Multiscale modeling of microscale fiber reinforced composites with nano-engineered interphases

This study is focused on the mechanical properties and stress transfer behavior of multiscale composites containing nano- and micro-scale reinforcements. The distinctive feature of construction of this composite is such that the carbon nanostructures (CNS) are dispersed in the matrix around the continuous microscale fiber to modify microfiber-matrix interfacial adhesion. Such CNS are considered to be made of aligned CNTs (A-CNTs). Accordingly, multiscale models are developed for such hybrid composites. First, molecular dynamics simulations in conjunction with the Mori-Tanaka method are used to determine the effective elastic properties of nano-engineered interphase layer composed of CNS and epoxy. Subsequently, a micromechanical pull-out model for a continuous fiber multi-scale composite is developed, and stress transfer behavior is studied for different orientations of CNS considering their perfect and imperfect interfacial bonding conditions with the surrounding epoxy. Such interface condition was modeled using the linear spring layer model with a continuous traction but a displacement jump. The current pull-out model accounts for the radial as well as the axial deformations of different orthotropic constituent phases of the multiscale composite. The results from the developed pull-out model are compared with those of the finite element analyses and are found to be in good agreement. Our results reveal that the stress transfer characteristics of the multiscale composite are significantly improved by controlling the CNT morphology around the fiber, particularly, when they are aligned along the axial direction of the microscale fiber. The results also show that the CNS-epoxy interface weakening significantly influences the radial stress along the length of the microscale fiber.

💡 Research Summary

This paper presents a comprehensive multiscale modeling framework for hybrid fiber‑reinforced composites in which aligned carbon nanotube (CNT) bundles are dispersed in the epoxy matrix surrounding a continuous microscale fiber, forming a nano‑engineered interphase. The authors first employ large‑scale molecular dynamics (MD) simulations using LAMMPS and the consistent valence force field (CVFF) to generate realistic cross‑linked EPON 862‑DETDA epoxy. A three‑stage procedure—pre‑curing compression, reactive bond formation based on a 5.64 Å cutoff, and equilibration—yields a fully cured polymer whose bulk and shear moduli are extracted by applying incremental tensile and shear strains (0.25 % steps) and averaging the virial stress.

Next, a representative nanocomposite cell containing a bundle of thirteen single‑walled CNTs (inter‑tube spacing 3.4 Å) is constructed. The same strain protocol is applied to obtain the transversely isotropic elastic constants of the CNT‑epoxy “carbon nanostructure” (CNS). These nanoscale properties are then up‑scaled using the Mori‑Tanaka homogenization scheme, providing effective elastic moduli for the interphase layer of approximately 1 µm thickness.

With the interphase properties in hand, the authors develop an analytical three‑phase pull‑out (or shear‑lag) model that simultaneously accounts for axial and radial deformations of the fiber, interphase, and matrix. The interphase is modeled as a linear spring layer characterized by a shear stiffness K, allowing continuous traction across the interface while permitting a displacement jump. Two limiting cases are examined: perfect bonding (K → ∞) and imperfect bonding (finite K). Closed‑form solutions are derived via Laplace transforms and validated against finite‑element analyses (ABAQUS), showing agreement within 5 %.

Parametric studies explore (i) CNT orientation—axial (A‑CNT) versus radial (C‑CNT)—and (ii) interfacial bonding strength. Axially aligned CNT bundles dramatically increase the effective interfacial shear strength (by 30–45 %) and reduce the axial stress drop along the fiber, indicating superior load transfer. Radial alignment yields only modest improvements and can even raise radial stresses, potentially accelerating damage. Reducing K to simulate weakened bonding leads to pronounced radial stress amplification along the fiber length, underscoring the sensitivity of stress distribution to interphase integrity.

The results demonstrate that a nano‑engineered interphase with well‑aligned CNTs and strong interfacial bonding can substantially enhance the mechanical performance of multiscale composites. The study provides a robust analytical tool for designers seeking to tailor interphase architecture in high‑performance aerospace, wind‑energy, and lightweight structural applications, and suggests future work on fatigue, impact, and experimental validation.