# Microstructure Study on Very High Cycle Fatigue of an
## 1 Introduction  
Fatigue is ubiquitous, and causes the vast majority failure of engineering structures and materials [1, 2]. In this paper, fatigue is defined as a degradation of mechanical properties leading to failure of a material or a component under cyclic loading [3], when the failure cycles \(N_{\mathrm{f}}\geq 10^{7}\), i.e., very high cycle fatigue (VHCF) [4, 5]. Additive manufacturing or 3D printing is a new promising technology with the aim being to produce net or near-net components with complex configurations, which is emerging to replace the traditionally subtractive machining, such as turning, milling, grinding, etc., as an alternative method [6]. In view of this point, additively manufactured (AM) metallic materials have drawn significant attention from both academia and industry [7]. For AM metallic materials, fatigue performance, especially in VHCF regime, has become a key factor restricting their engineering applications [6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. As the most abundant metallic element in the Earth's crust, aluminum and its alloys are widely applied in engineering as structural materials beneficial to their superior mechanical properties: high strength-to-weight ratio, low mass density, and good corrosion resistance [18]. Cast aluminum alloys [7; 18; 19], e.g., AlSi10 Mg [10; 17; 20], AlSi7 Mg [21], and AlSi12 [22], have excellent melting fluidity, which makes them extensively used in 3D printing of metals and alloys as one of the most popular AM metallic materials. According to the traditional paradigm of fatigue research, S-N (stress amplitude \(\sigma_{\rm a}\) versus \(N_{\rm f}\)) data have always been the most effective tools [23], and the fractography [24] is often used to conduct a post mortem analysis for understanding the fatigue failure process. With regard to the study of VHCF, fatigue crack initiation keeps crucial role for accounting a vast majority failure life, about 90% at \(N_{\rm f}\geq 10^{7}\), and greater than 99% at \(N_{\rm f}\geq 10^{8}\) in high-strength steels [25]. For high-strength steels, their S-N data exhibit typical duplex or staircase shapes, their fracture surfaces are well defined, and then the failure types can be determined [26]. In the first slope of S-N data from low-cycle to high-cycle fatigue (HCF), crack initiation tends to occur on the specimen surface due to persistent slip band or other mechanisms [27]. In the second slope of S-N data beyond a quite large number of failure cycles, usually \(N_{\rm f}\geq 10^{6}\), fatigue cracks prefer to specimen interior, and with \"fish eye\" (FiE) morphology frequently originated at nonmetallic inclusion [25; 26; 27]. Similar phenomena and S-N behaviors have also been reported in many titanium alloys with different microstructures [28; 29]. Nevertheless, there is no such type of S-N data in aluminum alloys [2; 3; 30]. On the contrary, even VHCF cracks may not initiate inside the specimen, and cannot cause internal FiE fracture like that in high-strength steels [25; 26; 27; 31; 32] and some titanium alloys [28; 29]. Besides S-N data and the fractography, the microstructure underneath the fracture surface is another important objective which can help us to comprehend the accumulative process of fatigue damage [1]. For high-strength steels, fine granular area (FGA) is a characteristic region of crack initiation in VHCF regime [25; 26; 27], which is identified as a thin layer with nanocrystalline and fine-grained structure [33; 34; 35; 36] top on the both side of a pair of fracture surfaces [35]. For many titanium alloys, there are several rough area (RA) regions with crack initiation from high-cycle to very high cycle stage [5]. While under stress ratio \(R=-1\), i.e., symmetric cyclic axial loading (push-pull), the microstructure underneath the fracture surface within the RA region of VHCF crack initiation is characterized as having layers of nanograins and refined grains with a thickness of tens to hundreds of nanometers [4; 5; 29].