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1.
Environ Res ; 259: 119523, 2024 Jul 02.
Article in English | MEDLINE | ID: mdl-38960352

ABSTRACT

Strengthening rhizosphere effects to enhance pollutant removal is a hotspot of constructed wetlands (CWs) research in recent years, and improving the root traits and metabolic capacity of macrophytes is crucial for strengthening rhizosphere effects. In the field experiment, two types of subsurface flow (SSF) CWs (CW10 and CW20, with substrate depths of 10 and 20 cm, respectively) under the vertical spatial stress of roots (VSSR) and two types of non-VSSR SSF CWs (CW40 and CW60) were adopted with Typha orientalis as cultivated plants to investigate the variability of root development, metabolism, and pollutant removal at different substrate depths. VSSR induced substantial redundant root development, which significantly increased root-shoot ratio, fine and lateral root biomass, root porosity, and root activity, with lateral and fine root biomass of CW20 reaching 409.17 and 237.42 g/m2, respectively, which were 3.18 and 5.28 times those of CW60. The radical oxygen loss (ROL) and dissolved organic carbon (DOC) levels of CW20 single plant were 1.36 and 4.57 times higher than those of CW60, respectively, and more types of root exudates were determined (e.g., aldehydes, ketones and amides). More aerobic heterotrophs (e.g., Massilia, Planomicrobium), nitrification bacteria (e.g., Ellin6067, Nitrospira), aerobic denitrification bacteria (e.g., Bacillu, Chryseobacterium, Pseudomonas) and denitrification phosphorus accumulating organisms (e.g., Flavobacterium) were enriched in the rhizosphere of CW20. This changed the main transformation pathways of pollutants and enhanced the removal of pollutants, with the COD, TN and TP average removal rates of CW20 increasing by 9.99%, 13.28% and 8.92%, respectively, compared with CW60. The ideotype root system architecture CW (RSACW; CW20) constructed in this study, which consists of a large number of fine and lateral roots, can stimulate more efficient rhizosphere effects stably and continuously.

2.
Heliyon ; 10(11): e32166, 2024 Jun 15.
Article in English | MEDLINE | ID: mdl-38912447

ABSTRACT

This study addressed the critical problem of repairing cracks in aging aircraft structures, a safety concern of paramount importance given the extended service life of modern fleets. Utilized a finite element (FE) method enhanced by the design of experiments (DOE) and adaptive neuro-fuzzy inference system (ANFIS) approaches to analyze the efficacy of piezoelectric actuators in mitigating stress intensity factors (SIF) at crack tips-a novel integration in structural repair strategies. Through simulations, we examined the impact of various factors on the repair process, including the plate, actuator, and adhesive bond size and characteristics. In this work, initially, the SIF estimation used the FE approach at crack tips in aluminum 2024-T3 plate under the uniform uniaxial tensile load. Next, numerous simulations have been performed by changing the parameters and their levels to collect the data information for the analysis of the DOE and ANFIS approach. The FE simulation results have shown that changing the parameters and their levels will result in changing of SIF. Several DOE and ANFIS optimization cases have been performed for the depth analysis of parameters. The current results indicated that optimal placement, size, and voltage applied to the piezoelectric actuators are crucial for maximizing crack repair efficiency, with the ability to significantly reduce the SIF by a quantified percentage under specific conditions. This research surpasses previous efforts by providing a comprehensive parameter optimization of piezoelectric actuator application, offering a methodologically advanced and practically relevant pathway to enhance aircraft structural integrity and maintenance practices. The study innovation lies in its methodological fusion, which holistically examines the parameters influencing SIF reduction in aircraft crack repair, marking a significant leap in applying intelligent materials in aerospace engineering.

3.
Materials (Basel) ; 17(10)2024 May 07.
Article in English | MEDLINE | ID: mdl-38793246

ABSTRACT

To understand the fracture properties of the nitrate ester plasticized polyether (NEPE) propellant, single-edge notched tension (SENT) tests were carried out at room temperature (20 °C) under different tensile rates (10-500 mm/min). The mechanical response, crack morphology, evolution path, and crack propagation velocity during the fracture process were studied using a combination of a drawing machine and a high-speed camera. The mode I critical stress intensity factor KIc was calculated to analyze the tensile fracture toughness of the NEPE propellant, and a criterion related to KIc was proposed as a means of determining whether the solid rocket motors can normally work. The experimental results demonstrated that the NEPE propellant exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. The fracture toughness of the NEPE propellant exhibited clear rate dependence. When the tensile rate increased from 10 mm/min to 500 mm/min, the magnitude of the critical stress intensity factor increased by 62.3%. Moreover, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the fracture process of the NEPE propellant, including the crack propagation speed and the load-displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

4.
Antioxidants (Basel) ; 13(4)2024 Apr 10.
Article in English | MEDLINE | ID: mdl-38671895

ABSTRACT

Under natural conditions, abiotic stresses that limit plant growth and development tend to occur simultaneously, rather than individually. Due to global warming and climate change, the frequency and intensity of heat and salt stresses are becoming more frequent. Our aim is to determine the response mechanisms of tomato to different intensities of combined heat and salt stresses. The physiological and morphological responses and photosynthesis/reactive oxygen species (ROS)-related genes of tomato plants were compared under a control, heat stress, salt stress (50/100/200/400 mM NaCl), and a combination of salt and heat stresses. The stomatal conductance (gs) of tomato leaves significantly increased at a heat + 50 mM NaCl treatment on day 4, but significantly decreased at heat + 100/200/400 mM NaCl treatments, compared with the control on days 4 and 8. The O2·- production rate of tomato plants was significantly higher at heat + 100/200/400 mM NaCl than the control, which showed no significant difference between heat + 50 mM NaCl treatment and the control on days 4 and 8. Ascorbate peroxidase 2 was significantly upregulated by heat + 100/200/400 mM NaCl treatment as compared with heat + 50 mM NaCl treatment on days 4 and 8. This study demonstrated that the dominant effect ratio of combined heat and salt stress on tomato plants can shift from heat to salt, when the intensity of salt stress increased from 50 mM to 100 mM or above. This study provides important information for tomato tolerance improvement at combined heat and salt stresses.

5.
Heliyon ; 10(8): e29423, 2024 Apr 30.
Article in English | MEDLINE | ID: mdl-38644892

ABSTRACT

In order to improve the accuracy of stress intensity factors (SIFs) calculated by traditional boundary element methods (BEM), the multi-domain wavelet boundary element method (WBEM) is proposed. Firstly, by adjusting the nodes of the B-spline wavelet element on the interval, crack-tip elements are constructed. Since B-spline wavelet on the interval (BSWI) has excellent compact support characteristics and is particularly suitable for describing solution domains with large gradient changes, the constructed crack-tip can reduce the numerical oscillation effect near the crack tip. Secondly, the crack-tip elements are implemented into WBEM. And the combination of WBEM and multi-domain technology can effectively handle interface cracks. Thirdly, the crack problem solving strategy based on multi-domain WBEM can directly evaluate the SIFs of cracks. Finally, several numerical examples involving homogeneous media and bi-material models are given to verify that the proposed method is simple and highly accurate.

6.
Behav Res Ther ; 177: 104550, 2024 Jun.
Article in English | MEDLINE | ID: mdl-38688821

ABSTRACT

BACKGROUND: Current research is moving from studying cognitive biases and maladaptive emotion regulation (ER) as relatively stable phenomena contributing to affective disturbances, adopting ecological methodologies, such as Experience Sampling Methods (ESM). However, there is still limited ESM evidence on the interactions between stress and ER strategies' use, and negative interpretation biases, regarding their relations with momentary affective states. In this study, we used a new ESM design to disentangle the contextual, regulatory and cognitive processes implicated in daily affective experiences. METHOD: A sample of 103 participants completed an ESM study (3 times a day for 10 days) that included self-reports of momentary affect, stress intensity, ER strategies' use and a cognitive task measuring momentary negative interpretation biases. RESULTS: Multilevel analyses supported significant interactions of both rumination and worry with stress intensity, to account for momentary higher negative and lower positive affect levels. Furthermore, higher state negative interpretation bias levels uniquely predicted both higher negative and lower positive momentary affect levels. CONCLUSION: This study implemented a novel online cognitive task within an ESM procedure, which helped to disentangle how contextual ER strategies' use and momentary cognitive biases uniquely relate to affective experiences in daily life.


Subject(s)
Affect , Cognition , Ecological Momentary Assessment , Emotional Regulation , Stress, Psychological , Humans , Female , Male , Adult , Young Adult , Stress, Psychological/psychology , Adolescent , Anxiety/psychology , Self Report , Middle Aged , Rumination, Cognitive/physiology , Activities of Daily Living/psychology
7.
Materials (Basel) ; 16(23)2023 Nov 24.
Article in English | MEDLINE | ID: mdl-38068045

ABSTRACT

In this paper, the application of the strong-form finite block method (FBM) to three-dimensional fracture analysis with functionally graded materials is presented. The main idea of the strong-form FBM is that it transforms the arbitrary physical domain into a normalized domain and utilizes the direct collocation method to form a linear system. Using the mapping technique, partial differential matrices of any order can be constructed directly. Frameworks of the strong-form FBM for three-dimensional problems based on Lagrange polynomial interpolation and Chebyshev polynomial interpolation were developed. As the dominant parameters in linear elastic fracture mechanics, the stress intensity factors with functionally graded materials (FGMs) were determined according to the crack opening displacement criteria. Several numerical examples are presented using a few blocks to demonstrate the accuracy and efficiency of the strong-form FBM.

8.
Materials (Basel) ; 16(24)2023 Dec 11.
Article in English | MEDLINE | ID: mdl-38138745

ABSTRACT

This paper presents an extensive literature review focusing on the utilisation of crack tip plasticity as a crucial parameter in determining and enhancing crack growth models. The review encompasses a comprehensive analysis of various methodologies, predominantly emphasising numerical simulations of crack growth models while also considering analytical approaches. Although experimental investigations are not the focus of this review, their relevance and interplay with numerical and analytical methods are acknowledged. The paper critically examines these methodologies, providing insights into their advantages and limitations. Ultimately, this review aims to offer a holistic understanding of the role of crack tip plasticity in the development of effective crack growth models, highlighting the synergies and gaps between theoretical, experimental, and simulation-based approaches.

9.
Materials (Basel) ; 16(18)2023 Sep 21.
Article in English | MEDLINE | ID: mdl-37763620

ABSTRACT

Selective laser melting is a form of additive manufacturing in which a high-power density laser is used to melt and fuse metallic powders to form the final specimen. By performing fatigue and tensile tests under various loading conditions, the study sought to establish the impact of internal defects on the specimens' fatigue life. Scanning electron microscopy and finite element simulation were conducted to determine the defect characteristics and the stress intensity factor of the specimens. Four different methods were used to determine the intrinsic defect length of the specimen, using data such as grain size, yield strength, and hardness value, among others. Kitagawa-Takahashi and El-Haddad diagrams were developed using the results. A correction factor hypothesis was established based on the deviation of measured data. Using Paris law, fatigue life was determined and compared to the experimental results later. The study aims to select one or more approaches that resemble experimental values and comprehend how internal defects and loading situations affect fatigue life. This study's findings shed light on how internal defects affect the fatigue life of selective laser-melted AlSi10Mg specimens and can aid in improving the fatigue life prediction method of additively manufactured components, provided an appropriate intrinsic crack criterion is selected.

10.
Materials (Basel) ; 16(12)2023 Jun 13.
Article in English | MEDLINE | ID: mdl-37374532

ABSTRACT

Over the past four decades, the use of composite materials for the repair of cracked structural plates with glued patches has been extensively studied. Attention has been focused on determining a mode-I crack opening displacement, which is important in tension load and in preventing the failure of a structure due to small damages. Therefore, the significance of conducting this work is to determine the mode-I crack displacement of the stress intensity factor (SIF) using analytical modeling and an optimization method. In this study, an analytical solution was obtained for an edge crack on a rectangular aluminum plate with single- and double-sided quasi-isotropic reinforcing patches, using linear elastic fracture mechanics and Rose's analytical approach. Additionally, an optimization technique with the Taguchi design was used to define the optimal solution of the SIF from the suitable parameters and levels. As a result, a parametric study was conducted to assess the mitigation of the SIF using analytical modeling, and the same data were used to optimize the results via the Taguchi design. This study successfully determined and optimized the SIF, demonstrating an energy- and cost-efficient approach to address damage control in structures.

11.
Materials (Basel) ; 16(10)2023 May 09.
Article in English | MEDLINE | ID: mdl-37241235

ABSTRACT

The efficient crack eliminated stop-hole measure was proposed to repair and reduce the stress concentration associated fracture risk of the corrugated plate girders by setting it at the critical joint of flange plate with tightened bolts and gaskets under preloading. To investigate the fracture behaviour of these repaired girders, parametric finite element analysis was conducted, focusing on the mechanical feature and stress intensity factor of crack stop-hole in this paper. The numerical model was verified against experimental results first, and then the stress characteristics due to the presence of crack open-hole were analysed. It was found that the moderate-sized open-hole was more effective than the over-sized open-hole in the reduction of stress concentration. For the model with prestressed crack stop-hole through bolt preloading, the stress concentration was nearly 50% with the prestress around open-hole increased to 46 MPa, but such a reduction is inconspicuous for even higher prestress. Relatively high circumferential stress gradients and the crack open angle of oversized crack stop-holes were decreased owing to additional prestress effects from the gasket. Finally, the shift from the original tensile area around the edge of the crack open-hole that was prone to fatigue cracking to a compression-oriented area is beneficial for the reduction of stress intensity factor of the prestressed crack stop-holes. It was also demonstrated that the enlargement of crack open-hole has limited influence on the reduction of stress intensity factor and crack propagation. In contrast, higher bolt prestress was more beneficial in consistently reducing the stress intensity factor of the model with the crack open-hole, even containing long crack.

12.
Materials (Basel) ; 16(10)2023 May 11.
Article in English | MEDLINE | ID: mdl-37241295

ABSTRACT

The finite element method was used to investigate the effect of the stress ratio on fatigue crack propagation behavior within the framework of the linear elastic fracture mechanics theory. The numerical analysis was carried out using ANSYS Mechanical R19.2 with the unstructured mesh method-based separating, morphing, and adaptive remeshing technologies (SMART). Mixed mode fatigue simulations were performed on a modified four-point bending specimen with a non-central hole. A diverse set of stress ratios (R = 0.1, 0.2, 0.3, 0.4, 0.5, -0.1, -0.2, -0.3, -0.4, -0.5), including positive and negative values, is employed to examine the influence of the load ratio on the behavior of the fatigue crack propagation, with particular emphasis on negative R loadings that involve compressive excursions. A consistent decrease in the value of the equivalent stress intensity factor (ΔKeq) is observed as the stress ratio increases. The observation was made that the stress ratio significantly affects both the fatigue life and the distribution of von Mises stress. The results demonstrated a significant correlation between von Mises stress, ΔKeq, and fatigue life cycles. With an increase in the stress ratio, there was a significant decrease in the von Mises stress, accompanied by a rapid increase in the number of fatigue life cycles. The results obtained in this study have been validated by previously published literature on crack growth experiments and numerical simulations.

13.
Materials (Basel) ; 16(9)2023 Apr 26.
Article in English | MEDLINE | ID: mdl-37176282

ABSTRACT

Impact energy tests are an efficient method of verifying adequate toughness of steel prior to it being put into service. Based on a multitude of historical correlations between impact energy and fracture toughness, minimum impact energy requirements that correspond to desired levels of fracture toughness are prescribed by steel bridge design specifications. Research characterizing the fracture behavior of grade 485 and 690 (70 and 100) high-performance steel utilized impact, fracture toughness, and crack arrest testing to verify adequate performance for bridge applications. Fracture toughness results from both quasi-static and dynamic stress intensity rate tests were analyzed using the most recently adopted master curve methodology. Both impact and fracture toughness tests indicated performance significantly greater than the minimum required by material specifications. Even at the AASHTO Zone III service temperature, which is significantly colder than prescribed test temperatures, minimum average impact energy requirements were greatly exceeded. All master curve reference temperatures, both for quasi-static and dynamic loading rates, were found to be colder than the Zone III minimum service temperature. Three correlations between impact energy and fracture toughness were evaluated and found to estimate reference temperatures that are conservative by 12 to 50 °C (22 to 90 °F) on average for the grades and specimen types tested. The evaluation of two reference temperature shifts intended to account for the loading rate was also performed and the results are discussed.

14.
J Mech Behav Biomed Mater ; 142: 105818, 2023 06.
Article in English | MEDLINE | ID: mdl-37068432

ABSTRACT

OBJECTIVE: This work used 3D finite element analysis (FEA) to analyze and directly compare the stress intensity factor (SIF) and stress distribution at the crack tip of identical cracked tooth models restored with different materials and crown parameters. METHODS: A 3D model of the cracked tooth was generated. Then, we applied 25 restorative models, including three parameters (shoulder height, width, and degree of polymerization), five restorative materials (GC, IPS, LU, ZC, VE), and two combinations of types of cement (RMGIC and GIC). An occlusal load of 800N was applied to the spherical part along the longitudinal axis. The stress distribution of the preparation and the SIF of the crack tip was analyzed. RESULTS: The crack tip SIF was minimal for a shoulder height offset of 0.8 mm (P = 0.032), a shoulder width of 0.6 mm (P = 0.045), a crown material of ZC (P < 2e-16), and a cement material of RMGIC (P < 0.05), respectively. In contrast, the effect of different polymerization degrees on SIF was insignificant (P = 0.95). CONCLUSION: Our results suggest that the selection of a larger modulus of elasticity (MOE) material for the crown, the preparation of a smaller shoulder width within a safe range, a reasonable increase in the crown length, and the selection of adhesive materials with high fracture toughness are favorable methods to prevent further crack extension.


Subject(s)
Crowns , Molar , Finite Element Analysis , Elasticity , Glass Ionomer Cements , Dental Stress Analysis , Materials Testing
15.
Materials (Basel) ; 16(4)2023 Feb 14.
Article in English | MEDLINE | ID: mdl-36837212

ABSTRACT

Over the last four decades, numerous studies have been conducted on the use of bonded composite repairs for aircraft structures. These studies have explored the repair of damaged plates through experimental, numerical, and analytical methods and have found that bonded composite repairs are effective in controlling crack damage propagation in thin plates. The use of double-sided composite repairs has been found to improve repair performance within certain limits. This study focuses on these limits and optimizes double-sided composite repairs by varying adhesive bond and composite patch parameters. The optimization process begins with a finite element analysis to determine the stress intensity factor (SIF) for various variables and levels, followed by the application of the Taguchi method to find the optimal combination of parameters for maximizing the normalized SIF. In conclusion, we successfully determined the stress intensity factor (SIF) for various variations and normalized it for optimization. An optimization study was then performed using the Taguchi design and the results were analyzed. Our findings demonstrate the repair performance of bonded composite patches using a cost-effective and energy-efficient approach.

16.
Materials (Basel) ; 17(1)2023 Dec 30.
Article in English | MEDLINE | ID: mdl-38204059

ABSTRACT

The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm's attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm.

17.
Materials (Basel) ; 15(23)2022 Dec 02.
Article in English | MEDLINE | ID: mdl-36500087

ABSTRACT

The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress-strain state of a piecewise homogeneous linear-elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic-numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress-strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation.

18.
Materials (Basel) ; 15(24)2022 Dec 19.
Article in English | MEDLINE | ID: mdl-36556897

ABSTRACT

In this paper, stress intensity factor (SIF) solutions are numerically obtained for notched bars subjected to tensile loading containing an eccentric circular inner crack located in the cross-section corresponding to the notch root. The finite element method and the J-integral have been used to obtain the SIF and to analyze the effect on it of three elliptical notch geometries (of equal radial depth). The results show how the SIF is greater in the notched bars than in the smooth bar and within the former when the axial semi-axis of the notch rises, its effect being greater as the diameter and eccentricity of the inner crack increase. In addition, the fatigue growth of an eccentric crack induces an increase in such eccentricity, greater as the notch axial semi-axis increases. The cause of these phenomena can be attributed to the constraint loss caused by the notch, which also facilitates bending of the specimen due to the asymmetry generated by the crack eccentricity.

19.
Metabolites ; 12(12)2022 Nov 29.
Article in English | MEDLINE | ID: mdl-36557228

ABSTRACT

Drought intensity modifies the assimilatory pathway of glutathione (GSH) synthesis. Abscisic acid (ABA) is a representative signaling hormone involved in regulating plant stress responses. This study aimed to investigate an interactive regulation of sulfate and/or ABA in GSH metabolism and redox. The drought-responsive alterations in sulfate assimilation and GSH-based redox reactions were assessed relative to ABA responses on the time-course of drought intensity. Drought-responsive H2O2 concentrations were divided into two distinct phases-an initial 4 days of no change (Ψw ≥ -0.49 MPa) and a phase of higher accumulation during the late phase of the drought (days 10-14; Ψw ≤ -1.34 MPa). During the early phase of the drought, GSH/GSSG redox state turned to the slightly reduced state with a transient increase in GSH, resulting from a strong activation of H2O2 scavenging enzymes, ascorbate peroxidase (APOX) and glutathione reductase (GR). The late phase of the drought was characterized by a decrease in GSH due to cysteine accumulation, shifting GSH- and NADPH-based redox states to higher oxidization, increasing sulfate and ABA in xylem, and causing ABA accumulation in leaves. Regression analysis revealed that sulfate in xylem sap was positively correlated with H2O2 concentrations and ABA was closely related to decreases in the GSH pool and the oxidation of GSH catalyzed by glutathione peroxidase (GPOX). These results indicate that drought-induced oxidation proceeds through the suppression of GSH synthesis and further GSH oxidation in a sulfate-activated ABA-dependent manner.

20.
Materials (Basel) ; 15(21)2022 Oct 30.
Article in English | MEDLINE | ID: mdl-36363222

ABSTRACT

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples.

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