Computational modeling of elastic properties of carbon nanotube/polymer composites with interphase regions. Part II: Mechanical modeling

Abstract We present two modeling approaches for predicting the macroscopic elastic properties of carbon nanotubes/polymer composites with thick interphase regions at the nanotube/matrix frontier. The first model is based on local continuum mechanics; the second one is based on hybrid local/non-local continuum mechanics. The key computational issues, including the peculiar homogenization technique and treatment of periodical boundary conditions in the non-local continuum model, are clarified. Both models are implemented through a three-dimensional geometric representation of the carbon nanotubes network, which has been detailed in Part I. Numerical results are shown and compared for both models in order to test convergence and sensitivity toward input parameters. It is found that both approaches provide similar results in terms of homogenized quantities but locally can lead to very different microscopic fields.

[1]  Jang‐Kyo Kim,et al.  Dispersion, interfacial interaction and re-agglomeration of functionalized carbon nanotubes in epoxy composites , 2010 .

[2]  Donald R Paul,et al.  Rheological behavior of multiwalled carbon nanotube/polycarbonate composites , 2002 .

[3]  J. Coleman,et al.  Morphological and mechanical properties of carbon-nanotube-reinforced semicrystalline and amorphous polymer composites , 2002 .

[4]  Gilles Lubineau,et al.  Computational modeling of elastic properties of carbon nanotube/polymer composites with interphase regions. Part I: Micro-structural characterization and geometric modeling , 2014 .

[5]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[6]  P. Moldenaers,et al.  Assessing the strengths and weaknesses of various types of pre-treatments of carbon nanotubes on the properties of polymer/carbon nanotubes composites: A critical review , 2010 .

[7]  Richard B. Lehoucq,et al.  Peridynamics as an Upscaling of Molecular Dynamics , 2009, Multiscale Model. Simul..

[8]  Sidney R. Cohen,et al.  Measurement of carbon nanotube-polymer interfacial strength , 2003 .

[9]  R. Rafiee,et al.  A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites , 2010 .

[10]  E. Pan,et al.  Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites , 2007 .

[11]  S. Frankland,et al.  Transverse mechanical properties of single-walled carbon nanotube crystals. Part I: determination of elastic moduli , 2003 .

[12]  S. Silling,et al.  Peridynamic States and Constitutive Modeling , 2007 .

[13]  F. Avilés,et al.  Modeling the influence of interphase on the elastic properties of carbon nanotube composites , 2010 .

[14]  Babak Ahmadimoghadam.  Comparison Between Different Finite Element Methods for Foreseeing the Elastic Properties of Carbon nanotube Reinforced Epoxy Resin Composite , 2008 .

[15]  S. R. Bakshi,et al.  Quantification of carbon nanotube distribution and property correlation in nanocomposites , 2009 .

[16]  Mario Di Paola,et al.  The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions , 2010 .

[17]  L. Brinson,et al.  Polymer nanocomposites: A small part of the story , 2007 .

[18]  Gilles Lubineau,et al.  A Morphing framework to couple non-local and local anisotropic continua , 2013 .

[19]  H. Golestanian,et al.  Effects of nanotube helical angle on mechanical properties of carbon nanotube reinforced polymer composites , 2011 .

[20]  Tingying Zeng,et al.  Influence of single-walled carbon nanotubes induced crystallinity enhancement and morphology change on polymer photovoltaic devices. , 2006, Journal of the American Chemical Society.

[21]  Gilles Lubineau,et al.  Coupling of nonlocal and local continuum models by the Arlequin approach , 2012 .

[22]  F. Bobaru,et al.  Studies of dynamic crack propagation and crack branching with peridynamics , 2010 .

[23]  Michael Griebel,et al.  Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites , 2004 .

[24]  Xin-Lin Gao,et al.  A shear-lag model for carbon nanotube-reinforced polymer composites , 2005 .

[25]  R. Naghdabadi,et al.  Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites , 2011 .

[26]  I. Szleifer,et al.  Control of carbon nanotube-surface interactions: the role of grafted polymers. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[27]  Christian Rey,et al.  A morphing strategy to couple non-local to local continuum mechanics , 2012 .

[28]  Erdogan Madenci,et al.  Predicting crack propagation with peridynamics: a comparative study , 2011 .

[29]  R. Lehoucq,et al.  Convergence of Peridynamics to Classical Elasticity Theory , 2008 .

[30]  H. Fukunaga,et al.  Prediction of elastic properties of carbon nanotube reinforced composites , 2004, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Serge Prudhomme,et al.  A force-based coupling scheme for peridynamics and classical elasticity , 2013 .

[32]  G. Failla,et al.  Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory , 2009 .

[33]  Stewart Andrew Silling,et al.  Linearized Theory of Peridynamic States , 2010 .

[34]  J. Coleman,et al.  Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites , 2006 .

[35]  William D. Callister,et al.  Materials Science and Engineering: An Introduction , 1985 .

[36]  G. Odegard,et al.  Constitutive Modeling of Nanotube- Reinforced Polymer Composite Systems , 2001 .

[37]  R. Batra,et al.  Uniform radial expansion/contraction of carbon nanotubes and their transverse elastic moduli , 2007 .

[38]  Donald W. Brenner,et al.  The stress–strain behavior of polymer–nanotube composites from molecular dynamics simulation , 2003 .

[39]  A. P. Davey,et al.  Observation of site selective binding in a polymer nanotube composite , 2000 .

[40]  N. Nishimura,et al.  Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method , 2005 .

[41]  Petra Pötschke,et al.  Dispersion, agglomeration, and network formation of multiwalled carbon nanotubes in polycarbonate melts , 2008 .

[42]  Frank T. Fisher,et al.  Direct Observation of Polymer Sheathing in Carbon Nanotube-Polycarbonate Composites , 2003 .

[43]  G. N. Labeas,et al.  Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites , 2008 .

[44]  M. Di Paola,et al.  The finite element method for the mechanically based model of non‐local continuum , 2011 .