• Title/Summary/Keyword: Constitutive Relation

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Dynamic recrystallization and microstructure evolution of a Nb-V microalloyed forging steel during hot deformation

  • Zhao, Yang;Chen, Liqing;Liu, Xianghua
    • Advances in materials Research
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    • v.3 no.4
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    • pp.217-225
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    • 2014
  • In this study, a forging steel alloyed with both Nb and V was used as experimental material and the hot deformation behavior has been studied for this steel by conducting the compressive deformation test at temperature of $900-1150^{\circ}C$ and strain rate of $0.01-0.01s^{-1}$ in a MMS-300 thermo-mechanical simulator. The microstructure evolution, particularly the dynamically recrystallized microstructure, of the experimental steel at elevated temperatures, strain rates and strain levels, was characterized by optical microstructural observation and the constitutive equation in association with the activation energy and Zener-Hollomon parameter. The curves of strain hardening rate versus stress were used to determine the critical strain and peak strain, and their relation was connected with Zener-Hollomon parameter. Under the conditions of processing temperature $900^{\circ}C$ and strain rate $0.01s^{-1}$, the dynamic recrystallization took place and the austenite grain size was refined from $164.5{\mu}m$ to $28.9{\mu}m$.

Localized Plastic Deformation in Plastic Strain Gradient Incorporated Combined Two-Back Stress Hardening Model (변형량 기울기 이론이 조합된 이중후방응력 경화모델에서의 국부적 소성변형)

  • Yun, Su-Jin;Lee, Sang-Youn;Park, Dong-Chang
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2011.11a
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    • pp.528-535
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    • 2011
  • In the present, the formation of shear band under a simple shear deformation is investigated using a rate-independent elastic-plastic constitutive relations. Moreover, the strain gradient terms are incorporated to obtain a non-local plastic constitutive relation, which in turn represented using combined two-back stress hardening model. Then, the continuum damage model is also included to the proposed model. The post-localization behavior are studied by introducing a small imperfection in a work piece. The strain gradient affects the shear localization significantly such that the intensity of shear band decreases as the strain gradient coefficient increases when the J2 flow theory is employed.

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Computational methodology to determine the strength of reinforced concrete joint

  • Sasmal, Saptarshi;Vishnu Pradeesh, L.;Devi, A. Kanchana;Ramanjaneyulu, K.
    • Advances in Computational Design
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    • v.1 no.1
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    • pp.61-77
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    • 2016
  • Seismic performance of structures depends on the force flow mechanism inside the structure. Discontinuity regions, like beam-column joints, are often affected during earthquake event due to the complex and discontinuous load paths. The evaluation of shear strength and identification of failure mode of the joint region are helpful to (i) define the strength hierarchy of the beam-column sub-assemblage, (ii) quantify the influence of different parameters on the behaviour of beam-column joint and, (iii) develop suitable and adequate strengthening scheme for the joints, if required, to obtain the desired strength hierarchy. In view of this, it is very important to estimate the joint shear strength and identify the failure modes of the joint region as it is the most critical part in any beam-column sub-assemblage. One of the most effective models is softened strut and tie model which was developed by incorporating force equilibrium, strain compatibility and constitutive laws of cracked reinforced concrete. In this study, softened strut and tie model, which incorporates force equilibrium equations, compatibility conditions and material constitutive relation of the cracked concrete, are used to simulate the shear strength behaviour and to identify failure mechanisms of the beam-column joints. The observations of the present study will be helpful to arrive at the design strategy of the joints to ensure the desired failure mechanism and strength hierarchy to achieve sustainability of structural systems under seismic loading.

The role of extensional rheology in polymer processing

  • Baird, Donald G.
    • Korea-Australia Rheology Journal
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    • v.11 no.4
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    • pp.305-311
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    • 1999
  • The shear behavior of polymers obtained by means of devices such as capillary and cone-and-plate rheo-meters is commonly used to assess their processing performance and as a characterization tool. However, the number of instances when two polymers have the same shear properties but perform differently during certain types of processing operations (e.g. film blowing and sheet extrusion) indicate that shear properties alone may not be sufficient to characterize polymeric fluids. We begin by defining the kinematics of shear-free or extensional flow and the associated material functions. The extensional and shear behavior of three different types of polyethylene (PE) are then compared to illustrate the points that one cannot ascertain the extensional properties of polymer melts from their shear properties and, furthermore, there may not be a simple relation between properties obtained from one type of extensional flow and those of another type. The kinematics of most processing flows are extensional rather than shear in nature, and , hence, the performance of polymers during processes such as fiber spinning, film casting, film blowing, thermoforming, blow molding, and even extrusion is more readily accounted for through extensional viscosity measurements. Methods for carrying out extensional flow measurements are then reviewed including approximate methods. To illustrate the sensitivity of extensional viscosity measurements to subtle changes in the molecular architecture of PEs, results are presented for samples with a narrow molecular weight distribution but with varying numbers of long chain branches. Finally, constitutive equations which allow one to separate shear and extensional flow behavior are discussed as any attempts to simulate the subtle processing differences between two polymers will require constitutive equations of this nature.

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Modeling refractory concrete lining of fluid catalytic cracking units of oil refineries

  • Silva, Ana B.C.G.;Andrade, Henrique C.C.;Fairbairn, Eduardo M.R.;Telles, Jose C.F.;Ribeiro, Fernando L.B.;Toledo-Filho, Romildo D.;Medeiros, Jorivaldo
    • Computers and Concrete
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    • v.25 no.1
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    • pp.29-36
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    • 2020
  • This work presents a numerical modeling procedure to simulate the refractory concrete lining in fluid catalytic cracking units of oil refineries. The model includes the simulation of the anchors that reinforce the contact between the refractory concrete and the steel casing. For this purpose, the constitutive relations of an interface finite element are set to values that represent the homogenized behavior of the anchored interface. The parameters of this constitutive relation can be obtained by experimental tests. The model includes also multi-surface plasticity, in order to represent the behavior of the refractory concrete lining. Since the complexity of real case applications leads to high computational costs, the models presented here were implemented in a high-performance parallelized finite element platform. A case study representing a riser similar to the ones used by the refinery industry demonstrates the potential of the model.

Design charts for estimating the consolidation times of reclaimed marine clays in Korea

  • Sang-Hyun Jun;Byung-Soo Park;Hyuk-Jae Kwon;Jong-Ho Lee
    • Geomechanics and Engineering
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    • v.32 no.1
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    • pp.1-20
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    • 2023
  • To predict the consolidation behavior of dredged and reclaimed marine clays exhibiting consolidation settlement with large strains, the finite strain consolidation theory must be used. However, challenges in appropriately applying the theory and determining input parameters make design and analysis studies difficult. To address these challenges, design charts for predicting the consolidation settlement of reclaimed marine clays are developed by a numerical approach based on the finite strain consolidation theory. To prepare the design charts, a sensitivity analysis of parameters is performed, and influencing parameters, such as initial void ratio and initial height, as well as the non-linear constitutive void ratio-effective stresspermeability relation, are confirmed. Six representative Korean marine clays obtained from different locations with different liquid limits are used. The design charts for estimating the consolidation times corresponding to various degrees of consolidation are proposed for each of the six representative clays. The consolidation settlements predicted from the design charts are compared to those in previous studies and at an actual construction site and are found to agree well with them. The proposed design charts can therefore be used to solve problems related to the consolidation of reclaimed marine clays having large strains.

Non-linear Dynamic Analysis of Reinforced Concrete Slabs Subjected to Explosive Loading Using an Orthotropic Concrete Constitutive Model (이등방성 콘크리트 모델을 이용한 폭발하중을 받는 철근콘크리트 슬래브의 비선형 동적해석)

  • Lee, MinJoo;Kwak, Hyo-Gyoung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.6
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    • pp.409-416
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    • 2019
  • An improved numerical model for non-linear analysis of reinforced concrete (RC) slabs subjected to blast loading is proposed. This approach considers a strain rate dependent orthotropic constitutive model that directly determines the stress state using the stress-strain relation acquired from the data obtained using the biaxial strength envelope. Moreover, the bond-slip between concrete and reinforcing steel is gradually enlarged after the occurrence of cracks and is concentrated in the plastic hinge region. The bond-slip model is introduced to consider the crack direction of the concrete under a biaxial stress state. Correlation studies between the numerical analysis and the experimental results were performed to evaluate the analytical model. The results show that the proposed model can effectively be used in dynamic analyses of reinforced concrete slab members subjected to explosive loading. Moreover, it was determined that it is important to consider biaxial behavior in the material model and the bond-slip effect.

Microplane Constitutive Model for Granite and Analysis of Its Behavior (마이크로플레인 모델을 이용한 화강암의 3차원 구성방정식 개발 및 암석거동 모사)

  • Zi Goangseup;Moon Sang-Mo;Lee In-Mo
    • Journal of the Korean Geotechnical Society
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    • v.22 no.2
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    • pp.41-53
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    • 2006
  • The brittle materials like rocks show complicated strain-softening behavior after the peak which is hard to model using the classical constitutive models based on the relation between strain and stress tensors. A kinematically constrained three-dimensional microplane constitutive model is developed for granite. The model is verified by fitting the experimented data of Westerly granite and Bonnet granite. The triaxial behavior of granite is well reproduced by the model as well as the uniaxial behavior. We studied the development of the fracture zone in granite during blasting impact using the model with the standard finite element method. All the results obtained from the microplane model developed are compared to those from the linear elasticity model which is commonly used in many researches and practices. It is found that the nonlinearity of rocks sigificantly affects the results of analysis.

Prediction of Stress-Strain Relation and Evolution of Compliance of Concrete by a Micromechanical Model (미세역학이론에 의한 콘크리트의 응력-변형도 관계와 연성도의 예측에 관한 연구)

  • 김진구
    • Magazine of the Korea Concrete Institute
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    • v.8 no.3
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    • pp.147-155
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    • 1996
  • In this study a model for the constitutive relation of a plane concrete is proposed using a micromechariical model. In this model a precursor crack is assumed to exist in the aggregate-cement paste interface, and the LEFM is used to predict the nucleation of the bond cracks and the grow th of mortar cracks. For computational convenience the bond crack-mortar crack configuration is transformed into a straight crack with a point force in the middle. 'The overall compliance and the cons,titutive relation are predicted from the damage due to microcracks, and the predicted stress-strain curves are compared with some experimental data. According to the results, the model predictions are better for under tensile loading than under compression, for high, strength concrete than for normal strength concrete.

A Study of A Nonlinear Viscoelastic Model for Elastomeric Bushing in Radial Mode (일래스토메릭 부싱의 반경방향모드 비선형 점탄성 모델연구)

  • Lee, Seong-Beom
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.415-419
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    • 2003
  • An elastomeric bushing is a device used in automotive suspension systems to reduce the load transmitted from the wheel to the frame of the vehicle. A bushing is an elastomeric hollow cylinder which is bonded to a solid steel shaft at its inner surface and a steel sleeve at its outer surface. The relation between the load applied to the shaft or sleeve and the relative deformation of elastomeric bushing is nonlinear and exhibits features of viscoelasticity. A load-displacement relation for elastomeric bushing is important for dynamic numerical simulations. A boundary value problem for the bushing response leads to the load-displacement relation which requires complex calculations. Therefore, by modifying the constitutive equation for a nonlinear viscoelastic incompressible material developed by Lianis, the data for the elastomeric bushing material was obtained and this data was used to derive the new load-displacement for radial response of the bushing. After the load relaxation function for the bushing is obtained from the step displacement control test, Pipkin-Rogers model was developed. Solutions were allowed for comparison between the results of Modified Lianis model and those of the proposed model. It is shown that the proposed Pipkin-Rogers model is in very good agreement with Modified Lianis model.

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