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Post-buckling behaviour of carbon-nanotube-reinforced nanocomposite plate

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Abstract

The aim of the present paper is to investigate the buckling and post-buckling behaviour of nanocomposite plate having randomly oriented carbon nanotubes (CNTs) reinforced in magnesium (Mg) under uni-axial compression. The effect of non-bonded interaction at the interface between CNT and matrix is considered through a cohesive zone model, used to predict the elastic property of the interphase, while evaluating the elastic properties of the nanocomposite using a representative volume element. A special purpose program based on finite-element formulation is developed to study the buckling and post-buckling behaviour of nanocomposite plate. The formulation is based on first-order shear deformation theory in conjunction with geometrical non-linearity as per von Karman’s assumptions. A parametric study is conducted to investigate the effects of interphase between CNT and matrix, short-CNT and long-CNT reinforcements and boundary conditions on buckling and post-buckling response of nanocomposite plate. It is found that imperfect bonding between CNT and Mg results in the loss of buckling and post-buckling strength, as compared with perfect bonding, of CNT–Mg nanocomposite plate. It is also concluded that buckling and post-buckling strength is higher for long-CNT-reinforced nanocomposite plate than that of short-CNT reinforcement, irrespective of bonding between CNT and matrix material.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Malaviya National Institute of Technology, Jaipur, 302017, India

    ASHISH SRIVASTAVA & DINESH KUMAR

Authors
  1. ASHISH SRIVASTAVA
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  2. DINESH KUMAR
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Corresponding author

Correspondence to ASHISH SRIVASTAVA.

Nomenclature

\( \phi \)

cohesive energy

σ

van der Waals radius

ε

bond energy at equilibrium distance

r

distance between the particles

\( \rho_{\text{C}} \)

area density of CNT

\( \rho_{m} \)

volume density of matrix material

\( h_{0} \)

equilibrium distance between the nanofiller and matrix material

E

elastic modulus

S

strain

a

side of square RVE

L

length of RVE

\( \sigma_{ij} , \varepsilon_{kl} \) and \( C_{ijkl} \)

stress, strain and stiffness tensor, respectively

\( \overline{\sigma _{ij}} \) and \( \overline{\varepsilon _{kl}} \)

volumetric average of stress and strain of RVE

\( C_{ijkl}^{e} \)

effective stiffness tensor

\( E_{1} \)

Young’s modulus in the axial direction of nanocomposite

\( E_{2} \)

Young’s modulus in the transverse direction of nanocomposite

V RVE

volume of represented volume element

\( v_{f} \)

volume fraction for CNT

r o and r i

external and internal radius of the CNT, respectively

t

thickness of CNT

r I

outer radius of interphase zone

b

width of square plate

h

thickness of square plate

u, v and w

displacements in x, y and z directions, respectively

θ x and θ y

rotation of normal to the undeformed mid-plane in xz- and yz-plane, respectively

\( \bar{W} \)

normalized maximum transverse deflection

N x

uni-axial edge compressive load

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SRIVASTAVA, A., KUMAR, D. Post-buckling behaviour of carbon-nanotube-reinforced nanocomposite plate. Sādhanā 42, 129–141 (2017). https://doi.org/10.1007/s12046-016-0581-9

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  • DOI: https://doi.org/10.1007/s12046-016-0581-9

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