Numerical model for composite material with polymer matrix reinforced by carbon nanotubes

Due to the high stiffness and strength, as well as their ability to act as conductors, carbon nanotubes are under intense investigation as fillers in polymeric materials. The nature of the carbon nanotube/polymer bonding and the curvature of the carbon nanotubes within the polymer have arisen as particular factors in the efficacy of the carbon nanotubes to actually provide any enhanced stiffness or strength to the nanocomposite. Here the effects of carbon nanotube curvature and interface interaction with the matrix on the nanocomposite stiffness are investigated using nanomechanical analysis. In particular, the effects of poor bonding and thus poor shear lag load transfer to the carbon nanotubes are studied. In the case of poor bonding, carbon nanotubes waviness is shown to enhance the composite stiffness.     

Screw dislocations and an interfacial blunt crack with viscoelastic interface

This work deals with the influence of Kelvin-type viscoelastic interface on the generation of screw dislocations near the interfacial blunt crack tip in light of a pair of concentrated loads. The stress fields for dislocation and concentrated load have been obtained by using the integral transform and conformal mapping, the stress intensity factor have been studied, the image force acting on dislocation has been analyzed. The region r_b where n screw dislocations are generated by a pair of concentrated loads and dislocation number are obtained by displacement compatibility and stress compatibility conditions of self-consistent and self-equilibrated systems. The results show that: the force acting on dislocation starts with the value that a perfectly bonded interface, then with relaxation of the imperfect interface; the shield effect for dislocation decreases as time goes by; in addition, with time elapsing, the influence of material shear modulus rate on shielding effect becomes weaker and weaker. The scale of multiplier α(r_b/a) increases with relaxation of imperfect interface, the larger ratio of crack geometry c/a and the smaller ratio of shear modulus μ₁/μ₂ will lead the higher scale of multiplier. When μ₁/μ₂ = 1, the screw dislocations number first increases and then decreases with relaxation of imperfect interface, In addition, it possesses the highest value at t₀ ≈ 1 and tends to vanish at t₀ = ∞. When μ₁ < μ₂, the screw dislocations number increases with relaxation of imperfect interface. When μ₁ > μ₂, the screw dislocations number first increases then decreases with relaxation of imperfect interface, and possesses the highest value at t₀ ≈ 1, the negative value are exclude from the discussion.     

Interaction of a screw dislocation in the interphase layer with the inclusion and matrix

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.     

Interaction between an edge dislocation and a circular inclusion with an inhomogeneously imperfect interface

This research presents an analytical study of the interaction problem of an edge dislocation with a circular inclusion with a circumferentially inhomogeneously imperfect interface. The interface, which is modeled as a spring (interphase) layer with vanishing thickness, is characterized by that in which there is a displacement jump across the interface in the same direction as the corresponding tractions, and the same degree of imperfection is realized in both the normal and tangential directions. Furthermore, the interface parameter is nonuniform along the interface. In order to arrive at an elementary form solution, we introduce a conformal mapping function. Then the stress field as well as the Peach–Koehler force acting on the edge dislocation can be obtained from the derived complex potentials. Calculations demonstrate that the nonuniform interface parameter has a significant influence on the stress field.     

Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites

The load transfer mechanisms and effective moduli of single-walled nanotube (SWNT) reinforced composites are studied using a continuum model. A “critical” fiber length is defined for full load transfer by numerically evaluating the strain-energy-changes for different fiber lengths. The effective longitudinal Young’s modulus and bulk modulus of the composite are derived. The effect of the interphase is also discussed. The results indicate the fiber length is critical both to the load transfer efficiency and effective moduli of the composite. The SWNT-matrix interphase plays an important role in load transfer efficiency but affects the effective moduli only slightly.     

Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes

This paper investigates the transverse and torsional wave in single- and double-walled carbon nanotubes (SWCNTs and DWCNTs), focusing on the effect of carbon nanotube microstructure on wave dispersion. The SWCNTs and DWCNTs are modeled as nonlocal single and double elastic cylindrical shells. Molecular dynamics (MD) simulations indicate that the wave dispersion predicted by the nonlocal elastic cylindrical shell theory shows good agreement with that of the MD simulations in a wide frequency range up to the terahertz region. The nonlocal elastic shell theory provides a better prediction of the dispersion relationships than the classical shell theory when the wavenumber is large enough for the carbon nanotube microstructure to have a significant influence on the wave dispersion. The nonlocal shell models are required when the wavelengths are approximately less than 2.36×10⁻⁹ and 0.95×10⁻⁹ m for transverse wave in armchair (15,15) SWCNT and torsional wave in armchair (10,10) SWCNT, respectively. Moreover, an MD-based estimation of the scale coefficient e₀ for the nonlocal elastic cylindrical shell model is suggested. Due to the small-scale effects of SWCNTs and the interlayer van der Waals interaction of DWCNTs, the phase difference of the transverse wave in the inner and outer tube can be observed in MD simulations in wave propagation at high frequency. However, the van der Waals interaction has little effect on the phase difference of transverse wave.     

Dispersion of multi-walled carbon nanotubes in poly（p-phenylene） thin films and their electrical characteristics

Dispersion of multi-walled carbon nanotubes in poly（p-phenylene） composite exposed to toluene was experimentally investigated. 3 mg of multi-walled carbon nanotubes with nominal size of 20 nm was compounded with 30 mg of poly（p-phenylene） with the presence of terpineol as binding initiator. To investigate an optimal condition for homogenizing all constituents, ultrasonication with an output power of 750W was employed with compounding time of 3, 10, 20 and 30 min. With FTIR analyses, it could be confirmed that homogeneous composite of multi-walled carbon nanotubes and poly（p-phenylene） could be prepared. SEM analyses were also conducted to examine the dispersion of multi-walled carbon nanotubes in the polymer matrix. Then intrinsic electrical resistance of the composites after being exposed to toluene was also investigated. It was found that the composite film prepared with ultrasonication for 20 min could provide sufficiently sensitive response with respect to varied concentration of toluene.     

Interaction between an interface crack and subinterface microcracks in metal/piezoelectric bimaterials

The J-integral analysis is presented for the interaction problem between a semi-infinite interface crack and subinterface matrix microcracks in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack subjected to different loads and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is deduced to a system of singular integral equations with the aid of a superimposing technique. The integral equations are then solved numerically and a conservation law among three values of the J-integral is presented, which are induced from the interface crack tip, the microcracks and the remote field, respectively. The conservation law not only provides a necessary condition to confirm the numerical results derived, but also reveals that the microcrack shielding effect in such materials could be considered as a redistribution of the remote J-integral. It is this redistribution that does lead to the phenomenological shielding effect.