• Title/Summary/Keyword: Strain Density Function

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Prediction of Mechanical Behavior for Carbon Black Added Natural Rubber Using Hyperelastic Constitutive Model

  • Kim, Beomkeun
    • Elastomers and Composites
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    • v.51 no.4
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    • pp.308-316
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    • 2016
  • The rubber materials are widely used in automobile industry due to their capability of a large amount of elastic deformation under a force. Current trend of design process requires prediction of functional properties of parts at early stage. The behavior of rubber material can be modeled using strain energy density function. In this study, five different strain energy density functions - Neo-Hookean model, Reduced Polynomial $2^{nd}$ model, Ogden $3^{rd}$ model, Arruda Boyce model and Van der Waals model - were used to estimate the behavior of carbon black added natural rubber under uniaxial load. Two kinds of tests - uniaxial tension test and biaxial tension test - were performed and used to correlate the coefficients of the strain energy density function. Numerical simulations were carried out using finite element analysis and compared with experimental results. Simulation revealed that Ogden $3^{rd}$ model predicted the behavior of carbon added natural rubber under uniaxial load regardless of experimental data selection for coefficient correlation. However, Reduced Polynomial $2^{nd}$, Ogden $3^{rd}$, and Van der Waals with uniaxial tension test and biaxial tension test data selected for coefficient correlation showed close estimation of behavior of biaxial tension test. Reduced Polynomial $2^{nd}$ model predicted the behavior of biaxial tension test most closely.

Derivation of constitutive equations of loose metal powder to predict plastic deformation in compaction (자유분말금속 압축시 소성변형예측을 위한 구성방정식의 유도)

  • Kim, Jin-Young;Park, Jong-jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.2
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    • pp.444-450
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    • 1998
  • In the present investigation, it is attempted to derive a yield function and associated flow rules of loose metal powders to predict plastic deformation and density change during compaction. The loose metal powders yield by shear stress as well as hydrostatic stress and the yield strength is much smaller in tension than compression. Therefore, a yield function for the powders is expressed as a shifted ellipse toward the negative direction in the hydrostatic stress axis in the space defined by the two stresses. Each of parameters A, B and .delta. used in the yield function is expressed as a function of relative density and it is determined by uniaxial strain and hydrostatic compressions using Cu powder. Flow rules obtained by imposing the normality rule to the yield function are applied to the analyses of unidirectional, bidirectional and hydrostatic compressions, resulting in an excellent agreement with experiments. The yield function is further examined by checking volume changes in plane stain, uniaxial strain and shear deformations.

Calculation of Critical Current Density Degradation in the HTS Magnet due to Mechanical Strain (고온초전도마그네트 내부의 스트레인에 의한 임계전류밀도 감소 계산)

  • Lee, In-Kyu;Nah, Wan-Soo
    • Proceedings of the KIEE Conference
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    • 1997.07a
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    • pp.260-263
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    • 1997
  • In this paper, we describe the mechanical strain effects on the critical current density of HTS (BSCCO) pancake-type-magnet. Firstly the strain of pancake coil is calculated in terms of coil length, which is also a function of angle, and then the critical current density degradation due to strain is calculated along the coil. We assumed that the critical current density degradation pattern is same with that of $Nb_{3}Sn$. We also modelled the effects of magnetic field on the critical curent degradation, and the results are compared with those with null magnetic field.

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Application for a BWIM Algorithm Using Density Estimation Function and Average Modification Factor in The Field Test (밀도추정함수와 평균보정계수를 이용한 BWIM 알고리즘의 현장실험 적용)

  • Han, Ah Reum Sam;Shin, Soobong
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.15 no.2
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    • pp.70-78
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    • 2011
  • The paper aims at developing a more reliable and accurate BWIM(Bridge Weigh-In-Motion) algorithm using measured strain data and examining its efficiency with various tests on bridges. It proposes a BWIM algorithm using density estimation function and average modification factor for moment-strain relationship. Density estimation function has been proved to be reliably applied when multiple axle loads are estimated. An average modification factor is applied to minimize overall error that can be encountered between theoretically computed moments and measured strains at multiple locations in a bridge. The developed algorithm has been successfully examined through numerical simulations, laboratory tests, and also by field tests on a multi-girder composite bridge.

Fatigue Strength Assessment of Spot-Welded Lap Joint Using Strain Energy Density Factor

  • Sohn, Ilseon;Bae, Dongho
    • Journal of Mechanical Science and Technology
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    • v.15 no.1
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    • pp.44-51
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    • 2001
  • One of the recent issues in design of the spot-welded structure such as the automobile body is to develop an economical prediction method of the fatigue design criterion without additional fatigue test. In this paper, as one of basic investigation for developing such methods, fracture mechanical approach was investigated. First, the Model I, Mode II and Mode III, stress intensity factors were analyzed. Second, strain energy density factor (S) synthetically including them was calculated. And finally, in order to decide the systematic fatigue design criterion by using this strain energy density factor, fatigue data of the ΔP-N(sub)f obtained on the various in-plane bending type spot-welded lap joints were systematically re-arranged in the ΔS-N(sub)f relation. And its utility and reliability were verified by the theory of Weibull probability distribution function. The reliability of the proposed fatigue life prediction value at 10(sup)7 cycles by the strain energy density factor was estimated by 85%. Therefore, it is possible to decide the fatigue design criterion of spot-welded lap joint instead of the ΔP-N(sub)f relation.

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Thermo-Elasto-Plastic Finite Element Analysis of Powder Hot Forging (열간분말단조 공정의 열탄소성 유한요소해석)

  • 김형섭
    • Journal of Powder Materials
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    • v.4 no.2
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    • pp.83-89
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    • 1997
  • A finite element analysis to solve the coupled thermomechanical problem in the plane strain upsetting of the porous metals was performed. The analysis was formulated using the yield function advanced by Lee and kim and developed using the thermo-elasto-plastic time integration procedure. The density and temperature dependent thermal and mechanical properties of porous metals were considered. The internal heat generation by the plastic deformation and the changing thermal boundary conditions corresponding to the geometry were incorporated in the program. The distributions of the stress, strain, pressure, density and temperature were predicted during the free resting period, deformation period and dwelling period of the forging process.

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A Study on the Resistance and Crack Propagation of ITO/PET Sheet with 20 nm Thick ITO Film (20 nm 두께의 ITO층이 코팅된 ITO/PET Sheet의 저항 및 균열형성 특성 연구)

  • Kim, Jin-Yeol;Hong, Sun-Ig
    • Journal of the Korean Ceramic Society
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    • v.46 no.1
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    • pp.86-93
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    • 2009
  • The crack formation and the resistance of ITO film on PET substrate with a thickness of 20 nm were investigated as a function of strain. The onset strain for the increase of resistance increased with increasing strain rate, suggesting the crack initiation is dependent on the strain rate. Electrical resistance increased at the strain of 1.6% at the strain rates below $10^{-4}/sec$ while it increased at ${\sim}2%$ at the strain rates above $10^{-3}/sec$. The critical strain at which the cracks were formed is close to the proportional limit. Upon loading, the initial cracks perpendicular to the tensile axis were observed and propagated the whole sample width with increasing strain. The spacing between horizontal cracks is thought to be determined by the fracture strength and the interfacial strength between ITO and PET. The crack density increased with increasing strain. However, the effect of the strain rate on the crack density was less pronounced in ITO/PET with 20 nm ITO thickness than ITO/PET with 125 nm ITO thickness, the strength of ITO film is thought to increase as the thickness on ITO film decreases. The absence of cracks on ITO film at a strain as close as 1.5% can be attributed to the compressive residual stress of ITO film which was developed during cooling after the coating process. The higher critical strain for the onset of the resistance increase and the crack initiation of ITO/PET with a thinner ITO film (20 nm) can be linked with the higher strength of the thinner ITO film.

Crack Length Estimation for Large Deformable Non-Linear Elastic Materials (대변형 비선형 탄성재료의 균열길이 예측)

  • Yang, Gyeong-Jin;Gang, Gi-Ju;Park, Sang-Seo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.1 s.173
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    • pp.103-109
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    • 2000
  • A method to measure the crack length in rubbery materials is described. Through dimensional analysis and experiments, an equation is derived to give the crack length as a function of the change of strain energy density in a region remote from the crack. The function is provided in a form of separated terms of loading and material, the validity of which is experimentally proved using separation parameters.

A Yield Function for Sintered Porous Metals (소결분말금속의 항복함수)

  • 박종진
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.5
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    • pp.1115-1122
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    • 1993
  • Several yield criteria for porous materials are compared with each other, defining the apparent yield stress as the yield stress of the porous material in simple compression. It was found that the plastic Poisson's ratio is the parameter needed to define the yield criterion, rather than the relative density. The plastic Poisson's ratio is regarded as a material characteristic that is obtained from a simple compression test. A new form of yield criterion was suggested, and it was applied to hydrostatic compression as well as uniaxial strain compression of sintered Al-2024 powder. The crossover point in the mean stress vs volume change curves of the processes was predicted. It is presented that the flow stress of the fully densed material can be obtained from that of the porous material using relations obtained from the yield criterion.

Effect of Microstructure on Dynamic Tensile Characteristics of SPRC440 Sheet (SPRC440 강판재의 미세조직 구성이 동적 인장 특성에 미치는 영향)

  • Lee, S.H.;Rhyim, Y.M.;Lee, J.H.;Kim, I.B.;Kim, Y.D.
    • Transactions of Materials Processing
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    • v.20 no.4
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    • pp.309-315
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    • 2011
  • The behavior of metallic materials at high strain rates shows different characteristics from those in quasi-static deformation. Therefore, the strain rate should be considered when simulating crash events. The objective of this paper is to evaluate the dynamic tensile characteristics of SPRC440 as a function of the volume fraction of phases. As-received SPRC440 is composed of ferrite and pearlite phases. However, ferrite and martensite phases were observed after heat treatment at $730^{\circ}C$ and $780^{\circ}C$ for 5 minutes, as expected by calculations based on the curves from dilatometry tests. High cross-head speed tensile tests were performed to acquire strain-stress curves at various strain rates ranging from 0.001 to $300\;s^{-1}$, which are typical in real vehicle crashes. It was observed that the flow stress increases with the strain rate and this trend was more pronounced in the as-received specimens consisting of ferrite and pearlite phases. It is speculated that the dislocation density in each phase has an influence on the strain rate sensitivity.