The effect of inclusion shape on the elastic moduli of a two-phase material

1966 ◽  
Vol 2 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Tai Te Wu
Keyword(s):  
Elastic Moduli ◽  
Two Phase ◽  
Inclusion Shape

scholarly journals Model Calculations of Elastic Moduli in Highly Deformed Composites

1989 ◽  
Vol 10 (2) ◽  
pp. 153-164 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Plastic Deformation ◽  
Simple Model ◽  
Elastic Moduli ◽  
Opposite Sign ◽  
Internal Stresses ◽  
Minor Importance ◽  
High Increase ◽  
Two Phase ◽  
Linear Elasticity Theory ◽  
Model Calculations

Young's modulus of heavily deformed two-phase composites shows an unusually high increase after plastic deformation. It is assumed that this is due to two reasons, i.e. texture changes and changes of the moduli of the constitutive phases on the basis of non-linear elasticity theory and internal stresses of opposite sign in the phases. Expressions of the two contributions are given on the basis of simple model assumptions. It is estimated that the changes of shape and arrangement of the phases and shape and arrangement of the crystallites in the phases are only of minor importance.

Mechanical Properties of Diverse High-Temperature Compounds–Thermal Variation of Microhardness and Crack Formation

1988 ◽  
Vol 133 ◽  
Author(s):  
Robert L. Fleischer
Keyword(s):  
Elastic Moduli ◽  
Crack Formation ◽  
The Other ◽  
Terminal Phase ◽  
Thermal Variation ◽  
Two Phase ◽  
Thermally Activated ◽  
High Melting Temperature ◽  
Binary Compounds ◽  
Single Crystal Plasticity

ABSTRACTMicrohardness vs temperature and elastic moduli have been measured for a suite of intermetallic compounds that melt above 1400°C. Binary intermetallics were selected to represent a variety of crystal structures and yet have optimal combinations of high melting temperature (Tm) and low specific gravity. Some deliberately two-phase alloys were prepared in which one phase is a terminal-phase metal and the other an intermetallic compound.Binary compounds can be described by two patterns. In those where plasticity is difficult, hardness decreased slowly with temperature up to Tm/2, the decrease being no more than that normally shown by the elastic moduli. In those compounds where single crystal plasticity is known (or at least plausible), microhardness decreases more rapidly than do elastic moduli, presumably due to thermally activated slip.

On a Spring-Network Model and Effective Elastic Moduli of Granular Materials

1999 ◽  
Vol 66 (1) ◽  
pp. 172-180 ◽  
Author(s):  
K. Alzebdeh ◽  
M. Ostoja-Starzewaski
Keyword(s):  
Granular Materials ◽  
Disordered Systems ◽  
Granular Media ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Medium ◽  
Solid State Physics ◽  
Two Phase ◽  
Effective Medium Theories ◽  
The Individual

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

Elastic Moduli of Thickly Coated Particle and Fiber-Reinforced Composites

1991 ◽  
Vol 58 (2) ◽  
pp. 388-398 ◽  
Author(s):  
Y. P. Qiu ◽  
G. J. Weng
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Elastic Moduli ◽  
Poisson Ratio ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Two Phase ◽  
Coated Particle ◽  
Replacement Method

Based on the models of Hashin (1962) and Hashin and Rosen (1964), the effective elastic moduli of thickly coated particle and fiber-reinforced composites are derived. The microgeometry of the composite is that of a progressively filled composite sphere or cylinder element model. The exact solutions of the effective bulk modulus κ of the particle-reinforced composite and those of the plain-strain bulk modulus κ23, axial shear modulus μ12, longitudinal Young’s modulus E11, major Poisson ratio ν12, of the fiber-reinforced one are derived by the replacement method. The bounds for the effective shear modulus μ and the effective transverse shear modulus μ23 of these two kinds of composite, respectively, are solved with the aid of Christensen and Lo’s (1979) formulations. By considering the six possible geometrical arrangements of the three constituent phases, the values of κ, and of κ23, μ12, E11, and ν12 are found to always lie within the Hashin-Shtrikman (1963) bounds, and the Hashin (1965), Hill (1964), and Walpole (1969) bounds, respectively, but unlike the two-phase composites, none coincides with their bounds. The bounds of μ and μ23 derived here are consistently tighter than their bounds but, as for the two-phase composites, one of the bounds sometimes may fall slightly below or above theirs and therefore it is suggested that these two sets of bounds be used in combination, always choosing the higher for the lower bound and the lower for the upper one.

scholarly journals Novel and efficient simulation approach for effective permeabilities of randomly ordered two-phase compounds

2019 ◽  
Vol 86 (10) ◽  
pp. 566-576
Author(s):  
Daniel Wöckinger ◽  
Wolfgang Amrhein ◽  
Stefan Schuster ◽  
Johann Reisinger
Keyword(s):  
Raw Materials ◽  
Simulation Method ◽  
Magnetic Characteristics ◽  
The Novel ◽  
Simulation Approach ◽  
Two Phase ◽  
Design And Optimization ◽  
Element Simulation ◽  
Inclusion Shape ◽  
Multi Phase

AbstractThis paper introduces a novel simulation approach for the magnetic properties of two-phase randomly ordered compounds. In industry, materials such as ferrous powder mixtures or metallic granulates are very often used as raw materials. Hence, their material characteristics are of utmost interest for material manufacturers in order to guarantee high quality standards. Typically, many parameters such as composition, inclusion shape, and the characteristics of the constituents affect the macroscopic physical behavior of such materials. In particular, the resulting permeability of multi-phase and randomly ordered materials exhibits a strong variation despite constant compounds. For the design and optimization of measurement setups, efficient simulators are necessary to estimate the effective permeability and its fluctuation range of a huge number of arrangements. In addition to the basic concept of the novel simulation method, this article presents some possible evaluations of the simulated results and their dependencies on the properties of the constituents. In the last century, a large number of different mixing formulas have been established in literature, which are summarized and compared to the simulation results. Finally, the simulated magnetic characteristics are evaluated with finite element simulation of a comparable particle arrangement.

Numerical Studies of the Correlation between Inclusion Shape and Effective Elastic Properties of the Particle Reinforced Composites

2019 ◽  
Vol 827 ◽  
pp. 234-239
Author(s):  
Romana Piat ◽  
Pascal A. Happ
Keyword(s):  
Material Properties ◽  
Three Dimensional ◽  
Reinforced Composites ◽  
Two Phase ◽  
Smooth Structures ◽  
Irregular Shapes ◽  
Numerical Studies ◽  
Effective Material Properties ◽  
Particle Reinforced Composites ◽  
Inclusion Shape

In present paper the effect of inclusions with irregular shapes on the elastic material properties of two-phase composites is studied. The irregular shapes of the real inclusions were approximated using smooth three-dimensional structures. For this needs the images of the microscopic particles were numerically approximated through smooth structures using methods of the computer algebra and were used for the following FE studies. The reference elements with typical inclusions with irregular shapes were determined and used for calculation of the effective material properties.

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.

Determination of closed form expressions of the second-gradient elastic moduli of multi-layer composites using the periodic unfolding method

2018 ◽  
Vol 24 (5) ◽  
pp. 1475-1502 ◽  
Author(s):  
Jean-François Ganghoffer ◽  
Gérard Maurice ◽  
Yosra Rahali
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Elastic Moduli ◽  
Gradient Elasticity ◽  
Constitutive Law ◽  
Two Phase ◽  
Linear Elastic ◽  
Second Gradient ◽  
Two Phases ◽  
Unfolding Method

The present paper aims at introducing a homogenization scheme for the identification of strain–gradient elastic moduli of composite materials, based on the unfolding mathematical method. We expose in the first part of this paper the necessary mathematical apparatus in view of the derivation of the effective first- and second-gradient mechanical properties of two-phase composite materials, focusing on a one-dimensional situation. Each of the two phases is supposed to obey a second-gradient linear elastic constitutive law. Application of the unfolding method to the homogenization of multi-layer materials provides closed form expressions of all effective first- and second-gradient elastic moduli as well as coupling moduli between first- and second-gradient elasticity. A comparison between the unfolding method and the method of oscillating functions shows that both methods, despite their differences, deliver the same effective second-gradient elastic constitutive law for stratified materials.

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