13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Longitudinal axis 0 2 4 6 8 10 12 -22 -20 -18 -16 -14 -12 -10 z (mm) y (mm) Simulation MTS notch 4.3. Crack propagation behavior of specimen S13 and S7 The crack growth path (path ①) for specimen S13 is plotted in Figure 6(a). An acceptable crack path compared with the experimental result from the notch root to point A was predicted by the MTS criterion. The transition fracture mode is expected following tension mode fracture. The simulated crack growth path for this specimen is not long enough to show a complete transition path. Nevertheless, it could be inferred that a shear mode fracture would occur as well as in specimen A8. The crack propagation path of specimen S13 is similar with specimen A8 (see Figure 3(b), Figure 4(b)), the final fracture is a coplanar crack extension perpendicular to the longitudinal axis which can be predicted by MSS criterion. Figure 6(b) illustrates one crack growth path (path ①) for specimen S7. It is found that the presented crack path has good agreement with the predicted crack path using MTS criterion. From the experimental result as shown in Figure 4(a), the crack growth paths did not deflect to the plane perpendicular to the longitudinal axis for coplanar shear crack extension, which means no shear mode fracture occurred in this specimen. Longitudinal axis 0 2 4 6 8 10 12 -22 -20 -18 -16 -14 -12 -10 z (mm) y (mm) Simulation MTS MSS notch Point A Figure 6. Crack growth path of (a) specimen S13, (b) specimen S7 4.4. Mode transition analysis The tension mode and shear mode competition under non-proportional mixed mode loading reflects the variation of KI and KII values. Figure 7 illustrates the KI and KII values in one loading cycle under combined tension and torsion with a phase angle of 90°. The equivalent stress intensity factors Keq reaches its peak values Keq,max at time tmax, which is taken as the crack growth driving force. The corresponding KI, KII components are marked as K*I and K*II. The K*II values of each crack propagation step for the four different specimens are shown in Figure 8 (①, ③ represent the corresponding crack paths) based on the calculation results from FRANC3D. The ordinate represents K*II values (absolute value), the abscissa represents the crack growth step. For all specimens the same tendency of increasing K*II with crack length is observed. From step 13 for specimen A7, step 15 for specimen A8 and S13, the transition mode started. It can be inferred that a threshold value K*II th exists in the transition mode. If the mode II component of the maximum equivalent stress intensity factor Keq,max in a loading cycle, K*II, is less than the threshold value, (a) (b)
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