Performance of monoleaf springs with functionally graded materials

Hassan S. Hedia; Hussein A. Saleem; Mohamed H. Hedia; Mona A. Soliman

doi:10.1515/mt-2025-0319

Article

Performance of monoleaf springs with functionally graded materials

Prof. Dr. Hassan S. Hedia, born in 1959, is Professor of Materials and Solid Mechanics at Mansoura University, Mansoura, Egypt. Now he is working at King Abdulaziz University, Jeddah Saudi Arabia. He received his BSc 1981 in the Mechanical Engineering Dept., Cairo University, Egypt, his MSc 1989 in Production Engineering, at Mansoura University, Egypt, and his PhD in 1996 in the Mechanical Engineering Dept., Leeds University, UK and Mansoura University, Egypt under the channel system. His field of interest is advanced materials, fracture mechanics, stress analysis optimum design, mechanics of materials, and biomechanics.
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Dr. Hussein A. Saleem is an accomplished Associate Professor in the Department of Mining Engineering, King Abdulaziz University, Jeddah Saudi Arabia. He earned his MSc and PhD in Mining Engineering from Assiut University, Assiut 71515, Egypt. His research expertise encompasses Mining Engineering. Also, he keenly involved in the quality procedures at the University and College levels.
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Mohamed H. Hedia, born in 1992, is Assistance Lecturer, Department of Structural Engineering, Mansoura University, Egypt. He is currently pursuing a PhD at the University of Nebraska at Lincoln, USA. With a master’s degree in structural engineering from Mansoura University, Egypt. Mr. Hedia’s research interests encompass a range of areas within structural engineering, including the strength of materials, finite element analysis, and behavior of structural elements, bridge engineering, and material science. His expertise and passion lie in exploring these subjects to contribute to the advancement of the field.
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Dr. Mona A. Soliman born in 1974, is assistant professor of Mechanical Design Engineering, Delta Higher Institute for Engineering and Technology, Talkha, Egypt. She graduated with BSc, MSc, and PhD from Production Engineering and Mechanical Design Department of Mansoura University at 1997, 2005, and 2015, respectively. Her research interests are in fracture mechanics and finite element analysis such as analysis of composite material leaf spring, analysis of FGM material, and its application in mechanical component, vibration analysis of car suspension system, fatigue life estimation, crack growth, & arresting methods.

Published/Copyright: January 13, 2026

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From the journal Materials Testing Volume 68 Issue 3

Abstract

Functionally Graded Materials (FGMs) improve fatigue resistance in leaf springs subjected to cyclic loading by optimizing the distribution of material properties throughout the component, thus enhancing both performance and durability. These materials feature a gradual variation in composition and structure, enabling customized mechanical properties that better resist the stresses and strains encountered during repeated loading cycles. This study focuses on the design of a monoleaf spring composed of an FGM composite that combines carbon fiber–reinforced polymer with 50R steel, analyzed using finite element analysis (FEA). The investigation examines the spatial distribution of von Mises stress and strain energy across the thickness of the functionally graded monoleaf spring. Three different grading functions are employed: a straightforward power-law function (P-FGM), a modified symmetric power-law function (S–P-FGM), and a Sigmoid function (S-FGM). The parameter k in the power-law functions was varied (0.2, 0.5, 1, 2, 5 and 10) to understand its influence on stress distribution and strain energy. Results indicate that the spring’s performance improves with increasing k, with the highest value, k = 10, yielding the greatest strain energy storage capacity, making it ideal for applications demanding high energy absorption and resilience. Additionally, at k = 10, the FGM exhibits the highest margin of safety (MOS), reflecting superior strength and reliability. Among the functions tested, P-FGM and S–P-FGM provide the best results in terms of margin of safety and strain energy, while the S-FGM function performs the least effectively. Ultimately, the optimal design for a monoleaf spring is an FGM composite of carbon fiber–reinforced polymer and 50R steel with a power exponent k = 10, offering excellent strain energy capacity, strength, and safety margin, thereby significantly enhancing spring performance.

Keywords: monoleaf spring; FGM; von Mises stress; strain energy; power law functions

Corresponding author: Hassan S. Hedia, King Abdulaziz University, Faculty of Maritime Studies, Marine Engineering Dept., Jeddah, Saudi Arabia, E-mail: hassanhedia87@yahoo.com

Funding source: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (IPP:90-980-2025). The authors, therefore, gratefully acknowledge with thanks DSR for technical and financial support

Award Identifier / Grant number: grant no. (IPP:90-980-2025).

About the authors

Hassan S. Hedia

Prof. Dr. Hassan S. Hedia, born in 1959, is Professor of Materials and Solid Mechanics at Mansoura University, Mansoura, Egypt. Now he is working at King Abdulaziz University, Jeddah Saudi Arabia. He received his BSc 1981 in the Mechanical Engineering Dept., Cairo University, Egypt, his MSc 1989 in Production Engineering, at Mansoura University, Egypt, and his PhD in 1996 in the Mechanical Engineering Dept., Leeds University, UK and Mansoura University, Egypt under the channel system. His field of interest is advanced materials, fracture mechanics, stress analysis optimum design, mechanics of materials, and biomechanics.

Hussein A. Saleem

Dr. Hussein A. Saleem is an accomplished Associate Professor in the Department of Mining Engineering, King Abdulaziz University, Jeddah Saudi Arabia. He earned his MSc and PhD in Mining Engineering from Assiut University, Assiut 71515, Egypt. His research expertise encompasses Mining Engineering. Also, he keenly involved in the quality procedures at the University and College levels.

Mohamed H. Hedia

Mohamed H. Hedia, born in 1992, is Assistance Lecturer, Department of Structural Engineering, Mansoura University, Egypt. He is currently pursuing a PhD at the University of Nebraska at Lincoln, USA. With a master’s degree in structural engineering from Mansoura University, Egypt. Mr. Hedia’s research interests encompass a range of areas within structural engineering, including the strength of materials, finite element analysis, and behavior of structural elements, bridge engineering, and material science. His expertise and passion lie in exploring these subjects to contribute to the advancement of the field.

Mona A. Soliman

Dr. Mona A. Soliman born in 1974, is assistant professor of Mechanical Design Engineering, Delta Higher Institute for Engineering and Technology, Talkha, Egypt. She graduated with BSc, MSc, and PhD from Production Engineering and Mechanical Design Department of Mansoura University at 1997, 2005, and 2015, respectively. Her research interests are in fracture mechanics and finite element analysis such as analysis of composite material leaf spring, analysis of FGM material, and its application in mechanical component, vibration analysis of car suspension system, fatigue life estimation, crack growth, & arresting methods.

Acknowledgment

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (IPP:90-980-2025). The authors, therefore, gratefully acknowledge with thanks DSR for technical and financial support.

Research ethics: The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013).
Informed consent: Informed consent was obtained from all individuals included in this study, or their legal guardians or wards.
Author contributions: The authors has accepted responsibility for the entire content of this manuscript and approved its submission.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors states no conflict of interest.
Research funding: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (IPP:90-980-2025). The authors, therefore, gratefully acknowledge with thanks DSR for technical and financial support.
Data availability: Not applicable.

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Published Online: 2026-01-13

Published in Print: 2026-03-26

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Articles in the same Issue

https://doi.org/10.1515/mt-2025-0319

Keywords for this article

monoleaf spring; FGM; von Mises stress; strain energy; power law functions