## 3 Numerical Results and Discussions
The data provided in these figures are valuable in understanding the relationship between the stress ratio and the equivalent range of SIFs in FCG. The presented data shows that an increase in the stress ratio leads to a decrease in the equivalent range of SIFs. This observation implies that crack propagation under higher stress ratios requires less energy compared to lower stress ratios to facilitate FCG. A thorough understanding of the relationship between stress ratio and stress intensity factors (SIFs) enables engineers to optimize the design and enhance the durability of structures, leading to improved performance and increased durability. Fatigue failure poses a significant concern in engineering applications exposed to fatigue loading. A comprehensive understanding of the relationship between stress ratios and fatigue life cycles is crucial when designing reliable and durable components. The stress ratio significantly influences fatigue life cycles. This study focuses on the impact of varying stress ratios, ranging from 0.1 to 0.9 with a step of 0.1, on the fatigue life cycles of materials. By examining the effects of stress ratio variation, engineers can make informed decisions to enhance the reliability and longevity of various structures. By systematically varying the stress ratio from 0.1 to 0.9 with a step of 0.1, valuable insights can be gained into the changes in fatigue life cycles. As shown in Figures 13 and 14 for CTS02 and CTS05, as the stress ratio increases from 0.5 to 0.9, there is a corresponding increase in the fatigue life cycles of the material. This indicates that higher stress ratios, such as \(R>0.5\), contribute to improved durability and a longer fatigue life under cyclic loading. The underlying mechanism driving this trend lies in the presence of compressive stress cycles. With higher stress ratios, there is a greater proportion of compressive stress cycles, which effectively mitigate the detrimental effects of tensile stress cycles. Compressive stresses retard crack initiation and slow down crack growth, thereby extending the fatigue life of the material. Consequently, increasing the stress ratio within this range enhances the material's resistance to fatigue failure, necessitating a larger number of stress cycles to induce failure. In contrast, when the stress ratio is relatively low, such as \(R<0.5\), the minimum cyclic stress is significantly lower than the maximum cyclic stress. This results in  
Figure 2:0 Equivalent range of stress intensity factors for CTS02. tensile stress conditions dominating the load cycle. Under these conditions, crack growth is accelerated, and the fatigue life cycles are typically shorter compared to higher stress ratios. Understanding the relationship between stress ratios and fatigue life cycles holds significant implications for engineering design. Designers can optimize the fatigue performance and durability of structures by considering different stress ratios. Figure 2:1 Equivalent range of stress intensity factors for CTS05. Figure 2:2 Fatigue life cycles for CTS02 under different stress ratios. Figure 15 illustrates the X-directional deformation for CTS02-CTS05. The presence of directional deformation in this axis can significantly affect the behavior of crack growth under cyclic loading. When subjected to alternating stress levels, cracks have the potential to initiate and propagate. Higher levels of deformation in the X-direction intensify stress at crack tips, accelerating the crack growth rate. Factors such as stress concentration, material properties, and the presence of stress corrosion factors in the environment further influence the rate of crack propagation. Therefore, precise control and management of X-directional deformation become imperative to minimize crack growth and extend the fatigue life of components. The number of cycles to failure exhibits an inverse relationship with the level of X-directional deformation. Generally, higher deformation levels tend to reduce the number of cycles required for failure due to fatigue.