Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 114-122; DOI: 10.3221/IGF-ESIS.41.16 117 position. In the case of specimens under pure axial loading, the fatigue cracks were initiated in both the weld start and end locations. The crack fronts spread toward each other at the weld toe on the outer tube side during cyclic loading and finally coalesced into one crack, Fig. 3a. In specimens subjected to torsional moment the cracks spread to the inner and outer tube halves, Fig. 3b. In the case of combined in-phase loading the fatigue cracks spread either into the outer pipe or through the weld metal, Fig. 3c. In contrast, the welds failed only with crack spreading through the weld metal when force and moment were phase shifted by 90°, Fig. 3d. The majority of fatigue life is spent during crack growth. A modelling of this mechanism is currently far behind numerical feasibilities, especially for the non-proportional loading cases [12]. Therefore, an approach based on notch stresses is applied as described in the next section. Figure 3 : Failure modes of welded joints under axial force a), torsional moment b) and proportional c) as well as non-proportional d) combinations, R =-1. The results are presented in form of S-N curves (nominal stresses versus number of cycles to failure) for stress-relieved specimens under alternating loading, Fig. 4, and also for as-welded specimens under alternating loading, Fig. 5. In each case, we have plotted normal stress amplitude (Figs. 4a and 5a), resulting from the axial force amplitude and shear stress amplitude (Figs. 4b and 5b), and from the torsional moment amplitude. A result was shown as run-out, when no cracks could be detected after 1·10 6 load cycles in the case of combined loadings or after 2·10 6 load cycles otherwise, symbols with horizontal arrows in Fig. 5. After such a test, the applied load(s) was/were doubled and the test was repeated, symbols with slanted arrows in Fig. 5. Regression lines are added for a 50% probability of survival. The slopes of the S-N curves, when described by a power law, vary within the range of 3.7 to 5.9 for stress-relieved specimens. The slopes of S- N curves are higher and vary between 6.1 ≤ k ≤7.7 for specimens not exposed to any heat treatment. The specimens in an as-welded state provide higher fatigue strengths as compared to stress-relieved specimens, especially in the area of higher fatigue lives. This indicates the existence of compressive residual stresses resulting from the welding process. Interaction lines Interaction diagrams make it possible to compare the experimental results shown as S-N curves among each other. Contours for constant fatigue lives can be plotted in a M T,a - F ٣ ,a (or  a -  a ) diagram. Also the phase shift for each contour is constant. In this way it is also possible to compare the experimental results as well as the out-of-phase behaviour. Indeed, the form of these contours is dependent upon fatigue life. An exceptional situation exists when the S-N curves all have the same slope. In this case, the form of the interaction lines is independent of the selected fatigue life. Fig. 6 shows the interaction lines in a M T,a - F ٣ ,a diagram corresponding to N f = 10 5 . The dashed lines representing the results on non- proportional loadings always lie below the solid lines for proportional loadings.