## 1 Introduction  
The main objective of fracture mechanics is to determine whether or not a structure will fail based on the presence of a crack. Crack analysis should start from field stresses in the crack tip, which are evaluated by the equivalent stress intensity factor (Keq). By comparing the Keq value to a material fracture toughness or threshold stress intensity factor, it is possible to determine whether or not a crack member would fail when subjected to static or fatigue loading, respectively. The prediction of curvilinear fatigue and fractures remains a topic of ongoing research. Few curved crack path propagation solutions have been obtained by mathematical analysis, but computational approaches can accurately reproduce experimental results [1; 2; 3]. Numerical simulations typically calculate the energy derivatives in the first order with respect to crack length or the equivalent stress intensity factors. A number of computational methods can be used to simulate a growing crack, including the mesh-free method and the bounding element method. However, as a versatile method to simulate crack propagation, the finite element method is still popular. For the safety and reliability of engineering structures, it is important to predict the crack propagation path. Therefore, in many industries, the accurate estimation of the crack path and fatigue life estimation are of primary importance in terms of the need for reliability. In various applications, such as aerospace manufacturing, experimental studies are necessary for fatigue analysis. However, due to high costs, a precise computational method is required for crack propagation analysis to predict the direction of crack growth and fatigue lifetime under static and dynamic loading conditions [4; 5; 6]. Failure is related to (a) the presence of flaws such as interfaces, cracks, and (b) the nature of loads that fluctuate. Cracks tend to initiate and propagate when subjected to fluctuating loads until a point when the structure does not bear the load, which contributes to complete failure. These cracks are considered fatigue cracks, and the expected life is one of the major parameters to determine the safety of the structure. This is computed by adding the number of loading cycles needed to nucleate the fatigue crack and lead to failure. The calculation of the growth rate of the crack is usually based on the relation between the range of stress intensity factors (SIFs) and the crack geometry. One way to predict SIFs is by using computational methods such as the extended finite element method. In general, the initiation and propagation of cracks must be associated with SIFs in a complicated way [7; 8; 9; 10]. The extended finite element method (XFEM) proposed by [PERSON] and [PERSON] in 1999 [11] has been widely used in recent studies. It is based on the standard finite element framework and uses a special displacement feature to allow discontinuities to occur, overcoming the need to re-mesh continuously throughout the crack tip expansion process. To evaluate SIF, XFEM [12; 13; 14] was used to perform crack growth analysis without updating the mesh [15]. Extensive work was undertaken to develop efficient models to evaluate the FCG and fatigue life in order to overcome fatigue failures. There are several experimental models proposed, but performing the experimental procedures is usually time-consuming and costly. An effective way to reduce the laboratory work, time, and costs is to incorporate a simulation methodology that involves numerical analysis and uses ANSYS APDL.19.2. Many fatigue crack problems identified to date by the literature use different computational approaches in terms of simulation for simple and complex geometries in two and three dimensions [3; 4; 16; 17; 18; 19; 20; 21; 22; 23; 24]. The present work, therefore, uses the ANSYS APDL 19.2 to accurately predict the mixed-mode stress intensity factors as well as the associated fatigue life for seven specimens of the modified compact tension specimen (MCTS).