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Analytical model for predicting the interfacial stresses of carbon nanotubes-reinforced nanocomposites

Shiuh-Chuan Her (Department of Mechanical Engineering, Yuan Ze University, Chung-Li, Taiwan)
Shou-Jan Liu (Department of Mechanical Engineering, Yuan Ze University, Chung-Li, Taiwan)

Engineering Computations

ISSN: 0264-4401

Article publication date: 25 February 2014




Carbon nanotubes (CNTs) with exceptional mechanical, thermal and electrical properties are considered to be ideal for reinforcing high-performance structures. The interfacial stresses between the CNTs and surrounding matrix are important phenomena which critically govern the mechanical properties of CNTs-reinforced nanocomposites. A number of methods have been proposed to investigate the stress transfer across the CNT/matrix interface, such as experimental measurement and molecular dynamics (MDs). Experimental tests are difficulty and expensive. MDs simulations, on the other hand, are computationally inefficient. The purpose of this paper is to present a reasonably simplified model. Incorporating the simplified model, the analytical expressions of the interface stresses including the shear stress and longitudinal normal stress are obtained.


The analytical model consists of two concentric cylinders, namely a single-walled carbon nanotube (SWCNT) cylinder and a matrix cylinder, as the representative volume element (RVE). The interfacial stress analysis is performed using the shear lag model for the axisymmetric RVE. Analytical solutions for the normal stresses in the SWCNT and matrix, and the interfacial shear stress across the SWCNT/matrix interface are obtained. The proposed model has a great ability to theoretical prediction of the stress transfer between the matrix and CNTs.


In order to demonstrate the simulation capabilities of the proposed model, parametric studies are conducted to investigate the effects of the volume fraction of SWCNT and matrix modulus on the stress transfer. The axial stress in the matrix is decreasing with the increase of the volume fraction and decrease of the matrix modulus. As a result of more loads can be transferred to the SWCNT for a large volume fraction and small matrix modulus. These results show that using a large volume fraction and a small matrix modulus improves the efficiency of the stress transfer from the matrix to the CNTs.


A simple but accurate model using a simplified 2D RVE for characterizing the stress transfer in CNT-reinforced nanocomposites is presented. The predictions from the current method compare favourably with those by existing experimental, analytical and computational studies. The simple and explicit expressions of the interfacial stresses provide valuable analysis tools accessible to practical users.



The authors thank for the finical support by National Science Council, Taiwan, under the Grant No. NSC-101-2221-E-155-013.


Her, S.-C. and Liu, S.-J. (2014), "Analytical model for predicting the interfacial stresses of carbon nanotubes-reinforced nanocomposites", Engineering Computations, Vol. 31 No. 2, pp. 353-364.



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