# Computational Simulation of 3D Fatigue Crack Growth under Mixed-Mode Loading
## 1 Introduction  
Most structures are subjected to cyclic loading, tension, and shear loads, known as mixed-mode fatigue loading. Fatigue failure is the most common type of failure in such configurations, caused by cracks and other defects in the components. The primary objective of fracture mechanics is to evaluate whether or not a structure will fail based on the presence of a crack. Crack growth is crucial in engineering structures, because it significantly impacts the quality and stability of engineering structures. Thus, the safety or reliability of engineering structures is vital to predicting the crack propagation path. As a result, in many industries, the accurate estimation of the crack path and fatigue life is essential in terms of reliability. Fracture mechanics is an essential tool in current materials science for enhancing the mechanical performance of mechanical components. A significant parameter for estimating a cracked structure's lifetime is the stress intensity factor (SIFs). The stress intensity factor is defined physically as the intensity of load transmitted through the crack tip area due to introducing a crack into the component [1]. The SIFs evaluate the severity of the stress induced by remote loading around the crack tip. The associated instantaneous value of SIFs would follow the changes in crack geometry and stresses during crack growth. The stress intensity factor has a complicated function of the load, boundary conditions, crack propagation, geometry, and material characteristics. The fatigue crack propagation is evaluated using the equivalent stress intensity factor in Paris' law. Experimental investigations are essential for fatigue assessment in several applications, such as the aerospace industry and the aviation industries. However, accurate calculation methods are needed to analyze crack propagation to prevent crack propagation and fatigue life in both static and dynamic loading [2]. The failure was caused by (a) faultssuch as interfaces and cracks and (b) the nature of fluctuating loads. When exposed to variable loads, cracks tend to initiate and grow until the structure no longer bears the load, leading to catastrophic failure. These cracks are characterized as fatigue cracks, and the predicted life is one of the most critical factors in determining the structure's reliability. It can be calculated by adding the required number of loading cycles to nucleate the fatigue crack and cause the failure. The crack propagation rate is generally determined using the relationship between SIFs and the crack geometry. Crack initiation and propagation are always associated with SIFs in a complicated state in general [3; 4; 5; 6]. In recent studies, the extended finite element technique (XFEM) introduced by [7] has frequently been adopted to study the fracture due to crack growth. Based on a standard finite element framework, it uses a unique displacement feature to allow for discontinuities, eliminating the need to re-mesh continuously during the crack tip growth process. XFEM was utilized to perform crack growth analysis without updating the mesh to evaluate SIFs [8; 9; 10]. Nowadays, numerous codes could be used to model cracks propagating through structures, e.g., FEM [11] and BEM [11; 12], both in mixed-mode [13; 14; 15; 16] or in-plane [17]. In addition, the methods used for calculating K values, kink angles, and crack-growth rates can be numerous [6; 7; 8]. Significant work was done to establish appropriate models for evaluating the fatigue crack growth (FCG) and fatigue life to avoid fatigue failures. Numerous experimental methods were proposed; nevertheless, the methods are frequently time-consuming and expensive to perform. Using a simulation strategy that involves numerical analysis and the ANSYS APDL19.2 finite element approach to decrease laboratory effort, time, and expenses is a great way to save time and money. Meanwhile, there are several of modern finite element simulation tools for fatigue crack propagation problems, including ANSYS, ABAQUS, FRANC3D, etc.