# Numerical Modeling of Crack Growth under Mixed-Mode Loading
## 1 Introduction
The XFEM has been one of the most recent fields of study in computational mechanics and has attracted many researchers. Its major benefit is that the crack will move through an element without being remeshed. To do this, the information from a crack must be described and updated by a so-called Level Set process. Convenient structures are often subjected to various loading mechanisms, such as stress, shear, and torsion, which lead to mixed-mode interactions. The stress status in front of a crack was therefore highly dependent on the form of interactions in mixed-mode \(I/II\), demonstrating the amount of the stresses at the crack tip. Mode \(I\) is the emphasis of scientific literature on the activity of the FCG, while cracks and defects are usually mixed-mode cracking, whereas crack growth in practical engineering structures such as the vessel pressure, pipelines, and fan blades appear to be mixed-mode too (\(I\)-\(II\)) [18]. The initiation and propagation of crack will usually refer in a complicated state to the governed stress intensity factors (SIFs) [19; 20; 21; 22]. Fatigue cracks in various fields of engineering are important because they are one of the key causes of catastrophic failure. The sustainability of main components and launch systems for operation must be ensured. The reliability of critical components must be ensured in the case of launching systems for service. Consequently, it is primarily important in terms of reliability requirements to precisely predict and assess fatigue life in many industries. In certain applications, for example in the aerospace industry, fatigue studies require experimentation that leads to high costs, thus precise computational processes for crack propagation analysis are essential to predict the direction of crack growth and durability in both static and dynamic loads. Comprehensive works have been performed to establish an efficient model to simulate the propagation of fatigue cracks and fatigue life in order to reduce fatigue failures. Numerical analyses using XFEM implemented by ANSYS APDL.19.2 are an effective method to reduce the computational time and expenses involved with performing experimental studies. SIFs are being used to characterize displacement and stress around the front of the crack and analyze the LEFM crack growth under dynamic loading for isotropic material. According to the parametric study, material anisotropy can have a significant impact on the direction of crack growth [23; 24; 25; 26]. Another study examined the influence of weak spots in composite structures that attract cracks and thereby prevent them from growing, such as the holes effect [27]. The SIF increases to a critical range as the crack grows, following which the structure might start deforming by starting a fracture. The general types of loads that depend on those used in fatigue life predictions attributed to the complex mode of applied loads and the geometry specificationsare regularly mixed modes (\(I/II\)) [28; 29; 30; 31]. The major motivations for this research were to contribute significantly to the use of ANSYS as an alternative approach for simulating fatigue crack propagation problems under mixed-mode loading, and monitoring the crack growth trajectory in the presence of holes in the geometry [32; 33; 34; 35]. This paper aims to study the effect of the crack tip location related to the presented holes in the trajectory of the crack propagation, SIFs, and fatigue life of a three-point-bending specimen with three holes and six different configurations using the XFEM implemented by ANSYS APDL 19.2. There are several different articles that were studied for this geometry, but no comprehensive analysis implements ANSYS software using the SMART CRACK feature (e.g., [36]).