• Title/Summary/Keyword: plastic shear strain

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Thermo-mechanical Behavior of WB-PBGA Packages with Pb-Sn Solder and Lead-free Solder Using Moire Interferometry (무아레 간섭계를 이용한 유연 솔더와 무연 솔더 실장 WB-PBGA 패키지의 열-기계적 변형 거동)

  • Lee, Bong-Hee;Kim, Man-Ki;Joo, Jin-Won
    • Journal of the Microelectronics and Packaging Society
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    • v.17 no.3
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    • pp.17-26
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    • 2010
  • Pb-Sn solder is rapidly being replaced by lead-free solder for board-level interconnection in microelectronic package assemblies due to the environmental protection requirement. There is a general lack of mechanical reliability information available on the lead-free solder. In this study, thermo-mechanical behaviors of wire-bond plastic ball grid array (WB-PBGA) package assemblies are characterized by high-sensitivity moire interferometry. Experiments are conducted for two types of WB-PBGA packages that have Pb-Sn solder and lead-free solder as joint interconnections. Using real-time moire setup, fringe patterns are recorded and analyzed for several temperatures. Bending deformations of the assemblies and average strains of the solder balls are investigated and compared for the two type of WB-PBGA package assemblies. Results show that shear strain in #3 solder ball located near the chip shadow boundary is dominant for the failure of the package with Pb-Sn solder, while normal strain in #7 most outer solder ball is dominant for that with lead-free solder. It is also shown that the package with lead-free solder has much larger bending deformation and 10% larger maximum effective strain than the package with Pb-Sn solder at same temperature level.

Studies on the Frost Heave Revelation and Deformation Behaviour due to Thawing of Weathered Granite Soils (화강암 풍화토의 동상 발현 및 융해에 따른 변형 거동에 관한 연구)

  • 류능환;최중대;류영선
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.37 no.3_4
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    • pp.61-71
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    • 1995
  • Natural ground is a composite consisted of the three phases of water, air and soil paircies. Among the three components, water as a material is weU understood but soil particles are not in foundation engineering. Especially, weathered granite soil generally shows a large volumetric expansion when they freeze. And, the stability and durability of the soil have shown decreased with repetitive freezing and thawing processes. These unique charcteristics may cause various construction and management problems if the soil is used as a construction material and foundation layers. This project was initiated to investigate the soil's physical and engineering characteristics resulting from freezing and freezing-thawing processes. Research results may be used as a basic data in solving various problems related to the soil's unique characteristics. The following conclusions were obtained: The degree of decomposition of weathered granite soil in Kangwon-do was very different between the West and East sides of the divide of the Dae-Kwan Ryung. Soil particles distributed wide from very coarse to fine particles. Consistency could be predicted with a function of P200 as LL=0.8 P200+20. Permeability ranged from 10-2 to 10-4cm/sec, moisture content from 15 to 20% and maximum dry density from 1.55 to 1.73 g /cmΥ$^3$ By compaction, soil particles easily crushed, D50 of soil particles decreased and specific surface significantly increased. Shear characteristics varied wide depending on the disturbance of soil. Strain characteristics influenced the soil's dynamic behviour. Elastic failure mode was observed if strain was less than 1O-4/s and plastic failure mode was observed if strain was more than 10-2/s. The elastic wave velocity in the soil rapidly increased if dry density became larger than 1.5 g /cm$^3$ and these values were Vp=250, Vg= 150, respectively. Frost heave ratio was the highest around 0 $^{\circ}C$ and the maximum frost heave pressure was observed when deformation ratio was less than 10% which was the stability state of soil freezing. The state had no relation with frost depth. Over freezing process was observed when drainage or suction freezing process was undergone. Drainage freezing process was observed if freezing velocity was high under confined pressure and suction frost process was occurred if the velocity was low under the same confined process.

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Experimental Performance Evaluation of Steel Mesh as Maintenance and Reinforcement Materials (Steel Mesh Cement Mortar의 보수⋅보강 성능 평가)

  • Kim, Yeon-Sang;Choi, Seung-Jai;Kim, Jang-Ho Jay
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.18 no.4
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    • pp.50-58
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    • 2014
  • Due to the cost burden of new construction, the necessity of repair and retrofitting of aged structures is sharply increasing as the domain of repair and retrofitting construction is expanding. Because of the necessity, new technologies for repair and retrofitting are continuously studied in Korea and foreign countries. Steel adhesive method, fiber reinforced plastic (FRP) surface adhesive method, and external prestressing method are used to perform the repair and retrofitting works in Korea. In order to consider a repair method using steel mesh reinforced cement mortar (SMCM), 3-point flexural member test was conducted considering repair area and layer number of SMCM. Five types of specimens including ordinary reinforced concrete (RC) specimen with dimensions of $1400{\times}500{\times}200$ (mm) were cast for testing the deflection measurement, a LVDT was installed at the top center of the specimens. Also, a steel strain gauge and a concrete strain gauge were placed at the center of the specimens. A steel strain gauge was also installed on the shear reinforcement. The 3 point flexural member test results showed that the maximum load of SMCM reinforced specimen was higher than that of basic RC specimen in all of the load-displacement curves. Also, the results showed that, when the whole lower part of the basic RC specimen was reinforced, the maximum load and strain were 1.18 and 1.37 times higher than that of the basic RC specimen, respectively. Each specimen showed a slightly different failure behavior where the difference of the results was caused by the difference in the adhesive level between SMCM and RC. Particularly, in SM-B1 specimen, SMCM spalled off during the experiment. This failure behavior showed that the adhesive performance for RC must be improved in order to utilize SMCM as repair and retrofitting material.

Unified Constitutive Model for RC Planar Members Under Cyclic Load (주기하중을 받는 철근 콘크리트 면부재에 대한 통합구성모델)

  • 김재요;박홍근
    • Journal of the Korea Concrete Institute
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    • v.14 no.2
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    • pp.239-248
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    • 2002
  • A constitutive model unifying plasticity and crack damage mode)s was developed to address the cyclic behavior of reinforced concrete planar members. The stress of concrete in tension-compression was conceptually defined by the sum of the compressive stress developed by the strut-action of concrete and the tensile stresses developed by tensile cracking. The plasticity model with multiple failure criteria was used to describe the isotropic damage of compressive crushing affected by the anisotropic damage of tensile cracking. The concepts of the multiple fixed crack damage model and the plastic flow model of tensile cracking were used to describe the tensile stress-strain relationship of multi-directional cracks. This unified model can describe the behavioral characteristics of reinforced concrete in cyclic tension-compression conditions, i.e. multiple tensile crack orientations, progressively rotating crack damage, and compressive crushing of concrete. The proposed constitutive model was implemented to finite element analysis, and it was verified by comparison with existing experimental results from reinforced concrete shear panels and walls under cyclic load conditions.

Deposition Behavior and Microstructure of Fe-based Amorphous Alloy Fabricated by Vacuum Kinetic Spraying Process (진공 저온 분사 공정을 통해 형성된 Fe계 비정질 재료의 적층거동 및 미세구조 변화 관찰)

  • Kwon, Juhyuk;Park, Hyungkwon;Lee, Illjoo;Lee, Changhee
    • Korean Journal of Materials Research
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    • v.24 no.1
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    • pp.60-65
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    • 2014
  • Fe-based amorphous coatings were fabricated on a soda-lime glass substrate by the vacuum kinetic spray method. The effect of the gas flow rate, which determines particle velocity, on the deposition behavior of the particle and microstructure of the resultant films was investigated. The as-fabricated microstructure of the film was studied by field emission scanning electron microscopy (FE-SEM) and high resolution transmission electron microscopy (HR-TEM). Although the activation energy for transformation from the amorphous phase to crystalline phase was lowered by severe plastic deformation and particle fracturing under a high strain rate, the crystalline phases could not be found in the coating layer. Incompletely fractured and small fragments 100~300 nm in size, which are smaller than initial feedstock material, were found on the coating surface and inside of the coating. Also, some pores and voids occurred between particle-particle interfaces. In the case of brittle Fe-based amorphous alloy, particles fail in fragmentation fracture mode through initiation and propagation of the numerous small cracks rather than shear fracture mode under compressive stress. It could be deduced that amorphous alloy underwent particle fracturing in a vacuum kinetic spray process. Also, it is considered that surface energy caused by the formation of new surfaces and friction energy contributed to the bonding of fragments.

A Study on the Microstructure and Anisotropic Mechanical Properties of Oxygen-Free Copper Fabricated by Equal Channel Angular Pressing (ECAP공법으로 제조된 무산소동의 미세조직 및 기계적 성질 이방성에 대한 고찰)

  • Lee, Jaekun;Hong, Younggon;Kim, Hyoungseop;Park, Sunghyuk
    • Journal of the Korea Institute of Military Science and Technology
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    • v.22 no.4
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    • pp.492-500
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    • 2019
  • Equal channel angular pressing(ECAP) is a severe plastic deformation technique capable of introducing large shear strain in bulk metal materials. However, if an ECAPed material has an inhomogeneous microstructure and anisotropic mechanical properties, this material is difficult to apply as structural components subjected to multi-axial stress during use. In this study, extruded oxygen-free copper(OFC) rods with a large diameter of 42 mm are extruded through ECAP by route Bc up to 12 passes. The variations in the microstructure, hardness, tensile properties, and microstructural and mechanical homogeneity of the ECAPed samples are systematically analyzed. High-strength OFC rods with a homogeneous and equiaxed-ultrafine grain structure are obtained by the repeated application of ECAP up to 8 and 12 passes. ECAPed samples with 4 and 8 passes exhibit much smaller differences in terms of the average grain sizes on the cross-sectional area and the tensile strengths along the axial and circumferential directions, as compared to the samples with 1 and 2 passes. Therefore, it is considered that the OFC materials, which are fabricated via the ECAP process with pass numbers of a multiple of 4, are suitable to be applied as high-strength structural parts used under multi-axial stress conditions.

Analytical Solutions for the Inelastic Lateral-Torsional Buckling of I-Beams Under Pure Bending via Plate-Beam Theory

  • Zhang, Wenfu;Gardner, Leroy;Wadee, M. Ahmer;Zhang, Minghao
    • International journal of steel structures
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    • v.18 no.4
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    • pp.1440-1463
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    • 2018
  • The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

Analysis of the Stability and Behavior of a Calcareous Rock Slope During Construction of a Tunnel Entrance (터널출입구 시공에 따른 석회암 사면의 안정성 및 거동 분석)

  • Song, Young-Suk;Yun, Jung-Mann
    • The Journal of Engineering Geology
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    • v.23 no.3
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    • pp.283-292
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    • 2013
  • A calcareous rock slope failed during excavation of the slope for construction of a tunnel entrance. The slope is located at the construction site for widening highway in Yeongwol, Korea. Field surveys, laboratory tests, and numerical analyses were performed to determine the reason for the slope failure. The numerical analysis revealed that the safety factor of the slope before construction of the entrance was less than 1, and that this decreased after construction. After construction of the entrance, the sliding zone of the slope increased and slope stability decreased because the shear strain and plastic zone in the slope over the tunnel entrance showed an increase relative to the lower part of the slope. To enhance the stability of the slope for construction of the tunnel entrance, countermeasures such as rock bolts, rock anchors, and FRP (Fiber glass Reinforced Plastic) grouting were adopted in light of the field conditions. Serial field monitoring performed to confirm the reinforcing effects of the adopted countermeasures revealed a small amount of horizontal deformation of the slope soils, most of the elastic deformation that can regain its former value. In addition, the axial forces of the rock bolt and anchor were more strongly affected by slope excavation during construction of the tunnel entrance than by tunnel excavation or the rainy season, and the axial forces tended to converge after excavation of the tunnel. Therefore, we can confirm that the slope is currently safe.

Molecular Theory of Plastic Deformation (Ⅲ)$^*$

  • Kim, Jae-Hyun;Ree, Tai-Kyue;Kim, Chang-Hong
    • Bulletin of the Korean Chemical Society
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    • v.2 no.3
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    • pp.96-104
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    • 1981
  • (1) The flow data of f (stress) and ${\dot{s}$ (strain rate) for Fe and Ti alloys were plotted in the form of f vs. -ln ${\dot{s}$ by using the literature values. (2) The plot showed two distinct patterns A and B; Pattern A is a straight line with a negative slope, and Pattern B is a curve of concave upward. (3) According to Kim and Ree's generalized theory of plastic deformation, pattern A & B belong to Case 1 and 2, respectively; in Case 1, only one kind of flow units acts in the deformation, and in Case 2, two kinds flow units act, and stress is expressed by $f={X_1f_1}+{X_2f_2}$where $f_1\;and\;f_2$ are the stresses acting on the flow units of kind 1 and 2, respectively, and $X_1,\;X_2$ are the fractions of the surface area occupied by the two kinds of flow units; $f_j=(1/{\alpha}_j) sinh^{-1}\;{\beta}_j{{\dot{s}}\;(j=1\;or\;2)$, where $1/{\alpha}_j\;and\;{\beta}_j$ are proportional to the shear modulus and relaxation time, respectively. (4) We found that grain-boundary flow units only act in the deformation of Fe and Ti alloys whereas dislocation flow units do not show any appreciable contribution. (5) The deformations of Fe and Ti alloys belong generally to pattern A (Case 1) and B (Case 2), respectively. (6) By applying the equations, f=$(1/{\alpha}_{g1}) sinh^-1({\beta}_{g1}{\dot{s}}$) and $f=(X_{g1}/{\alpha}_{g1})sinh^{-1}({\beta}_{g1}{\dot{s}})+ (X_{g2}/{\alpha}_{g2})\;shih^{-1}({\beta}_{g2}{\dot{s}})$ to the flow data of Fe and Ti alloys, the parametric values of $x_{gj}/{\alpha}_{gj}\;and\;{\beta}_{gs}(j=1\;or\;2)$ were determined, here the subscript g signifies a grain-boundary flow unit. (7) From the values of ($({\beta}_gj)^{-1}$) at different temperatures, the activation enthalpy ${\Delta}H_{gj}^{\neq}$ of deformation due to flow unit gj was determined, ($({\beta}_gj)^{-1}$) being proportional to , the jumping frequency (the rate constant) of flow unit gj. The ${\Delta}H_{gj}\;^{\neq}$ agreed very well with ${\Delta}H_{gj}\;^{\neq}$ (self-diff) of the element j whose diffusion in the sample is a critical step for the deformation as proposed by Kim-Ree's theory (Refer to Tables 3 and 4). (8) The fact, ${\Delta}H_{gj}\;^{\neq}={\Delta}H_{j}\;^{\neq}$ (self-diff), justifies the Kim-Ree theory and their method for determining activation enthalpies for deformation. (9) A linear relation between ${\beta}^{-1}$ and carbon content [C] in hot-rolled steel was observed, i.e., In ${\beta}^{-1}$ = -50.2 [C] - 40.3. This equation explains very well the experimental facts observed with regard to the deformation of hot-rolled steel..

Rheological Properties of Cement Paste Mixed with Aqueously Dispersed Single-Walled Carbon Nanotubes (Single-Walled 탄소나노튜브 수용액 혼입 시멘트 페이스트의 유변학적 특성)

  • Kim, Ji-Hyun;Chung, Chul-Woo
    • Journal of the Korea Institute of Building Construction
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    • v.19 no.2
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    • pp.113-121
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    • 2019
  • Single walled carbon nanotube (SWCNT) has been used as a material for reinforcing various advanced materials because it has superior mechanical properties. However, pure SWCNT that does not have any functional group has a hydrophobic character, and exists as bundles due to the strong Van der Waals attraction between each SWCNT. Due to these reasons, it is very difficult to disperse SWCNTs in the water. In this work, in order to use SWCNT for production of cementitious composites, SWCNT was first dispersed in water to make an aqueous solution. Sodium deoxycholate (DOC) and Sodium dodecyl sulfate (SDS) were chosen as surfactants, and the dosage of DOC and SDS were 2wt% and 1wt%, respectively. Sonication and ultracentrifugation were applied to separate each SWCNT and impurities. Using such processed SWCNT solutions, cement paste was prepared and its shear stress vs. strain rate relationship was studied. The yield stress and plastic viscosity of cement paste were obtained using Bingham model. According to the results in this work, cement pastes made with DOC and SDS showed similar rheological behavior to that of air entrained cement paste. While cement paste made with DOC 2 wt.% SWCNT solution showed similar rheological behavior to that of plain cement paste, cement paste made with SDS 1 wt.% SWCNT solution showed different rheological behavior showing much less yield stress than plain cement paste.