• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• Journal of Welding and Joining
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• v.24 no.6
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• pp.21-27
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• 2006

This study was focused on the evaluation of the thermo-mechanical board-level reliability of Pb-bearing and Pb-free surface mount assemblies. The composition of Pb-bearing solder was a typical Sn-37Pb and that of Pb-free solder used in this study was a representative Sn-3.0Ag-0.5Cu in mass %. Thermal shock test was chosen for the reliability evaluation of the solder joints. Typical $Cu_6Sn_5$ intermetallic compound (IMC) layer was formed between both solders and Cu lead frame at the as-reflowed state, while a layer of $Cu_3Sn$ was additionally formed between the $Cu_6Sn_5$ and Cu lead frame during the thermal shock testing. Thickness of the IMC layers increased with increasing thermal shock cycles, and this is very similar result with that of isothermal aging study of solder joints. Shear test of the multi layer ceramic capacitor(MLCC) joints was also performed to investigate the degradation of mechanical bonding strength of solder joints during the thermal shock testing. Failure mode of the joints after shear testing revealed that the degradation was mainly due to the excessive growth of the IMC layers during the thermal shock testing.

• Journal of Korean Society of Steel Construction
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• v.11 no.4 s.41
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• pp.373-384
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• 1999

The shell structures with composite materials have the advantages in strength, corrosion resistance, and weight reduction. The objective of this study is to analyze anisotropic composite circular cylindrical shells with shear deformation theory. In applying numerical methods to solve differential equations of anisotropic shells, this paper use finite difference method. The accuracy of the numerical method can be improved by taking higher order of interval ${\Delta}$ to reduce error. This study compares the results of finite difference method with the results of ANSYS based on finite element method. Several numerical examples show the advantages of the stiffness increasement when the composite materials aroused. Therefore, it is expected that results of this study give various guides for change of the subtended angles, load cases, boundary conditions, and side-to-thickness ratio.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.4
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• pp.759-764
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• 2012

Copper Pillar Tin Bump (CPTB) was investigated for high density chip interconnect technology development, which was prepared by electroplating and electro-less plating methods. Copper pillar tin bumps that have $100{\mu}m$ pitch were introduced with fabrication process using a KM-1250 dry film photoresist (DFR), with copper electroplating for Copper Pillar Bump (CPB) formation firstly, and then tin electro-less plating on it for control oxidation. Electric resistivity and mechanical shear strength measurements were introduced to characterize the oxidation effects and bonding process as a function of thermo-compression. Electrical resistivity increased with increasing oxidation thickness, and shear strength had maximum value with $330^{\circ}C$ and 500 N at thermo-compression process. Through the simulation work, it was proved that the CPTB decreased in its size of conduction area as time passes, however it was largely affected by the copper oxidation.

• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.3
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• pp.134-141
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• 2013

Reflow soldering process is essential in electronic package. Reflow process for a long time results from the decrease of reliability because IMC is formed excessively. Solder alloys of Sn-37Pb and Sn-Ag with different kinds of Cu contents (0, 0.5 and 1 wt.%) as compared with Ni and Cu plate joints are investigated according to varying reflow time. The interfaces of solder joints are observed to analyze IMC (intermetallic compound) growth rate by scanning electron microscope (SEM). Shear test is also performed by using SP (Share-Punch) tester. The test results are compared with the solder joints of two different plates (Ni and Cu plate). $Cu_6Sn_5$ IMCs are formed on Cu plate interfaces after reflows in all samples. Ni3Sn4 and $(Cu,Ni)_6Sn_5$ IMCs are also formed on Ni plate interfaces. The IMC layer forms are affected by reflow time and contents of solder alloy. These results show that mechanical strength of solder joints strongly depends on thickness and shape of IMC.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Asian-Australasian Journal of Animal Sciences
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• v.28 no.8
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• pp.1061-1065
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• 2015

Data collected from 690 purebred Duroc pigs from 2009 to 2012 were used to estimate the heritability, and genetic and phenotypic correlations between production and meat quality traits. Variance components were obtained through the restricted maximum likelihood procedure using Wombat and SAS version 9.0. Animals were raised under the same management in five different breeding farms. The average daily gain, loin muscle area (LMA), backfat thickness (BF), and lean percent (LP) were measured as production traits. Meat quality traits included pH, cooking loss, lightness ($L^*$), redness ($a^*$), yellowness ($b^*$), marbling score (MS), moisture content (MC), water holding capacity (WHC), and shear force. The results showed that the heritability estimates for meat quality traits varied largely from 0.19 to 0.79. Production traits were moderate to highly heritable from 0.41 to 0.73. Genotypically, the BF was positively correlated (p<0.05) with MC (0.786), WHC (0.904), and pH (0.328) but negatively correlated with shear force (-0.533). The results of genetic correlations indicated that selection for less BF could decrease pH, moisture content, and WHC and increase the shear force of meat. Additionally, a significant positive correlation was recorded between average daily gain and WHC, which indicates pork from faster-growing animals has higher WHC. Furthermore, selection for larger LMA and LP could increase MS and lightness color of meat. The meat quality and production traits could be improved simultaneously if desired. Hence, to avoid further deterioration of pork characteristics, appropriate selection of traits should be considered.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.53-66
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• 2018

This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton's principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.

• Journal of Korean Society of Steel Construction
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• v.12 no.6
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• pp.749-758
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• 2000

This study presents a governing equations of bending behavior of sandwich plates with thick metal, polymer composite facings. Based on zig-zag models for through thickness deformations, the transverse shear deformation of composite facings is included. All edges of plate are assumed to be simply supported. Results of the bending analysis under lateral loads are presented for the influence of various lay up sequences of antisymmetric angle-ply laminated facings. The accuracy of the approach is ascertained by comparing solutions from the sandwich plates theory with composite facings to the laminated plates theory. Since the present analysis considers the bending stiffness of the core and also the transverse shear deformations of the laminated facings, the proposed method showed higher than that calculated according to the general laminated plates theory. The information presented might be useful to design sandwich plates structure with metal, polymer matrix composite facings.

• Journal of Korean Society of Steel Construction
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• v.27 no.1
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• pp.1-12
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• 2015

Well-designed bolted connections can exhibit excellent ductile behavior through bearing mechanism until the occurrence of bolt shear rupture. The ultimate strength analysis of eccentric bolted connections is an economical and mechanistic approach which uses such ductility. However, the bolt load-deformation relationship, which forms basis of the current practice, is based on very limited combinations of bolt and steel materials. The primary objective of this study was to establish the general bolt force-deformation relationship based on systematic single-bolt bearing connection tests. The test results showed that the projected area of the bolt hole and the strength and thickness of the plate to be connected are the main factors affecting the force-deformation relationship. The results of this study can be used for the instantaneous center of rotation method (ICRM) to achieve more accurate analysis and economical design of a variety of group-bolted connections subjected to eccentric shear.