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.

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.

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.

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.

scholarly journals Local elastic moduli of simple random composites computed at different length scales

2020 ◽  
Vol 53 (6) ◽  
Author(s):  
E. J. Garboczi ◽  
P. Lura
Keyword(s):  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Delta Function ◽  
Two Phase ◽  
Length Scales ◽  
Average Value ◽  
Young’S Moduli ◽  
Three Phase ◽  
Overlapping Spheres

AbstractTechniques like nanoindentation and atomic force microscopy can estimate the local elastic moduli in a region surrounding the probe used. For composites with phase regions much larger than the size of the probe, these procedures can identify the phases via their different elastic moduli but identifying phase regions that are on the same size scale as the indent is more problematic. This paper looks at three random 3D 8003 voxel composite models, each consisting of a matrix and spherical inclusions. One model has non-overlapping spheres and two models have overlapping spheres, with two and three distinct phases. The linear elastic problem is solved for each microstructure, and histograms are made of the local Young’s moduli over a number of sub-volumes (SVs), averaged over progressively larger SVs. The number and shape of histogram peaks change from N delta functions, where N is the number of elastically distinct phases, at the 1 voxel SV limit, to a single delta function located at the value of the effective global Young’s modulus, when the SV equals the unit cell volume. The phase volume fractions are also tracked for each bin in the Young’s modulus histograms, showing the phase make-up of bin in the histogram. There are clear differences seen between the non-overlapping and three-phase overlapping models and the two-phase overlapping sphere model, because of different size microstructural features, characterized by the average value of size as computed by the W(q) function. In the three-phase model, a peak that is originally all phase 3 persists at its same location, but as the size of the SVs increase, it is made up of a mixture of phases, so that it cannot be identified with a single phase even though it remains a clear peak. These results give some guidance as to what probe size might be useful in distinguishing different phases by local elastic moduli measurements, and how the length scales of the probe and the microstructure interact.

Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites

2005 ◽  
Vol 461 (2057) ◽  
pp. 1475-1504 ◽  
Author(s):  
Lianxi Shen ◽  
Jackie Li
Keyword(s):  
Strain Energy ◽  
Elastic Moduli ◽  
Radial Direction ◽  
Analytical Models ◽  
Effective Elastic Moduli ◽  
The Finite Element Method ◽  
Central Idea ◽  
Two Phase ◽  
Three Phase ◽  
Replacement Model

An effective interphase model (EIM) and a uniform replacement model (URM) are proposed to study the effect of an inhomogeneous interphase with varying elastic properties in the radial direction on the effective elastic moduli of composites reinforced by fibres/spheres. The central idea of these models is to convert a fibre/sphere with its interphase into a two-phase or homogeneous fibre/sphere. Then, the strain energy changes can be obtained using the three-phase model or Eshelby's solution. Detailed comparisons with the finite-element method (FEM) results of the strain energy changes for various possible material combinations of fibre/sphere, interphase and matrix are carried out to check the validity of the two models. Moreover, the other two existing models, the uniform interphase model (UIM) and differential replacement model (DRM), are compared with the new ones. It is shown that the validity of these analytical models depends on the material combinations. The EIM can be valid for general cases, while the simple URM is only valid for some cases. The validity ranges of the two existing models lie between those of the two new ones. Finally, the expressions of the effective elastic moduli of composites involving an inhomogeneous interphase are given by combining these models and the Mori–Tanaka method. The application of these expressions is illustrated through three examples and further comparisons with FEM results are also given.

Elastic Moduli of Gray and Nodular Cast Iron

1980 ◽  
Vol 47 (4) ◽  
pp. 821-826 ◽  
Author(s):  
G. R. Speich ◽  
A. J. Schwoeble ◽  
B. M. Kapadia
Keyword(s):  
Cast Iron ◽  
Elastic Moduli ◽  
Elevated Temperatures ◽  
Gray Cast Iron ◽  
Volume Fraction ◽  
Nodular Cast Iron ◽  
Theoretical Models ◽  
Two Phase ◽  
Wave Technique ◽  
Pulse Echo

The elastic moduli of both gray and nodular cast iron were measured by a pulse-echo elastic-wave technique at ambient and elevated temperatures up to 760°C. When compared at similar graphite contents, the elastic moduli of gray cast iron were much lower than those of nodular cast iron. These results are satisfactorily explained by theoretical models for the elastic moduli of two-phase solids which take into account not only the volume fraction but also the shape of the graphite particles. The temperature-dependence of the elastic moduli of both gray and nodular cast iron can also be correctly predicted from these same models.

The generated power of multipole induction generator with secondary winding on the stator

2009 ◽  
Vol 25 (25) ◽  
pp. 31-34
Author(s):  
Guntis Diļevs ◽  
Edgars Jakobsons
Keyword(s):  
Rotation Speed ◽  
Induction Generator ◽  
Two Phase ◽  
Three Phase ◽  
Secondary Winding

The generated power of multipole induction generator with secondary winding on the statorThis paper posses the construction of induction generator, which has the ability to operate at a low rotation speed. This generator can be applied for directly driven turbine without using the gearbox. The generator is multi pole with all of the windings placed on the stator. Rotor is tooth-like and has no windings on it. Primary winding is three phase, secondary winding is two phase.

Inductor Saturation Compensation in Three-Phase Three-Wire Voltage-Source Converters via Inverse System Dynamics-I

2020 ◽  
Author(s):  
Ziya Özkan ◽  
Ahmet Masum Hava
Keyword(s):  
Dynamic Model ◽  
Dynamic Performance ◽  
Current Control ◽  
Inverse System ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Two Phase ◽  
Inverse Dynamic ◽  
Three Phase ◽  
Steady State Current

In three-phase three-wire (3P3W) voltage-source converter (VSC) systems, utilization of filter inductors with deep saturation characteristics is often advantageous due to the improved size, cost, and efficiency. However, with the use of conventional synchronous frame current control (CSCC) methods, the inductor saturation results in significant dynamic performance loss and poor steady-state current waveform quality. This paper proposes an inverse dynamic model based compensation (IDMBC) method to overcome these performance issues. Accordingly, a review of inductor saturation and core materials is performed, and the motivation on the use of saturable inductors is clarified. Then, two-phase exact modelling of the 3P3W VSC control system is obtained and the drawbacks of CSCC have been demonstrated analytically. Based on the exact modelling, the inverse system dynamic model of the nonlinear system is obtained and employed such that the nonlinear plant is converted to a fictitious linear inductor system for linear current regulators to perform satisfactorily.

Transport of organochlorine pesticides in soil columns enhanced by dissolved organic carbon

1997 ◽  
Vol 35 (7) ◽  
pp. 139-145 ◽  
Author(s):  
Jiann-Yuan Ding ◽  
Shian-Chee Wu
Keyword(s):  
Organic Carbon ◽  
Dissolved Organic Carbon ◽  
Organochlorine Pesticides ◽  
Transport Model ◽  
Phase Model ◽  
Soil Columns ◽  
Two Phase ◽  
Three Phase ◽  
Phase Transport ◽  
Remediation Of Soil

The objective of this study is to quantify the effects of humic acid solution infiltration on the transport of organochlorine pesticides (OCPs) in soil columns using a three-phase transport model. From experimental results, it is found that the dissolved organic carbon enhances the transport of OCPs in the soil columns. In the OCPs-only column, the concentration profiles of OCPs can be simulated well using a two-phase transport model with numerical method or analytical solution. In the OCPs-DOC column, the migrations of aldrin, DDT and its daughter compounds are faster than those in the OCPs-only column. The simulation with the three-phase model is more accurate than that with the two-phase model. In addition, significant decrease of the fluid pore velocities of the OCPs-DOC column was found. When DOC leachate is applied for remediation of soil or groundwater pollution, the decrease of mean pore velocities will be a crucial affecting factor.

A Novel Two-phase Soft Starter Used for Three-phase Asynchronous Motors

2020 ◽  
Vol 13 (8) ◽  
pp. 1175-1182
Author(s):  
Jingwen Chen ◽  
Hongshe Dang
Keyword(s):  
Pulse Generation ◽  
Power Module ◽  
Two Phase ◽  
Power Semiconductor ◽  
Starting Current ◽  
Semiconductor Switches ◽  
Soft Starter ◽  
Three Phase ◽  
And Control ◽  
Driving Circuit

Background: Traditional thyristor-based three-phase soft starters of induction motor often suffer from high starting current and heavy harmonics. Moreover, both the trigger pulse generation and driving circuit design are usually complicated. Methods: To address these issues, we propose a novel soft starter structure using fully controlled IGBTs in this paper. Compared to approaches of traditional design, this structure only uses twophase as the input, and each phase is controlled by a power module that is composed of one IGBT and four diodes. Results: Consequently, both driving circuit and control design are greatly simplified due to the requirement of fewer controlled power semiconductor switches, which leads to the reduction of the total cost. Conclusion: Both Matlab/Simulink simulation results and experimental results on a prototype demonstrate that the proposed soft starter can achieve better performances than traditional thyristorbased soft starters for Starting Current (RMS) and harmonics.

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