# Fatique Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel
## 3 Numerical Results and Discussions  
### Compact Tensile Shear (CTS) Specim  
The experimental studies by [13; 15] utilizing a mixed-mode (I/II) compact tensile shear (CTS) specimen provided the basis for the present numerical simulation for the modelled geometry shown in Figure 2. The CTS material was AISI 316 austenitic stainless steel alloy with the material properties shown in Table 1, and of 15 mm thickness. The CTS geometries are loaded in the original direction of cracking at various angles of 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) at a constant load \(F_{max}\) = 36 kN and fatigue-loading ratio of \(R\) = 0.1  
Figure 1: Flowchart for the ANSYS SMART crack growth procedures. (\(R=F_{min}/Fmax\)) with constant amplitude under a plane stress assumption. Figure 3 illustrates the loading and boundary conditions used in the present analyses. The holes located at the bottom are restricted from moving in both the \(x\) and \(y\) directions. The applied force \(F\) is distributed among three punctual loads, namely \(F_{1}\), \(F_{2}\), and \(F_{3}\), which are applied at their corresponding holes. These loads are applied at different loading angles, and their respective values are determined by the following formulas [18; 47; 48]:  
\[F_{1}=F(0.5\cos\alpha+\frac{c}{b}\sin\alpha) \tag{5}\]  
\[F_{2}=F\sin\alpha \tag{6}\]  
\[F_{3}=F(0.5\cos\alpha-(c/b)\sin\alpha) \tag{7}\]  
where \(\alpha\) is the load angle, \(c\) and \(b\) are a specified length defined in Figure 3 (\(c=b=54\) mm). The evaluated forces at the three loading angles are displayed in Table 2.  
Figure 2: Geometrical representation of CTS specimen. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Metric Units Value** \\ \hline Elasticity Modulus, \(E\) & 192 GPa \\ [PERSON]’s ratio, \(v\) & 0.27 \\ Yield strength, \(\sigma_{y}\) & 295 MPa \\ Ultimate strength, \(gu\) & 582 MPa \\ Paris law coefficient, \(C\) & 4.051 \(\times\) 10\({}^{-8}\) \\ Paris law exponent, \(m\) & 2.348 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of the CTS specimen. Figure 4: The initial mesh for the compact tension shear specimen. Figure 3: (**a**) Force division; (**b**) loading angles. The relationship between the crack growth path and loading angles in the compact tension shear (CTS) specimen is influenced by the specific loading configuration and material properties. Therefore, the loading angle can have a significant influence on the crack growth path in the CTS specimen, with shear-dominated fracture modes becoming more prominent with increasing loading angles. Figure 5 shows a comparison between the crack growth direction obtained from the present study and the experimental crack growth directions predicted by [PERSON] et al. [36] for all three loading angles (\(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\)) with an average error of less than 0.5%. The results presented in the figure reveal a high level of agreement between the simulated and experimental crack growth paths. The study's findings revealed that under mode I loading, cracks had a tendency to propagate in a direction that was nearly perpendicular to the loading direction. This observation provides valuable insights into the failure mechanisms of the material under investigation, which can aid in the development of more precise predictive models for crack propagation in similar materials. By understanding how cracks propagate under specific loading conditions, engineers and researchers can design more reliable and durable materials and structures that are less prone to failure. Figures 6-8 illustrate a comparison between the predicted crack growth trajectories for the various loading angles \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\) and the experimental results obtained by [15]. The comparison between the predicted and experimental results is a crucial step in determining the reliability of the predictive models used in the present study.