Investigation of stress-strain behavior of single walled carbon nanotube-rubber composites

Investigation of stress–strain behavior of single walled carbon

nanotube/rubber composites by a multi-scale finite element method

S.K.Georgantzinos,G.I.Giannopoulos,N.K.Anifantis *

Mechanical and Aeronautics Engineering Department,University of Patras,2500Rio,Patras,Greece

a r t i c l e i n f o Article history:

Available online 12October 2009Keywords:Nanotube Rubber

Nanocomposite Fracture

Finite element

a b s t r a c t

The excellent properties of carbon nanotubes have generated technological interests in the development of nanotube/rubber composites.This paper describes a finite element formulation that is appropriate for the numerical prediction of the mechanical behavior of rubber-like materials which are reinforced with single walled carbon nanotubes.The considered composite material consists of continuous aligned single walled carbon nanotubes which are uniformly distributed within the rubber material.It is assumed that the carbon nanotubes are imperfectly bonded with the matrix.Based on the micromechanical theory,the mechanical behavior of the composite may be predicted by utilizing a representative volume element.Within the representative volume element,the reinforcement is modeled according to its atomistic microstructure.Therefore,non-linear spring-based line elements are employed to simulate the discrete geometrical structure and behavior of the single-walled carbon nanotube.On the other hand,the matrix is modeled as a continuum medium by utilizing solid elements.In order to describe its behavior an appropriate constitutive material model is adopted.Finally,the interfacial region is simulated via the use of special joint elements of variable stiffness which interconnect the two materials in a discrete ing the proposed multi-scale model,the stress–strain behavior for various values of reinforcement volume fraction and interfacial stiffness is extracted.The influence of the single walled carbon nanotube addition within the rubber is clearly illustrated and discussed.

Ó2009Elsevier Ltd.All rights reserved.

1.Introduction

Rubber composites can be classified as particulate,laminated,or fibrous depending on their construction.The most commonly available elastomeric composites are reinforced with carbon black particles [1]which range in size from a few hundred to thousand of angstroms.Fillers are added to rubber products as car tires and shock mounts to enhance their stiffness and toughness properties.The unique behavior of carbon black-filled elastomers results due to a rigid,particulate phase and the interaction of the elastomer chains with this phase [2].It is well known that such composites usually exhibit highly anisotropic response due to directionality in material properties.Unfortunately,among the existing strain energy functions,both the polynomial as well as Ogden models are unable to capture the sharp decrease in stiffness for filled rub-bers at small strains.

As there is a demand in modern technological applications for superior elastomeric composites,innovative reinforcements hav-ing superior properties should be introduced.Such reinforcements could be found in the field of nanotechnology.Single walled carbon

nanotubes (SWCNTs)are the stiffest and strongest known fibbers,having also remarkable electronic and conductive properties and many other unique characteristics [3].However,these properties are obviously of limited value in individual tubes.The develop-ment of SWCNT based elastomeric composites [4]could demon-strate both the excellent energy absorption characteristics of the rubber component as well as the advanced structural properties of the nanotubes.Recent experimental observations have shown that significant improvements in the mechanical properties of polymeric materials can be achieved by using even small volume fractions of carbon nanotubes as reinforcement [5–7].

Molecular dynamics (MD)[8–10]and continuum mechanics [11–14]based approaches have been adopted to simulate carbon nanotube (CNT)composite behavior.The performance of CNT-based composites is greatly influenced by the interface which has different properties from those of the matrix and the CNT.Gener-ally,the three main mechanisms of interfacial load transfer are micromechanical interlocking,chemical bonding,and the van der Waals interactions between the matrix and the reinforcements.Al-Ostaz et al.[15]investigated SWCNT-polymer interface interac-tions in nanoscale via MD.To represent the CNT-polymer load transfer characteristics and consequently the interface between the CNTs and the polymer,Frankland et al.[16]employed just

0167-8442/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.tafmec.2009.09.005

*Corresponding author.

E-mail address:nanif@mech.upatras.gr (N.K.Anifantis).

Theoretical and Applied Fracture Mechanics 52(2009)

158–164

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