Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 260-268; DOI: 10.3221/IGF-ESIS.41.35 264          1/2 3/2 2 5/2 1 3 4 7 8 11 12 1/2 4 3r 8 r 5 r 12 r 7 r r rr a a a a a a a (7a)        1/2 3/2 5/2 1 4 8 12 1/2 3r 5 r 7 r r a a a a (7b)       1/2 3/2 5/2 2 5 9 13 1/2 3r 5 r 7 r r r a a a a (7c) Along the direction    , the unique non vanishing stress component is the radial stress   rr :          1/2 3/2 2 5/2 2 3 5 7 9 11 13 1/2 2 4 6r 8 r 10 r 12 r 14 r r rr a a a a a a a (8) It is important to underline that, for the welded lap joint shown in Fig. 1, the polar angle  providing the maximum tangential stress   and the corresponding provisional crack propagation angle is close to   /2 due to the high contribution due to mode II in this kind of geometry. In the light of this consideration the expression of the stress components in that direction are of particular interest. Along the direction     we have:             1/2 1/2 3/2 4 5 8 1 2 1/2 1/2 3/2 2 5/2 5/2 9 13 12 11 3 3 5 3 r r r 2 2 2 2 2 2 2 2r 2 2r 15 35 21 r 12 r r r 2 2 2 2 2 2 rr a a a a a a a a a (9a)                1/2 1/2 4 5 1 2 3 6 1/2 1/2 3/2 3/2 2 5/2 5/2 8 9 13 12 11 9 15 3 4 r r 8 2 2 2 2 2 2r 2 2r 25 35 63 49 r r 24 r r r 2 2 2 2 2 2 2 2 a a a a a ra a a a a a (9b)               1/2 1/2 3/2 4 5 8 1 2 7 1/2 1/2 3/2 2 5/2 5/2 9 13 12 10 3 9 15 r r 8 r 2 2 2 2 2 2 2 2r 2 2r 25 49 35 r 12 r r r 2 2 2 2 2 2 r a a a a a ra a a a a (9c) S TRESS FIELD AT THE SLIT TIP OF A THIN WELDED LAP JOINT he geometry of lap joint subjected to tensile-shear loading is shown in Fig. 1. The initial value of the thickness is t=1 mm, whereas the ratio d/t ranges from 0.5 to 5.0. The applied load F results in a membrane nominal stress F/t = 10 MPa. On the slit edge side of point O, the membrane stress (10 MPa) and the bending stress (30 MPa) are superimposed, resulting in a total nominal stress of 40 MPa. Parameters a 1 , a 2 , a 3 are derived directly from K I , K II and the T-stress respectively by means of Eq. (3). The original values of K I , K II and T stress match those reported in Lazzarin et al. (2009). The parameters a 4 , a 5 , a 7 are set by imposing the condition that numerical values of the stress components     rr ,  r  coincide with theoretical prediction along the slit ligament far from the tip. This distance varied as a function of the ratio d/t. Dealing with the ratio d/t=1, a 4 and a 5 have been directly determined along the bisector line by a condition on    and    r  at a distance r=0.1 mm and r=0.4 mm, respectively. The parameter a 7 has been then derived by a condition T