• Title/Summary/Keyword: Deformation Modulus

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A Description of Thermomechanical Behavior Using a Rheological Model (리올러지 모델을 이용한 열적 기계적 변형 거동 모사)

  • Lee Keum-Oh;Hong Seong-Gu;Lee Soon-Bok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.7 s.250
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    • pp.757-764
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    • 2006
  • Isothermal cyclic stress-strain deformation and thermomechanical deformation (TMD) of 429EM stainless steel were analyzed using a rheological model employing a bi-linear model. The proposed model was composed of three parameters: elastic modulus, yield stress and tangent modulus. Monotonic stress-strain curves at various temperatures were used to construct the model. The yield stress in the model was nearly same as 0.2% offset yield stress. Hardening relation factor, m, was proposed to relate cyclic hardening to kinematic hardening. Isothermal cyclic stress-strain deformation could be described well by the proposed model. The model was extended to describe TMD. The results revealed that the hi-linear thermomechanical model overestimates the experimental data under both in-phase and out-of-phase conditions in the temperature range of $350-500^{\circ}C$ and it was due to the enhanced dynamic recovery effect.

Non-classical plate model for single-layered graphene sheet for axial buckling

  • Safaei, Babak;Khoda, Farzad Hamed;Fattahi, A.M.
    • Advances in nano research
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    • v.7 no.4
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    • pp.265-275
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    • 2019
  • In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

The Effect of Stress on Borehole Deformability (응력이 공내 변형률에 미치는 영향)

  • 윤건신
    • Geotechnical Engineering
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    • v.14 no.5
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    • pp.219-234
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    • 1998
  • Modulus measurements in vertical boreholes under simulated horizontal in-situ stress conditions were performed on laboratory rock specimens. The experimental program was focused on the examination of modulus change with the variation of the orientation, magnitude and ratios of horizontal biaxial stresses. The experiment results show that the modulus increases when the magnitude of the horizontal stresses increases. The modulus measured in the minimum principal direction increased when the ratio between the horizontal principal stresses increased, while the modulus measured in the maximum principal direction decreased when the ratio of the horizontal principal stresses increased. These were caused by the tangential stresses that vary depending upon the magnitude of horizontal stresses, the applied pressure and the orientation of measurement. Also, the measured moduli were determined under tensile stress, compressive stress, or both stresses. Thus, the stress effect on deformation modulus should be considered, not only for the interpretation of the results of borehole deformability measurement, but also for the design of underground gas storage and pressure tunnel, and for the interpretation of tunnel monitoring.

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Relation between Cone Tip Resistance and Deformation Modulus of Cemented Sand (고결모래의 콘선단저항과 변형계수의 관계)

  • Lee, Moon-Joo;Choi, Sung-Kun;Choo, Hyun-Wook;Lee, Woo-Jin
    • Journal of the Korean Geotechnical Society
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    • v.24 no.12
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    • pp.53-63
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    • 2008
  • In this study, the cone tip resistances of cemented sand are measured by performing a series of miniature cone penetration tests in large calibration chamber, and the relations with constrained modulus, unconfined compressive strength, and shear strength of cemented sand are suggested. Experimental results show that both the cone tip resistance and constrained modulus of sand increase with increasing cementation effect as well as relative density and confining stress. However, it is observed that the relative density and confining stress have more significant influence on cone tip resistance than constrained modulus of cemented sand. Since the cone penetration into the ground induces the damage of cementation, the cone tip resistance can't properly reflect the cementation effect of sand. An analysis based on the constrained modulus shows that the measured cone tip resistance underestimates the deformation modulus of cemented sand by about $70{\sim}85%$. In addition, this study establishes various relationships among the above soil properties from the regression analysis.

A Study on Temperature Dependency of Strength and Deformation Behavior of Rocks (암석의 강도 및 변형거동의 온도의존성에 관한 연구)

  • 이형원;이정인
    • Tunnel and Underground Space
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    • v.6 no.2
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    • pp.101-121
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    • 1996
  • The thermomechanical characteristics of rocks such as temperature dependency of strength and deformation were experimentally investigated using Iksan granite, Cheonan tonalite and Chung-ju dolomite for proper design and stability analysis of underground structures subjected to temperature changes. For the temperature below critical threshold temperature $T_c$, the variation of uniaxial compressive strength, Young's modulus, Brazilian tensile strength and cohesion with temperature were slightly different for each rock type, but these mechanical properties decreased at the temperatures above $T_c$ by the effect of thermal cracking. Tensile strength was most affected by $T_c$, and uniaxial compressive strength was least affected by $T_c$. To the temperature of 20$0^{\circ}C$ with the confining prressure to 150 kg/$\textrm{cm}^2$, failure limit on principal stress plane and failure envelope on $\sigma$-$\tau$ plane of Iksan granite were continuously lowered with increasing temperature but those of Cheonan tonalite and Chung-ju dolomite showed different characteristics depending on minor principal stress on principal stress plane and normal stress on $\sigma$-$\tau$ plane. The reason for this appeared to be the effect of rock characteristics and confining pressure. Young's modulus was also temperature and pressure dependent, but the variation of Young's modulus was about 10%, which was small compared to the variation of compressive strength. In general, Young's modulus increased with increasing confining pressure and increased or decreased with increasing temperature to 20$0^{\circ}C$ depending on the rock type.

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Failure and Deformation Characteristics of Rock at High and Low Temperatures (고온 및 저온하에서의 암석의 변형, 파괴 특성)

  • 정재훈;김영근;이형원;이희근
    • Tunnel and Underground Space
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    • v.2 no.2
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    • pp.224-236
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    • 1992
  • It is very important to determine the thermo-mechanical characteristics of the rock mass surrounding the repository of radioctive waste and the LPG storage cavern. In this study, Hwasoon-Shist. Dado-Tuff adn Chunan-Tonalite were the selected rock types. Temperature dependence of the mechanical properteis such as uniaxial compressive strength, tensile strength, Young's modulus was investigated by measuring the behaviour of these properties due to the variation of temperature. Also, the characteristics of strength and deformation of these rocks were examined through high-temperature triaxial compression tests with varing temperatures and confining pressures. Important results obtained are as follows: In high temperature tests, the uniaxial compressive strength and Yong's modulus of Tonalite showed a sligth increase at a temperature up to 300$^{\circ}C$ and a sharp decrease beyond 300$^{\circ}C$, and the tensile strength showed a linear decrease with increasing heating-temperature. In high-temperature triaxial compression test, both the failure stress and Young's modulus of Tonalite increased with the increase of confining pressure at constant heating-temperature, and the failure stress decreased at 100$^{\circ}C$ but increased at 200$^{\circ}C$ under a constant confining pressure. In low temperature tests, the uniaxial compressive and tensile strengths and Young's modulus of these rocks increased as the cooling-temperature is reduced. Also, the uniaxial compressive and tensile strengths of wet rock specimens are less than those of dry rock specimens.

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Effect of Pad Thickness on Removal Rate and Within Wafer Non-Uniformity in Oxide CMP (산화막 CMP에서 패드 두께가 연마율과 연마 불균일도에 미치는 영향)

  • Bae, Jae-Hyun;Lee, Hyun-Seop;Park, Jae-Hong;Nishizawa, Hideaki;Kinoshita, Masaharu;Jeong, Hae-Do
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.23 no.5
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    • pp.358-363
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    • 2010
  • The polishing pad is important element for polishing characteristic such as material removal rate(MRR) and within wafer non-uniformity(WIWNU) in the chemical mechanical planarization(CMP). The result of the viscoelasticity measurement shows that 1st elastic modulus is increased and 2nd elastic modulus is decreased when the top pad is thickened. The finite element analysis(FEA) was conducted to predict characteristic of polishing behavior according to the pad thickness. The result of polishing experiment was similar with the FEA, and it shows that the 1st elastic modulus affects instantaneous deformation of pad related to MRR. And the 2nd elastic modulus has an effect on WIWNU due to the viscoelasticity deformation of pad.

Method of Deciding Elastic Modulus of Left and Right Ventricle Reconstructed by Echocardiography Using Finite Element Method and Stress Analysis

  • Han, Geun-Jo;Kim, Sang-Hyun
    • Journal of Biomedical Engineering Research
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    • v.15 no.2
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    • pp.217-224
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    • 1994
  • In order to study the shape and dimensions of heart, a procedure to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images was studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and by optimization techniques which compared the computer predicted 3D deformation with the experimentally determined deformation. Elastic modulus ranged from 3.5g/$cm^2$ at early diastole to l53g/$cm^2$ at around end diastole showing slightly nonlinear relationship between the modulus and the pressure. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed. The maximum and minimum of ${\sigma}_1$ (max. principal stress) occurred at nodes on the second level intersection points of x-axis with endocardium and with epicardium, respectively. And the tendency of the interventricular septum to be flattened was observed from the compressive ${\sigma}_1$ on the anterior, posterior nodes of left ventricle and from the most significant change of dimension in $D_{RL}$ (septal-lateral dimension of right ventricle).

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The Characteristic of Strength for a Lime Stone in Donghae Area and Harden Cement Milk of Super Injection Grouting (동해 석회암과 SIG 고결체의 강도특성)

  • Park, Young-Ho;Kim, Nak-Young;Hong, Sa-Myun;Yook, Jeong-Hoon;Kim, Ki-Seog
    • Proceedings of the Korean Geotechical Society Conference
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    • 2004.03b
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    • pp.137-145
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    • 2004
  • Limestone zone in korea have been distributed to diagonal line so that it is wide from the Gangwondo to the Jeonlanamdo. The limestone cavity and fractured zone were formed by chemical weathering. Limestone cavity and fractured zone was reinforced with cemented milk(w/c=60%)by high pressure jet grouting by tripple -pipe to establish bridge foundation on the ground condition like limestone cavity. To analyze property of limestone and solid of cement milk(w/c=65%), mixed solid of cement, core NX size in the limestone cavity and fractured zone and compressive strength. Seismic tomograpy exploration was pcrforn1cd to analyze deformation modulus of limestone. The analysis suggests that deformation modulus of limestone has effect on uniaxial compressive strength, seismic velocity, seismic elasticity modulus. Average static elasticity modulus of limestone is $5.08{\times}10^5kgf/cm^2$, cement and coal mixed solid is $0.25{\times}10^5kgf/cm^2$, $0.095{\times}10^5kgf/cm^2$. Average seismic velocity of limestone is 5.240m/sec, cement and coal mixed solid is 2,211.3m/sec, 1,447.5m/sec. Average uniaxial compressive strength of limestone was $1,221.3kgf/cm^2$ and limestone specimen mixed with cement milk and solid of cement milk mixed with coal were $125.22kgf/cm^2$, $35kgf/cm^2$ each other. Average friction angle of limestone was $49.14^{\circ}$ and limestone specimen mixed with cement milk and solid of cement milk mixed with coal were $38.39^{\circ}, 25.83^{\circ}$ each other. Average cohesion of limestone was $137.7kgf/cm^2$ and limestone specimen mixed with cement milk and solid of cement milk mixed with coal were $23.5kgf/cm^2$, $15.5kgf/cm^2$ each other. Average deformation modulus of limestone was $2.84{\times}10^5kgf/cm^2$ and limestone specimen mixed with cement milk and solid of cement milk mixed with coal were $0.4{\times}10^5kgf/cm^2, 0.12{\times}10^5kgf/cm^2$ each other. It was analyzed that the elasticity and uniaxial compressive strength, seismic velocity of solid of cement milk mixed limestone pieces and coal had an highly interrelation regardless of existence of limestones pieces and coal but it had shown that limestones had an lower interrelation. In case of field seismic velocity and deformation of limestone, SIC solid of cement milk mixed with coal and limestone pieces had an highly interrelation.

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Dynamic Deformation Properties of Coarse Granular Materials with Respect to Gradation Characteristics (조립재료의 입도특성에 따른 동적 변형특성 평가)

  • Ha, Ik-Soo;Kim, Nam-Ryong
    • Journal of the Korean Geotechnical Society
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    • v.29 no.8
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    • pp.5-14
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    • 2013
  • Coarse granular geomaterials containing large gravels are broadly used for construction of large geotechnical systems such as dams, levees, railways and backfills. It is necessary to evaluate deformation characteristics of these materials for dynamic analysis, e.g. seismic design. This study presents evaluation of dynamic deformation characteristics of coarse materials using large scale resonant column testing apparatus, which uses specimens with 200 mm in diameter and 400 mm in height, and the effects of gradation characteristics on maximum shear modulus, shear modulus reduction curve and damping characteristics were investigated. From experimental study using rock-fill materials for a dam, we could see that the largest or mean particle size affects the shape of shear modulus reduction curve. When the specimens are prepared under the same conditions for maximum particle size, the coefficient of uniformity affects the confining stress exponent of maximum shear modulus. It could be concluded that the maximum particle size is an factor which affects shear modulus reduction curve, and that the coefficient of uniformity is for small strain shear modulus, especially for the sensitivity to confining stress.