Electromechanical peridynamics modeling of piezoresistive response of carbon nanotube nanocomposites

Abstract In this work, a coupled electromechanical peridynamics formulation is presented which is used to study the electrical and piezoresistive response of a carbon nanotube (CNT) reinforced polymer nanocomposite material. CNT nanocomposites are multiscale materials which have unique piezoresistive properties arising from mechanisms operating from the nanoscale to the macroscale. The origin of piezoresistivity in CNT nanocomposites is a nanoscale phenomenon known as electron hopping or the electrical tunneling effect which allows an electric current to flow between neighboring CNTs even when not in contact, thereby forming a conductive network. A nanoscale representative volume element of a CNT bundle is chosen, i.e. a local region of high CNT volume fraction within the polymer matrix, wherein coupled electromechanical peridynamic equations are solved to evaluate the effective electrical and piezoresistive properties. The peridynamics formulation is used to introduce electron hopping in a unique way, through electron hopping bonds which have a horizon distance and conductivity dictated by the appropriate physics operating at the nanoscale. The effective electromechanical response depends on parameters such as CNT volume fraction, properties of the polymer matrix between CNTs and applied strain which are investigated in detail. Both quasistatic and dynamic loading conditions are considered where the effective electromechanical response is found to depend on variations in the local conductivity of intertube regions.

[1]  P. Ajayan,et al.  Multifunctional composites using reinforced laminae with carbon-nanotube forests , 2006, Nature materials.

[2]  Youn Doh Ha,et al.  MODELING DYNAMIC FRACTURE AND DAMAGE IN A FIBER-REINFORCED COMPOSITE LAMINA WITH PERIDYNAMICS , 2011 .

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

[4]  Y. Hwang,et al.  Photoluminescence characteristics of Cd1-xMnxTe single crystals grown by the vertical Bridgman method , 2012, Nanoscale Research Letters.

[5]  G. Seidel,et al.  Computational micromechanics analysis of electron-hopping-induced conductive paths and associated macroscale piezoresistive response in carbon nanotube–polymer nanocomposites , 2014 .

[6]  F. Avilés,et al.  Self-sensing of elastic strain, matrix yielding and plasticity in multiwall carbon nanotube/vinyl ester composites , 2013 .

[7]  P. Ma,et al.  Correlations between Percolation Threshold, Dispersion State, and Aspect Ratio of Carbon Nanotubes , 2007 .

[8]  Electrical and Mechanical Properties of Twisted Carbon Nanotubes , 1999, cond-mat/9904411.

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

[10]  V. Chalivendra,et al.  Sensitivity and dynamic electrical response of CNT-reinforced nanocomposites , 2012, Journal of Materials Science.

[11]  Yiping Guo,et al.  Effects of carbon nanotube functionalization on the mechanical and thermal properties of epoxy composites , 2009 .

[12]  D. Suh,et al.  Magnetoresistance of an entangled single-wall carbon-nanotube network , 1998 .

[13]  Mukul M. Sharma,et al.  A peridynamic formulation of pressure driven convective fluid transport in porous media , 2014, J. Comput. Phys..

[14]  F. Bobaru,et al.  Characteristics of dynamic brittle fracture captured with peridynamics , 2011 .

[15]  A. Shukla,et al.  Electrical Response of Carbon Nanotube Reinforced Nanocomposites Under Static and Dynamic Loading , 2012 .

[16]  Tsu-Wei Chou,et al.  Coupled carbon nanotube network and acoustic emission monitoring for sensing of damage development in composites , 2009 .

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

[18]  Xiang Ren,et al.  Computational micromechanics modeling of inherent piezoresistivity in carbon nanotube–polymer nanocomposites , 2013 .

[19]  Gary D. Seidel,et al.  Analysis of clustering, interphase region, and orientation effects on the electrical conductivity of carbon nanotube–polymer nanocomposites via computational micromechanics , 2011 .

[20]  Jifeng Xu,et al.  Peridynamic analysis of damage and failure in composites. , 2006 .

[21]  N. Hu,et al.  Tunneling effect in a polymer/carbon nanotube nanocompositestrain sensor , 2008 .

[22]  Youn Doh Ha,et al.  ADAPTIVE REFINEMENT AND MULTISCALEMODELING IN 2D PERIDYNAMICS , 2011 .

[23]  G. Seidel,et al.  Computational micromechanics analysis of electron hopping induced piezoresistive response in carbon nanotube-polymer nanocomposites , 2013 .

[24]  Tianxi Liu,et al.  Morphology and Mechanical Properties of Multiwalled Carbon Nanotubes Reinforced Nylon-6 Composites , 2004 .

[25]  Meijie Tang,et al.  Reversible electromechanical characteristics of carbon nanotubes underlocal-probe manipulation , 2000, Nature.

[26]  H. Garmestani,et al.  Enhancement of thermal and electrical properties of carbon nanotube polymer composites by magnetic field processing , 2003 .

[27]  Engin C. Sengezer,et al.  Experimental Characterization of Damage Evolution in Carbon Nanotube-Polymer Nanocomposites , 2015 .

[28]  U. Pal,et al.  Effects of crystallization and dopant concentration on the emission behavior of TiO2:Eu nanophosphors , 2012, Nanoscale Research Letters.

[29]  H. Wagner,et al.  Evaluation of Young’s Modulus of Carbon Nanotubes by Micro-Raman Spectroscopy , 1998 .

[30]  Florin Bobaru,et al.  A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities , 2012, J. Comput. Phys..

[31]  Bodo Fiedler,et al.  Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites – A comparative study , 2005 .

[32]  S. Silling,et al.  Peridynamic modeling of membranes and fibers , 2004 .

[33]  Dimitris A. Saravanos,et al.  Piezoresistive behavior of CNT nanocomposites using atomistic and micromechanics models , 2009, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[34]  D. Carroll,et al.  Dynamic electrical properties of polymer-carbon nanotube composites: Enhancement through covalent bonding , 2006 .

[35]  K. Schulte,et al.  Two percolation thresholds in carbon nanotube epoxy composites , 2007 .

[36]  A. Rinzler,et al.  Electronic structure of atomically resolved carbon nanotubes , 1998, Nature.

[37]  K. Tserpes,et al.  Modeling of carbon nanotubes, graphene and their composites , 2014 .

[38]  S. Silling,et al.  Convergence, adaptive refinement, and scaling in 1D peridynamics , 2009 .

[39]  G. Seidel,et al.  Computational micromechanics analysis of electron hopping and interfacial damage induced piezoresistive response in carbon nanotube-polymer nanocomposites , 2014 .

[40]  R. Ruoff,et al.  Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load , 2000, Science.

[41]  Mark J. Schulz,et al.  A carbon nanotube strain sensor for structural health monitoring , 2006 .

[42]  F. Avilés,et al.  Modeling of mesoscale dispersion effect on the piezoresistivity of carbon nanotube-polymer nanocomposites via 3D computational multiscale micromechanics methods , 2015 .

[43]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

[44]  Tsu-Wei Chou,et al.  Modeling of damage sensing in fiber composites using carbon nanotube networks , 2008 .

[45]  Chunyu Li,et al.  Dominant role of tunneling resistance in the electrical conductivity of carbon nanotube-based composites , 2007 .

[46]  Wolfgang Bauhofer,et al.  A review and analysis of electrical percolation in carbon nanotube polymer composites , 2009 .

[47]  Ravi Bhatia,et al.  Electrical Percolation studies of Polystyrene‐multi wall carbon nanotubes Composites , 2009 .

[48]  E. Madenci,et al.  Peridynamic theory for progressive damage prediction in center-cracked composite laminates , 2009 .

[49]  R. Ruoff,et al.  Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties , 2000, Physical review letters.

[50]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[51]  A. Rinzler,et al.  Resistance vs. pressure of single-wall carbon nanotubes , 1998 .

[52]  Arun Shukla,et al.  Electro-mechanical Behavior of Graphene–Polystyrene Composites Under Dynamic Loading , 2015, Journal of Dynamic Behavior of Materials.

[53]  T. Chou,et al.  Carbon Nanotube Networks: Sensing of Distributed Strain and Damage for Life Prediction and Self Healing , 2006 .

[54]  Michael L. Parks,et al.  ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY , 2011 .

[55]  G. Seidel,et al.  Computational micromechanics modeling of piezoresistivity in carbon nanotube–polymer nanocomposites , 2013 .

[56]  E. Madenci,et al.  Prediction of crack paths in a quenched glass plate by using peridynamic theory , 2009 .

[57]  Richard E. Smalley,et al.  METALLIC RESISTIVITY IN CRYSTALLINE ROPES OF SINGLE-WALL CARBON NANOTUBES , 1997 .

[58]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .

[59]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

[60]  C. Lieber,et al.  Atomic structure and electronic properties of single-walled carbon nanotubes , 1998, Nature.

[61]  Shaker A. Meguid,et al.  Tunneling resistance and its effect on the electrical conductivity of carbon nanotube nanocomposites , 2012 .

[62]  B. Kilic,et al.  Peridynamic Theory for Thermomechanical Analysis , 2010, IEEE Transactions on Advanced Packaging.

[63]  J. Simmons.  Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film , 1963 .

[64]  F. Bobaru,et al.  The Meaning, Selection, and Use of the Peridynamic Horizon and its Relation to Crack Branching in Brittle Materials , 2012, International Journal of Fracture.

[65]  Christian A. Martin,et al.  Formation of percolating networks in multi-wall carbon-nanotube–epoxy composites , 2004 .

[66]  Dimitris C. Lagoudas,et al.  Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites , 2006 .

[67]  Wei Zhou,et al.  Nanotube Networks in Polymer Nanocomposites: Rheology and Electrical Conductivity , 2004 .

[68]  Shaker A. Meguid,et al.  Recent Developments in Multifunctional Nanocomposites Using Carbon Nanotubes , 2010 .

[69]  Florin Bobaru,et al.  The peridynamic formulation for transient heat conduction , 2010 .

[70]  F. Avilés,et al.  On the contribution of carbon nanotube deformation to piezoresistivity of carbon nanotube/polymer composites , 2013 .

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

[72]  H. Wagner,et al.  Correlation between interfacial molecular structure and mechanics in CNT/epoxy nano-composites , 2010 .

[73]  Karl Schulte,et al.  Load and health monitoring in glass fibre reinforced composites with an electrically conductive nanocomposite epoxy matrix , 2008 .

[74]  V. Castaño,et al.  Improvement of Thermal and Mechanical Properties of Carbon Nanotube Composites through Chemical Functionalization , 2003 .

[75]  G. Seidel.  Micromechanics modeling of the multifunctional nature of carbon nanotube-polymer nanocomposites , 2007 .

[76]  Dimitris A. Saravanos,et al.  Numerical investigation of mechanisms affecting the piezoresistive properties of CNT-doped polymers using multi-scale models , 2010 .

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

[78]  Yang Wang,et al.  Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes , 2002, Microscopy and Microanalysis.

[79]  Jifeng Xu,et al.  Peridynamic Analysis of Impact Damage in Composite Laminates , 2008 .

[80]  S. Silling,et al.  Viscoplasticity using peridynamics , 2010 .