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.

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.

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.

Modelling transversely isotropic fiber-reinforced composites with unidirectional fibers and microstructure

2019 ◽  
Vol 24 (11) ◽  
pp. 3444-3455 ◽  
Author(s):  
Ryan Barrage ◽  
Stanislav Potapenko ◽  
Maria Anna Polak
Keyword(s):  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Constitutive Law ◽  
Fiber Reinforced Composites ◽  
Isotropic Case ◽  
Reinforced Composites ◽  
Homogenization Procedure ◽  
Isotropic Composite ◽  
Unidirectional Fibers ◽  
Micropolar Medium

This paper develops a micropolar constitutive model for a transversely isotropic composite material comprised of a polymer matrix and unidirectional fibers. The constitutive law follows Eringen’s model for a generally anisotropic micropolar medium and reduces the model to the transversely isotropic case. The model is then used to develop a boundary value problem with a homogenization procedure, with the goal of obtaining an analytical solution for the homogenized elastic moduli once solved. A variational principle is used to develop the boundary conditions.

scholarly journals On the Theory of Elasticity of Microinhomogeneous Media with Account for Stochastic Changes in the Connectivity of Constituent Components

2021 ◽  
pp. 132-143
Author(s):  
L. A Saraev
Keyword(s):  
Differential Equation ◽  
Composite Material ◽  
Composite Materials ◽  
Numerical Solution ◽  
Elastic Moduli ◽  
Production Factor ◽  
Effective Elastic Moduli ◽  
Connectivity Function ◽  
Isotropic Composite ◽  
Random Connectivity

The paper proposes a mathematical model aimed at calculating the effective elastic moduli of a micro-inhomogeneous two-component isotropic composite material, which components are connected randomly depending on the level of their relative volumetric contents. A stochastic equation is formulated for the connectivity parameter of the constituent components, according to which, with an increase in the volumetric content of the filler, individual inclusions build the structures of the matrix mixture in the form of interpenetrating frameworks, and then turn into a new binding matrix with individual inclusions from the material of the rest of the old matrix. The algorithm for the numerical solution of this stochastic differential equation is constructed in accordance with the Euler-Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random connectivity function of the constituent components of the composite material. A variant of the method aimed at calculating the mathematical expectation of a random connectivity function of the constituent components has been developed and the corresponding differential equation has been obtained for it. It is shown that the numerical solution of this equation and the average value of the production factor function calculated for all realizations of stochastic trajectories give close numerical values. New macroscopic constitutive relations are found for microinhomogeneous materials with a variable microstructure and their effective elastic moduli are calculated. It is noted that the formulas for these effective elastic moduli generalize the known results for isotropic composite materials. The values of the effective elastic moduli, constructed according to the expressions obtained in the paper, lie within the Khashin-Shtrikman range for the lower and upper bounds of the effective elastic moduli of the composite materials. The numerical analysis of the developed models showed a good agreement with the known experimental data.

scholarly journals Extraction of void fraction in metal matrix composite using morphological image processing

1994 ◽  
Vol 3 (2) ◽  
pp. 096369359400300
Author(s):  
Lun X. He ◽  
David K. Hsu ◽  
John P. Basart
Keyword(s):  
Image Processing ◽  
Void Fraction ◽  
Metal Matrix ◽  
Volume Fraction ◽  
Matrix Material ◽  
Void Content ◽  
Matrix Composites ◽  
Cross Sectional ◽  
Morphological Image Processing ◽  
The Matrix

In continuous fiber reinforced metal matrix composites, the volume fraction of voids in the matrix material is an important parameter for material property characterization. In analyzing a cross-sectional micrograph of such a composite, the presence of fiber images and voids occurring on the perimeter of fibers complicates the determination of void content. This paper describes image processing steps using mathematical morphology for the extraction of void fraction in a composite.

Evaporating Meniscus of Ethanol and Ethanol-Based Nanofluids in Single Micro-Channels

2013 ◽  
Vol 390 ◽  
pp. 685-690
Author(s):  
Yuan Wang ◽  
Khellil Sefiane ◽  
Zhen Guo Wang
Keyword(s):  
Heat Flux ◽  
Aspect Ratio ◽  
Evaporation Rate ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Volume ◽  
Cross Sectional ◽  
Stick Slip ◽  
Micro Channels ◽  
Sink Effect

Evaporating meniscus of ethanol and ethanol-based nanofluids (0.01vol.%) in micro-channels were experimentally studied. Visualisation and thermographic results of the stationary meniscus confined in high-aspect-ratio rectangular micro-channels (hydraulic diameters are 571 μm, 727 μm and 1454 μm, channel cross sectional aspect ratio is 20, 20, 10 respectively) were obtained. It was found that interface evaporation rate increases with heat flux. The meniscus interface becomes deformed when the evaporation rate increases. The use of nanofluids largely enhances the interface stability even though the particle volume fraction is at a very low level. Besides, a stick-slip and back-jump behaviour of the nanofluids meniscus was captured during the transition from stable to deformed interface. Moreover, sink effect at the liquid-vapour interface was discussed based on the IR results.

An Analytical Modeling for Effective Thermal Conductivity of Multi-Phase Transversely Isotropic Fiberous Composites Using Generalized Self-Consistent Method

2012 ◽  
Vol 249-250 ◽  
pp. 904-909 ◽  
Author(s):  
Syed Aadil Hassan ◽  
Hassaan Ahmed ◽  
Asif Israr
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Composite System ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Balance Principle ◽  
Isotropic Composite ◽  
Self Consistent ◽  
Consistent Method ◽  
Multi Phase

In this paper a theoretical relationship for the effective thermal conductivity of a multiphase transversely isotropic composite system is obtained. The Generalized Self-Consistent Method and simple energy balance principle is employed to derive a more appropriate model. In the derivation, it is assumed that the orientation of fiber within the transversely isotropic composite system is unidirectional and surrounded by two different phases of porous and matrix phase. A combined effect of these three different phases on the effective thermal conductivity of the composite system in transverse direction is studied. The effect of the interfacial contact conductance between the fibers and porous medium is also considered. Results of effective thermal conductivity are plotted against volume fraction and conductance which shows extremely good agreement.

A Methodology for Synthesizing High-Performance Robots Fabricated With Optimally Tailored Composite Laminates

1987 ◽  
Vol 109 (1) ◽  
pp. 74-86 ◽  
Author(s):  
C. K. Sung ◽  
B. S. Thompson
Keyword(s):  
Composite Laminates ◽  
High Performance ◽  
Volume Fraction ◽  
Three Dimensional ◽  
High Strength ◽  
Fiber Volume ◽  
Cross Sectional ◽  
Fiber Properties ◽  
Robot Arms ◽  
The Matrix

An essential ingredient of the next generation of robotic manipulators will be high-strength lightweight arms which promise high-performance characteristics. Currently, a design methodology for optimally synthesizing these essential robotic components does not exist. Herein, an approach is developed for addressing this void in the technology-base by integrating state-of-the-art techniques in both the science of composite materials and also the science of flexible robotic systems. This approach is based on the proposition that optimal performance can be achieved by fabricating robot arms with optimal cross-sectional geometries fabricated with optimally tailored composite laminates. A methodology is developed herein which synthesizes the manufacturing specification for laminates which are specifically tailored for robotic applications in which both high-strength, high-stiffness robot arms are required which also possess high material damping. The parameters in the manufacturing specification include the fiber-volume fraction, the matrix properties, the fiber properties, the ply layups, the stacking sequence and the ply thicknesses. This capability is then integrated within a finite-element methodology for analyzing the dynamic response of flexible robots. An illustrative example demonstrates the approach by simulating the three-dimensional elastodynamic response of a robot subjected to a prescribed spatial maneuver.

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