# Notch Effect on the Fatigue Behavior of a TC21 Titanium Alloy in Very High Cycle Regime
## 1 Introduction  
Titanium alloys are widely used for aeronautical structures because of their high specific strength, toughness, and damage tolerance [1]. Due to the very high vibration frequency of aeronautical structures, their fatigue failure occurs in the very high cycle fatigue (VHCF, i.e., more than \(10^{7}\) cycles) regime, and fatigue cracks are inclined to initiate at the subsurface of high strength titanium alloys [2; 3]. In practice, notches in aeronautical structures are a common problem resulting from the sharp change of a complex geometry, such as a screw thread, groove, scratch, and foreign object damage (FOD). A notch in a component can produce a local stress concentration at the notch root, consequently leading to the crack initiation from the notch root [4]. Therefore, it is a great concern to investigate the VHCF crack initiation mechanism due to the interaction between the notch stress gradient and microstructure for aeronautical structures applications.  
Recently, the notch effect on very high cycle fatigue has attracted much attention. [PERSON] [5] and [PERSON] [6] reported that the crack initiation sites of the notched specimens were always at the root of the notch independent of the number of cycles, and the notches remarkably decreased the VHCF property. However, the investigation by [PERSON] [7] and [PERSON] [8] showed that VHCF crack can initiate from the subsurface for some high-strength steel and titanium alloy specimens where a fine granular area was observed at the crack initiation site. However, the fatigue crack initiation mechanism of notched titanium alloys is not well understood in the very high cycle regime.  
In sharp notches (with high stress concentration factor K\({}_{\text{t}}\)), the stress concentration is the determining factor, and VHCF cracks initiate from the notch root due to its experiencing high enough stress [5,6]. However, a blunt notch (small K\({}_{\text{t}}\)) exhibits microstructurally short non-propagating cracks (crack length on the order of the microstructural dimensions). As for high cycle fatigue, the fatigue crack that initiated from the blunt notch can overcome the strongest microstructural barrier and is sufficient to cause continuous propagation; thus, the fatigue strength of a blunt-notched specimen is determined by a \(\Delta\sigma\) criterion [9]. It was reported that the stress amplitude in the very high cycle regime was lower than that in the high cycle regime for high strength titanium alloys [8], which indicated that very high cycle fatigue cracks may not initiate from the notch root due to the inadequate stress drive force. Thus, fatigue crack initiation under a low stress amplitude depended on the interaction between the stress gradient and the microstructure around the notch root, especially for high strength titanium alloys. On the other hand, theory of critical distance (TCD) methods [10] had been proposed to evaluate the high cycle fatigue limit of notched components, and TCD methods that are modified for very high cycle fatigue are investigated in this paper.  
The blunt-notched effect on very high cycle fatigue behavior of a TC21 titanium alloy is investigated in this paper. The VHCF initiation mechanism of blunt-notched specimen is discussed based on the interaction between the stress gradient effect and the microstructure. Fatigue limits of blunt-notched specimens are also evaluated based on TCD methods.