Semi-Empirical Analysis of Polyamide 11 Hybrid Composites: Unveilingthe Journey from Simple Models to Complex Theories

Introduction: Predicting the properties of hybrid composites is challenging due to their mechanical and thermal heterogeneity, anisotropy, and complex microstructures. This has led to the development of various theoretical models, each tailored to assess specific microstructures and optimize material properties for targeted applications. Methods: The present paper presents a semi-empirical analysis of hybrid Polyamide 11 (PA11) composites reinforced with wood and carbon fibers. To predict the tensile modulus of natural fiber composites, methods such as ROM, IROM, Halpin-Tsai, Halpin-Tsai for random fiber orientations, and shear lag model equations were employed and accordingly modified. Employing the "effective matrix" approach, the modified single fiber system equations were further employed for hybrid fiber systems. The HROM, Halpin-Tsai, Halpin-Tsai for random fiber orientations, Halpin-Tsai for hybrid composites, and shear lag model equations were applied and modified for hybrid composites. objective: The objectives of this research are to develop a mathematical model for predicting the mechanical properties of hybrid composites and to validate this model with experimental data. The model will utilize predictive frameworks such as the Rule of Mixtures (ROM), Inverse Rule of Mixtures (IROM), Shear Lag model, and adaptations of the Halpin-Tsai equations. It aims to effectively capture the inherent heterogeneity and anisotropy of the composites, enhancing predictive accuracy for various microstructural configurations. Validation of the developed model through experimental comparison is crucial, ensuring its efficacy and reliability in accurately reflecting the mechanical behavior of hybrid composites under operational conditions. Results and Discussion: The Halpin-Tsai equations for randomly distributed fibers demonstrated the highest level of agreement with the experimental findings. The best-fit values for λL (longitudinal direction) and λT (Transverse direction) for randomly distributed fibers in Halpin-Tsai models were 0.372 and 0.568. These values were in excellent agreement with the original Halpin-Tsai equations for randomly dispersed fibers, which are reported as 0.375 and 0.625, respectively. Similarly, the experimental findings strongly correlate with the Halpin-Tsai equations for hybrid composites documented in the literature. Furthermore, this study effectively derived and employed modified equations from several micromechanical models to accurately predict the tensile modulus for single and hybrid fiber-reinforced composites. Conclusion: Hybrid composites of PA11 reinforced with natural and carbon fibers represent a promising approach for sustainable, high-performance materials. This study';s experimental results closely align with several established micromechanical models, including the Halpin-Tsai model for both randomly distributed short fibers and hybrid composites. Additionally, existing models for single-fiber composites, such as ROM and shear lag theory, were effectively modified to match the study';s experimental data. These modifications accounted for fiber misalignment, inadequate fiber-matrix interaction, fiber breakage, and natural fiber degradation. The modified models'; predicted moduli were consistent with the experimental findings for both single- fiber and hybrid systems.