Novel Formulations for Higher-Order Bounds on Effective Transverse Elastic Moduli of Three-Phase Cylindrical Fiber Reinforced Composites

2012 ◽  
Author(s):  
Yu-Fu Ko ◽  
J. W. Ju
Keyword(s):  
Elastic Properties ◽  
Elastic Moduli ◽  
Homogenization Method ◽  
Higher Order ◽  
Two Phase ◽  
Special Event ◽  
Three Phase ◽  
Cylindrical Fiber ◽  
Theoretical Predictions ◽  
Order Bounds

A higher-order multiscale structure for three-phase composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area multi-level homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. In the special event, two-phase composites with same elastic properties and sizes of fibers are studied. Two non-equivalent micromechanical formulations are considered to derive effective transverse elastic moduli of two-phase composites leading to new higher-order bounds. Furthermore, the effective transverse elastic moduli for an incompressible matrix containing randomly located and identical circular rigid fibers and voids are derived. It is demonstrated that significant improvements in the singular problems and accuracy are achieved by the proposed methodology. Numerical examples and comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered to illustrate the potential of the present method.

Elastic Moduli of Composites Reinforced by Multiphase Particles

1995 ◽  
Vol 62 (4) ◽  
pp. 1023-1028 ◽  
Author(s):  
M. L. Dunn ◽  
H. Ledbetter
Keyword(s):  
Elastic Moduli ◽  
Aluminum Matrix ◽  
Recent Analysis ◽  
Simple Extension ◽  
Two Phase ◽  
Elastic Fields ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Concentration Factors ◽  
Pulse Echo

A theoretical approach is proposed to estimate the elastic moduli of three-phase composites consisting of a matrix phase reinforced by two-phase particles. The theoretical predictions are based on a simple extension to nondilute concentrations of the mechanical concentration factors obtained from the recent analysis of the average elastic fields in a double inclusion by Hori and Nemat-Nasser (1993). The proposed micromechanics theory can account for the effects of shapes and concentrations of both the particles and the dispersed phase in the particles. Theoretical estimates of the concentration factors and the effective elastic moduli are obtained in closed form and are diagonally symmetric and fall within the Hashin-Shtrikman-Walpole bounds for all cases considered. The theoretical predictions are in excellent agreement with experimental results obtained from pulse-echo and rod-resonance measurements of the elastic moduli of a three-phase composite consisting of an aluminum matrix reinforced by mullite/alumina particles.

Micromechanical analysis of effective mechanical properties of graphene/ZrO2-hybrid poly (methyl methacrylate) nanocomposites

2021 ◽  
pp. 251659842110388
Author(s):  
Ankit Rathi ◽  
S. I. Kundalwal
Keyword(s):  
Methyl Methacrylate ◽  
Elastic Properties ◽  
Mechanical Performance ◽  
Volume Fraction ◽  
Element Model ◽  
Two Phase ◽  
Effective Elastic Properties ◽  
Poly Methyl Methacrylate ◽  
Three Phase ◽  
Effective Mechanical Properties

In this study, the tensile properties of two-phase and three-phase graphene/ZrO2-hybrid poly (methyl methacrylate) (PMMA) nanocomposites are investigated by developing finite element model using ANSYS. Primarily, the effective elastic properties of two- and three-phase graphene/ZrO2-hybrid PMMA nanocomposites (GRPCs) are estimated by developing mechanics of material (MOM) model. Results indicated that the effective elastic properties of GRPCs increase with an increase in the volume fraction of graphene. Also, the stiffness of GRPCs is increased by 78.12% with increasing in the volume fraction of graphene from 0.1 to 0.5 Vf. The incorporation of an additional ZrO2 interphase significantly improved the mechanical performance of resulting GRPCs.

Effective Thermal Conductvity of Three-Phase Soils

2012 ◽  
Author(s):  
Fabio Gori ◽  
Sandra Corasaniti
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Heat Fluxes ◽  
Water Volume ◽  
Two Phase ◽  
Empirical Constant ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Porosity Ratio ◽  
Good Agreement

The aim of the present paper is to determine the effective thermal conductivity of three-phase soils, made of a quasi-spherical solid grain, and surrounded by two phase, which can be water and air or water and ice. The effective thermal conductivity is obtained theoretically by integrating the conduction equation under the thermal distribution of parallel heat fluxes in steady-state. The effective thermal conductivity is evaluated at a given degree of porosity (ratio between the void volume and the total one) and different degrees of saturation (ratio between the water volume and the void one) from dryness up to saturation. Comparisons between experimental data and theoretical predictions confirm that the present model can predict the effective thermal conductivity with a fairly good agreement without using any empirical constant.

Effective Transverse Elastic Properties of Composites Containing Two Types of Continuous Fibers

2007 ◽  
Vol 23 (4) ◽  
pp. 309-318
Author(s):  
P. J. Lin
Keyword(s):  
Elastic Properties ◽  
Current Approach ◽  
Two Phase ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Three Phase ◽  
Local Solutions ◽  
Rigid Fibers ◽  
Interaction Problem ◽  
Properties Of Composites

AbstractBased the previously published model on the two-dimensional micromechanical fiber interaction framework of two-phase composites, effective transverse elastic properties of composites containing two types of randomly located yet unidirectionally aligned circular fibers are studied in this paper. Approximate local solutions for the interaction problem of two randomly located circular fibers of different elastic properties are presented. A fiber-reinforced composite material containing two extreme types of inclusions, voids and rigid fibers, is also investigated. Comparison with Hashin's variational bounds and Mori-Tanaka method, the current approach provides reasonably accurate predictions for three-phase composites. Finally, numerical simulation examples are implemented to demonstrate the capability of the proposed model.

A Three-Phase Constitutive Model for Estimating the Elastic Moduli and The Strengths of Granular Composite Materials

2013 ◽  
Vol 29 (4) ◽  
pp. 675-683 ◽  
Author(s):  
P.-J. Lin
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Elastic Moduli ◽  
Matrix Interface ◽  
Predictive Capability ◽  
Two Phase ◽  
Granular Composite ◽  
Three Phase ◽  
Analytical Formulas ◽  
Inclusion Matrix

ABSTRACTThis paper proposes a three-phase constitutive model for estimating the elastic moduli and strength of granular composite. The three-phase granular composite material containing aggregate (inclusion), matrix, and aggregate/matrix interface were investigated in this study. It was observed that significant improvement in predictive capability for three-phase granular composite materials can be achieved by using the proposed method. By using micromechanics and adopting the double-inclusion concept initiated by Hori and Nemat-Nasser and the two-phase model introduced by Yang et al.; the predicted elastic moduli for three-phase granular composite materials were evaluated. Moreover, analytical formulas were obtained to predict the strengths of three-phase granular composite materials. The potential of the proposed framework was also explored by comparing the analytical predictions in this study with other analytical methods as well as experimental data of other studies.

Quantum-Mechanical Study of Single-Crystalline and Polycrystalline Elastic Properties of Mg-Substituted Calcite Crystals

2013 ◽  
Vol 592-593 ◽  
pp. 335-341 ◽  
Author(s):  
Martin Friák ◽  
Li Fang Zhu ◽  
Liverios Lymperakis ◽  
Hajjir Titrian ◽  
Ugur Aydin ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Mean Field ◽  
Homogenization Method ◽  
Quantum Mechanical ◽  
Two Phase ◽  
Single Crystalline ◽  
Mechanical Study ◽  
Quantum Mechanical Study ◽  
Mg Content ◽  
Stiffening Effect

We use quantum-mechanical calculations to study single-crystalline elastic properties of (Ca,Mg)CO3crystals with concentrations ranging from calcite CaCO3to magnesite MgCO3. By analyzing results for a dense set of distributions of Ca and Mg atoms within 30-atom supercells, our theoretical study shows that those atomic configurations, that minimize the total energy for a given concentration, are characterized by elastic constants that either increase with the Mg content or remain nearly constants. Employing theseab initiocalculated single-crystalline elastic parameters, the polycrystalline elastic properties of (Ca,Mg)CO3aggregates are determined using a mean-field self-consistent homogenization method. The computed integral elastic moduli (bulk and shear) show a significant stiffening impact of Mg atoms on calcite crystals. Our analysis also demonstrates that it is not advantageous to use a granular two-phase composite of stoichiometric calcite and magnesite instead of substituting individual Ca and Mg atoms. Such two-phase aggregates are not significantly thermodynamically favorable and do not offer any strong additional stiffening effect.

Micro-Macro Characterization of Effective Properties for Fibrous Composites With Parallelogram Cells and Imperfect Contact Condition

2011 ◽  
Author(s):  
Reinaldo Rodriguez-Ramos ◽  
Juan Carlos Lo´pez-Realpozo ◽  
Rau´l Guinovart-Di´az ◽  
Julia´n Bravo-Castillero ◽  
J. A. Otero ◽  
...  
Keyword(s):  
Effective Properties ◽  
Transverse Isotropy ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Two Phase ◽  
Imperfect Contact ◽  
Three Phase ◽  
Asymptotic Homogenization Method ◽  
Theoretical Results

In this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Two types of imperfect contact at the interface of the composites are studied: a) imperfect contact via spring model, b) three phase model. Simple closed-form formulae are obtained for the effective properties of the composites with both types of contact and different parallelogram cells by means of the asymptotic homogenization method (AHM). Some numerical examples and comparisons with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of parallelogram cells and imperfect contacts.

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