growth of cracks [9-13]. The difference between two stages of nucleation and growth of fatigue crack is “qualitatively distinguishable but quantitatively ambiguous” [14]. In this regard, NSIFs were used for prediction of crack nucleation and also the total fatigue life [15-19]. Prediction of the total fatigue life using NSIFs is only limited for the cases in which a large amount of fatigue life is consumed at short crack depth, within the zone governed by the notch singularity at the weld toe or root. Lassen [20] reported that up to 40 percent of fatigue life of transverse non-load-carrying fillet welded joints was related to nucleation of a microcrack with a length of 0.1 mm. Singh et al. [21,22] showed that 70 percent of the total fatigue life of fillet joints in AISI 304L was related to crack nucleation up to a size of 0.5 mm. According to the theoretical formulations related to the NSIF approach, this method cannot be employed for the joints characterized by weld flank angles very different from 135 degrees or for comparing failures at the weld root (2α =0°) or weld toe (2 α =135°). That is due to the units which are used for mode I NSIF as MPa(m) β , where the exponent β depends on the V-notch angle, according to the expression β = 1-λ 1 , λ 1 being Williams’ eigenvalue (Williams 1952). This problem was solved later by using the average strain energy density range present in a critical volume of radius R c surrounding the weld toe or the weld root. Using some closed form formulations, the strain energy density range was defined as a function of the relevant NSIFs. The NSIF approach was later extended to welded joints under multiaxial loading [23]. The simple volume is approximately similar to that of proposed by Sheppard [24], while proposing a volume criterion based on local stresses to predict fatigue limits of notched components. Sonsino [25] proposed the highly stressed volume (the region where 90% of the maximum notch stress is exceeded) to predict the high cycle strength of welded joints. The same methodology based on strain energy is employed in this paper for fatigue analysis of streel rollers made by Rulmeca [26] with failure occurring at the weld root. The rollers studied in the present paper belong to the category PSV which is mainly suitable for conveyors that operate in very difficult conditions with high level of working loads where large lump size material is conveyed; and yet, despite these characteristics, they require minimal maintenance. The bearing housings of the PSV series are welded to the tube body using autocentralising automatic welding machines utilizing a continuous wire feed. Considering the fatigue behavior of the component, the weakest point of the entire structure is the lack of penetration of the weld root. Hence, if the roller is loaded well above its declared nominal admitted load [26] it would experience fatigue failure starting at the level of the weld root. The current paper aims to describe the modelling method of the roller by using the finite element method combined with three-dimensional analyses (the procedure is described in more detail in [27] and implementation of the SED method in a control volume for two different tested geometries belonging to the family of rollers called PSV4 and characterized by a different lengths. A PPROACH BASED ON THE LOCAL SED: ANALYTICAL PRELIMINARIES he degree of singularity of the stress fields due to re-entrant corners was established by Williams both for mode I and mode II loading [28]. When the weld toe radius ρ is set to zero, NSIFs quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip. By using a polar coordinate system (r, θ) having its origin located at the sharp notch tip, the NSIFs related to mode I and mode II stress distribution are [29]: 1 1 1 0 2 lim ( , 0) N r K r r           (1) 2 1 2 0 2 lim ( , 0) N r r K r r           (2) where the stress components σ θθ and τ rθ have to be evaluated along the notch bisector (θ = 0). Dealing with mode III loading an extension of the definition proposed by Gross and Mendelson [29] has been carried out in [30,31]: 3 1 3 0 2 lim ( , 0) N z r K r r           (3) By means of Eqs. (1,2), it is possible to present Williams’ formulae for stress components as explicit functions of the NSIFs. Then, mode I stress distribution is [32]: T