Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions

1999 ◽  
Vol 14 (1) ◽  
pp. 49-63 ◽  
Author(s):  
L. V. Gibiansky ◽  
S. Torquato
Keyword(s):  
Effective Properties ◽  
Matrix Material ◽  
Transversely Isotropic ◽  
Effective Moduli ◽  
Phase Volume ◽  
Laminate Composites ◽  
Effective Coefficients ◽  
The Matrix ◽  
Axis Of Symmetry ◽  
Free Parameters

This paper is concerned with the effective piezoelectric moduli of a special class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the matrix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symmetry. The exact expressions for the effective coefficients of such structures are obtained. They can be used to approximate the effective properties of any transversely isotropic dispersion. The advantages of our approximations are that they are (i) realizable, i.e., correspond to specific microstructures; (ii) analytical and easy to compute even in nondegenerate cases; (iii) valid for the entire range of phase volume fractions; and (iv) characterized by two free parameters that allow one to “tune” the approximation and describe a variety of microstructures. The new approximations are compared with known ones.

The Effect of Debonding Angle on the Reduction of Effective Moduli of Particle and Fiber-Reinforced Composites

2002 ◽  
Vol 69 (3) ◽  
pp. 292-302 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Transversely Isotropic ◽  
Fiber Composites ◽  
Fiber Reinforced Composites ◽  
Anisotropic Damage ◽  
Reinforced Composites ◽  
Effective Moduli ◽  
Loading Mode ◽  
Interfacial Cracks ◽  
The Matrix ◽  
Composite Stiffness

In an effort to uncover the effect of interfacial partial debonding on the reduction of composite stiffness, a reduced moduli approach is proposed for the fictitious inclusions which are used to replace the original partially debonded inclusions. The fictitious inclusions are now perfectly bonded to the matrix and any micromechanical theory can be called upon to estimate the moduli of the composite. Using the volume of the inclusion directly beneath the interfacial cracks under the considered loading mode as a measure of damage, a set of anisotropic damage parameters is established in terms of the debonding angle, providing the reduced moduli for the fictitious inclusions. Specific considerations include debonding on the top and bottom of spheres and prolate inclusions, debonding on the lateral surface of spheres and oblate inclusions, and debonding on the top and bottom of circular fibers and elliptic cylinders. The reductions of the five transversely isotropic moduli for the partially debonded particle composites and the nine orthotropic moduli for the partially debonded fiber composites are examined as the debonding angle increases. The theory is also compared with some finite element results, and it suggests that the concept proposed to estimate the reduced moduli of the fictitious inclusions is a viable one.

A translated rigid ellipsoidal inclusion in an elastic medium

1991 ◽  
Vol 434 (1892) ◽  
pp. 571-585 ◽  
Keyword(s):  
Elastic Medium ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Ellipsoidal Inclusion ◽  
Arbitrary Orientation ◽  
Isotropic Matrix ◽  
The Matrix ◽  
Ellipsoidal Surface ◽  
Axis Of Symmetry ◽  
Anisotropic Elastic

A rigid ellipsoidal inclusion is embedded at arbitrary orientation in a homogeneous, arbitrarily anisotropic, elastic matrix and is translated infinitesimally by an externally imposed force. We find directly the relation between the force and translation vectors, and the stress, strain and rotation concentrations over the ellipsoidal surface, without having to solve the equations of equilibrium in the matrix, or the fundamental ones of a point force. We refer particularly then to a spheroid aligned along the axis of symmetry of a transversely isotropic matrix, and subsequently to the full elastic field of a general ellipsoid in an isotropic matrix.

Critical Fiber Length for Load Transfer in Carbon Nanotube (CNT) Reinforced Composites

Aerospace ◽  
2004 ◽  
Author(s):  
Feridun Delale ◽  
Huapei Wan
Keyword(s):  
Carbon Nanotube ◽  
Polymer Matrix ◽  
Fiber Length ◽  
Strain Energy ◽  
Load Transfer ◽  
Effective Properties ◽  
Critical Length ◽  
Polymeric Composite ◽  
Effective Moduli ◽  
The Matrix

In this paper the load transfer mechanism in a carbon nanotube (CNT) reinforced polymeric composite is considered. It is assumed that the polymer matrix is reinforced with single-walled carbon nanotubes and that the continuum model with adjustments is valid in estimating the effective properties of the composite. The existing studies contradict each other with respect to effective load transfer between the matrix and the nanotubes. In this study we show that there is a critical CNT length below which the load transfer is not effective. Thus for an effective load transfer the CNT length must exceed a critical length. To determine the critical length we consider a CNT embedded in a polymer matrix. The polymer/CNT interface is modeled as a distinct layer with elastic properties different than those of the CNT and the matrix. The strain energy change due to the inclusion of a CNT in a polymer matrix is then computed for various interphase stiffnesses using the finite element method. The variation of the strain energy per unit fiber length ΔU/L is plotted versus the aspect ratio of the CNT, L/D. It is observed that ΔU/L first increases steeply with L/D and then reaches a plateau. Since the region of constant ΔU/L is associated with uniform stress distribution, we define the critical CNT length as 90% of the asymptotic value of ΔU/L. It is shown that the load transfer is affected by the nature of the interphase. Next, using a dilute solution the effective moduli of the composite are derived for the cases of both hard and soft interphase. The results indicate that the nature of matrix/CNT interface affects the effective moduli of the composite only slightly.

Application of Variational Asymptotic Micromechanical Method to Strength Analysis of Composite Materials

2019 ◽  
Vol 801 ◽  
pp. 95-100
Author(s):  
Dileep Kumar ◽  
Dineshkumar Harursampath
Keyword(s):  
A Priori ◽  
Plastic Region ◽  
Mathematical Formulation ◽  
Matrix Material ◽  
Transversely Isotropic ◽  
Constitutive Relationship ◽  
Strength Analysis ◽  
The Matrix ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumption regarding the kinematics. The 3-D strain generated in each constituent material is explicitly expressed in 1-D strains and initial curvatures. The advantage of using VAM is that the stress state correlation of constituent materials is taken care of while applying warping constraints. Prandtl-Reuss plasticity theory has been implemented for the plastic region constitutive relationship. The other advantage of this work is that the load-bearing capacity of the composite beyond the elastic region has been considered. Good agreement has been found between experimental data and VAM analysis.

scholarly journals Semi-Analytical Method for Computing Effective Thermoelastic Properties in Fiber-Reinforced Composite Materials

2021 ◽  
Vol 11 (12) ◽  
pp. 5354
Author(s):  
Rodolfo Avellaneda ◽  
Suset Rodríguez-Alemán ◽  
José A. Otero
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Analytical Method ◽  
Effective Properties ◽  
Fibrous Composite ◽  
Transversely Isotropic ◽  
Homogenization Method ◽  
Elliptical Cross ◽  
Periodic Cell ◽  
Effective Coefficients

Effective elastic and thermal properties for isotropic or transversely isotropic thermoelastic fibrous composite materials are obtained. Fibers are distributed with the same periodicity along the two perpendicular directions to the fiber orientation. The periodic cell of the composite has a square or hexagonal distribution. Perfect contact between the fiber and the matrix is presented. The effective properties are calculated using a semi-analytical method. The semi-analytical method consists of obtaining the differential equations that describe the local problems using the Asymptotic Homogenization Method. Then, these equations are solved using the Finite Element Method. Effective elastic coefficient (C¯), effective thermal expansion coefficient (α¯) and the effective thermal conductivity (κ¯) are obtained. The numerical results are compared with the semi-analytical solution and with results reported by other authors. Additionally, the effective properties for a fiber with an elliptical cross section are calculated. Distributions of the fiber’s cross section with different orientations are also studied. A MATLAB program for computing the effective coefficients is presented.

Modeling of Carbon Nanotube Reinforced Rubber Seals

2015 ◽  
Author(s):  
Haitao Zhang ◽  
Ke Li ◽  
Masaei Ito ◽  
Tony Collins
Keyword(s):  
High Pressure ◽  
Structural Integrity ◽  
Oil And Gas ◽  
Effective Properties ◽  
Matrix Material ◽  
Critical Element ◽  
High Concentration ◽  
The Matrix ◽  
Exploration And Production ◽  
Increasing Demand

The increasing demand for oil and gas has incited exploration and production of deeper wells that reach high pressure and high temperature (HPHT) reservoirs. One critical element that is required to this end is rubber seals that can withstand HPHT conditions while meeting the requirements of sealability and structural integrity. Novel nanocomposites that comprise of natural rubber (NR) reinforced by well dispersed, high-concentration carbon nanotubes (CNTs) were recently developed to achieve the desired performance and were experimentally shown to exhibit significantly higher storage modulus than the matrix material. Understanding of the underlying reinforcing mechanism of this class of nanocomposites subjected to large deformation, especially in the real application conditions, has been very limited. In this study, a multiscale modeling method is developed to understand the mechanical behavior of CNT-rubber seals installed in a groove and subjected to high pressure. A micromechanics model is first constructed to evaluate the effective stress-strain responses of a representative volume element under different loading conditions, including uniaxial tension, equal biaxial extension, and planar tension. The effective properties thus established are then inputted into an appropriate hyperelasticity model, which is then used to model a CNT-rubber O-ring installed and pressurized. Sealability and structural integrity are evaluated in terms of contact pressure and strain. The numerical results are compared with the available experimental data. A parametric study is then conducted to assess the effects of CNT concentrations.

Exact Results Concerning the Local Fields and Effective Properties in Piezoelectric Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 260-267 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Effective Properties ◽  
Transversely Isotropic ◽  
Local Fields ◽  
The Other ◽  
Effective Moduli ◽  
Piezoelectric Composites ◽  
Arbitrary Phase ◽  
New Findings ◽  
Piezoelectric Solids ◽  
Underlying Theme

This paper consists of two parts: (a) a concise summary and discussion is given of the recent contributions of the author in the micromechanics of piezoelectric composites. The underlying theme here is the derivation of exact connections for the local fields and effective moduli of heterogeneous piezoelectric solids. Composites of arbitrary phase geometry as well as fibrous systems are considered. (b) New results are presented on the effective behavior of fibrous piezoelectric systems. Fibrous composites with transversely isotropic constituents and cylindrical microgeometry are considered. The exact connections of the author (Benveniste (1993), Proc. R. Soc., Series A, Vol. 441, pp. 59-81) are extended to include the most generally possible overall symmetry of the composite aggregate. The other category of the new findings concerns exact expressions for the effective thermal terms of fibrous systems which possess the same shear modulus GT.

Fabrication of Metal Laminate Composites with Interface Reinforcement by Semi-Solid Sintering

2016 ◽  
Vol 256 ◽  
pp. 205-215
Author(s):  
Mina M.H. Bastwros ◽  
Gap Yong Kim
Keyword(s):  
Spray Deposition ◽  
Matrix Material ◽  
Reference Sample ◽  
Az31 Alloy ◽  
Laminate Composites ◽  
Nanoparticle Layer ◽  
The Matrix ◽  
Magnesium Az31 ◽  
Three Point Bend Test ◽  
Semi Solid

Semi-solid sintering technique has been introduced to alter the interfaces of a metal laminate composite material. A thin layer of reinforcement nanoparticles was applied on substrate metallic sheets using an ultrasonic spray deposition method. The sheets were then stacked, pressed, and sintered in the semi-solid regime of the metallic sheet. The liquid phase present in the matrix material penetrates and diffuses into the nanoparticle layer during consolidation and helps to form a gradual, nanostructured interface. Aluminum (Al6061) and magnesium (AZ31) alloy foils were used as the matrix sheets while various species of reinforcement particles were investigated, including silicon carbide (SiC), silicon (Si), and a mix of Si+SiC. Multilayered metal composites with nanostructured interfaces were successfully consolidated and were evaluated by performing a three-point bend test. AZ31 composites reinforced with SiC nanoparticle interface showed an improvement of 49% in flexural yield strength when compared with a reference sample without such interfaces.

Effective Electromechanical Properties of 622 Piezoelectric Medium With Unidirectional Cylindrical Holes

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Adair Roberto Aguiar ◽  
Julián Bravo Castillero ◽  
Reinaldo Rodríguez Ramos ◽  
Uziel Paulo da Silva
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Matrix Material ◽  
Piezoelectric Medium ◽  
Composite State ◽  
Periodic Distribution ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Cylindrical Holes

The asymptotic homogenization method (AHM) yields a two-scale procedure to obtain the effective properties of a composite material containing a periodic distribution of unidirectional circular cylindrical holes in a linear transversely isotropic piezoelectric matrix. The matrix material belongs to the symmetry crystal class 622. The holes are centered in a periodic array of cells of square cross sections and the periodicity is the same in two perpendicular directions. The composite state is antiplane shear piezoelectric, that is, a coupled state of out-of-plane shear deformation and in-plane electric field. Local problems that arise from the two-scale analysis using the AHM are solved by means of a complex variable method. For this, the solutions are expanded in power series of Weierstrass elliptic functions, which contain coefficients that are determined from the solutions of infinite systems of linear algebraic equations. Truncating the infinite systems up to a finite, but otherwise arbitrary, order of approximation, we obtain analytical formulas for effective elastic, piezoelectric, and dielectric properties, which depend on both the volume fraction of the holes and an electromechanical coupling factor of the matrix. Numerical results obtained from these formulas are compared with results obtained by the Mori–Tanaka approach. The results could be useful in bone mechanics.

Effective Elastic Properties of Porous Materials With Randomly Dispersed Pores: Finite Deformation

2000 ◽  
Vol 67 (4) ◽  
pp. 667-670 ◽  
Author(s):  
V. A. Levin ◽  
V. V. Lokhin ◽  
K. M. Zingerman
Keyword(s):  
Finite Deformation ◽  
Constitutive Equations ◽  
Effective Properties ◽  
Matrix Material ◽  
Finite Deformations ◽  
Cylindrical Shape ◽  
Ensemble Averaging ◽  
Elastic Materials ◽  
The Matrix ◽  
Nonlinear Elastic

A method is developed for the analysis of the effective properties of porous nonlinear elastic materials with randomly distributed interacting pores under finite deformations. The method is based on the solution of the problems of nonlinear elasticity for a representative region using Signorini’s expansion. The constitutive equations for the matrix material and for the comparison material are written in a form corresponding to Murnaghan’s potential. The technique, which is used for ensemble averaging, approximately simulates the uniform distribution of pores. The computations are performed for plane strain, when pores are equal in size, and a circular cylindrical shape in the undeformed state is assumed. [S0021-8936(00)01802-X]

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