• Transactions of Materials Processing
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• v.10 no.5
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• pp.396-401
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• 2001

The concept of the mixtures can be used not only in the composites but also in the materials with precipitates and matrix. In this investigation, the finite element method of axisymmetric unit cell models and the rule of mixtures of the Voigt and the Reuss models are used to analyze the overall mechanical response of composites with homogeneously distributed particles. The calculations have been cameo out by taking the materials as i) hardening and ii) perfect plastic materials. The Plastic properties are predicted for various volume fractions of the soft and hard particles. The computational results are compared with the results of the rule of mixtures. It is found that the plastic flow curves agree well with the Voigt model when the volume fraction of the particles is high. On the other hand, the calculated flow curves exist between the Voigt model and the Reuss model when the volume fraction of the particles is low.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.399-406
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• 2006

The natural frequencies of Al square plates with a brass inclusion were analyzed by the rule of mixtures. The rule of mixtures is the method to derive natural frequency mutiplying effective inplane wane speed and nondimensional frequency parameters. Numerical models were Al square plates with an inclusion with cantilever type, 2 clamped edge-2 free edge type, 3 clamped edge-1 free edge type and fully clamped edge type. In cantilever type plates, 2 clamped edge-2 free edge type plates and 3 clamped edge-1 free edge plates with an inclusion, good agreement within 10% obtained from rule of mixtures' results and numerical analysis results within inclusion area ratio 1/9. It was found that the natural frequencies of the cantilever type, 2 clamped edge-2 free edge type and 3 clamped edge-1 free edge type plates with an inclusion decrease as the size of inclusion increases when inclusion is located center of plates. And when the density of inclusion is less than the plates, natural frequency of plates with an inclusion increases as the size of inclusion increases.

• Preventive Nutrition and Food Science
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• v.14 no.3
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• pp.233-239
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• 2009

The effects of guar gum (GG) and xanthan gum (XG) at different concentrations (0, 0.2, 0.4, and 0.6% w/w) on the rheological properties of Korean waxy rice starch (WRS) pastes were evaluated under both steady and dynamic shear conditions. The flow properties of WRS-gum mixtures were determined from the rheological parameters of the power law model. The addition of GG and XG to WRS resulted in an increase in the apparent viscosity ($\eta_{a,100}$) and consistency index (K) values obtained from power law model. The flow behavior index (n) values of the WRS-XG mixtures decreased with an increase in gum concentration while there was only a marginal difference between n values for the WRS-GG mixtures. Dynamic moduli (G', G", and $\eta^*$) values in the WRS-gum mixture systems also increased with an increase in gum concentration. WRS-XG mixtures had higher dynamic moduli and lower tan $\delta$ (ratio of G"/G') values than WRS-GG mixtures, indicating that the higher dynamic rheological properties of WRS-XG can be attributed to an increase in the viscoelasticity of the continuous phase in the starch-gum mixture systems, which was due to the higher viscoleastic properties of XG compared to GG. The dynamic ($\eta^*$) and steady shear ($\eta_a$) viscosities of the WRS-XG paste at a 0.2% gum concentration followed the Cox-Merz superposition rule.

• Journal of the Korean Wood Science and Technology
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• v.12 no.3
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• pp.3-8
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• 1984

It is shown that Paul and Jones' Rule of Mixtures modified by Smith and Cox's theory can be used for the fiber-reinforced, sulfur-based composites, when the constant for the linear regression equation is given. The computation results, programmed by Hewlett Packard 75C (HP 75C) using math rom pack for the linear regression form, expressed as $E_c=\frac{1}{3}aE_fV_f+bE_mV_m$, turn out to be a=3.27-3.54 b=-2.47~-2.80. This results indicate that the factors such as density of fiber mat and the amount of matrix used have nothing for affecting the numerical value of the constants a and b of the linear regression form. Conclusively this results also show that the Paul and Jones' Rule of Mixtures which has been used for the composites made by randomly-oriented long fiber can also be used for the composites made by short fiber with the same fiber orientation such as wood and lignocellulosic fibers.

• International Journal of Concrete Structures and Materials
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• v.8 no.1
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• pp.27-41
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• 2014

The use of carbon fibers (CF) and glass fibers (GF) were combined to strengthen concrete flexural members. In this study, data of tensile tests of 94 hybrid carbon-glass FRP sheets and 47 carbon and GF rovings or sheets were thoroughly investigated in terms of tensile behavior. Based on comparisons between the rule of mixtures and test data, positive hybrid effects were identified for various (GF/CF) ratios. Unlike the rule of mixtures, the hybrid sheets with relatively low (GF/CF) ratios also produced pseudo-ductility. From the calibrated results obtained from experiments, a new analytical model for the stress-strain relationship of hybrid FRP sheets was proposed. Finally, the hybrid effects were verified by structural tests of concrete members strengthened with hybrid FRP sheets and either carbon or glass FRP sheets.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.399-404
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• 2000

Functionally graded materials(FGMs) involve dual-phase graded layers in which two different constituents are mixed continuously and functionally according to a given volume fraction. For the analysis of their thermo-mechanical response, conventional homogenized methods have been widely employed in order to estimate equivalent material properties of the graded layer. However, such overall estimations are insufficient to accurately predict the local behavior. In this paper, we compare the thermo-elastic behaviors predicted by several overall material-property estimation techniques with those obtained by discrete analysis models utilizing the finite element method, for various volume fractions and loading conditions.

• Korean Journal of Metals and Materials
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• v.47 no.9
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• pp.567-572
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• 2009

The densification behaviors of mixtures of copper and steel powders during cold die compaction were investigated. We proposed the pressure-dependent yield function based on the rule of the mixtures of each yield function of a critical relative density type. The constitutive equations were implemented into a finite element program (DEFORM2D) to analyze the densification and deformation behavior of powder mixtures, and the simulated results are in good agreement with the experimental results in reference studies.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.03a
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• pp.73-76
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• 1997

Nanocrystalline materials have been modeled as a mixture of the crystallite and the grain boundary phases. The mechanical property has been calculated using the rule of mixtures based on the volume fractions. The critical grain size concept suggested by Nieh and Wadsworth and porous material model suggested by Lee and Kim were applied to the calculation. The theoretical results fit very well with the experimental values

• Journal of the Korean Wood Science and Technology
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• v.15 no.2
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• pp.99-104
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• 1987

Fiber mats were made at various density levels, using fibers from papermill sludge, ricestraw and various mixtures of the two. The paper mill sludges were collected from Moorim Papermill Co, and Jeonjoo Papermill Co. They were soaked in the liquid sulfur compounds, sulfur-tall oil and sulfurpolyester compounds, and made into fiber-reinforced, sulfur-based composition board. Under optimum conditions of fiber mat preparation and saturation with molten sulfur and modified sulfur, the Young's moduls of the manufactured tiber-reinforced composition board are superior to those of conventional wood-based composition boards. For example, the moduli of elasticity of the composition board made from papermill sludge, with a density of 0.40gm/$cm^3$, were greater than 1,400,000psi as compared 800,000psi for high density hardboard(1.28gm/$cm^3$). The modulus of rupture of the best reinforced composition board manufactured was over 9000psi, comparable to 6000psi of high density hardboard. The proposed Bryant and Lee's theory, "Modified Rule of Mixtures" can be applicable to the nonoriented and short fibrous composition board, when it was modified from "Rule of Mixtures" established by Paul an Jones, and supplemented by Smith and Cox's theory, In the Bryant and Lee's theory of $E_c=\frac{1}{3}aE_fV_f+bE_mV_m$, the constants "a" and "b" for the composition boards made from papermill sludge and the mixtures of ricestraw and the sludge were identified to be in the ranges of 3.29~3.54 and -2.47~-2.80 respectively.

• Journal of the Korean Society of Safety
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• v.16 no.4
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• pp.103-108
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• 2001

Explosive limit is one of the major physical properties used to determine the fire and explosion hazards of the flammable substances. Explosive limits are used to classify flammable liquids according to their relative flammability. Such a classification is important for the safe handling of flammable liquids which constitute the solvent mixtures. Explosive limits of all compounds and solvent mixtures can be calculated with the appropriate use of the fundamental laws of Raoult, Dalton, Le Chatelier and activity coefficient models. In this paper, Raoult,s law and van Laar equation(activity coefficient model) are shown to be applicable for the prediction of the explosive limits in the flammable ethylacetate-toluene system. The values calculated by the proposed equations were a good agreement with literature data within a given percent. From a given results, by the use of the proposed equations, it is possible to predict explosive limits of the other flammable mixtures. It is hoped eventually that this method will permit the estimation of the explosive Properties of flammable mixtures with improved accuracy and the broader application for other flammable stances.