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This study presents a comparative analysis of the Voigt and self-consistent models for predicting the Young’s modulus of functionally graded materials (FGMs) composed of aluminum reinforced with silicon carbide (SiC), alumina (Al₂O₃), and magnesium oxide (MgO). Utilizing a sigmoidal power-law distribution to model volume fraction variations across the thickness, the investigation evaluates modulus behavior under varying power indices (p = 0.1 to 10). Results indicate that the Voigt model overestimates stiffness in phase-dominant regions (e.g., 400 GPa for Al–SiC at z/h = −0.5) and underestimates it in intermediate zones (e.g., 230.29 GPa for Al–SiC at z/h = 0), failing to account for phase interactions. In contrast, the self-consistent model provides more accurate modulus predictions (e.g., 194.19 GPa for Al–SiC at z/h = 0) and captures steeper gradients (e.g., 392.86 GPa for Al–SiC at z/h = 0.25 for p = 5), aligning with experimental FGM trends. The self-consistent approach’s ability to iteratively model the effective medium enhances its reliability, positioning it as a preferred tool for designing FGMs with optimized mechanical properties for aerospace, biomedical, and energy applications.

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Comparative Analysis of Voigt and Self-consistent Models for Predicting Young’s Modulus in Al–SiC, Al–Al₂O₃, and Al–Mgo Functionally Graded Materials

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  • 发表日期：

    2026年

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  • Taoufik Hachimi,
  • Fouad Ait Hmazi,
  • Fatima Ezzhra Arhouni,
  • Mohammed Remaidi,
  • Hicham Doghmi,
  • Fatima Majid

摘要

This study presents a comparative analysis of the Voigt and self-consistent models for predicting the Young’s modulus of functionally graded materials (FGMs) composed of aluminum reinforced with silicon carbide (SiC), alumina (Al₂O₃), and magnesium oxide (MgO). Utilizing a sigmoidal power-law distribution to model volume fraction variations across the thickness, the investigation evaluates modulus behavior under varying power indices (p = 0.1 to 10). Results indicate that the Voigt model overestimates stiffness in phase-dominant regions (e.g., 400 GPa for Al–SiC at z/h = −0.5) and underestimates it in intermediate zones (e.g., 230.29 GPa for Al–SiC at z/h = 0), failing to account for phase interactions. In contrast, the self-consistent model provides more accurate modulus predictions (e.g., 194.19 GPa for Al–SiC at z/h = 0) and captures steeper gradients (e.g., 392.86 GPa for Al–SiC at z/h = 0.25 for p = 5), aligning with experimental FGM trends. The self-consistent approach’s ability to iteratively model the effective medium enhances its reliability, positioning it as a preferred tool for designing FGMs with optimized mechanical properties for aerospace, biomedical, and energy applications.