Issue 50

P. Livieri et alii, Frattura ed Integrità Strutturale, 50 (2019) 613-622; DOI: 10.3221/IGF-ESIS.50.52

2 2 x y    , w x i y   , Q  is equivalent to:   0 1 1 Re Im r r r r r A A w B w       

By setting

(23)

1

For example, if ( ) 1 cos R A    

2 A   , the condition Q  becomes

with

0

2



   

0 Ax

(24)

Finally, the equation for SIF assessments can be rewritten as:

( ') I K Q K Q Q D O        ( , ') ( ') ( ) I

(25)

with



) Q B jk ij

(



2



( , ') 

(26)



K Q

I



k

(for more details see reference [21]).

N UMERICAL EXAMPLE n order to verify the accuracy of the proposed procedure, now we analyse two reference cases: the first is a circular defect at the weld toe, the second is an irregular crack under uniform tensile loading. Fig. 4 shows a welded T-joint under tensile nominal stress. In Fig. 4, a disc is put at the weld toe of the welded T-joint and the stress intensity factor is evaluated by considering the asymptotic stress field as reported in [22–23]. The crack lies along the bisector at variable distance d from the weld corner. The T-joint is subjected to a tensile nominal stress, but along the bisector of the weld corner the hoop stress assumes the simple form: I

326 .0 rK 

(27)

399 .0





N



where K N is the Notch Stress Intensity Factors of mode I and it is equal to 2.46 MPa mm 0.326 for a nominal tensile stress σ n of 1 MPa. This value was calculated by means of a careful notch stress analysis by considering the T-joints of Fig. 5 as three dimensional components without taking into account the effects of the width as analysed in [24].

Figure 4 : Welded T-joint under tensile loading.

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