A novel approach for the practical estimation of the elastic modulus in randomly oriented short fiber reinforced composites

This paper introduces new rule-of-thumb equations for estimating the effective elastic modulus of randomly oriented short fiber reinforced composites (SFRCs), developed using the Tandon and Weng method combined with the simplifications from the Tsai-Pagano model. These types of rule-of-thumb equations are useful for a quick first approximation when designing SFRCs. The analysis reveals a linear relationship between the effective Young’s modulus of randomly oriented SFRCs and the effective axial and transverse elastic moduli of unidirectional SFRCs, highlighting that the slope of this relationship is sensitive to the axial-to-transverse modulus ratio. Equations are provided to estimate this slope. Additionally, the study utilizes a two-step homogenization analysis, applied theoretically in this work, which proved to be a practical method for predicting the elastic modulus of randomly oriented SFRCs. Finally, a comprehensive comparative analysis with similar theoretical models demonstrates that the proposed approach delivers comparable prediction performance in two-dimensional random fiber distribution cases and slightly superior performance in three-dimensional random fiber distribution cases. Notably, the rule-of-thumb model developed in this work outperformed other two-step homogenization rule-of-thumb models, achieving better predictions of Young’s modulus.