• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.7
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• pp.2931-2938
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• 2011

Effective thermal conductivity of three-phase composites, consisting of matrix and two kinds of spherical inclusions, has been derived as an explicit form by extending modified Eshelby model (MEM) for two-phase composites. The present results are compared with those by differential effective medium model (DEMM), which are also compared with the experimental results of two- and three-phase composites in the literatures to be validated. For two-phase composites, the results by MEM are better than those by DEMM for the inclusion volume fraction smaller than 0.5. Comparisons between the results by two models and experimental results have been made for three-phase composite, resulting in that MEM predicts better than DEMM for smaller volume fraction of the inclusion having larger inclusion-to-matrix thermal conductivity ratio, but DEMM predicts better as its volume fraction increases. It has been observed through parametric study that its volume fraction is the critical factor affecting the deviation of predictions by the two models. The results by them show a good agreement with the three-phase composite proposed by Molina et al..

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.321-332
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• 2009

Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young's modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby's theorem, which states, for two-phase, infinite composites, the inclusion's stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.

• Journal of Welding and Joining
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• v.12 no.4
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• pp.141-150
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• 1994

The residual stress is inevitably introduced into composites because of the mismatch of the coefficient of thermal expansion, and it is different in each phase. The X-ray technique can detect separately the stress in each phase, so will wield useful information for analyzing the toughening mechanisms of composites. In order to apply the law of mixture to alloy steels with composite microstructures, two phase stainless steel, consisted of ferrite (.alpha.-Fe) and austenite (.gamma.-Fe) structures, was selected. The tensile elastic deformation was loaded, and then the X-ray diffraction technique was used to measure the X-ray elastic constants, the X-ray stress constants and the phase stresses. The law of mixture was investigated and the separation of macrostress and microstress was carried out. The phase stresses (the residual stresses of phase) in each phase, which were measured by X-ray technique, was directly proportional to the applied stress. The macrostress calculated from the phase stresses by using the law of mixture was nearly equal to the applied stress.

• Korean Journal of Materials Research
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• v.11 no.11
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• pp.929-935
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• 2001

Two-dimensional computer simulations were conducted on percolation structure in which second phases of various aspect ratios were arranged in a lattice (matrix). The second phases were randomly arranged in an array with two different computational programs; one prohibiting an overlap among second phases and the other allowing the overlap. From the simulation prohibiting the overlap, it was predicted that a complete path was formed at less amounts of the second phase with higher aspect ratios. In the simulation allowing the overlap, a complete path throughout the array was formed by arranging the second phase of an aspect ratio of 1. 5, 20, 100 with less than 59%, 43%, 19%, 4% in the array, respectively.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.23 no.4
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• pp.189-194
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• 2013

Single phase crystalline powders of $Mg_3Sb_2$ and $Mg_3Bi_2$ were prepared by mechanical alloying Mg, Sb and Bi metals with planetary ball milling for 24~48 h. The compositions of starting raw materials for single phase $Mg_3Sb_2$ and $Mg_3Bi_2$ were 3Mg : 1.8Sb and 3Mg : 1.6Bi, respectively. Two types of mechanically alloyed powders obtained were mixed at some ratios for the fabrication of $Mg_3Sb_2-Mg_3Bi_2$ composites and then hot pressed under uniaxial pressure of 70 MPa at 723 K for 1 h. The main phase of composites was a stable phase similar to $Mg_3Bi_2$ phase with a small amount of Bi phase. The distributions of Sb and Bi elements on EDS mapping images were discontinuous and their compositional contours were clear, which means that the hot pressed specimens were composites composed of two compounds of $Mg_3Sb_2$ and $Mg_3Bi_2$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2181-2193
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• 1995

The effective elasticity and conduction of composite materials containing arbitrarily oriented multiple phases has been analyzed using the concept of orientation-dependent average fields and concentration factors. The analysis provided closed form expressions for the effective stiffnesses and conductivities. Under the prescribed boundary conditions, the concentration factors were evaluated by the equivalent inclusion principle, through which the interaction between various phases is approximated by the Mori-Tanaka mean-field approximation. SiC particulate(SiC$_{p}$) reinforce aluminum(Al) matrix composites were fabricated and their elastic constants and electrical conductivities were measured together with a careful study of their microstructure. The measured properties showed a systematic anisotropy and this behavior could be attributed to the preferred orientation of SiC$_{p}$. The theoretical model developed was applied to the computation of the anisotropic properties of these composites. Both two-phase and three-phase composites were considered based on the microstructural information. The SiC$_{p}$ was modeled as an ellipsoid with planar random orientation distribution in the extruded Al/SiC$_{p}$ composites. The effect of extraneous phase such as intermetallic compounds was also investigated.tigated.

• Journal of the Korean Ceramic Society
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• v.35 no.12
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• pp.1266-1273
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• 1998

Al2O3/(5~20vol%)LaAl11O18 composites in which the second phase was dispersed with a elongated grain shape were fabricated using Al2O3 and La2O3 composition by hot-pressing. In order investigate the in-fluence of LaAl11O18 on the toughening of LaAl11O18 on the toughening of Al2O3 matrix composites AE(acoustic emission) analysis was con-ducted together with an evaluation of fracture toughness using of SEPB technique. The degree of AE events occurred in composites were more than those in monolithic alumina. The occurrences of AE event increased with increasing the amount of LaAl11O18 phase in the Al2O3/LaAl11O18 composite is two times higher compared to monolithic alu-mina. The main toughening mechanism was attributed to the bridging of LaAl11O18 grains at tip of pro-pagating crack.

• Journal of Powder Materials
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• v.6 no.1
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• pp.18-35
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• 1999

Phase equilibria in the system Si3N4-TiC-TiCxN1-x-C-N were determined by thermodynamic calculations (CALPHAD-method). The reaction peaction paths for Si3N4-TiC and SiC-TiC composites in the Ti-Si-C-n system were simulated at I bar N2-pressure and varying terpreatures. At a temperature of 1923 K two tie-triangles (TiC0.34N0.66+SiC+C and TiC0.13N0.87+SiC+Si3N4) and two 2-phase fieds (TiCxN1-x+SiC; 0.13

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.04a
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• pp.135-140
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• 1997

The influences of ZrB$_2$ additions to SiC on microstructural, DDM(Electrical Discharge Machining), mechanical and electrical properties were investigated. composites were prepared by adding 15, 30, 45 vol.% ZrB$_2$particles as a second phase to SiC matrix. SiC-ZrB$_2$ composites obtained by hot pressing for high temperature structural application were fully dense with the relative densities over 99%. The fracture toughness of the composites were increased with the ZrB$_2$contents. In case of composite containing 30vol.% ZrB$_2$, the flexural strength and fracture toughness showed 45% and 60% increase, respectively compared to that of monolithic SiC sample. The electrical resistivities of SiC-ZrB$_2$ composites decreased significantly with the ZrB$_2$ contents. The electrical resistivity of SiC-30vol.% ZrB$_2$ composite showed 6.50$\times$10$^{-4}$ $\Omega$.cm. Cutting velocity of EDM of SiC-ZrB$_2$ composites are directly proportional to duty factor of pulse width. Surface roughness, however, are not all proportional to pulse width. Higher-flexural strength composites show a trend toward smaller crater volumes, leaving a smoother surface; the average surface roughness of the SiC-ZrB$_2$ 15 vol.% composite with the flexural strengthe of 375㎫ was 3.2${\mu}{\textrm}{m}$, whereas the SiC-ZrB$_2$ 30.vol% composite of 457㎫ was 1.35${\mu}{\textrm}{m}$. In the SEM micrographs of the fracture surface of SiC-ZrB$_2$ composites, the SiC-ZrB$_2$ two phases are distinct; the white phase is the ZrB$_2$and the gray phase is the SiC matrix. In the SEM micrographs of the EDM surface, however, these phases are no longer distinct because of thicker recast layer of resolidified-melt-formation droplets present. It is shown that SiC-ZrB$_2$ composites are able to be machined without surface cracking.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.11
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• pp.1249-1255
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• 2009

Cord-rubber composites widely used in tires show very complicated mechanical behavior such as nonlinearity and large deformation. Three-phase(cord, rubber and the interface) modeling has been used to analyze the stress distribution in the cord-rubber composites more accurately. In this study, finite element methods were performed using two-dimensional generalized plane strain element and plane strain element to investigate the stress distribution and effective modulus of cord-rubber composites. Neo Hookean model was used for rubber property and several interface properties were assumed for various loading directions. It was found that the interface properties affect the effective modulus and the distributions of shear stress.