Engineering Reports
Volume 7, Issue 3 e70053
RESEARCH ARTICLE
Open Access

Fatigue Analysis and Load Spectrum Generation for Wing-Fuselage Lug Joint With a Focus on Human Safety Transport Category Aircraft

Rajadurai Murugesan, 

Rajadurai Murugesan

Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, Karnataka, India

Contribution: ​Investigation, Formal analysis, Data curation, Writing - original draft

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Srikanth Holalu Venkataraman, 

Srikanth Holalu Venkataraman

Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, Karnataka, India

Contribution: Writing - review & editing, Software, Visualization

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Pradeep Kumar Sahoo, 

Pradeep Kumar Sahoo

Structural Technological Division, CSIR—National Aerospace Laboratories, Bangalore, Karnataka, India

Contribution: Writing - review & editing, Resources, Supervision

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Praveena Bindiganavile Anand, 

Praveena Bindiganavile Anand

Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, Karnataka, India

Contribution: Conceptualization, Funding acquisition, ​Investigation, Writing - original draft, Writing - review & editing, Visualization, Validation, Methodology, Software, Formal analysis, Project administration, Resources, Supervision, Data curation

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Rithick Rithick, 

Rithick Rithick

Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, Karnataka, India

Contribution: Conceptualization, Writing - review & editing, Methodology

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Muhammad Imam Ammarullah, 

Corresponding Author

Muhammad Imam Ammarullah

Department of Mechanical Engineering, Faculty of Engineering, Universitas Diponegoro, Semarang, Central Java, Indonesia

Undip Biomechanics Engineering & Research Centre (UBM-ERC), Universitas Diponegoro, Semarang, Central Java, Indonesia

Correspondence: Muhammad Imam Ammarullah ([email protected])

Contribution: Writing - review & editing, Validation, Project administration

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First published: 18 March 2025
https://doi.org/10.1002/eng2.70053

Funding: The authors received no specific funding for this work.

ABSTRACT

This research work focuses on fluctuating load spectrum generation and fatigue analysis of a wing-fuselage attachment lug joint, in accordance with the requirements outlined in 14 CFR Part 25 for transport category aircraft. The study involves the generation of a fatigue load spectrum using an exceedance curve, followed by finite element analysis of a simple round-ended lug. The exceedance curve is a statistical tool used to represent the probability of a variable exceeding a particular threshold over a specified time period. It is particularly useful in fatigue analysis as it helps quantify the likelihood of stress levels surpassing critical limits, aiding in the assessment of structural integrity and durability. The CAD model of the lug is created in CATIA, and the corresponding FE model is obtained using Altair HyperMesh. The investigation pertains to a turboprop aircraft weighing approximately 25,000 kg and accommodating 70–90 seats, with ATR 72 and Dash Q 400 being the prominent choices in this category within India. Mission Profiles for these aircraft are obtained from the Directorate General of Civil Aviation (DGCA) website, utilizing scheduled flight data. To ensure the structural integrity of the lug, a static analysis is performed for FE model convergence, leading to the determination of stress concentration factors. Subsequently, fatigue analysis is conducted using Nastran Embedded Fatigue (NEF), considering constant amplitude loading with stress ratios of −1 and 0.1. the fatigue life of the component is predicted based on Goodman and Gerber failure criteria. The analysis yields crucial insights into the fatigue life of the lug and its damage accumulation over time.

1 Introduction

Human safety is a paramount consideration in the design, manufacturing, and maintenance of aircraft. Among the critical factors influencing safety is the fatigue behavior of aircraft components, which can lead to progressive and often undetectable damage under repeated loading conditions [1-3]. Fatigue failures, if not addressed, pose significant risks to structural integrity, potentially compromising an aircraft's operational safety [4-6]. By identifying potential failure points and assessing damage tolerance, fatigue analysis prevents catastrophic failures, thereby safeguarding passengers and crew. This approach underpins the industry's commitment to achieving the highest safety standards while maintaining efficiency and performance [1].

Fatigue analysis is crucial in aircraft design to ensure structural integrity and safety, as it helps predict and prevent potential failures caused by cyclic stresses [7-11]. In addition, it enhances environmental sustainability by optimizing materials and extending component lifespan while maintaining passenger health and safety standards [12-15].

Lug joints, particularly wing-fuselage attachments, are critical elements in aerospace structural applications that provide structural integrity and load transfer between these primary structural components [16, 17]. Understanding the behavior and predicting the fatigue life of lug joints is of utmost importance to ensure the overall reliability and safety of aircraft structures. This research aims to contribute to the existing knowledge by providing comprehensive insights into the behavior of lug joints used for wing-fuselage attachments. The FEA and fatigue analysis results will help validate the structural performance of these critical components, thereby enhancing the overall safety and performance of complex structures [19, 18, 20].

The primary objective of this research is to perform an FEA analysis of lug joints subjected to the load spectrum derived from a specific load exceedance spectrum representative of realistic flight conditions. The construction of this load spectrum is tailored to the unique mission profile data of a specific aircraft. This customization is essential due to the distinct mission profiles that vary among different aircraft, influenced by diverse environmental conditions and operational requirements. By utilizing Altair HyperMesh and MSC Nastran Embedded Fatigue (NEF), the mechanical response of the lug joints under these loads can be simulated and evaluated. The analysis will consider factors such as material properties, geometric configurations, and load distribution as inputs to assess the potential fatigue life and damage of the component accurately.

2 Literature Survey

2.1 Mission Profile Data

The frequencies of operation for ATR 72 aircraft at different sector lengths are obtained from the DGCA website [1]. The data available on the website specifically pertain to the aircraft operations in India by airlines such as SpiceJet, IndiGo, Alliance Air, and TrueJet, as of March 31, 2019.

2.2 Load Spectrum Generation

The AFGROW data hand book [2] provides comprehensive information on the utilization of load exceedance spectra to develop fatigue load sequences. It offers a detailed procedure for deriving load sequences using load exceedance spectra specifically for aircraft wings of various categories. The handbook extensively explains the concepts of number of exceedances and occurrences of a load, which are derived from the mission profile details of an aircraft. The typical load spectrum plot for transport category aircraft is derived from this data handbook for deriving the load spectrum.

2.3 Fatigue Analysis Using the Finite Element Method

The journal article by Shridhar [3] focuses on conducting a fatigue analysis of the wing-fuselage lug section of a transport aircraft. The research commences with a static analysis, considering three different radius ratios of the lug (1.5, 2, and 3) under a test load of 50 kN. The study concludes that the lug with a radius ratio of 3 exhibits lower stress concentration at the hole section compared to the other ratios.

2.4 Importance of Stress Concentration Factor

Peterson's stress concentration factors textbook [4] serves as a valuable resource, offering in-depth insights into the geometric parameters of diverse lug configurations and their consequential effects. This textbook also encompasses essential formulas for determining the stress concentration factor and nominal stresses, particularly applicable to simple rounded lugs.

2.5 Technical Assessment of Fatigue Analysis

Shigley's Mechanical Engineering Design textbook [5] provides a comprehensive exploration of failures resulting from fatigue loading. It extensively covers the properties of stress cycles and their distinct characteristics. In addition, the book thoroughly delves into the concept of fatigue, offering in-depth discussions on design philosophies and failure criteria. This comprehensive coverage has significantly fortified the theoretical foundation of the research [13-17].

3 Methodology

3.1 Mission Profile Data

Table 1 shows the flight frequency and duration of ATR 72 aircraft as provided on the DGCA website. The time for all the mission operations is derived and approximated from the flight schedule documents.

TABLE 1. Flight frequency and duration of ATR 72 for various sector lengths [1].
Sector length (NM) Cruise altitude (ft) Cabin differential pressure (psi) Percentage of total operations (%) Time (min)
Taxi (take off) Mission (climb + cruise +  descent) Taxi (landing) Total
100 15,000 2.62 2 45 35 30 110
150 20,000 4.16 19 45 50 30 125
200 22,000 4.8 22 45 64 30 139
250 25,000 5.46 27 45 77 30 152
300 25,000 5.46 20 45 85 30 160
350 25,000 5.46 5 45 96 30 171
400 25,000 5.46 4 45 107 30 182
450 25,000 5.46 1 45 118 30 193

3.2 Exceedance and Occurrence Data

The typical exceedance spectra for a transport category aircraft are derived from the AFGROW data handbook [2]. In this context, the number of occurrences is determined through a stepped approximation method of the spectrum. The accuracy of this approximation in capturing the spectrum shape improves as the discrete load levels become more numerous. To achieve this precision, we employ a step size of 0.25, as outlined in Table 8. The resulting occurrence plot is visually presented in Figure 1, generated using the Matplotlib library.

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FIGURE 1
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Occurrence versus load factor for transport category, plotted using matplotlib.

3.3 Lug Joint Geometry, CAD Model, and Material Properties

According to [3], a radius ratio of 3 was selected for the lug model. The 7075T-6 alloy, which primarily consists of aluminum (87.1–91.4 wt%) and zinc (5–6.1 wt%), was chosen for this lug joint. According to ASTM documentation, aluminum–zinc alloys tend to exhibit superior fatigue life for a lug joint compared to aluminum–magnesium and aluminum–manganese alloys. Furthermore, 7075T-6 demonstrates favorable fatigue strength when compared to aluminum 2024-T351, aluminum 2014-T6, and 2014-T651 alloys. Figure 2 illustrates the CAD model and geometric details of the simple rounded lug. Table 2 contains the mechanical and fatigue properties of aluminum 7075T-6 material.

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FIGURE 2
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(a) CAD model of round-ended lug; (b) geometric details of simple rounded lug.
TABLE 2. Aluminum 7075T-6 mechanical and fatigue properties [6].
Sl. no. Material properties Values
Mechanical properties
1 Young's modulus (E) 71,700 MPa
2 Poison's ratio (μ) 0.33
3 Density (ρ) 0.28335e−9 t/mm3
4 Ultimate tensile strength (Sult) 572 MPa
5 Yield strength (Sy) 503 MPa
6 Shear modulus (G) 26,900 MPa
Fatigue properties
7 Fatigue strength (Se) 159 MPa
8 Cycle corresponding to Se 5E+8 cycles

3.4 Finite Element Model Mesh Quality and Boundary Conditions

Figure 3a depicts the finite element (FE) model of the round-ended lug, utilizing a solid mesh due to the component's solid nature. A four-noded tetrahedral element is employed, with mesh refinement applied near the lug hole and a mesh transition, as depicted in Figure 3a. The lug pin is simulated using an RBE3 MPC element for a perfectly fitting pin, as shown in Figure 3c. The applied force is axially directed along the x-axis at the MPC node, and the model is effectively constrained in all directions, as shown in Figure 3b,c. As indicated in Table 3, the mesh quality adheres to industry standards, with a maximum tet collapse value above 0.6, indicating an acceptable/good quality mesh. The aspect ratio is maintained within 2.5. Furthermore, Figure 3d portrays a graph demonstrating how reducing the mesh size gradually increases the number of elements. The model used to perform fatigue analysis assumed homogeneous, isotropic, and linear elastic [21] conditions without considering thermal changes [22].

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FIGURE 3
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(a) Finite element model of round-ended lug; (b) FEM model showing boundary conditions; (c) RBE3 node (MPC) at the center of the lug hole; (d) plot for mesh size versus number of elements.
TABLE 3. The details of round-ended lug FE model parameters and quality criteria.
Sl. no. Parameters Values
1 Mesh size 1 mm 0.5 mm 0.25 mm 0.125 mm
2 No. of elements created 45,094 2,20,278 6,37,950 10,45,781
3 Maximum aspect ratio 1.98 2.01 2.13 2.38
4 Maximum equiangular skew 0.728335 0.73161 0.75935 0.798535
5 Minimum Jacobian 1 1 1 1
6 Minimum tetra collapse 0.725465 0.700693 0.695846 0.682002
7 Minimum tria face angle 35.31 35.45 30.61 29.53
8 Maximum tria face angle 100.01 100.21 111.23 115.30

3.5 Stress Concentration Factor Prediction

The stress concentration factor is determined using the data available in the table. The stress concentration factor is obtained through the convergence of a FE model. The equations used to find the stress concentration factor (Kt) and nominal stress are given below.
K t = σ max σ nom $$ {K}_{\mathrm{t}}=\frac{\sigma_{\mathrm{max}}}{\sigma_{\mathrm{nom}}} $$ (1)
σ nom = P ( H − d ) h $$ {\sigma}_{\mathrm{nom}}=\frac{P}{\left(H-d\right)h} $$ (2)

3.6 High Cycle S-N Life Prediction

In MSC NEF analysis, the default setting involves conducting stress or fatigue analysis for a stress ratio of −1. To perform a fatigue analysis for a stress ratio of 0.1, a mean stress correction is performed by creating a spatial field in the form of a time domain within the dat file, as outlined in the Nastran documentation [7]. In this context, the time (t) corresponds to the number of cycles. The S-N life prediction for the lug component is performed by applying load at the MPC node, as a constant amplitude loading. Based on the available fatigue properties of the material, Basquin's equations (3)–(5) are utilized for slope calculations, and the S-N life is predicted by applying the Goodman and Gerber failure criteria, Equations (6) and (7), for stress ratios −1 and 0.1 and at a constant amplitude loading.
N f = σ rev a 1 b $$ {N}_{\mathrm{f}}={\left(\frac{\sigma_{\mathrm{rev}}}{a}\right)}^{\frac{1}{b}} $$ (3)
a = f S ult 2 S e $$ a=\frac{{\left(f{S}_{\mathrm{ult}}\right)}^2}{S_e} $$ (4)
b = − 1 3 log f S ult S e $$ b=-\frac{1}{3}\log \left(\frac{f{S}_{\mathrm{ult}}}{S_e}\right) $$ (5)
σ a S e + σ m S ult = 1 n $$ \frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_{\mathrm{ult}}}=\frac{1}{n} $$ (6)
n σ a S e + n σ m S ult 2 = 1 n $$ \frac{{n\sigma}_a}{S_e}+{\left(\frac{n{\sigma}_m}{S_{\mathrm{ult}}}\right)}^2=\frac{1}{n} $$ (7)

3.7 Fatigue Load Spectrum Generation

In this research, we aim to create a fluctuating stress cycle-based fatigue load spectrum. To visualize this dynamic load spectrum, we employ Python scripts within the Jupyter Lab notebook, leveraging the Pandas and Matplotlib libraries. The methodology involves calculating occurrences from the exceedance spectra using a discrete but manageable number of data points. It is important to strike a balance and do not want an excessive number of points. This is because, for plotting stress points against time (i.e., number of cycles), we employ a randomization function. If we have too many points, it can result in an overwhelming number of combinations of random numbers, based on load factor occurrences within the specified time frame (i.e., for the estimated number of cycles).

4 Results and Discussion

4.1 Stress Convergence Study

A static analysis is performed on four FE models with varying mesh refinement sizes of 1, 0.5, and 0.25 mm. A load of 150 kN is applied at the MPC node, and the resulting maximum principal stress is recorded. Table 4 presents the maximum stress values for each mesh size element. The model converges at a mesh size of 0.125 mm, with an incremental stress difference of 0.13%. For further analysis, the model with a mesh size of 0.25 mm is chosen as it has fewer elements than the 0.125 mm mesh size. The stress plot for mesh size 0.25 mm is shown in Figure 4a. Figure 4b,c show the plots of element size, maximum stress, and its incremental difference, respectively.

TABLE 4. Stress convergence study for the finite element model.
Mesh size (mm) Maximum principal stress (MPa) Vonmises stress Displacement (mm) Maximum principal stress incremental % difference
1 287.8 309 0.2229 —
0.5 291.1 319.3 0.2229 1.15
0.25 298.6 339.4 0.2219 2.58
0.125 299 341 0.2219 0.13
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FIGURE 4
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(a) Maximum stress plot for a mesh refinement size of 0.25 mm; (b) plot for element size versus maximum principal stress; (c) plot for element size versus maximum principal stress incremental % difference.

4.2 Stress Concentration Factor (Kt)

Table 5 and Figure 5 present the results of the convergence study conducted on the stress concentration factor for the FE lug model. The Kt value is found to converge from 1.9185 to 1.9931, with a decrease in the incremental percentage difference of Kt to 0.0013 when the mesh size is set to 0.125. therefore, based on the FE analysis, Kt is determined as 1.99 (rounded to two decimal places).

TABLE 5. Stress concentration factor based on FE analysis.
Element size (mm) Maximum principal stress (MPa) Applied nominal stress (MPa) Stress concentration factor (Kt) Stress concentration factor (Kt) incremental % difference
1 287.8 150.015 1.9185 —
0.5 291.1 150.015 1.9405 1.1467
0.25 298.6 150.015 1.9905 2.5767
0.125 299 150.015 1.9931 0.0013
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FIGURE 5
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Plot for element size versus stress concentration factor.

4.3 Fatigue Life Prediction and Correlation Using S-N Approach

Node 4081, located near the lug hole, exhibits the maximum stress within the finite element method (FEM) model. The fatigue analysis will be focused on the elements surrounding this region. Considering the ultimate load factor of 3g and a factor of safety of 1.5g, static analysis will be performed on the FEM model with a load of 150 kN. Based on the material fatigue parameters provided in Table 2, an S-N life exceeding 5E+08 cycles is considered to be infinite. Table 6 compares the analytically predicted and FE-predicted S-N life values, based on the Goodman and Gerber Criteria, for stress ratios −1 and 0.1, respectively. Figure 6 illustrates the fatigue analysis plots.

TABLE 6. High cycle (S-N) fatigue life prediction and comparison.
Sl no. Load applied at the MPC node (kN) FE analysis maximum stress (MPa) Stress ratio Fatigue life calculations
Analytically calculated life (cycle) NEF life (cycle) for 99.9% certainty of survival Percentage error %
Based on Goodman criteria
1 150 298.6 −1 2.37E+04 2.31E+04 2.6
2 150 298.6 0.1 3.64E+05 3.61E+05 0.83
Based on Gerber criteria
3 150 298.6 0.1 1.63E+06 1.59E+06 2.52
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FIGURE 6
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(a) Fatigue life for the elements surrounding the lug hole for the stress ratio equal to −1 based on the Goodman criterion for a constant load of 150 kN; (b) fatigue damage for the elements surrounding the lug hole for the stress ratio equal to −1 based on the Goodman criterion; (c) log of life for the elements surrounding the lug hole for the stress ratio equal to −1 based on the Goodman criterion.

When The stress ratio is −1, the fatigue life determined by the Gerber failure criteria will be identical to that obtained using Goodman criteria since the mean stress is zero. Figure 6a–c illustrate the fatigue results for the elements adjacent to the lug hole region under an applied load of 150 kN. In Figure 6a, the fatigue life results based on Goodman criteria are shown, with node 4081 exhibiting the lowest fatigue life of 2.31E+04. Figure 6b illustrates the fatigue damage results, with node 4081 having the highest damage value of 4.33E−05. In addition, Figure 6c displays the log life results, revealing that node 4081 has a minimum log life of 4.36.

4.4 Fatigue Load Spectrum

The fatigue load spectrum is generated in a dynamic format by utilizing exceedance spectra data for a transport category aircraft. Specifically, we employ mission profile data from Table 1 for the ATR 72 aircraft to determine the number of cycles, the duration of each cycle, and the total duration, all with respect to a 1000-h flight. Table 7 presents a total duration for all flight sectors of approximately 995.89 h, which can be approximated as 1000 h. This approximation highlights the accuracy of our calculations for estimating the number of cycles and the duration of each cycle. This data analysis process is based on the information contained in Tables 7 and 8. Figure 7 displays a one block of the load spectrum for a 1000-h flight, offering a visual representation of the dynamic load variations experienced by the aircraft during its operational mission.

TABLE 7. Number of cycles based on ATR 72 mission profile data for the exceedance spectra for 1000 h flight.
Serial no. Sector length Percentage of operation % Number of cycles Duration of each cycle (min) Total duration (h)
1 100 2 11 110 20.17
2 150 19 91 125 189.58
3 200 22 95 139 220.08
4 250 27 106 152 268.53
5 300 20 75 160 200
6 350 5 17 171 48.45
7 400 4 13 182 39.43
8 450 1 3 193 9.65
Total 411 995.89
TABLE 8. Stress acting on the lug for various load factors based on FE static analysis.
Load factor (nz) Exceedances Occurrences Stress (MPa)
3 1 1 298.62
2.75 5 4 273.74
2.5 18 13 248.85
2.25 80 62 223.97
2 302 222 199.08
1.75 1343 1041 174.2
1.5 5756 4413 149.31
1.25 25,137 19,381 124.43
1 92,808 67,671 99.54
0.75 34,521 24,063 74.66
0.5 10,458 7290 49.77
0.25 3168 2153 24.89
0 1015 651 0
−0.25 364 252 −24.89
−0.5 112 79 −49.77
−0.75 33 23 −74.66
−1 10 7 −99.54
−1.25 3 2 −124.43
−1.5 1 1 149.31
Details are in the caption following the image
FIGURE 7
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One block of fatigue load spectrum for 1000 h based on ATR 72 mission profile data.

5 Conclusion

Stress convergence in the FE model was achieved at a mesh size of 0.125 mm, resulting in a maximum principal stress of 299 MPa and a final incremental difference of 0.13%. The converged model exhibited a stress concentration of 1.99 with a final incremental difference of 0.0013%. Consequently, a 0.25 mesh size model was considered for further analysis, which saved time for both static and fatigue analysis. In addition, further research is to be conducted to determine the stress concentration factor analytically using “Peterson's Stress Concentration” plots for perfectly fit pins. The life of the lug joint for constant load of 150 kN (3g) is 23,000 flights. But the lug does not experience a constant load but a fluctuating load condition. Hence a crack growth model is to be developed to perform damage tolerance analysis using the fluctuating load spectrum obtained. Software's like Nasgro and FRANC 3D can be used for this type of fluctuating loading sequence for further research to complete the F&DT analysis. NEF does not have variable loading sequence interface. The developed load spectrum contains 411 stress cycles considered as one block for a 1000 h flight.

Nomenclature

  • E
  • Young's Modulus of the material, N/mm2 or MPa
  • μ
  • Poisson's ratio
  • ρ
  • density of the material, t/mm3
  • Sult, Sy, and Se
  • ultimate tensile strength, yield strength, and endurance limit or fatigue strength of the material, respectively, MPa
  • G
  • shear modulus of the material, MPa
  • H, d, and h
  • width, diameter, and thickness of the lug respectively, mm
  • Kt
  • stress concentration factor
  • P
  • applied load, N
  • σmax, σnom, σm, and σa
  • maximum stress, nominal stress, mean stress, and stress ratio of the component, respectively, MPa
  • n
  • factor of safety
  • f
  • fatigue strength fraction

    • Author Contributions

    Rajadurai Murugesan: investigation, formal analysis, data curation, writing – original draft. Srikanth Holalu Venkataraman: writing – review and editing, software, visualization. Pradeep Kumar Sahoo: writing – review and editing, resources, supervision. Praveena Bindiganavile Anand: conceptualization, methodology, supervision. Rithick Rithick: conceptualization, writing – review and editing, methodology. Muhammad Imam Ammarullah: writing – review and editing, validation, project administration.

    Acknowledgments

    The authors gratefully thank the authors' respective institutions for their strong support in this study. The authors declare the use of generative artificial intelligence (AI) and AI-assisted technologies to improve the readability and language of this article.

      Ethics Statement

      The authors have nothing to report.

      Consent

      The authors have nothing to report.

      Conflicts of Interest

      The authors declare no conflicts of interest.

      Data Availability Statement

      The necessary data used in the manuscript are already present in the manuscript.

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