Issue34

C. Fischer et alii, Frattura ed Integrità Strutturale, 34 (2015) 99-108; DOI: 10.3221/IGF-ESIS.34.10 102 difference between variant 4 and 5 is only the support of the lower longitudinal plate changing also the kind of loading, but not  s or  eff and  at the hot-spot. COMPUTED FATIGUE LIVES Crack Propagation Analysis half-circular initial crack is assumed at the critical weld toe for all variants. The crack initiation phase was considered by choosing a small initial crack length a i = 0.15 mm. The crack growth increments d a and d c were computed for a defined number of cycles d N via individual integrations of the law by Paris and Erdogan [16]:   , m I a da C K dN   (3) Eq. (3) links the crack propagation rate d a /d N to the range of the stress intensity factor (SIF)  K I,a at the deepest point of the crack by using the material parameter C = 3·10 -13 and m = 3 (unit: N and mm). The integrations, however, must be done discretely because the SIF varies non-linearly and depends on the crack depth and crack shape. In order to avoid an under- or overestimation of cycles, the average value of the cyclic SIF was used when the crack grows from one stage (1) to the next (2):       ,1 ,2 log 0.5 log log I I I K K K          (4) A separate block of elements was added to the FE models. It includes half of the semi-elliptical crack shape with half crack depth a and width c . The block was connected with the surrounding model by contact elements transferring all kinds of forces and moments (bonded conditions). The block is 10 mm long and high, whereas the width depends on the actual half crack width c . The 20-node solid elements size 0.1· a at the crack front, and the midsize nodes are shifted to the quarter points towards the crack front to improve the accuracy. No weld toe radius was considered to simplify the modelling, but this causes an additional stress singularity and a steep increase of the SIF. Due to this, the SIF K I,c at the plate surface was estimated by extrapolating the SIF values computed at the three previous nodes. Generally, K I at each node along the crack front was determined individually via the J -integral using six contour integrations. Fischer and Fricke [4] described the modelling of the crack and the estimation of K I,c in detail. They applied the procedure to a load-carrying cruciform joint and obtained a satisfying agreement with experimental results. 1) Transverse attachment 2) Transverse attachment w. gradient 3) Supported transverse attachment 4) Additional longitudinal attachment 5) Complex structure Degree of bending  0.0 0.315 0.315 0.315 0.315 Final crack depth a f [mm] 8.48 8.51 8.43 8.44 8.45 Final crack width 2 c f [mm] 36.1 49.2 42.3 39.8 38.3 Fatigue life N P 300,000 385,600 452,200 456,200 509,600 Rel. fatigue life 1.00 1.29 1.51 1.52 1.70 Table 1 : Computed fatigue life N p for the same structural hot-spot stress  s = 176 MPa. Fatigue Lives Referring to Same Structural Hot-Spot Stress Between nine and eleven integrations with up to 14 internal loops were performed until the crack had reached the final depth a f ≈ 8.5 mm, being close to the opposite plate surface. In this process, smaller increments d N are considered for small cracks. Fig. 3 shows the evolution of the crack depth of the variants for the same structural HSS  s = 176 MPa. Here, the additional longitudinal attachment (4) is omitted since the crack grows similarly as for the supported transverse A