scholarly journals Improved Bounds on the Effective Elastic Moduli of Random Arrays of Cylinders

1992 ◽  
Vol 59 (1) ◽  
pp. 1-6 ◽  
Author(s):  
S. Torquato ◽  
F. Lado
Keyword(s):  
Elastic Moduli ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Circular Cylinders ◽  
Effective Elastic Moduli ◽  
Random Arrays ◽  
The Matrix ◽  
Rigorous Bounds ◽  
Fiber Reinforced Material ◽  
The Hill

Improved rigorous bounds on the effective elastic moduli of a transversely isotropic fiber-reinforced material composed of aligned, infinitely long, equisized, circular cylinders distributed throughout a matrix are evaluated for cylinder volume fractions up to 70 percent. The bounds are generally shown to provide significant improvement over the Hill-Hashin bounds which incorporate only volume-fraction information. For cases in which the cylinders are stiffer than the matrix, the improved lower bounds provide relatively accurate estimates of the elastic moduli, even when the upper bound diverges from it (i.e., when the cylinders are substantially stiffer than the matrix). This last statement is supported by accurate, recently obtained Monte Carlo computer-simulation data of the true effective axial shear modulus.

Effective Elastic Moduli of Ribbon-Reinforced Composites

1990 ◽  
Vol 57 (1) ◽  
pp. 158-167 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Aspect Ratio ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Effective Elastic Moduli ◽  
Cross Sectional ◽  
Isotropic Composite ◽  
The Matrix ◽  
The Hill

Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. These moduli are given in terms of the cross-sectional aspect ratio and the volume fraction of the elliptic cylinders. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. It turns out that, in the transversely isotropic case, the effective elastic moduli of the composite coincide with Hill’s and Hashin’s upper bounds if ribbons are harder than the matrix, and coincide with their lower bounds if ribbons are softer. These results are in direct contrast to those of circular fibers. Since the width of the Hill-Hashin bounds can be very wide when the constituents have high modular ratios, this analysis suggests that the ribbon reinforcement is far more effective than the traditional fiber reinforcement.

Modeling of the Effective Elastic Properties of Multifunctional Carbon Nanocomposites Due to Agglomeration of Straight Circular Carbon Nanotubes in a Polymer Matrix

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Chetan Shivaputra Jarali ◽  
Somaraddi R. Basavaraddi ◽  
Björn Kiefer ◽  
Sharanabasava C. Pilli ◽  
Y. Charles Lu
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Properties ◽  
Transverse Isotropy ◽  
Effective Elastic Moduli ◽  
Effective Elastic Properties ◽  
The Matrix ◽  
Nanotube Composites

In the present study, the effective elastic properties of multifunctional carbon nanotube composites are derived due to the agglomeration of straight circular carbon nanotubes dispersed in soft polymer matrices. The agglomeration of CNTs is common due to the size of nanotubes, which is at nanoscales. Furthermore, it has been proved that straight circular CNTs provide higher stiffness and elastic properties than any other shape of the nanofibers. Therefore, in the present study, the agglomeration effect on the effective elastic moduli of the CNT polymer nanocomposites is investigated when circular CNTs are aligned straight as well as distributed randomly in the matrix. The Mori–Tanaka micromechanics theory is adopted to newly derive the expressions for the effective elastic moduli of the CNT composites including the effect of agglomeration. In this direction, analytical expressions are developed to establish the volume fraction relationships for the agglomeration regions with high, and dilute CNT concentrations. The volume of the matrix in which there may not be any CNTs due to agglomeration is also included in the present formulation. The agglomeration volume fractions are subsequently adopted to develop the effective relations of the composites for transverse isotropy and isotropic straight CNTs. The validation of the modeling technique is assessed with results reported, and the variations in the effective properties for high and dilute agglomeration concentrations are investigated.

Rigorous link between the conductivity and elastic moduli of fibre-reinforced composite materials

1995 ◽  
Vol 353 (1702) ◽  
pp. 243-278 ◽  
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli ◽  
Effective Conductivity ◽  
Transversely Isotropic ◽  
Circular Cylinders ◽  
Upper And Lower Bounds ◽  
Two Phase ◽  
Sharp Estimates ◽  
Reinforced Composite ◽  
Random Arrays

We derive rigorous cross-property relations linking the effective transverse electrical conductivity cr* and the effective transverse elastic moduli of any transversely isotropic, two-phase ‘fibre-reinforced’ composite whose phase boundaries are cylindrical surfaces with generators parallel to one axis. Specifically, upper and lower bounds are derived on the effective transverse bulk modulus k* in terms of cr* and on the effective transverse shear modulus //* in terms of cr*. These bounds enclose certain regions in the ct*-ac* and cr*-/r* planes, portions of which are attainable by certain microgeometries and thus optimal. Our bounds connecting the effective conductivity cr* to the effective bulk modulus ft* apply as well to anisotropic composites with square symmetry. The implications and utility of the bounds are explored for some general situations, as well as for specific microgeometries, including regular and random arrays of circular cylinders, hierarchical geometries corresponding to effective-medium theories, and checkerboard models. It is shown that knowledge of the effective conductivity can yield sharp estimates of the effective elastic moduli (and vice versa), even for infinite phase contrast.

Theoretical Prediction of the Anisotropic Effective Thermal Conductivity of Composite Materials

2012 ◽  
Author(s):  
Fabio Gori ◽  
Sandra Corasaniti ◽  
Jean-François Ciparisse
Keyword(s):  
Thermal Conductivity ◽  
Composite Material ◽  
Composite Materials ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Silica Matrix ◽  
Flux Lines ◽  
The Matrix ◽  
Fiber Reinforced Material ◽  
Thermal Conductivities

The composite is made of a matrix and a fiber-reinforced material to form a non-homogeneous anisotropic material. Thermal behaviour of composite materials is very important in many applications as heat shields and heat guides. The present paper investigates theoretically a composite material made of a silica matrix and a fiber reinforcement made of steel. The steady state effective thermal conductivity in the main directions are calculated theoretically for two extreme thermal assumptions, i.e. parallel isothermal lines and parallel heat flux lines. The effective thermal conductivity of the composite is evaluated for a variable thickness of the reinforcement, i.e. for a variable volume fraction. The anisotropy degree, defined as the ratio between the thermal conductivities along the two main directions, increases with the ratio between the thermal conductivities of the reinforcement material and the matrix. The composite material, made of two homogeneous and isotropic materials, is thermally anisotropic and can be used to drive heat towards colder regions. This phenomenon is very useful when a device, such as a spacecraft, must be thermally protected.

Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials

1992 ◽  
Vol 59 (3) ◽  
pp. 539-546 ◽  
Author(s):  
Tungyang Chen ◽  
George J. Dvorak ◽  
Yakov Benveniste
Keyword(s):  
Composite Materials ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
Explicit Formulae ◽  
Cylindrically Orthotropic ◽  
Multiphase Composite

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

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