A Surface-Energy-Based Extension of the Cox–Krenchel Model for Stiffness Prediction of Short-Fiber-Reinforced Thermoplastics

Abstract

Short-fiber-reinforced thermoplastics are widely used in lightweight structural applications, but reliable prediction of their Young’s modulus remains challenging because classical analytical models usually neglect interfacial effects. In this study, the Cox–Krenchel model was extended by an adhesion efficiency factor derived from surface-energy-based interfacial tension to account for incomplete elastic load transfer at the fiber–matrix interface. Injection-molded polypropylene (PP) and polyamide 6.6 (PA 6.6) composites reinforced with basalt and glass fibers were produced and characterized experimentally. Model inputs comprised the matrix and fiber modulus, measured fiber volume fraction, experimentally determined individual fiber lengths incorporated through an effective Cox length efficiency factor, and experimentally determined fiber orientation factors. Interfacial tension was calculated from polar and dispersive surface-tension components using the Owens–Wendt–Rabel–Kaelble approach. The classical Cox–Krenchel model described the PA–basalt system with high accuracy but systematically overestimated the stiffness of the PP-based systems. Using a single globally calibrated proportionality constant of ω = 0.8, the adhesion-extended model reduced the mean absolute percentage error on the full condition-specific dataset of 55 data points from 14.2% to 2.7%. The results indicate that morphology remains the dominant basis of stiffness prediction, while surface-energy-based interfacial compatibility provides a relevant additional descriptor for residual system-dependent error. For the investigated systems, the proposed extension improved predictive accuracy while preserving the analytical simplicity of the Cox–Krenchel framework.

The authors' abstract, as published at the source. Fibers, 2026 · DOI ↗