PSI - Issue 57

2

Mehdi Ghanadi et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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

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Nomenclature ref A

1 t 2 t

Thickness of load-carrying plate

Reference surface area

i A 

Sub-area

Thickness of stiffener plate

a

ref t eff t

Weld throat size

Reference thickness

C

Constant in the equation of S-N curve

Effective thickness

( ) f t

W

Weld length

Thickness reduction factor

 

L m

Attachment length

Weibull shape parameter

Exponent of S-N curve

Stress

n

FEM 

First principal stress

Thickness correction exponent

ref 

chain n

Number of links

Reference stress

nom   ENS   equ  

N

Fatigue life in cycles

Nominal stress range

f p

Effective notch stress range

Failure probability

( ) q s

Number of critical defects in specimen

Equivalent stress range

r

Fictitious radius

misalignment. High residual stress in thicker plates due to constraints against thermal contraction , variations in microstructure and surface roughness can also be addressed by the technological size effect (O.Öjasäter, 1995). Another cause of the size effect can be explained in terms of the geometry of the joint, named as geometrical size effect (Niemi et al., 2018). This may be defined with respect to stress gradient through thickness along crack propagation path caused by geometrical discontinuities, bending or torsional loads(Berge, 1985; O.Öjasäter, 1995). In the case of the geometrical size effect, the stress gradient through thickness at the weld toe becomes steeper for thinner joints; therefore, by assuming the same nominal stress and at a similar initial crack length the stress at crack tip becomes less intense in thin plates compared to thick plates. In this matter, the toe radius does not change by increasing plate thickness, namely incomplete scaling; hence the stress concentration is higher in thicker plates (Pedersen, 2019). Two size measures most commonly used when studying the thickness effect are the load-carrying plate thickness and the distance between weld toes, including attachment thickness. The latter, named the attachment length, covers the effect of weld size, including weld leg length as local geometry and the thickness of the transverse plate, both of which contribute to the fatigue capacity of the joint (Zhao & Hsu, 2020a). This is illustrated in Fig. 1(a). Investigations of the size effect in welds date back decades ago when Gurney showed that among variables affecting the fatigue strength of welded components, the size of the specimen is of great importance (Gurney, 1979, 1991). He compared the theoretical results, calculated based on fracture mechanics, with fatigue test data with different joint types under axial and bending loading. The results showed that the fatigue strength decreases under axial load until the attachment length equals twice the plate thickness. While above this value, the fatigue strength is not affected by the attachment length. Gurney also suggests that in the case of non load-carrying cruciform joints, the apparent thickness can be used instead of the actual thickness. Pedersen (Pedersen, 2019) discussed the factors indicating the positive and negative sides of the thickness effect on the fatigue strength by comparison of results for axially loaded butt weld joints with different thicknesses. The high stress concentration factor, less steep stress gradient through the thickness, and increasing residual stress in the thick plates are mentioned as negative factors of plate thickness. On the other hand,the governing role of weld length instead of the thickness on statistical size effect together with longer crack propagation length, decreasing misalignment and flank angle in thicker plates are some of the positive influences of plate thickness. Takahashi showed that the combination of both stress concentration and the residual stresses influence the plate thickness effect (Takahashi et al., 1993). Yamamoto’s studies show that the thickness effect in large-scale welded components is very small compared with small specimens. He also showed that stress concentration and stress gradient at the weld toe are influential factors in the reduction of fatigue strength(Yamamoto et al., 2014). Some attention has been paid to probabilistic modelling of size effect on fatigue strength considering the weakest link approach. The research by Mikkel et al. (Larsen, 2022), for instance, is focused on the probabilistic and statistical framework of the thickness effect. In this research, the Karhunen-Loéve expansion has been implemented to formulate the stochastic size effect considering the weld length and by using the stochastic stress concentration factor. Based on the literature review, it is found that although the majority of investigations have been made towards the thickness effect on fatigue strength, few researchers draw attention to the thinness effect which benefits from plate thickness. The current study gives an increased understanding of the thinness effect on fatigue behaviour by studying the variation of fatigue strength in terms of the thickness of thin-walled welded joints in conjunction with experimental fatigue data from literature and statistical analysis. The investigation has been carried out through numerical simulations, comparing a probabilistic weakest-link model with the effective notch stress method (ENS) and the nominal stress method with thickness correction.