Alternative Formulation of Elastic Fields due to Inhomogeneous Isotropic Spherical Inclusions Undergoing Shape-Conserving Volume Change

1992 ◽  
Vol 59 (4) ◽  
pp. 1026-1027
Author(s):  
S. Schmauder ◽  
W. Mader
Keyword(s):  
Shear Modulus ◽  
Elastic Constants ◽  
Volume Change ◽  
Spherical Inclusion ◽  
Infinite Medium ◽  
Alternative Formulation ◽  
Elastic Fields ◽  
Spherical Inclusions ◽  
The Matrix ◽  
Initial Strains

In this Note alternative formulae are derived for the elastic fields due to homogeneous initial strains in an isotropic spherical inclusion embedded in an isotropic infinite medium, assuming a shape conserving volume change of the inclusion. The bulk modulus of the inclusion and the shear modulus of the matrix are the only physically relevant elastic constants necessary to describe analytically displacements, strains, and stresses in the inclusion and the matrix.

Micromechanics Analysis of Elastic Modulus of Alumina-Carbon Refractories

2015 ◽  
Vol 1095 ◽  
pp. 175-179
Author(s):  
Tian Fei Ma ◽  
Hong Xia Li ◽  
Xin Fu Wang ◽  
Guo Qi Liu
Keyword(s):  
Elastic Modulus ◽  
Elastic Constants ◽  
Phenolic Resin ◽  
Raw Materials ◽  
Spherical Inclusion ◽  
Great Influence ◽  
Effective Elastic Modulus ◽  
Carbon Phase ◽  
Spherical Inclusions ◽  
Multi Phase

Based on the micromechanics theory, Alumina-carbon refractories were regarded as resin-carbon bonded composites, including alumina, graphite and pores derived from particles packing gaps and phenolic resin pyrolysis. Graphite was regarded as isotropic spherical inclusions; particles packing gaps and phenolic resin pyrolysis pores were regarded as pore phase all together. Applying Mori-Tanaka multi-phase spherical inclusion method, firstly, elastic constants of resin-carbon phase were computed reversely by the elastic constants known alumina-carbon refractories, alumina and graphite, and then the effective elastic modulus of alumina-carbon refractories were estimated by the calculated elastic constants of resin-carbon and other raw materials. The results show that: the predicted elastic modulus by Mori-Tanaka model are higher than the experimental measurement values; resin carbon residue and pores have a great influence on effective elastic modulus of alumina-carbon refractories.

A Spherical Inclusion in an Elastic Half-Space Under Shear

1997 ◽  
Vol 64 (3) ◽  
pp. 471-479 ◽  
Author(s):  
I. Jasiuk ◽  
P. Y. Sheng ◽  
E. Tsuchida
Keyword(s):  
Half Space ◽  
Spherical Inclusion ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Elastic Fields ◽  
Surrounding Matrix ◽  
Uniform Shear ◽  
The Matrix ◽  
Displacement Potentials ◽  
Space Matrix

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to its traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclusion and the surrounding matrix is either perfectly bonded or is allowed to slip without friction. We obtain an analytical solution to this problem using displacement potentials in the forms of infinite integrals and infinite series. We include numerical examples which give the local elastic fields due to the inclusion and the traction-free surface.

The microstructure change of low-carbon electrical steels by residual aluminum

1989 ◽  
Vol 47 ◽  
pp. 286-287
Author(s):  
C.K. Hou ◽  
C.T. Hu ◽  
Sanboh Lee
Keyword(s):  
Annealing Treatment ◽  
Low Carbon ◽  
Electrical Steels ◽  
Vacuum Degassing ◽  
Spherical Inclusions ◽  
Residual Aluminum ◽  
Average Grain Size ◽  
The Matrix ◽  
Fine Size ◽  
To Come

The fully processed low-carbon electrical steels are generally fabricated through vacuum degassing to reduce the carbon level and to avoid the need for any further decarburization annealing treatment. This investigation was conducted on eighteen heats of such steels with aluminum content ranging from 0.001% to 0.011% which was believed to come from the addition of ferroalloys.The sizes of all the observed grains are less than 24 μm, and gradually decrease as the content of aluminum is increased from 0.001% to 0.007%. For steels with residual aluminum greater than 0. 007%, the average grain size becomes constant and is about 8.8 μm as shown in Fig. 1. When the aluminum is increased, the observed grains are changed from the uniformly coarse and equiaxial shape to the fine size in the region near surfaces and the elongated shape in the central region. SEM and EDAX analysis of large spherical inclusions in the matrix indicate that silicate is the majority compound when the aluminum propotion is less than 0.003%, then the content of aluminum in compound inclusion increases with that in steel.

scholarly journals Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
O. N. Senkov ◽  
D. B. Miracle
Keyword(s):  
Crystal Structure ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Single Crystal ◽  
Elastic Constants ◽  
Mechanical Analysis ◽  
Quantum Mechanical ◽  
Modulus Ratio ◽  
Cubic Crystal ◽  
The Difference

AbstractTwo classical criteria, by Pugh and Pettifor, have been widely used by metallurgists to predict whether a material will be brittle or ductile. A phenomenological correlation by Pugh between metal brittleness and its shear modulus to bulk modulus ratio was established more than 60 years ago. Nearly four decades later Pettifor conducted a quantum mechanical analysis of bond hybridization in a series of intermetallics and derived a separate ductility criterion based on the difference between two single-crystal elastic constants, C12–C44. In this paper, we discover the link between these two criteria and show that they are identical for materials with cubic crystal structures.

Optimization of thermal conductivity in composites loaded with the solid-solid phase-change materials

2018 ◽  
Vol 25 (6) ◽  
pp. 1157-1165
Author(s):  
Taoufik Mnasri ◽  
Adel Abbessi ◽  
Rached Ben Younes ◽  
Atef Mazioud
Keyword(s):  
Thermal Conductivity ◽  
Phase Change ◽  
Phase Change Materials ◽  
Solid Phase ◽  
Spherical Inclusions ◽  
First Case ◽  
The Matrix ◽  
Composite Conductivity ◽  
First Time

AbstractThis work focuses on identifying the thermal conductivity of composites loaded with phase-change materials (PCMs). Three configurations are studied: (1) the PCMs are divided into identical spherical inclusions arranged in one plane, (2) the PCMs are inserted into the matrix as a plate on the level of the same plane of arrangement, and (3) the PCMs are divided into identical spherical inclusions arranged periodically in the whole matrix. The percentage PCM/matrix is fixed for all cases. A comparison among the various situations is made for the first time, thus providing a new idea on how to insert PCMs into composite matrices. The results show that the composite conductivity is the most important consideration in the first case, precisely when the arrangement plane is parallel with the flux and diagonal to the entry face. In the present work, we are interested in exploring the solid-solid PCMs. The PCM polyurethane and a wood matrix are particularly studied.

scholarly journals Role of temperature in the numerical analysis of CaO under high pressure

2010 ◽  
Vol 8 (1) ◽  
pp. 126-133 ◽  
Author(s):  
Purvee Bhardwaj ◽  
Sadhna Singh
Keyword(s):  
Phase Transition ◽  
High Pressure ◽  
Numerical Analysis ◽  
Thermodynamic Properties ◽  
Elastic Constants ◽  
Volume Change ◽  
Thermodynamical Properties ◽  
Phase Transition Pressure ◽  
Different Temperatures

AbstractIn this paper we focus on the elastic and thermodynamic properties of the B1 phase of CaO by using the modified TBP model, including the role of temperature. We have successfully obtained the phase transition pressure and volume change at different temperatures. In addition elastic constants and bulk modulus of B1 phase of CaO at different temperatures are discussed. Our results are comparable with the previous ones at high temperatures and pressures. The thermodynamical properties of the B1 phase of CaO are also predicted.

scholarly journals Mechanical and Thermal Conductivity Properties of Enhanced Phases in Mg-Zn-Zr System from First Principles

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2010
Author(s):  
Shuo Wang ◽  
Yuhong Zhao ◽  
Huijun Guo ◽  
Feifei Lan ◽  
Hua Hou
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Intermetallic Compounds ◽  
Elastic Constants ◽  
First Principles ◽  
Strengthening Phases ◽  
Zr Alloy ◽  
Zr Alloys

In this paper, the mechanical properties and minimum thermal conductivity of ZnZr, Zn2Zr, Zn2Zr3, and MgZn2 are calculated from first principles. The results show that the considered Zn-Zr intermetallic compounds are effective strengthening phases compared to MgZn2 based on the calculated elastic constants and polycrystalline bulk modulus B, shear modulus G, and Young’s modulus E. Meanwhile, the strong Zn-Zr ionic bondings in ZnZr, Zn2Zr, and Zn2Zr3 alloys lead to the characteristics of a higher modulus but lower ductility than the MgZn2 alloy. The minimum thermal conductivity of ZnZr, Zn2Zr, Zn2Zr3, and MgZn2 is 0.48, 0.67, 0.68, and 0.49 W m−1 K−1, respectively, indicating that the thermal conductivity of the Mg-Zn-Zr alloy could be improved as the precipitation of Zn atoms from the α-Mg matrix to form the considered Zn-Zr binary alloys. Based on the analysis of the directional dependence of the minimum thermal conductivity, the minimum thermal conductivity in the direction of [110] can be identified as a crucial short limit for the considered Zn-Zr intermetallic compounds in Mg-Zn-Zr alloys.

scholarly journals 3D MORPHOLOGICAL ANALYSIS OF COMPOSITE MATERIALS WITH AGGREGATES OF SPHERICAL INCLUSIONS

2011 ◽  
Vol 22 (1) ◽  
pp. 153 ◽  
Author(s):  
Arnaud Delarue ◽  
Dominique Jeulin
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Empirical Distribution ◽  
Geodesic Distance ◽  
Shortest Paths ◽  
Morphological Properties ◽  
3D Images ◽  
Spherical Inclusions ◽  
New Information ◽  
The Matrix

Composite materials containing aggregates of spherical inclusions are studied from 3D images obtained by X-ray microtomography. Using two point statistics in different directions, and the empirical distribution of orientations of pairs of inclusions, interesting details concerning the anisotropy of the distribution of inclusions are obtained and are related to the method of construction for these materials. Some 3D morphological properties, available on the 3D images, give new information on the shape and the distribution of aggregates: tortuosity of shortest paths in the matrix, local volume fraction, geodesic distance function, local histograms of numbers of objects.

Elastic Constants in C-plane of Single Crystal Bi 2Sr 2Ca Cu 208 between 80 K and 260 K

1990 ◽  
Vol 193 ◽  
Author(s):  
Jin Wu ◽  
Yening Wang ◽  
Yifeng Yan ◽  
Zhongxian Zhao
Keyword(s):  
Shear Modulus ◽  
Single Crystal ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Wide Temperature Range ◽  
Sound Propagation ◽  
Anisotropic Elasticity ◽  
Ultrasonic Velocities ◽  
Temperature Range

ABSTRACTThe temperature dependence of the in-plane C11 C22. C12 and C66 modes between 80 and 260 K of superconducting crystals of Bi2Sr2Ca1Cu208 have been obtained via the measurements of ultrasonic-velocities. The anisotropic elasticity in the a-b plane of single crystal Bi2 Sr2Ca1Cu2O8 is manifest. The shear modulus of sound propagation along the [110] with the polarization has been also calculated and shows an overall trend of softening over a wide temperature range above Tc. The shear modulus C6 6 shows three obvious softening minima around 240–250 K, 150 K and 100 K.

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

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