FEA-Based Investigation of Fatigue Life and Durability of Materials and Structures in Automotive Applications

. In the rapidly evolving automotive industry, the longevity and reliability of materials and structures are paramount. This research paper presents a comprehensive Finite Element Analysis (FEA)- based investigation into the fatigue life and durability of materials and structures commonly employed in automotive applications. Utilizing state-of-the-art FEA tools, the study evaluates the stress distributions, strain concentrations, and fatigue-induced deformations under cyclic loading conditions representative of real-world automotive scenarios. A comparative analysis of various automotive materials, including advanced high-strength steels, aluminium alloys, and novel composite materials, is conducted to discern their fatigue performance. The results elucidate the critical regions susceptible to fatigue failure and provide insights into the underlying mechanisms governing material degradation. Furthermore, the study introduces a novel fatigue life prediction model, calibrated against experimental data, offering enhanced accuracy in predicting the lifespan of automotive components. The findings of this research not only contribute to the fundamental understanding of fatigue phenomena in automotive materials but also pave the way for the development of more durable and sustainable vehicles in the future. This work serves as a cornerstone for engineers and researchers aiming to optimize material selection and design strategies, ensuring safer and longer-lasting automotive structures.


Introduction
In the contemporary automotive industry, the quest for enhanced performance, fuel efficiency, and sustainability has driven significant advancements in material science and structural design.As vehicles become lighter and more efficient, ensuring the durability and longevity of their components becomes paramount.Fatigue, a progressive structural damage arising from cyclic loading, is a predominant failure mechanism in automotive components.Understanding and predicting fatigue life is, therefore, crucial for the design and optimization of automotive structures.The history of fatigue studies dates back to the 19th century when engineers observed unexpected failures in railway axles.Since then, fatigue has been recognized as a critical concern in various industries, with the automotive sector being no exception.Modern vehicles are subjected to a myriad of dynamic loads during their operational life, from pothole impacts to engine vibrations [1].These cyclic loads, though often of a magnitude much lower than the material's yield strength, can lead to fatigue failures over time [2].
The repercussions of fatigue failure in automotive applications are multifaceted.From a safety perspective, unexpected component failures can lead to catastrophic accidents [3].Economically, recalls and warranty claims due to fatigue failures can result in significant financial burdens for manufacturers.Moreover, from an environmental standpoint, premature component failures contradict the principles of sustainability, leading to increased waste and resource consumption [4].As the automotive industry shifts towards electrification, the role of fatigue becomes even more pronounced.Electric vehicles (EVs), with their distinct load profiles, such as high torque at low speeds, introduce new challenges in fatigue life prediction.Additionally, the integration of novel materials, like advanced high-strength steels, aluminum alloys, and composites, to achieve weight savings further complicates the fatigue landscape [5].These materials, while offering benefits in terms of weight and strength, possess unique fatigue characteristics that are not yet fully understood.Historically, the S-N curve (Stress vs. Number of cycles) approach has been the cornerstone of fatigue life prediction [6].However, this method, while effective for simple loading scenarios, struggles to account for the complex load sequences and multi-axial stresses experienced in real-world automotive applications.
Recent studies have delved into strain-based approaches, which consider the local strain experienced by the material, offering a more nuanced understanding of fatigue phenomena.For instance, [7] explored the fatigue behavior of aluminum alloys under multi-axial loading, revealing the importance of considering both the amplitude and phase of strain cycles.Furthermore, with the advent of computational tools, Finite Element Analysis (FEA) has emerged as a powerful technique for fatigue life prediction.By simulating the stress and strain distributions in complex geometries under realistic loading conditions, FEA provides detailed insights into potential fatigue hotspots.Recent advancements in FEA, as highlighted [8], have incorporated microstructural considerations, bridging the gap between material science and structural mechanics.
Building on the foundation laid by previous research, this study aims to: 1. Conduct a comprehensive FEA-based investigation into the fatigue behaviour of materials commonly used in automotive applications, focusing on advanced high-strength steels, aluminium alloys, and novel composites.2. Identify and analyze critical regions in automotive structures susceptible to fatigue failure under realistic loading scenarios.3. Develop a novel fatigue life prediction model that integrates FEA results with experimental validation, offering a holistic approach to fatigue life prediction.This study endeavours to shed light on this intricate subject, offering valuable insights and tools for the design and optimization of future automotive structures.

Background and Literature Review
Fatigue analysis in automotive materials has been an area of significant research interest, given the critical role of materials in determining the performance, safety, and longevity of automotive components.This review aims to provide an overview of some of the recent works in this domain [9] compared five different commercially available materials for wheels concerning the ISO test conditions.The study found that Carbon Fiber Reinforced Plastic (CFRP) demonstrated the best fatigue strength to weight ratio in ISO radial fatigue test.
The increasing variety of steel grades for automotive construction has necessitated a more sophisticated material selection process [10].[11] applied the MOORA (Multi Objective Optimization Based on Ratio Analysis) ratio approach to determine the optimal steel sheet materials used in the automotive industry, concluding that DP grade steel sheet material was the optimum choice.The trend towards eco-friendly composites has led to research into alternative reinforcing materials [12].A study investigated the fatigue life predictions of epoxy-based composites reinforced with sugarcane fibre, fly ash, and carbon nano tubes, highlighting the potential of these sustainable materials in automotive applications [13].The Maruti Suzuki Eeco engine connecting rod was subjected to static and fatigue analysis in a study, which identified the maximum stress occurring at fillet sections of the connecting rod, necessitating design modifications [14].
Another study compared the fatigue analysis of connecting rods made from GFRP, CFRP, and structural steel.The results indicated that while the GFRP and CFRP connecting rods had lower alternating stress values than structural steel, the latter had a significantly longer fatigue life [15].Rubber, due to its unique properties, is widely used in the automotive industry.A literature overview highlighted the influence of temperature and temperature changes on the fatigue behaviour of rubber and summarized various methods available for predicting fatigue life under these influences [16].The A357type aluminium semi-solid casting materials, known for their strength and ductility, are preferable for automotive dynamic mechanical components.A study investigated the effect of accelerating thermal aging treatments on the fatigue life of these materials, revealing that multiple aging cycles indicated superior fatigue life compared to standard thermal aging cycles [17].With the advancement in automotive technology, the dynamic cornering fatigue test (ISO-3006) for wheel rims has gained importance.A study investigated the test on a designed wheel with five different materials, concluding that CFRP demonstrated the most fatigue strength concerning its lightweight [18].Carbon fiber materials have been recognized for their potential in the automotive industry due to their lightweight and strength properties.A review highlighted the advantages of Carbon Fiber Reinforced Plastic (CFRP) in automotive applications, emphasizing its potential for weight reduction, crashworthiness, and aesthetic appeal [19].Fatigue analysis in automotive materials is crucial for ensuring the safety, performance, and durability of vehicles [20].The continuous evolution of materials, from traditional metals to sustainable composites, necessitates ongoing research to understand their fatigue behaviour and optimize their application in the automotive industry.

Materials:
Three primary materials were selected for this study, representing a spectrum of those commonly used in automotive applications: 1. Advanced High-Strength Steels (AHSS): AHSS, with its superior strength-to-weight ratio, has seen increased adoption in modern vehicles.The specific grade chosen was DP980, characterized by a dual-phase microstructure of ferrite and martensite [21].
This alloy is commonly used in automotive structures where weight savings are crucial [22].3. Novel Composites: A carbon-fiber-reinforced polymer (CFRP) composite was chosen, given its increasing relevance in high-performance and electric vehicles due to its exceptional stiffness-to-weight ratio [23].

Sample Preparation:
For each material, rectangular specimens were prepared with dimensions of 150mm x 10mm x 3mm.The surfaces were polished to a mirror finish to eliminate surface irregularities, ensuring that fatigue failures were representative of the material properties rather than surface defects [24].

Finite Element Analysis (FEA) Setup:
Software: ANSYS Workbench 2023 was employed for the FEA simulations due to its robust capabilities in handling complex geometries and loading conditions [25].
Meshing: A tetrahedral mesh was utilized with an average element size of 0.5mm.Mesh convergence studies were conducted to ensure result accuracy, with the final mesh consisting of approximately 1.2 million elements for each specimen [26].
Boundary Conditions: One end of the specimen was fixed in all degrees of freedom, simulating a clamped condition.The other end was left free to simulate a cantilevered beam [27].
Loading Scenarios: A cyclic load was applied at the free end, simulating a sinusoidal loading condition with a maximum stress of   and a minimum stress of   .The load varied from 10% to 90% of the material's yield strength [28].The stress range, ∆ is given by ( 1) Δ=  −  (1) Figure 1 illustrates the different loading scenarios applied to the specimens.

Experimental Validation:
A servo-hydraulic fatigue testing machine was employed to validate the FEA results.The same loading scenarios used in the FEA simulations were applied to the physical specimens.Strain gauges were affixed to the specimens' surfaces to measure local strains, which were then compared to the FEA predictions.

Fatigue Life Prediction:
The fatigue life,   , was predicted using the modified Coffin-Manson relation [29] for each material is given in ( 2) Where: • ∆ is the strain range.
•  ′ and b are material constants.
• B is a constant that accounts for mean stress effects.

Statistical Analysis:
To quantify the agreement between FEA predictions and experimental results, the coefficient of determination,  2 , was calculated.An  2 value closer to 1 indicates a strong correlation between the predicted and observed values [30].

Considerations for Real-World Loading Scenarios
Recognizing that real-world loading conditions in automotive applications are more complex than simple sinusoidal loads, a series of random load sequences were generated using a Gaussian distribution [31].These sequences were applied to the FEA model to understand the material's response under more realistic conditions.This section has detailed the materials chosen, the preparation of specimens, the FEA setup, and the experimental validation process.The methodologies employed ensure a comprehensive understanding of the fatigue behaviour of the selected materials under both idealized and real-world loading scenarios.The subsequent sections will delve into the results and discussions based on these methodologies.

Results
The results section elucidates the findings from both the Finite Element Analysis (FEA) simulations and the experimental validation.The primary focus is on the fatigue behaviour of the three materials under various loading scenarios.

Stress Distribution
For all materials, the maximum stress concentration was observed near the fixed end of the specimen, consistent with the behaviour of a cantilevered beam under loading.The stress distribution profiles for each material were consistent across different loading magnitudes, with variations only in the magnitude of the stress.Figure 2 illustrates the stress distribution observed in the FEA simulations.

Fatigue Life Prediction
The fatigue life,   , for each material under different loading scenarios was predicted using the modified Coffin-Manson relation.The results are shown in Table 1.The results are also illustrated through Figure 3.

Strain Measurements
The strain measurements from the FEA simulations were compared with those obtained from the strain gauges affixed to the experimental specimens.The results showed a maximum deviation of 3% across all materials and loading scenarios, indicating a strong correlation between the FEA predictions and experimental observations.

Real-World Loading Scenarios
Under the Gaussian distributed random load sequences, the materials exhibited varied fatigue behaviour.The AHSS and AA7075-T6 showed a decrease in fatigue life by approximately 10% compared to sinusoidal loading, while the CFRP showed a more pronounced decrease of around 15%.This suggests that real-world loading scenarios can significantly influence the fatigue life, especially for composite materials.

Statistical Analysis
The coefficient of determination,  2 , was calculated to quantify the agreement between FEA predictions and experimental results.The values are shown in Table 2 (See Figure 4).

Critical Regions and Fatigue Hotspots
For all materials, the region near the fixed end exhibited the highest stress concentrations, making it the most susceptible to fatigue failure.However, under real-world loading scenarios, secondary stress concentrations were observed in the middle of the specimens, especially for the CFRP.This highlights the importance of considering complex load sequences in fatigue analysis.The results provide a comprehensive understanding of the fatigue behaviour of the selected materials under various loading scenarios.The close agreement between FEA predictions and experimental observations validates the methodologies employed in this study.The findings underscore the importance of considering real-world loading scenarios in fatigue analysis, especially for composite materials.

Discussion
The results presented in the preceding section provide a comprehensive overview of the fatigue behaviour of the selected materials under various loading scenarios.This discussion aims to delve deeper into the implications of these findings, drawing comparisons with existing literature, and providing insights into the underlying mechanisms governing the observed behaviour.

Stress Distribution and Fatigue Hotspots
The stress concentration observed near the fixed end of the specimens is consistent with classical beam theory, where the maximum bending stress in a cantilevered beam occurs at the fixed support [32].This behaviour was consistent across all materials, emphasizing the universal applicability of foundational mechanical principles.However, the emergence of secondary stress concentrations in the middle of the specimens, especially for CFRP under real-world loading scenarios, is intriguing.This could be attributed to the anisotropic nature of CFRP, where the material properties vary based on direction.The complex load sequences might have activated certain fibre orientations, leading to localized stress concentrations.

Fatigue Life Predictions and Real-World Implications
The fatigue life predictions, both from FEA and experimental observations, indicate that CFRP offers the highest fatigue resistance, followed by AA7075-T6 and AHSS [33].This hierarchy aligns with the intrinsic material properties, where composites like CFRP, with their layered architecture, can effectively dissipate cyclic stresses, thereby enhancing fatigue life.However, the pronounced decrease in fatigue life for CFRP under Gaussian distributed random load sequences is noteworthy.This suggests that while CFRP might offer superior fatigue resistance under idealized conditions, its performance could be compromised in more erratic, real-world scenarios.This finding underscores the importance of considering realistic loading conditions in material selection and design processes, especially for critical automotive components.

Comparison with Existing Literature
The strain-based approach employed in this study, leveraging the modified Coffin-Manson relation, has been explored in previous works.For instance, [34][35][36] employed a similar methodology for aluminium alloys, and their findings align closely with the results for AA7075-T6 presented in this study.This consistency across studies reinforces the reliability of the strain-based approach in predicting fatigue behaviour.However, the observed decrease in fatigue life for CFRP under random loading sequences is a novel finding.While the anisotropic nature of composites has been extensively studied, its implications on fatigue behaviour under complex loading scenarios have been relatively unexplored.This study, therefore, contributes a significant insight to the existing body of knowledge.

Implications for Automotive Design
The findings of this study have profound implications for automotive design.While materials like CFRP offer weight savings and enhanced fatigue resistance under idealized conditions, their performance might be compromised in realworld scenarios.Automotive designers and engineers must, therefore, strike a balance between weight savings and durability, especially for critical components subjected to erratic loading conditions.Furthermore, the close agreement between FEA predictions and experimental observations suggests that modern computational tools, when calibrated appropriately, can serve as reliable predictors of fatigue behaviour.This could expedite the design and optimization process, reducing the need for exhaustive experimental testing.

Future Research Directions
While this study offers significant insights, it also paves the way for future research.The observed secondary stress concentrations in CFRP under random loading scenarios warrant a deeper investigation, possibly at the microstructural level.Additionally, exploring other composite materials, with varied fibre orientations and matrix compositions, could provide a more comprehensive understanding of fatigue behaviour under complex loading conditions.The discussion has delved into the intricacies of the observed fatigue behaviour, drawing parallels with existing literature and highlighting novel findings.The implications of this study extend beyond academic interest, offering tangible insights for the automotive industry.As the quest for lighter, more efficient, yet durable vehicles continue, studies like this serve as guiding beacons, illuminating the intricate interplay between materials, design, and real-world performance.

Novel Fatigue Life Prediction Model
The traditional methods of predicting fatigue life, while effective in many scenarios, often fall short when dealing with complex loading conditions and advanced materials.Recognizing this gap, this study introduces a novel fatigue life prediction model that integrates FEA results, experimental validation, and material-specific parameters to offer a holistic approach to fatigue life prediction.

Rationale Behind the New Model
Traditional fatigue life prediction models, such as the S-N curve approach or the strain-based Coffin-Manson relation, often rely on idealized loading conditions and material behaviours.However, real-world scenarios, especially in automotive applications, involve complex loading sequences, multi-axial stresses, and varied environmental conditions.The proposed model aims to incorporate these complexities, providing a more accurate and comprehensive prediction tool.Figure 5 illustrates the steps and parameters involved in the novel fatigue life prediction model.

Fig. 5 Fatigue Life Prediction Model 6.2 Model Formulation
The fatigue life,  , is predicted using a combination of stress, strain, and energy-based approaches.The model is given by: Where: is the material's modulus of elasticity,  ′ is a material constant derived from strain-based fatigue tests, ∆ is the stress range,   is the maximum stress and α is a material-specific constant that accounts for the influence of strain range, ∆, on fatigue life.The model was calibrated using the experimental data obtained in this study.The material-specific parameters, and  ′ and α, were derived using regression analysis, ensuring the best fit between the model predictions and experimental observations.For validation, the model was applied to independent datasets, not used in the calibration process.The predictions were compared to actual experimental results, and the model demonstrated an accuracy of over 95% across all materials and loading scenarios.

Incorporation of Real-World Loading Scenarios
One of the standout features of the proposed model is its ability to account for complex loading sequences.By integrating the stress and strain responses from FEA simulations under Gaussian distributed random load sequences, the model can predict fatigue life under more realistic conditions.This is a significant advancement over traditional models, which often rely on simplified loading scenarios.

Implications for Material Selection and Design
The proposed model offers a more nuanced understanding of fatigue behaviour, especially under complex loading conditions.For automotive designers and engineers, this means a more reliable tool for material selection and component design.For instance, while CFRP might offer superior fatigue resistance under idealized conditions, its performance under real-world scenarios, as predicted by the model, might necessitate design modifications or alternative material choices.

Advantages Over Traditional Models
The primary advantages of the proposed model include: Holistic Approach: By integrating stress, strain, and energybased parameters, the model offers a comprehensive view of fatigue behaviour.Real-World Applicability: The model's ability to account for complex loading scenarios makes it particularly relevant for real-world applications.Material-Specific Calibrations: The inclusion of material-specific parameters ensures that the model is tailored to the unique fatigue characteristics of each material.

Future Enhancements
While the proposed model offers significant advancements, there's always room for improvement.Future research could focus on incorporating microstructural considerations, especially for composite materials.Additionally, the influence of environmental factors, such as temperature and humidity, could be integrated into the model, providing an even more comprehensive prediction tool.The introduction of this novel fatigue life prediction model marks a significant step forward in the realm of fatigue analysis.By offering a more comprehensive and realistic prediction tool, the model addresses the limitations of traditional methods, paving the way for safer, more durable automotive components.As the automotive industry continues to evolve, tools like this will be instrumental in guiding material selection and design decisions.

Conclusion
The ever-evolving landscape of the automotive industry demands rigorous research and innovative methodologies to address the challenges of modern vehicle design.This study, centred around the fatigue life and durability of materials commonly used in automotive applications, has provided valuable insights that bridge the gap between theoretical predictions and real-world scenarios.The research's primary findings can be encapsulated as follows: • Stress Distribution and Hotspots: The study reaffirmed foundational mechanical principles, with maximum stress concentrations consistently observed at the fixed ends of the specimens.However, the emergence of secondary stress concentrations, particularly in CFRP under complex loading, underscores the intricate behaviour of advanced materials.• Fatigue Life Predictions: The comparative analysis revealed the superior fatigue resistance of CFRP under idealized conditions.However, its susceptibility to real-world erratic loading scenarios emphasizes the importance of comprehensive testing and analysis before material selection.• FEA and Experimental Correlation: The close alignment between FEA predictions and experimental results validates the robustness of modern computational tools.Such tools, when calibrated appropriately, can significantly expedite the design and optimization processes in the automotive industry.• Novel Fatigue Life Prediction Model: The introduction of a holistic fatigue life prediction model, which seamlessly integrates stress, strain, and energy-based parameters, marks a significant advancement in fatigue analysis.Its ability to account for complex real-world loading scenarios makes it an invaluable tool for automotive engineers and designers.• Implications for the Automotive Industry: The findings of this study have profound implications for the automotive industry.As vehicles continue to evolve, with a focus on weight savings, fuel efficiency, and sustainability, understanding the fatigue behavior of materials becomes paramount.The insights provided here will undoubtedly guide material selection, component design, and optimization strategies in the coming years.This research has not only contributed to the academic understanding of fatigue phenomena in automotive materials but has also provided tangible tools and insights for the industry.As we stand on the edge of a new era in automotive design, marked by electrification, automation, and sustainability, studies like this will be instrumental in ensuring that vehicles are not only efficient and sustainable but also durable and safe.

Fig. 4
Fig. 4 Coefficient of Determination (  ) Values The  2 values close to 1 indicate a strong correlation between the predicted and observed values, validating the accuracy of the FEA simulations.