Issue34

S. Henkel et alii, Frattura ed Integrità Strutturale, 34 (2015) 466-475; DOI: 10.3221/IGF-ESIS.34.52 472 Fig. 8 shows the retardation cycles after the overloads for the tested samples. A tendency was observed that the overload delay of crack growth is higher at R = 0.1 with a force F X = 40 kN parallel to the crack while at R = 0.5 and R = 0.8 it is equal or lower. Figure 8 : Crack retardation for the tested overloads depending on R-ratio and loading parallel to the crack growth direction. For the starting notch with an orientation of 45° to the loading axes the crack tips propagate straight forward. A change to 45° phase shift between the sine functions for 100,000 cycles did not result in a change in crack growth rate. After changing from proportional loading to 90° phase shifted loading the two crack tips branched after a short incubation period app. 45° to the starting notch direction (Fig. 9). All four cracks propagated simultaneously. The crack length measurement with the crack gage is not valid from this point because the electric resistance is changing more with the two branched cracks on each gage and the two crack lengths cannot be separated. Therfore, further measurements were done with a high resolution camera system [19]. Between both measurements is a gap because crack branching was not expected. Fig. 10 shows the crack length for the two crack tips (signals of the crack gages) and four crack tips from the camera measurements versus number of cycles. Crack branching occurred at app. 0.63 million cycles. It can be seen that all four crack tips propagated quite simultaneously until 1.6 million cycles. From that time a pair of two cracks grow faster than the other ones (Fig. 9). Similar crack branching was found by Mall and Perel [20] for the aluminum alloy 7075 T6 for 90° and 180° phase shifted loading of a cruciform specimen with starting crack position 45° to the loading arms. The authors found by FEA calculations that the sum of the strain energy release rates of the two split cracks is equal to that of a single crack under biaxial fatigue without a phase shift. A principal understanding for that branching can be given by calculating the stress intensity factors for a configuration with two cracks compared to a branched configuration in Fig. 11. Due to the symmetry of the cracks only one end or one pair of branched crack tips are shown. Comparing the time dependent mode I and mode II fractions it can be seen that for each of the four branched crack tips in Fig. 11a the  K I has a significant higher value, than for the unbranched configuration with two crack tips shown in Fig. 11b. The mode II  K II is significantly lower for the branched configuration. The used FEA model does not consider crack surface contact and calculates therefore negative mode I stress intensity factors K I which are not possible in the real configuration. Figure 11c in addition to Fig. 3c shows the von Mises stress field on the two branched crack tips during one cycle. Both cracks ends are opened time shifted in mainly mode I.