Semi-Empirical Analysis of Polyamide 11 Hybrid Composites: Unveiling the Journey from Simple Models to Complex Theories
Authors: Armioun Shaghayegh , Tjong Jimi , Sain Mohini 
Published: February 2025

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.