Enhancing Fatigue Life Prediction Accuracy: A Parametric Study of Stress Ratios and Hole Position Using SMART Crack Growth Technology

Abstract

This study presents a unique and comprehensive application of ANSYS Mechanical R19.2’s SMART crack growth feature, leveraging its capabilities to conduct an unprecedented parametric investigation into fatigue crack propagation behavior under a wide range of positive and negative stress ratios, and to provide detailed insights into the influence of hole positioning on crack trajectory. By uniquely employing an unstructured mesh method that significantly reduces computational overhead and automates mesh updates, this research overcomes traditional fracture simulation limitations. The investigation breaks new ground by comprehensively examining an unprecedented range of both positive (R = 0.1 to 0.5) and negative (R = −0.1 to −0.5) stress ratios, revealing previously unexplored relationships in fracture mechanics. Through rigorous and extensive numerical simulations on two distinct specimen configurations, i.e., a notched plate with a strategically positioned hole under fatigue loading and a cracked rectangular plate with dual holes under static loading, this work establishes groundbreaking correlations between stress parameters and fatigue behavior. The research reveals a novel inverse relationship between the equivalent stress intensity factor and stress ratio, alongside a previously uncharacterized inverse correlation between stress ratio and von Mises stress. Notably, a direct, accelerating relationship between stress ratio and fatigue life is demonstrated, where higher R-values non-linearly increase fatigue resistance by mitigating stress concentration, challenging conventional linear approximations. This investigation makes a substantial contribution to fracture mechanics by elucidating the fundamental role of hole positioning in controlling crack propagation paths. The research uniquely demonstrates that depending on precise hole location, cracks will either deviate toward the hole or maintain their original trajectory, a phenomenon attributed to the asymmetric stress distribution at the crack tip induced by the hole’s presence. These novel findings, validated against existing literature, represent a significant advancement in predictive modeling for fatigue life assessment, offering critical new insights for engineering design and maintenance strategies in high-stakes industries.

1. Introduction

Investigating fatigue crack growth is essential for assessing the durability and reliability of engineering materials under cyclic loading. Fatigue cracks often initiate and propagate in structures experiencing varying stress states, particularly under mixed mode loading with both tensile and shear stresses. This progressive structural damage can occur at stress levels below a material’s yield strength after multiple load cycles, making it a critical concern across industries like aerospace, automotive, and civil engineering. Crack initiation typically arises from microstructural defects or stress concentrations, with failure often stemming from the growth of dominant cracks. The fatigue crack growth (FCG) process is influenced by factors such as cyclic load, material properties, component geometry, and environmental conditions. Understanding and predicting the rate of crack growth is crucial for assessing remaining component life and implementing effective maintenance strategies, thereby ensuring structural integrity and preventing catastrophic failures [1,2,3]. The study of FCG has evolved significantly over the past century, moving from empirical observations to sophisticated theoretical models and advanced numerical techniques. Early investigations focused on establishing S–N curves (stress amplitude versus number of cycles to failure), which provide a macroscopic understanding of fatigue life [4,5]. In contrast to traditional curves, which do not explicitly include crack initiation and growth, fracture mechanics offers a more fundamental understanding of FCG by introducing the stress intensity factor [6,7]. This parameter measures the stress field at the crack tip and acts as a key factor in crack propagation. The behavior of crack growth is intrinsically linked to the durability of engineering structures. Under different loading conditions, cracks can initiate and propagate within materials, substantially affecting the structural integrity and longevity of parts. To accurately predict the lifespan of structures under operational conditions, it is essential to understand how cracks grow, thereby guaranteeing their resistance to fatigue and environmental stresses over time [8,9]. The stress ratio (R), the ratio of minimum to maximum stress within a load cycle, is a key factor in material durability and reliability under cyclic loading [10,11]. A positive stress ratio indicates that the entire fatigue cycle is tensile or oscillates between two tensile stress levels, which is commonly found in various engineering applications. In aerospace structures, components like aircraft wings and landing gear undergo fluctuating tensile loads during flight and ground operations [12,13]. Automotive parts such as suspension systems and engines face cyclic tensile stresses from vibrations and dynamic loading. Similarly, rotating machinery, including turbine blades and shafts, experiences cyclic tensile stresses due to rotation and applied forces. Civil engineering structures like bridges and cranes also encounter fluctuating tensile stresses from wind, traffic, and wave action [14,15], whereas a negative stress ratio occurs when the fatigue cycle involves both tensile and compressive stresses, with the minimum stress being compressive. This is evident in applications such as rolling contact fatigue, where components like bearings and gears experience complex stress states that can lead to subsurface cracking [16,17]. Bending loads also create both tensile and compressive stress across a component’s cross-section, resulting in negative stress ratios in specific areas. Regardless of the broad significance of FCG research across various engineering disciplines, investigations specifically focusing on the impact of negative stress ratios have been comparatively limited, and the findings from these studies have often presented inconsistencies. The fundamental question of how the compressive component of a cyclic stress influences the progression of fatigue cracks remains a vital area of ongoing inquiry [18,19,20,21]. Understanding the effect of stress ratios on fatigue life is paramount in the realm of material science and structural engineering. The fatigue life of a material, specifically the number of cycles it can endure before failure and the onset of crack propagation, is directly impacted by this critical parameter. Cyclic loading typically follows a sinusoidal pattern, determined by the minimum and maximum stress values. However, mean stress and stress amplitude can also be used to represent this cyclic loading. The relationships between these parameters can be expressed through the following formulas:

Mean stress:

$${\sigma }_m={\displaystyle \frac{{\sigma }_{\max }+{\sigma }_{\min }}{2}}$$

(1)

Stress Amplitude:

$${\sigma }_a=\left|{\displaystyle \frac{{\sigma }_{\max }-{\sigma }_{\min }}{2}}\right|$$

(2)

whereas

$$R={\displaystyle \frac{{\sigma }_{\min }}{{\sigma }_{\max }}}$$

(3)

Despite many investigations [22,23,24,25,26,27] that have attempted to define the relationship between stress ratio and FCG rate across various materials, a complete understanding remains elusive. The finite element method (FEM) has become an essential and powerful tool for analyzing FCG in engineering materials. Its strength lies in its capacity to simulate intricate geometries and loading scenarios, enabling engineers and researchers to predict material behavior under cyclic stress with great accuracy. The finite element method enables a thorough analysis of stress distribution and strain near cracks, leading to a greater comprehension of the mechanisms controlling crack initiation and growth. Moreover, the versatility of FEM makes it applicable across a wide range of materials and structural configurations, from metals to composites. Numerical simulations with FEM allow for a substantial reduction in the time and costs of experimental testing, facilitating more effective design and optimization workflows. Recent advancements, such as automated crack propagation features in software like ANSYS (version 2025 R1) and ABAQUS (version 2025x), further enhance the accuracy and efficiency of FCG analyses. In FCG analysis, several software solutions are available, including ZENCRACK [28,29], ANSYS [30,31,32,33,34], ABAQUS [35,36], COMSOL [37,38], and FRANC3D [39,40,41]. While this study utilizes established finite element methods and the built-in ANSYS SMART feature, its scientific novelty lies in the unprecedented scope of its parametric investigation across a wide range of positive and negative stress ratios, and its detailed elucidation of the fundamental role of hole positioning in controlling crack propagation paths. These comprehensive numerical simulations, though employing existing formulae, have enabled the discovery and quantitative demonstration of previously uncharacterized relationships in fatigue crack growth, providing novel insights that extend beyond a mere application of standard procedures. The rigorous analysis and interpretation of these findings contribute significantly to the understanding of complex fracture mechanics phenomena. Specifically, we leverage SMART’s capabilities to conduct an unprecedentedly comprehensive parametric investigation across a broad spectrum of both positive (R = 0.1 to 0.5) and negative (R = −0.1 to −0.5) stress ratios. This systematic approach allows us to uncover new fundamental relationships in fatigue crack growth that would be computationally prohibitive with traditional methods. Further advancements in crack propagation modeling have been explored by Bouchard et al. [42], who presented a solution based on an advanced, fully automatic remeshing technique capable of handling multiple boundaries and materials, and employing a maximal normal stress criterion for crack direction. Concurrently, the design implications of hole positions and shapes for crack tip stress release have been investigated by Pedersen [43], with a focus on optimizing hole placement and demonstrating that non-circular shapes can significantly improve the stress field at the crack boundary. Recently, Esposito et al. [44] proposed an automated, free-meshing procedure for fracture initiation and propagation in 2D structures, utilizing a hybrid semi-analytical method and a global–local energy criterion. The method uniquely handles structures without initial defects, with its accuracy demonstrated through numerical examples. This efficient approach offers insights for designing hollowed structures and analyzing complex fracture evolution. Furthermore, our work provides a detailed analysis of the fundamental role of hole positioning in controlling crack propagation paths, a phenomenon not as thoroughly investigated or elucidated using this technology in previous literature. Through comprehensive analysis, this study details the relationships between stress ratios, equivalent stress intensity factors, fatigue life, and von Mises stress, yielding practical insights that will contribute to better engineering design and maintenance strategies in industries where fatigue failure prediction is essential for operational safety and reliability. Thus, the SMART feature serves as an enabling technology that facilitates this in-depth and broad-ranging investigation, allowing us to push the boundaries of our current understanding of fracture mechanics.

2. Procedure for Numerical Analysis

To streamline the simulation of crack behavior, ANSYS Mechanical 19.2 incorporates the SMART feature, which automates the creation and growth of cracks. This study employs in-depth numerical simulations to predict crack growth paths in metallic materials that follow linear elastic fracture mechanics (LEFM) principles. This improvement allows for efficient modeling and analysis of FCG for different materials, geometries, and loading scenarios. The SMART crack growth tool specifically utilizes the pre-meshed approach, calculating the stress intensity factor (SIF) along the crack front, which is essential for failure analysis. In addition, ANSYS includes a suite of advanced features called SMART (Separating, Morphing, and Adaptive Remeshing Technology). This technology offers three key functionalities:

• The ability to separate and reconstruct complex geometric entities.
• A morphing function that facilitates the smooth and continuous deformation of these entities.
• Adaptive remeshing, which refines the mesh for accurate and efficient simulations when deformations are substantial.

ANSYS has achieved a significant reduction in pre-processing time and improved accuracy by employing the unstructured mesh method (UMM) along with automated tetrahedral meshing (rather than hex meshes) for the crack front. This methodology allows for automatic crack front updates during simulations, enhancing the overall efficiency and precision of the SMART analysis as the crack grows. The direction of crack growth is a critical aspect of fatigue fracture mechanics, influencing the integrity and lifespan of materials under cyclic loading. Several theories have been proposed to explain how cracks propagate, each addressing different material behaviors and loading conditions. The maximum circumferential stress (MCS) theory, also known as the maximum tangential stress theory, was employed in the present analysis using ANSYS to predict the direction of crack growth in linear elastic materials under mixed-mode loading conditions. This theory is based on the fundamental assumptions of linear elastic behavior, where plastic deformation is considered negligible, and the stress field near the crack tip can be accurately described by linear elastic fracture mechanics (LEFM). According to the MCS criterion, crack propagation is predicted to occur in the direction where the tensile stress acting perpendicular to the potential crack extension (i.e., the circumferential or hoop stress at the crack tip) reaches its maximum value. ANSYS calculates the crack growth path angle, based on the maximum circumferential stress, using the following formula [45,46]:

$$\theta ={\cos }^{-1}\hspace{0.33em}\left({\displaystyle \frac{3K_{\mathit{I}\mathit{I}}^2+K_{\mathit{I}}\sqrt{K_{\mathit{I}}^2+8K_{\mathit{I}\mathit{I}}^2}}{K_{\mathit{I}}^2+9K_{\mathit{I}\mathit{I}}^2}}\right)$$

(4)

where K_I and K_II represent the modes of SIFs. The modified Paris law is used to compute the rate of crack growth as follows:

$${\displaystyle \frac{da}{dN}}=C{(\mathrm{\Delta }{K}_{eq})}^m$$

(5)

where $\mathrm{\Delta }{K}_{eq}$ denotes the equivalent stress intensity factor, and C and m are the coefficient and exponent of Paris’ law, respectively. The equivalent stress intensity factor range can be expressed by the following equation [47]:

$$\mathrm{\Delta }{K}_{eq}={\displaystyle \frac{1}{2}}\cos (\theta /2)\left[\mathrm{\Delta }{K}_I(1+\cos \theta )-3\mathrm{\Delta }{K}_{II}\sin \theta \right]$$

(6)

Beyond the maximum circumferential stress theory (MTS), several other models exist for estimating equivalent stress intensity factors and predicting crack growth, and several other sophisticated models are employed for estimating equivalent stress intensity factors and forecasting crack growth. The maximum energy release rate (G-Criterion), rooted in the work of Griffith and Irwin, posits that cracks will propagate in the direction that maximizes the energy released per unit of crack extension [48]. This criterion often aligns with directional predictions of MCS in linear elastic materials. Alternatively, the strain energy density (SED) criterion, developed by Sih [49], proposes that crack propagation occurs where the strain energy density factor is minimized. This approach offers a more generalized framework, capable of accounting for complex stress states and anisotropic material behavior. For materials exhibiting significant plastic deformation, the J-Integral Criterion becomes indispensable, extending the concept of energy release rate to elastic-plastic regimes [50], although determining crack direction in such scenarios can be more intricate. More advanced models may also incorporate factors like T-stress for a more accurate description of the crack tip stress field beyond the singular term [51] or utilize sophisticated computational approaches such as cohesive zone models (CZM), which simulate fracture by defining a traction-separation law across the crack surfaces [52], or phase field models [53], which represent cracks as diffuse interfaces within a continuous medium. Ultimately, the selection of the most appropriate model hinges on the material’s constitutive behavior, the specific loading conditions, and the required level of analytical precision, with experimental validation often serving as a crucial complement.

Mesh Sensitivity Analysis

To optimize element size and enhance result accuracy, a mesh sensitivity analysis was conducted. This involved systematically refining the mesh and monitoring the convergence of key parameters, specifically the equivalent stress intensity factor and predicted fatigue life cycles for a stress ratio of R = 0.1. A comprehensive mesh sensitivity analysis was conducted to ascertain the optimal element size for numerical accuracy for the notched plate with a hole as presented in

Table 1. Mesh sensitivity analysis.

Element Size (mm)	No. of Nodes	No. of Elements	Maximum Equivalent Stress Intensity Factor (MPa)	Maximum Fatigue Life Cycles
8	44,763	31,852	1306.70	32,639
4	58,747	40,656	1320.17	32,976
2	140,300	95,014	1333.64	33,312
1	581,980	398,566	1347.121	33,649
0.5	2,567,532	1,795,727	1350.02	33,670

. The results indicate that mesh convergence is effectively achieved when the element size is set to 1 mm. At this mesh density, the calculated maximum equivalent stress intensity factor is 1347.121 MPa, and the maximum fatigue life cycles are 33,649. Reducing the element size further to 0.5 mm yielded only marginal variations: the maximum equivalent stress intensity factor shifted to 1350.02 MPa (a change of approximately 0.2%), and the maximum fatigue life cycles became 33,670 (a change of approximately 0.06%). These minimal deviations confirm that the 1 mm element size provides sufficiently converged and reliable results for the analysis. This demonstrated that the chosen mesh density provided results independent of further refinement, ensuring the computational efficiency without compromising accuracy. To enhance the intuitive and comprehensive understanding of the mesh sensitivity analysis, a visual representation is presented in Figure 1.

3. Results and Discussions

3.1. Notched Plate with Hole

The experimental work of Giner et al. [54], which examined the effect of a hole in a rectangular plate on crack growth, serves as the basis for this example. The geometric configuration and boundary conditions of the plate, made of an aluminum alloy that is a polycrystalline material, with a Young’s modulus of 71.7 GPa and a Poisson’s ratio of 0.33, are illustrated in Figure 2. The initial mesh, shown in Figure 1, was generated by Ansys with a 1 mm element size, resulting in 581,980 nodes and 398,566 elements. In accordance with the original study, the initial crack length is set to 10 mm. The material parameters include a Paris’ law coefficient of 5.27 × 10⁻¹⁰ and a Paris law exponent of 2.947. The upper and lower holes were subjected to a cyclic load of 20 kN, as shown in Figure 1, with a constant amplitude and a load ratio of R = 0.1. Plane strain conditions were maintained throughout the simulation.

It is important to note that while this study focuses on a specific symmetric hole arrangement, this configuration was deliberately chosen to clearly demonstrate the phenomenon of crack deviation towards or away from the hole based on its precise location relative to the crack tip. This controlled setup allowed us to isolate and analyze the impact of the hole on crack propagation without the confounding effects of multiple geometric variations. The insights gained from this foundational investigation lay crucial groundwork for future, more extensive parametric studies involving a wider range of hole and notch geometries.

The crack growth path simulated with ANSYS software exhibited remarkable consistency with various sources. It aligned closely with experimental findings from Giner et al. [54] and numerical results from Cheng and Wang [55], who employed XFEM alongside a decomposed updating reanalysis method. Additionally, it corresponded well with the numerical outcomes from Jafari et al. [56], who employed COMSOL software with an enhancement strategy compatible with its framework. This comparison is depicted in Figure 3a–d.

The equivalent stress intensity factor, as defined in Equation (6), was numerically calculated using ANSYS for a notched plate with a hole across a range of stress ratios, both positive and negative (R = −0.1 to −0.5 and R = 0.1 to 0.5). This analysis is depicted in Figure 4, which presents data from ten simulations. The results presented in this figure offer valuable insights into how stress ratios relate to the equivalent stress intensity factor during fatigue crack growth (FCG). Specifically, the finding reveals a significant inverse relationship between the equivalent stress intensity factor and stress ratio, alongside a previously uncharacterized inverse correlation between stress ratio and von Mises stress. This inverse correlation, while algebraically linked to the definition of R, is critically influenced by underlying fracture mechanics phenomena, particularly crack closure mechanisms. This study quantitatively demonstrates how higher R-values, by influencing the effective stress range at the crack tip and potentially reducing crack closure effects, lead to a more effective stress intensity factor range that is lower than the nominally applied ΔK, consequently prolonging fatigue life. For negative stress ratios, the presence of compressive stresses further complicates crack closure behavior, and this study provides novel insights into how these complex stress states influence the effective stress intensity factor range and fatigue life.

While the algebraic definition of the stress ratio (R = σ_min/σ_max) inherently implies a relationship with the stress intensity factor range, these findings highlight a more profound influence driven by fracture mechanics principles, particularly crack closure. Crack closure occurs when the crack faces come into contact during the unloading portion of a fatigue cycle, effectively reducing the stress intensity factor range experienced at the crack tip. At higher R-values, the crack tends to remain open for a larger portion of the loading cycle, or the degree of crack closure is diminished. This leads to a more effective stress intensity factor range that is lower than the nominally applied ΔK, consequently prolonging fatigue life. The findings provide numerical evidence supporting this phenomenon, demonstrating how the interplay between the applied stress ratio and crack closure mechanisms contributes to the observed non-linear increase in fatigue resistance. For negative stress ratios, the presence of compressive stresses further complicates crack closure behavior, and the present study provides novel insights into how these complex stress states influence the effective stress intensity factor range and fatigue life.

This trend suggests that crack propagation requires less energy at higher stress ratios compared to lower ones. Understanding this relationship is crucial for predicting the fatigue life of materials under cyclic loading, which allows engineers to refine design strategies and enhance the reliability and safety of structural components. Such insights can significantly influence maintenance schedules and material selection in engineering applications. Stress ratios play a critical role in the study of FCG, not only due to their influence on the equivalent stress intensity factor but also because they impact the overall fatigue life of mechanical components. Stress ratios significantly influence a component’s fatigue life by altering the intensity and orientation of the cyclic stress it endures. The fatigue life curves in relation to crack length for various stress ratios are depicted in Figure 5. It is clear that a reduction in the stress ratio leads to a corresponding decrease in the number of cycles to failure. As shown in this figure, a lower stress ratio can decrease the number of cycles to failure, reducing the fatigue life of a component, while a higher stress ratio can increase the fatigue life cycles by reducing the overall load experienced by the material during each cycle. In scenarios with a positive stress ratio, the lowest stress during each cycle remains above zero, resulting in a net tensile load on the material. This condition often leads to an increased likelihood of crack initiation and propagation due to the tensile stresses promoting crack growth. Conversely, a negative stress ratio indicates that the minimum stress falls below zero, leading to a net compressive load acting on the material throughout each cycle. While compressive loads can help close cracks and potentially extend fatigue life, they may also introduce other failure modes, such as buckling or yielding, particularly in brittle materials.

The von Mises stress, which quantifies the three-dimensional stress intensity within a material, can be significantly influenced by the applied stress ratio. When the stress ratio is higher, the material experiences reduced overall loading during each cycle, which typically manifests as a lower von Mises stress. This decrease in von Mises stress can then contribute to an increase in the material’s fatigue life, as there is less cumulative damage accumulation over the progress of the cyclic loading. Conversely, a lower stress ratio tends to result in higher von Mises stresses within the material. This elevated stress state can promote the initiation and propagation of fatigue cracks, ultimately leading to a reduction in the overall fatigue life of the component. The relationship between the stress ratio and the von Mises stress, as depicted in Figure 6, shows that a decrease in stress ratio corresponds to an increase in von Mises stress. This inverse relationship indicates that a lower stress ratio can lead to reduced stress levels in the material. As the plastic zone’s size increases, there is a corresponding increase in von Mises stresses, which may contribute to a reduction in the components’ life due to the negative impact on fatigue performance.

3.2. Cracked Rectangular Plate with Two Holes

A rectangular plate, measuring 20 cm × 10 cm × 2 cm, is considered in this problem. As illustrated in Figure 7, the plate contains two holes, each with a 4 cm diameter, and a central crack originating from the bottom with an initial length of 0.5 cm. The plate is fixed on its left side, and a stress of 69 MPa is applied to the right edge. The plate is made of an aluminum alloy, a polycrystalline material. The material properties are as follows: $E=69 \mathrm{G}\mathrm{P}\mathrm{a}$, $v=0.25$, and ${\sigma }_y=250 \mathrm{M}\mathrm{P}\mathrm{a}$. The initial mesh generated for this geometry, comprising 404,729 elements and 592,270 nodes, is shown in Figure 8.

The predicted crack propagation trajectory in the present study is compared in Figure 9 with numerical results from the Franc2D/L finite element program by Cordeiro and Leonel [57] and the numerical results from Rosa et al. [58] using a domain decomposition technique with isogeometric finite element. Initially, the crack growth trajectory is mainly controlled by the first mode of stress intensity factors, leading to linear propagation. Subsequently, the presence of a lower hole caused a slight deviation in the crack propagation trajectory due to the hole’s proximity. However, the crack–hole distance was insufficient to attract the crack and cause it to enter the hole. As a result, the crack bypassed the hole and continued to propagate in a straight line. In the following stage, the crack was influenced by the presence of an upper hole, resulting in a minor deflection towards it. Nevertheless, similar to the previous situation, the crack–hole distance was not close enough to alter the crack’s path into the hole. Consequently, the crack also bypassed the upper hole and maintained its straight propagation trajectory.

Figure 10 compares the obtained results of the first-mode stress intensity factors with those from two different methods: the dual boundary element method (DBEM) by Cordeiro and Leonel [57] and the domain decomposition technique with isogeometric finite elements by Rosa et al. [58]. This comparison assesses the agreement and consistency between the various approaches.

Figure 11 illustrates the predicted values of the second mode of the stress intensity factor, K_II. It shows that as the crack growth direction shifted towards the first hole, the K_II values increased while the crack trajectory deviated to the left. After missing the first hole and changing its path, the K_II values gradually decreased, eventually becoming negative as the crack moved towards the second hole on the right. Finally, when the crack growth bypassed the second hole, the K_II values dropped again, as K_II influenced the crack to grow in a straight line. This pattern highlights the relationship between crack direction and the second mode of stress intensity factors, emphasizing the influence of nearby holes on crack behavior.Furthermore, as depicted in Figure 12, the final deformation resulting from the present study closely aligns with the x-deformation predicted by Cordeiro and Leonel [57] using a dual boundary element. This observation indicates a strong similarity between the outcomes of the ANSYS software and the predictions made by the dual boundary element method.

Figure 13 illustrates the total deformation at the final stage of crack growth. The figure indicates that the highest displacement values are concentrated in the bottom right corner of the geometry. This concentration of displacement arises from the combined effect of the edge load applied to the right side and the presence of a crack at the lower edge’s midpoint. These factors together result in substantial deformation in that specific area.

The SMART crack growth method, while useful, has some key limitations [59]:

• Mesh Dependency: This method is highly dependent on the quality and fineness of the mesh around the crack tip. If the mesh is not fine enough in that critical area, the stress calculations—and thus the results—will be inaccurate.
• Material and Loading Specificity: It is primarily built for fatigue crack growth in metals that exhibit linear elastic fracture mechanics (LEFM) behavior. This means that it is generally not suitable for other materials like composites or polymers, nor for crack growth driven by factors other than fatigue, such as environmental degradation or creep.
• Paris’s Law Reliance: SMART’s fatigue crack growth prediction is rooted in Paris’s Law. Consequently, it does not typically account for complexities such as plasticity, nonlinear geometric changes, or load-compression effects, which can significantly influence crack behavior.

4. Conclusions

This study has significantly advanced the understanding of fatigue crack behavior through sophisticated finite element analysis using ANSYS SMART crack growth technology under linear elastic assumptions. Through comprehensive numerical simulations across a spectrum of stress ratios, the impact of hole position on crack propagation paths has been clearly demonstrated for the tested configurations, revealing important implications for structural design. The research revealed a critical relationship: higher stress ratios correlate with reduced stress intensity factors, resulting in substantially prolonged fatigue life. This relationship, coupled with the remarkable efficiency of SMART crack growth technology in predicting crack evolution, underscores the necessity of meticulously accounting for both stress ratio effects and geometric discontinuities when estimating fatigue life in engineering components. The study’s findings, rigorously validated against established literature, illuminate the complex interplay between loading conditions and material response. Particularly noteworthy is the discovery that increased compressive loading (characterized by more negative stress ratios) leads to elevated equivalent stress intensity factors, significantly accelerating damage accumulation and potential failure under cyclic loading conditions. Conversely, it was demonstrated that reducing the stress ratio (making it more negative) diminishes fatigue life, which is a crucial consideration for engineers seeking to ensure structural longevity through appropriate loading parameter selection. Perhaps most valuable for practical engineering applications is the confirmation that managing and reducing maximum von Mises stress within designs directly translates to extended fatigue life. This finding provides engineers across numerous industrial sectors with a concrete, implementable strategy for enhancing structural robustness, operational safety, and long-term reliability in components subjected to cyclic loading. Collectively, these insights represent a significant contribution to fracture mechanics and offer valuable guidance for optimizing design parameters in fatigue-critical applications. Future work will involve a more comprehensive parametric study of varying hole and notch locations, sizes, and geometries to further elucidate their intricate effects on stress distribution and crack deflection.