Fatigue Lifetime Research Articles

Critical length parameter of HDPE and its use in fatigue lifetime predictions

The contribution describes the fatigue lifetime predictions of polyethylene notched specimens based on the theory of critical distance. The approach uses the line method, which averages the axial stress over the critical distance. The critical distance is determined from experimental data of Cracked Round Bar (CRB) specimens and specimens with a model notch. From these two sets of experimental fatigue data and corresponding axial stress distributions, the critical distance is determined. The critical distance depends on the number of cycles to failure and notch radius. For this reason, the critical distance is modified by the ratio of stress concentration factors and the modified distance is used for fatigue lifetime predictions of notched specimens with various notch radii. Using this approach significant savings in testing time can be achieved. CRB fatigue tests are commonly used tests for ranking PE pipe grades and are easily available. Adding the fatigue tests of notched specimens with a model notch, the critical parameter can be found, and fatigue lifetime predictions of various notches can be calculated.

Impact of Combined Zr, Ti, and V Additions on the Microstructure, Mechanical Properties, and Thermomechanical Fatigue Behavior of Al-Cu Cast Alloys

The effects of minor additions of the transition elements Zr, Ti, and V on the microstructure, mechanical properties, and out-of-phase thermomechanical fatigue behavior of 224 Al-Cu alloys were investigated. The results revealed that the introduction of the transition elements led to a refined grain size and a finer and much denser distribution of θ″/θ′ precipitates compared to that of the base alloy, which enhanced the tensile strength but reduced the elongation at both room temperature and 300 °C. Constitutive analyses based on theoretical strength calculations indicated that precipitation strengthening was the primary mechanism contributing to the strength of both tested alloys at room temperature and 300 °C. The out-of-phase thermomechanical fatigue test results showed that the addition of transition elements caused a slight decrease in the fatigue lifetime, which was mainly attributed to the reduced ductility and higher peak tensile stress at low temperatures. During the fatigue process, the transition element-added alloy exhibited a lower coarsening ratio, indicating higher thermal stability, which mitigated the negative impact of the reduced ductility on the fatigue performance to some extent. Considering their various properties, the addition of Zr, Ti, and V is recommended to improve the overall performance of Al-Cu 224 cast alloys.

Rotating Bending Fatigue Durability of Wrought 304 Stainless Steel: A Comparative Study of Surface-Treated vs. Untreated Specimen

The rotating bending fatigue test, which is a common durability test for industrial components, was employed in this study to examine the impact of the surface treatment procedure on the material's performance under room temperature. The studied material in this research is a wrought stainless steel (SS) 304 alloy that has undergone a specialized surface treatment to enhance the fatigue properties of this unique material. The fatigue endurance of untreated materials was 405 MPa (65% of untreated specimen’s yield strength) on 5 million runout cycles, while the surface-treated samples exhibited 545 MPa (85% of treated specimen’s yield strength), a significantly greater value compared to the untreated ones (even up to 10 million runout cycles). The experimental results demonstrated that the surface-treated samples exhibited no signs of cracking. Instead, all failures were attributed to plastic bending, particularly at higher stress levels. Furthermore, the samples displayed a limited range of stress levels, spanning from endurance to plastic bending conditions. This finding suggests that the hypothesis of an increase in stiffness in the surface layer is more pronounced than in the material interior. It also indicates that the surface layer material was not cracked under the maximum stress level, while the layer beneath it experienced plastic deformation. A comparison has been made between the Basquin equation and a statistical machine learning model (for a limited amount of data) to incorporate the impact of surface treatment on predicting fatigue lifetime, and the random forest regressor model would be able to predict the lifetime with the accuracy of R2= 87% which was much higher than the classical model.

The effect of variable humidity on corrosion fatigue of AA7085-T7451 with surface salt deposits

Corrosion fatigue (CF) crack growth is quantified as a function of relative humidity (RH) using AA7085-T7451 samples with NaCl deposited to understand the effect of deliquesced surface electrolyte droplets on CF performance when humidity varies. Fracture mechanics testing holding mechanical driving forces for cracking constant and incrementally increasing humidity show that crack growth rate (da/dN) more than doubles once RH moves above 78–80% RH. When decreasing RH, some amount of drying below the efflorescence RH (ERH) and/or a sufficient time is needed to pass in order for da/dN to return to that expected for a dry crack tip. All in all, this study establishes time of crack tip wetness as an important parameter for predicting fatigue lifetimes in atmospheric conditions, a parameter that cannot be solely predicted by RH, as accelerated cracking can continue for a limited amount of time even when RH is brought below the ERH.

Statistical Lifetime of Composites Subjected to Random and Ordered Block Loadings

ABSTRACTThis study presents a procedure based on constant amplitude (CA) fatigue data to predict the statistical fatigue lifetime of glass/orthopolyester composites subjected to repeated ordered and random two, three, and six sequences of block loadings. A numerical routine was developed to detect cycle‐by‐cycle the statistical strength degradation progression until failure, assuming that the strength at the end of a block cycle equals the strength at the start of the successive one and that the individual samples' static strength, the amount of degraded strength, and fatigue life share the same rank in their respective cumulative distribution function. Predictions conform to the statistically undetectable loading sequence effects and lightly overestimate the lifetimes of random and ordered high‐to‐low (1/100 cycles) repeated two‐block loadings. The vanishing effect of the loading sequence when the block extents remain fixed, the block extent effects for a given three‐block sequence, and the lifetimes of three‐block loadings were fully predicted. The six‐block sequence's experimental lifetimes with different block loading orders and block extent fell within the predicted lifetimes' cumulative distribution function. A reliable damage rule based on residual strength was proposed and compared to the Miner's rule.

High temperature fatigue behavior of coated and uncoated nickel-based single crystal superalloy DD6: Microstructures evolution, damage mechanisms and lifetime prediction

Thermal barrier coatings (TBCs) are widely used to further extend the lifetime of turbine blades by protecting the blades from high temperature corrosion and oxidation. However, the mechanical behavior of turbine blades is obviously affected by the TBCs. In this study, microstructures evolution, damage mechanisms and life prediction of coated and uncoated nickel-based single crystal (NBSX) superalloy DD6 under isothermal fatigue load were investigated at 980 °C. The effects of TBCs on fatigue failure behavior and lifetime of DD6 were addressed. The results showed that the fatigue lifetime reduced with the increase of load. The effect of TBCs on the fatigue lifetime was related to the stress amplitude, as the effect was beneficial at high stress but almost negligible at low stress. Fracture morphologies showed that the cracks more likely initiated and propagated from basal defects for both coated and uncoated DD6, and the microstructure evolution also showed stress amplitude dependence. The crack density of uncoated DD6 increased first and then decreased with the increase of stress amplitude. However, the TBCs reduced the number of cracks that penetrate into the DD6 substrate, and the stress amplitude exerted a significant effect on crack propagation paths. In addition, the rafting behaviors of the DD6 substrate of coated and uncoated samples was compared, and results showed that TBCs could reduce the rafting degree of DD6. Finally, the fatigue lifetime of coated samples was predicted based on the modified Basquin model, and the prediction results fitted well with the experimental results.

Elevated-temperature performances of Al-Si-Cu casting alloys for cylinder head applications

In this study, high-temperature properties of two newly developed Al-Si-Cu alloys (2Cu and 3.5Cu alloys) were investigated and compared to the commercial-grade A356 + 0.5Cu alloy (R alloy). 3.5Cu alloy exhibited the highest strength, outperforming R alloy by over 50 MPa at room temperature and by more than 20 MPa at elevated temperatures in ultimate tensile strength. However, R alloy demonstrated three to four times higher elongation than 3.5Cu alloy at room temperature, though this difference diminished at high temperatures. The minimum creep rate of 3.5Cu alloy was 2.4 times lower than that of 2Cu alloy and 14.5 times lower than that of R alloy, showing the superior creep resistance. Under low cycle fatigue loadings, the fatigue lifetimes of R and 2Cu alloys were similar, and slightly longer than that of 3.5Cu alloy. Conversely, in the high cycle fatigue regime, 3.5Cu alloy exhibited the highest fatigue resistance, followed by 2Cu and R alloys. The superior high-temperature performances of 3.5Cu alloy were attributed to the enhanced thermal stability of θ' precipitates compared to β' precipitates in R alloy, as confirmed during long-term thermal exposures at 250 and 300 °C. These findings suggest that 3.5Cu alloy is a promising candidate to replace the traditional A356 + 0.5Cu alloy for cylinder head applications.

Mechanical Properties and Fatigue Life Evaluation under High Temperature and Shot Peening Application using AA7001

In some applications, AA7001 may be subjected to high temperature and fatigue. This interaction leads to varying the mechanical and fatigue properties of the above alloy. This work deals with the effects of tensile properties and constant fatigue amplitude performance. Aluminum alloys have a low specific strength, are simple to produce, and are lightweight, which has made them popular in the construction, automotive, marine, and aviation industries. The history of stress and temperature applied to the component has a significant impact on the time-dependent process of creep and strain damage. The purpose of this research is to investigate the behavior of AA7001-T6 when two phenomena, high temperatures creep and fatigue, are combined. Compared to the fatigue life interaction employing shot peening thereby, the fatigue lifetimes were The influence of shot peening on the mechanical and fatigue characteristics of AA7001-T6 was investigated utilizing four different temperatures, including RT, SP+RT, 330°C, and SP+330°C. It has been observed The application of 330°C to the tensile process lowered the ultimate tensile strength of UTS and YS by 21.9 % and 22.3 %, respectively. Shot peening improved the aforesaid percentage, lowering it to 19.2 % and 19.7%, respectively. At a stress level of 400MPa, fatigue life was lowered by 18.18 % owing to an increased temperature of 330°C, and this percentage was reduced to 10.16 % due to creating the compressive residual stresses (CRS) (SP). At (RT), the fatigue strength (endurance fatigue limit) was 229 MPa, but after Shot Peening, it improved to 237 MPa. At 330°C, shot peening increased the improved fatigue limit from 217MPa to 229MPa, resulting in a 5.24 % improvement.

Ultrasonic fatigue of superelastic Nitinol and in situ synchrotron observation of strain and damage

Superelastic Nitinol was tested at ultrasonic frequency in the high and very high cycle fatigue regime. Thin sheet specimens were initially preloaded to mimic crimping and deployment of Nitinol implants, which lead to a sample in a multi-phase state with martensitic phase in the middle and adjacent zones with austenitic phase. In situ synchrotron X-ray diffraction (XRD) was used to monitor cyclic strains over an entire ultrasonic cycle, and to compare the results with low frequency loading. Both austenitic and martensitic regimes showed similar sinusoidal elastic deformation at cycling frequencies 0.1 Hz and 18.3 kHz, and strains were comparable over the entire gauge section of the specimen. XRD data showed progressive growth of austenitic bands in formerly martensitic areas with increasing numbers of ultrasonic cycles. This increased specimen stiffness and cyclic stresses promoting crack initiation, which nearly exclusively occurred at cracked surface inclusions. The strain versus fatigue lifetime diagram shows a pronounced change in slope below 106 cycles. The overlapping properties measured at low and ultrasonic frequency demonstrate that ultrasonic fatigue testing is in principle appropriate for rapid characterization of the cyclic properties of Nitinol.

Study on the improvement of fatigue and crack resistance of semi-flexible pavement materials using the mixing -molding method

This study focuses on two significant issues pertaining to conventional grout-molded semi-flexible pavement material (P-SFP): the difficult of achieving a high grouting rate and the limited scope for enhancing asphalt content, both of which contribute to the poor crack resistance of the SFP. To address these problems, the Mixed-Molding Method Semi-Flexible Pavement Material (M-SFP) is proposed, which utilizes a combination of mixed-molding method to enhance the crack resistance and fatigue life of SFP. In order to investigate the effects of asphalt film thickness and gradation type, four different gradations and five different asphalt contents of M-SFP were designed based on the volume filling theory. The effects of asphalt film thickness and gradation type on the cracking resistance and fatigue life of M-SFP were investigated through various tests, including low-temperature bending, semi-circular bending tensile, and four-point bending fatigue test. The results were then compared with those of the control P-SFP. The test results show that the strain energy density of M-SFP is increased by 24.9 % and the fracture energy is increased by 52.1 % compared with the conventional P-SFP; the number of fatigue life times under 200με, 225με, and 250με microstrain are increased by 53.6 %, 41.3 %, and 47.3 %, respectively. Based on crack resistance test results, it is recommended that the design asphalt film thickness of M-SFP exceed 10μm. Furthermore, measurements of the air void content reveal that the M-SFP exhibits significantly better compactness compared to the P-SFP. In conclusion, it shows that the Mixing-Molding method can be used to obtain semiflexible pavement materials with higher asphalt dosage, better cracking resistance, better degree of compactness, and longer fatigue life. In addition, the correlation analysis between the cracking resistance results and the rigid-flex ratio indicates that the recommended design rigid-flex ratio for SFP should be less than 2.06.

Improvement mechanism of fretting fatigue lifetime of turbine dovetail tenon by shot peening combined with CuNiIn coating at 500 °C

In this study, turbine dovetail tenon specimens made of iron-based superalloy were composite treated by shot peening and CuNiIn coating, and the fretting fatigue performance at room temperature and 500 °C high temperature was investigated. The surface integrity of the composite-treated dovetail specimens and the wear, fracture morphology, and microstructure after the fretting fatigue tests were characterized. The results showed that the composite treatment of shot peening and CuNiIn coating made the surface roughness of iron-based superalloy from 0.405 μm to 11.279 μm, 46 % reduction in surface hardness and the residual compressive stress layer of about 100 μm was introduced. Compared with the as-received (AS) specimens, the fretting fatigue lifetime of shot peening and CuNiIn coating composite treatment (SC) specimens was increased by 437 % at room temperature, and the fretting fatigue lifetime of SC specimens at high temperature was reduced by 54 % compared with that at room temperature. The cracks in SC specimens were still initiated by multiple fatigue sources, but the number of crack sources decreased and the position of crack sources moved down. At room temperature, CuNiIn coating first underwent shear grinding and then entered delamination wear, while at high temperature, the presence of a large number of coating oxides would lead to serious abrasive wear of CuNiIn coating. Fretting fatigue resulted in obvious orientation differences in the contact region, and the formation and propagation of cracks were related to the plastic deformation and dislocation accumulation of the contact region. The good plasticity of CuNiIn coating is an important reason why it can improve the fretting fatigue performance. The surface hardening caused by shot peening and the introduction of residual compressive stress layer can effectively inhibit crack initiation and propagation. The composite treatment of shot peening and CuNiIn coating can effectively improve the fretting fatigue performance of the dovetail structure of superalloy.

Study on vibration fatigue of lifeguard in a metro bogie and methodology for damage estimation based on the measured acceleration

The lifeguard is more like a cantilever beam installed on the end of bogie frame, used to remove foreign body on the rail. Due to severe vibration condition, the lifeguard has been reported to be subjected to fatigue failure by railway operators. This paper thus studied on fatigue failure mechanisms of lifeguard through both the field test and numerical simulation. In the field test, the vibration acceleration and dynamic stress developed on the lifeguard were measured to identify main contributors to the fatigue failure. The test results showed that the structural resonance arising from the rail corrugation-induced high frequency impact serves as the main causal factor. To better understanding the failure mechanism, a numerical model considering the flexibility of lifeguard was established to determine the stress field of lifeguard based on the modal method, which was further used to estimate the residual fatigue lifetime for given loading conditions. The results showed that the obtained dynamic stress for given position on lifeguard is quite comparable with those obtained through the field test. Based on the obtained dynamic stress, the fatigue damage was further estimated and concluded that the fatigue lifetime of lifeguard is much less than the designed lifetime under the considered loading condition. The rail grinding and the structural improvement are thus suggested to mitigate the vibration fatigue of lifeguard.

A data‐assisted physics‐informed neural network (DA‐PINN) for fretting fatigue lifetime prediction

AbstractIn this study, we present for the first time the application of physics‐informed neural network (PINN) to fretting fatigue problems. Although PINN has recently been applied to pure fatigue lifetime prediction, it has not yet been explored in the case of fretting fatigue. We propose a data‐assisted PINN (DA‐PINN) for predicting fretting fatigue crack initiation lifetime. Unlike traditional PINN that solves partial differential equations for specific problems, DA‐PINN combines experimental or numerical data with physics equations as part of the loss function to enhance prediction accuracy. The DA‐PINN method, employed in this study, consists of two main steps. First, damage parameters are obtained from the finite element method by using critical plane method, which generates a data set used to train an artificial neural network (ANN) for predicting damage parameters in other cases. Second, the predicted damage parameters are combined with the experimental parameters to form the input data set for the DA‐PINN models, which predict fretting fatigue lifetime. The results demonstrate that DA‐PINN outperforms ANN in terms of prediction accuracy and eliminates the need for high computational costs once the damage parameter data set is constructed. Additionally, the choice of loss‐function methods in DA‐PINN models plays a crucial role in determining its performance.

Fatigue crack growth rate under mixed-mode loading conditions (I+III) of a carbide-free bainitic steel designed for rail applications

Carbide-free bainitic steel was designed for railway infrastructure application, focusing on high-speed and heavy-loaded freight tracks. Considering the complex state of stresses occurring on the rails running surface, mode III plays a significant role in the initiation and propagation of fatigue cracks of rails during service. Thus, the Fatigue Crack Growth Rate (FCGR) under mixed-mode loading conditions (I+III) was evaluated. It was revealed, that fatigue lifetime increases with loading angle modes. In the area of fatigue fracture, transgranular cracking mechanisms dominated. For the stable fatigue crack growth, a trend was observed related to the decrease in the fraction of intergranular fracture with the increasing loading angle modes (α). Secondary cracks indicated privileged cracking directions related to the crystallographic structure of bainite. The influence of the mechanical stability of retained austenite during mixed-mode FCGR requires further in-depth research. These studies contribute to understanding the factors influencing the reliability of railway tracks in terms of designing new materials and modeling the rate of crack growth to precise assessment of the life cycle of rails.

Using physics-informed neural networks to predict the lifetime of laser powder bed fusion processed 316L stainless steel under multiaxial low-cycle fatigue loading

Axial-torsional Low-Cycle Fatigue (LCF) tests were conducted under strain control on Additively Manufactured (AM) 316L stainless steel using laser powder bed fusion. The tests covered various strain amplitudes under tension-compression, proportional, and pure shear loading paths. The AM 316L stainless steel exhibited cyclic softening and transgranular cracking under all the investigated loading conditions. The presence of deposition defects, predominantly the lack of fusion type, was identified as the main factor influencing the crack initiation and propagation, as well as the scatter in the fatigue lifetime. Therefore, to account for the damaging effects of these deposition related defects on fatigue lifetime, a novel physics-informed neural network was proposed. Subsequently, this neural network was combined with the critical plane approach, based on the tensile mode of failure, in order to predict the lifetime of AM 316L stainless steel. The predicted data exhibited a good correlation with the experimental results.

Influence of connection design and material properties on stress distribution and fatigue lifetime of zygomatic implants: A finite element analysis

Zygomatic implants (ZIs) were developed as a graftless alternative to rehabilitate severely reabsorbed maxillae. This study aims to employ three-dimensional finite element analysis (FEA) to simulate the impact of external hexagonal implant connection (EHC) and internal hexagonal implant connection (IHC) on the stress distribution and fatigue lifetime within the ZI systems using parameters defined in ISO 14801:2016. Two ZI assemblies (Nobel Biocare and Noris Medical) were scanned in a micro-CT scanner and reconstructed using Nrecon software. Three-dimensional models were generated by Simpleware ScanIP Medical software. All models were exported to FEA software (ABAQUS) and subsequently to a fatigue analysis software (Fe-safe). A compressive 150 N load was applied at a 40° angle on the cap surface. A 15 Hz frequency was applied in the in silico cyclic test. The implant components had material properties of commercially pure grade 4 titanium (CPTi) and Titanium-6Aluminum-4Vanadium alloy (Ti64). Von Mises stress data, contour plots, and fatigue limits were collected and analyzed. EHC models exhibited higher peak stresses in implant components for both materials compared to IHC models. However, simulated bone support results showed the opposite trend, with higher stresses on IHCthan EHC models. The fatigue analysis revealed that assemblies with both designs exceeded ISO 14801:2016 number of cycles limits using Ti64, while CPTi groups exhibited comparatively lower worst life-repeats. In conclusion, ZIs with IHC were found to have a more homogeneous and advantageous stress distribution within both materials tested. Ti64 demonstrates a prolonged service life for both design connections.

Lifetime prediction of copper pillar bumps based on fatigue crack propagation

2.5D package realizes the interconnection of multiple dies through Si interposers, which can greatly improve the data transmission rate between dies. However, its multi-layer structure and high package density also place higher reliability requirements on the interconnection structure. As a key structure for interconnection, copper pillar bump (CPB) has small size, high heat generation, and thermal mismatch with silicon chips. The thermal fatigue failure of CPB has gradually become the main failure mode in 2.5D package. Due to the small size of CPB and the large proportion of intermetallic compound (IMC) layers, the lifetime prediction method of spherical solder joints is no longer suitable for CPB. Therefore, it is necessary to establish a fatigue lifetime prediction method for CPB. This paper establishes a method for obtaining the lifetime of CPB based on the basic theory of fatigue crack propagation. Using the extended finite element simulation method, the crack propagation lifetime of CPB under thermal cycling was obtained, and the influence of different IMC layer thickness on the fatigue lifetime of CPB was analyzed. The results indicated that the fatigue lifetime of cracks propagating in the IMC layer is lower than that of cracks propagating in the solder layer, and an increase in the thickness of the IMC layer leads to a significant decrease in the fatigue lifetime of CPB. The lifetime prediction method for CPB proposed in this paper can be used for reliability evaluation of 2.5D package, and has certain reference value for the study of the lifetime of CPB.

Impact of biological environment on bending fatigue lifetime in additive-manufactured polylactic acid fabricated by 3D-printing

Polylactic acid (PLA) has become desirable for biomedical applications, particularly implantable devices. However, the degradation of PLA in biological environments under mechanical stress remains incompletely understood and requires further investigation. This study compared the plain fatigue (PF) and the biodegraded fatigue (BDF) behavior of 3D-printed PLA. For this purpose, two sets of standard fatigue specimens were additively manufactured by the fused filament fabrication (FFF) method. One set was used for plain fatigue testing, and the other was immersed for 330 days in simulated body fluid (SBF). After immersion, the samples were dried and weighed before fatigue testing. The fully reversed rotary bending fatigue tests were conducted on both sets of specimens, and the stress-lifetime (S-N) curves were obtained. Additionally, the fatigue properties of PF and BDF specimens were evaluated. Moreover, the fracture behaviors of the materials were studied using field emission scanning electron microscopy (FESEM). The outcomes implied that the weight of the samples extended during the immersion period, primarily due to water absorption by the PLA. However, after drying, the final weights did not change compared to the weights before immersion. The SBF immersion significantly reduced the fatigue performance of the biodegraded samples comparing the PF result.

The Evolution of Surfaces on Medium-Carbon Steel for Fatigue Life Estimations

Early in fatigue life, fatigue cracks are often initiated at persistent slip bands (PSBs), which play the main role in surface evolution when the components are subjected to cyclic loading. Therefore, this paper aims to study the behavior of the surface development of medium-carbon steel, specifically 42CrMo4 (SAE 4140). Tests were conducted using tension–compression fatigue testing with stress amplitudes set at 30%, 40%, and 50% of the ultimate tensile strength (UTS); a load ratio of R = −1; and a frequency of f = 10 Hz. The ultimate number of test cycles was 2 × 105. The fatigue test specimens with as-machined surface quality (Ra < 100 nm) were tested on a servo-hydraulic push–pull testing machine, and the tests were interrupted a few times to bring the specimens out for surface measuring with a confocal microscope. The linear roughness values of the arithmetic mean deviation (Ra), maximum height (Rz), maximum profile peak height (Rp), and maximum profile valley depth (Rv) were investigated and further used to determine the roughness evolution during cyclic loading (REC) by analyzing the inclinations of the fitting curves of roughness and number-of-cycles diagrams. REC could then be used to estimate and classify the fatigue lifetime.

Influence of Non-Metallic Inclusions on Very High-Cycle Fatigue Performance of High-Strength Steels and Interpretation via Crystal Plasticity Finite Element Method

The fatigue behaviors of high-strength bearing steel were investigated with rotating bending fatigue loading with a frequency of 52.5 Hz. It was revealed that the high-strength steel tended to initiate at interior non-metallic inclusions in a very high-cycle fatigue regime. During fractography observation, it was also seen that the inclusion acting as a failure-originating site was seldom smaller than 10 μm. Moreover, prior austenite grains could also act as the originating source of failure when inclusion was absent. The crystal plasticity finite element method (CPFEM) was adopted to simulate the residual stress distribution around non-metallic inclusions of different sizes under different loading amplitudes. The accumulated plastic strain around the inclusion suggested that the existence of inclusion may reduce material strength and lead to more fatigue damage. The value of accumulated plastic strain around different inclusion sizes also resembled the crack nucleation or propagation of the materials. The simulation results also indicated that inclusions smaller than 5 μm had little influence on fatigue lifetimes, while inclusions larger than 10 μm had a significant influence on fatigue lifetimes.