# Fatique Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel
## 2 ANSYS Procedure for Fatigue Analysis  
Mixed-mode fatigue life evaluation is an essential process for predicting the durability of materials that undergo cyclic loading conditions with different loading modes. ANSYS is a powerful software package commonly used in engineering applications, including fatigue life evaluation. ANSYS has the capability to model three types of cracks: arbitrary, semi-elliptical, and pre-meshed cracks. Among these, the pre-meshed crack approach is used in the \"Smart Crack Growth\" analysis tool. This tool utilizes the crack front to calculate the stress-intensity factor, which is the failure criterion. The \"Smart Crack Growth\" simulation tool uses this approach to simulate the propagation of cracks. The separating, morphing, and adaptive remeshing technologies (SMART) is a set of advanced capabilities in ANSYS that enable the simulation of complex and large deformations in structural mechanics problems. SMART technology includes three main features:  
* Separating technology: this feature allows for the separation of different components within a model, making it possible to simulate the deformation of individual parts separately. This is particularly useful when simulating complex structures that have many moving parts. * Morphing technology: this feature enables the morphing of a mesh to match the deformation of the structure during simulation. This is achieved by updating the nodal positions of the mesh based on the deformation of the structure. * Adaptive remeshing technology: this feature enables the automatic refinement of the mesh in regions where high deformation gradients are present, improving the accuracy of the simulation. This feature is especially useful in simulating crack propagation, where accurate stress gradient capture necessitates mesh refinement around the crack tip. The variation in crack initiation angle under different mixed-mode loading conditions is a well-established phenomenon. To address this issue, several researchers have proposed various fracture criteria. Within linear elastic fracture mechanics (LEFM), fracture criteria are typically categorized into three groups: stress-based, strain-based, and energy-based. The stress-based group includes the maximum tangential stress (MTS) criterion [37], the strain-based group includes the maximum tangential strain (MTSN) criterion [38], and the energy-based group includes the strain energy density (SED) criterion [39] and the maximum energy release rate (MERR) criterion [40]. The maximum circumferential stress criterion is one of the criteria that ANSYS uses to evaluate the crack growth under mixed-mode loading conditions which was used in the present study. This criterion is based on the assumption that the crack growth occurs in the direction of maximum circumferential stress. The criterion involves calculating the stress-intensity factors for each mode of loading and combining them to obtain the total stress-intensity factor. The crack growth direction is then determined based on the direction of the maximum circumferential stress, which is perpendicular to the direction of the total stress-intensity factor. The ratio of modes of stress-intensity factors (SIFs) at the crack tip can be used to estimate the angle \(\theta\), which defines the path of crack propagation [41; 42; 43]. The formula used in this criterion to determine the direction of crack propagation is [44; 45]:  
\[\theta=\cos^{-1}\,\left(\frac{3K_{II}^{2}+K_{I}\sqrt{K_{I}^{2}+8K_{II}^{2}}}{K _{I}^{2}+9K_{II}^{2}}\right) \tag{1}\]  
where:  
\(K_{I}\) and \(K_{II}\) correspond to the opening and in-plane shear modes, respectively. The ANSYS simulation performed in this study is limited to region II of a typical cyclic-loading-induced crack growth pattern.