Issue34

C. Fischer et alii, Frattura ed Integrità Strutturale, 34 (2015) 99-108; DOI: 10.3221/IGF-ESIS.34.10 103 attachment (3). First differences in crack growth occur at a small crack depth a ≈ 0.5 mm. This corresponds to ca. 10 5 cycles. Afterwards, faster crack propagation can be observed at variants 1 and 2. The curves of the other two variants deviate beyond a ≈ 1.5 mm. Finally, the transverse attachment (1) achieves the shortest fatigue life N p , see also Tab. 1. The next are the transverse attachment with stress gradient over the plate thickness (2), the supported transverse attachment (3), and, finally, the complex structure (5). Tab. 1 also lists in the last line the relative fatigue life referring to that of variant 1. The largest influence (29%) is caused by the stress gradient over the plate thickness (2). Both the apparent plate thickness (3) and the bending constraint (5) increase N P by about 12%, compared with the previous variants. It is worth noting that the stress gradient along the weld line does not affect the life since the same N p is computed for variants 3 and 4. Although the two variants differ with respect to the load-carrying grade of the weld, the same stress distribution over the plate thickness occurs. The gradient along the weld line, however, has an impact on the aspect ratios of the crack, see Tab. 1. The final ratio is relatively small at variant 2 because the stress level is constant along the weld line, whereas the level decreases over the plate thickness. The final aspect ratio increases from the supported transverse attachment (3) to the complex structure (5) as the stress gradient along the weld line gets more pronounced and slows down the crack growth in this direction. 0 2 4 6 8 0,E+00 1,E+05 2,E+05 3,E+05 4,E+05 5,E+05 Quersteife Quersteife mit Gradient unterstützte Quersteife komplexes Bauteil 0 10 5 2∙1 5 3∙1 5 4∙1 5 5∙1 5 crack depth a [mm] cycles N transv rse attachment (1) transv rse attachment w. gradient (2) supported transvers attachment (3) c plex tructure (5) Figure 3 : Determined crack depth vs. applied cycles. 0 4 8 0 4 8 12 16 20 24 Risstiefe a [mm] halbe Rissbreite c [mm] 0 4 8 0 4 8 12 16 20 24 Risstiefe a [mm] halbe Rissbreite c [mm] 0 4 8 0 4 8 12 16 20 24 Risstiefe a [mm] halbe Rissbreite c [mm] transverse attachment (1) N p = 300,000 N = 150,000 0 4 8 0 4 8 12 16 20 24 Risstiefe a [mm] halbe Rissbreite c [mm] supported transverse attachment (3) transverse attachment w. gradient (2) complex structure (5) N = 360,000 N = 150,000 N = 360,000 N = 150,000 N = 360,000 N = 150,000 N p = 385,000 N p = 510,000 N p = 452,000 half crack w dth c [ m] half crack w dth c [ m] half crack width c [ m] half crack w dth c [ m] crack depth a [mm] crack depth a [mm] crack depth a [mm] crack depth a [ ] Figure 4 : Calculated crack shapes for variants 1 to 3 and 5. 1) Transverse attachment 2) Transverse attachment w. gradient 3) Supported transverse attachment 4) Additional longitudinal attachment 5) Complex structure Weld shape factor K W 2.41 2.24 2.17 2.35 2.43 Fatigue life N P 297,000 308,500 329,000 418,700 515,000 Rel. fatigue life 1.00 1.04 1.11 1.41 1.73 Table 2 : Computed fatigue life N p for the same effective notch stress  eff = 425 MPa. This influence is also visible when comparing the crack shapes for defined number of cycles, see Fig. 4 showing half crack shapes of variant 1 to 3 and 5 for the same number of cycles ( N p = 150,000; N p = 360,000 and at final life) and σ s = 176 MPa. The transverse attachment (1) does not reach N p = 360,000 since it has the highest crack propagation rate. While the crack shapes of the variants are almost similar for N p = 150,000, after this they start to differ obviously between the simple transverse attachments (1 and 2) and the more complex variants 3 and 5. Nevertheless, semi-elliptical crack shapes evolve in all cases and the more effects are present, the smaller the computed crack size is. Fatigue Lives Referring to Same Effective Notch Stress The computed life can be converted by adjusting the load level in order to consider the same effective notch stress σ eff = 425.3 MPa on the radius r ref at symmetry plane, see Tab. 2. Here, the stress gradient over the plate thickness (variant 2) as