# Fatique Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel
## 1 Introduction  
Studying the behavior of fatigue crack growth under mixed-mode loading conditions at different angles is a crucial research area with significant implications for the safety and design of various engineering structures. It entails examining how cracks respond to cyclic loading when subjected to a combination of different modes of loading, such as tensile, shear, or bending modes, at varying angles relative to the crack plane. The understanding of this behavior is essential in predicting the remaining useful life of structures and ensuring their safe and reliable operation. Therefore, investigating fatigue crack growth under mixed-mode loading conditions at various angles is a critical aspect of structural analysis and design, particularly in fields such as aerospace, aircraft wings, automotive components, and turbine blades [1; 2]. The safe and reliable operation of structures and components that are subjected to cyclic loading over time is heavily reliant on the accurate prediction of fatigue crack growth behavior. Structures designed without taking the effects of mixed-mode loading and loading angles into account can experience premature failure, which can result in catastrophic consequences such as loss of life and property damage. Therefore, itis crucial to consider the effects of mixed-mode loading and loading angles when designing structures, to predict their fatigue life accurately. Many real-world structures are subjected to mixed-mode loading and differing loading angles, and failure due to fatigue crack growth is a common problem [3; 4; 5]. Understanding the behavior of cracks under these loading conditions, engineers can design more reliable and durable structures [6; 7; 8; 9]. There are various methods available for demonstrating the analysis of fatigue in materials, but three methods are most commonly used. The first one is the stress-life (S-N) method, which was proposed by [PERSON] [10]. This approach involves plotting the stress amplitude against the number of cycles until failure, represented in an S-N curve. It is mostly utilized for metallic materials and assumes that the material's failure is related to its stress level and the number of cycles it undergoes. The second method is the strain-life (\(\epsilon\)-N) method, introduced by [PERSON] [11]. This technique involves plotting the strain amplitude against the number of cycles until failure, represented in an \(\epsilon\)-N curve. It is primarily used for non-metallic materials, such as composites and polymers, as they exhibit strain-based failure mechanisms. Lastly, [PERSON] and [PERSON] [12] developed the fracture mechanics method, which correlates the rate of crack propagation with the stress-intensity factor range. This technique monitors the growth of a pre-existing crack under cyclic loading conditions until it reaches a critical size and leads to catastrophic failure. It is commonly used for predicting the fatigue life of materials that contain pre-existing cracks or defects, such as castings or welded structures. For a more comprehensive understanding of mixed-mode fracture behavior, researchers recommend using different loading devices and specimen types in experimental studies. In this study, the third method was utilized to predict the fatigue life of materials. This approach involves describing the crack tip separately by using stress-intensity factors (SIFs). Research on fatigue crack growth under mixed-mode loading has been ongoing for several decades. Many studies have investigated the effects of different loading conditions on the growth rate and direction of fatigue cracks, as well as the corresponding SIFs [13; 14; 15; 16]. Researchers have conducted significant studies to create reliable and effective models for accurately predicting the propagation of fatigue cracks and the corresponding fatigue life in order to prevent fatigue failure. Although various experimental models have been suggested, conducting such experiments can often be a costly and time-consuming process.