# Notch Effect on the Fatigue Behavior of a TC21 Titanium Alloy in Very High Cycle Regime
## 3 Results  
### S-N Curves  
The S-N curves for smooth and blunt-notched specimens are shown in Figure 5. The smooth and notched specimens still fail beyond 10\({}^{7}\) cycles, which corresponds to the cycle life of the conventional fatigue limit. It is indicated that there is no tradition fatigue limit for a TC21 titanium alloy, and it is dangerous to estimate fatigue limits using conventional fatigue strength data. As for smooth specimens, a step-wise characteristic can be observed in S-N curves over the wide range of the 10\({}^{5}\)-10\({}^{9}\) cycle regimes. Surface cracks were initiated from the specimen surface in the regime of less than 10\({}^{6}\) cycles, while internal crack initiation occurred in the above-10\({}^{6}\) cycle regime. The transition of the crack initiation site existed in the plateau around 10\({}^{6}\) cycles. However, a continuous decrease in the S-N curve with a horizontal line shape was observed for blunt-notched specimens. The fatigue crack initiation site shifted from the specimen surface in the high cycle regime to the specimen subsurface in the very high cycle regime. At the same stress amplitude, fatigue life for the subsurface initiation was far higher than that for the surface initiation. It is clear that the fatigue life shows a large scatter for notched specimens. However, [PERSON] [5] indicated that the notched specimens of high strength steel displays a continuous decrease in the S-N characteristic, which is owed to the crack initiation at the surface of notch root. Furthermore, the notch significantly decreased the fatigue property in the high cycle and very high cycle regimes, and the fatigue limit of the smooth specimen decreased from 430 MPa to 270 MPa for the notched specimen, respectively.  
Considering that the smooth specimens with the diameter of 3 mm was smaller than that of notched specimens, the specimen size effect on the decrease of fatigue strength was not neglected in this experiment. The risk volumes of notched specimens, estimated as the region subjected to >90% of maximal stress, was larger than that of the smooth ones. Fatigue strength decreased in proportion to the increased risk volume [14]. On the other hand, the risk volume could be restricted at the notch root for the notched specimens, which have a smaller risk volume than that of smooth specimens with the same diameter. The investigation of the notch effect by using the same diameter specimens will carry to eliminate the specimen size effect in the future.  
For a given fatigue life, the fatigue notch factor K\({}_{f}\) is expressed by the following equation:  
\[\text{K}_{f}=\frac{\sigma_{e}(smooth)}{\sigma_{n}( notch)} \tag{1}\]  
Figure 5: S–N curves for smooth and notched specimens of TC21 titanium alloys (arrows denote the run-out specimens).  
The K\({}_{f}\) values are summarized in Table 1. The fatigue notch factor tends to be almost constant regardless of the number of cycles between the high cycle and very high cycle regime, which can be attributed to the fact that the fatigue strength of the smooth and notched specimens continuously decreased with the number of cycles and obtained VHCF limits above 2 \(\times\) 10\({}^{7}\) cycles. However, as for high strength steels, the very high cycle fatigue notch factor K\({}_{f}\) can be lower than high cycle fatigue because the VHCF strength of high steels continuously decreases with the number of cycles, while the notched specimens obtained the VHCF limit [7].