Issue 41

F. Chebat et alii, Frattura ed Integrità Strutturale, 41 (2017) 447-455; DOI: 10.3221/IGF-ESIS.41.56 449                         1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 cos 1 cos 1 1 3 cos 1 1 cos 1 1 1 2 1 sin 1 sin 1 N rr r r K                                                                                       (4) Mode II stress distribution is:                         2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 0 1 sin 1 sin 1 1 3 sin 1 1 sin 1 1 1 2 1 cos 1 cos 1 N rr r r K                                                                                         (5) Mode III stress distribution is:     3 3 1 3 3 1 3 3 sin 2 cos 2 N zr N z K τ r K τ r              (6) All stress and strain components in the highly stressed region are correlated to mode I, mode II and mode III NSIFs. Under plane strain hypothesis, the strain energy included in a semicircular sector is [33,34]: 3 1 2 2 2 2 3 3 1 1 2 2 1 1 1 N N N C C C e K e K e K W E R E R E R                                (7) where R C is the radius of the semicircular sector and e 1 , e 2 are functions that depend on the opening angle 2 α and on the Poisson’s ratio ν, while e 3 depends only on the notch opening angle. A rapid calculation, with ν = 0.3, can be made for e 1 and e 2 by using the following expressions [33]: 6 4 2 1 5.373 10 (2 ) 6.151 10 (2 ) 0.1330 e          (8) 6 2 3 2 4.809 10 (2 ) 2.346 10 (2 ) 0.3400 e          (9) where 2 α is in degrees. Dealing with failures originated at the crack tip (i.e. weld root) Eq. (7) can be simplified as follows: 2 2 2 1 1 2 2 3 3 1 C W e K e K e K ER            (10) The material parameter R C can be estimated by using the fatigue strength Δ σ A of the butt ground welded joints (in order to quantify the influence of the welding process, in the absence of any stress concentration effect) and the NSIF-based fatigue