• Title, Summary, Keyword: Viscoplastic Constitutive Equation

### Viscoplastic Solution of Thick Walled Cylinder Considering Axial Constraint (축방향 경계 조건을 고려한 두꺼운 실린더의 점소성 응력해)

• Yoon, Sam-Son;Lee, Soon-Bok
• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1555-1561
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• 2003
• Finite element analysis using modern constitutive equation is one of the most general tools to simulate the deformation behavior and to predict the life of the structure. Constitutive equation becomes complicated so as to predict the material behavior more accurately than the classical models. Because of the complexity of constitutive model, numerical treatment becomes so difficult that the calculation should be verified carefully. One-element tests, simple tension or simple shear, are usually used to verify the accuracy of finite element analysis using complicated constitutive model. Since this test is mainly focused on the time integration scheme, it is also necessary to verify the equilibrium iteration using material stiffness matrix and to compare FE results with solution of structures. In this investigation, viscoplastic solution of thick walled cylinder was derived considering axial constraints and was compared with the finite element analysis. All the numerical solutions showed a good coincidence with FE results. This numerical solution can be used as a verification tool for newly developed FE code with complicated constitutive model.

### A THERMO-ELASTO-VISCOPLASTIC MODEL FOR COMPOSITE MATERIALS AND ITS FINITE ELEMENT ANALYSIS

• Shin, Eui-Sup
• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.45-65
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• 2002
• A constitutive model on oorthotropic thermo-elasto-viscoplasticity for fiber-reinforced composite materials Is illustrated, and their thermomechanical responses are predicted with the fully-coupled finite element formulation. The unmixing-mixing scheme can be adopted with the multipartite matrix method as the constitutive model. Basic assumptions based upon the composite micromechanics are postulated, and the strain components of thermal expansion due to temperature change are included In the formulation. Also. more than two sets of mechanical variables, which represent the deformation states of multipartite matrix can be introduced arbitrarily. In particular, the unmixing-mixing scheme can be used with any well-known isotropic viscoplastic theory of the matrix material. The scheme unnecessitates the complex processes for developing an orthotropic viscoplastic theory. The governing equations based on fully-coupled thermomechanics are derived with constitutive arrangement by the unmixing-mixing concept. By considering some auxiliary conditions, the Initial-boundary value problem Is completely set up. As a tool of numerical analyses, the finite element method Is used with isoparametric Interpolation fer the displacement and the temperature fields. The equation of mutton and the energy conservation equation are spatially discretized, and then the time marching techniques such as the Newmark method and the Crank-Nicolson technique are applied. To solve the ultimate nonlinear simultaneous equations, a successive iteration algorithm is constructed with subincrementing technique. As a numerical study, a series of analyses are performed with the main focus on the thermomechanical coupling effect in composite materials. The progress of viscoplastic deformation, the stress-strain relation, and the temperature History are careful1y examined when composite laminates are subjected to repeated cyclic loading.

### Plane Strain Analysis of Sheet Metal with Arbitrary Forming Conditions (임의의 성형조건을 갖는 박판의 평면변형율 해석)

• Keum, Y.T.;Lee, S.Y.;Wagoner, R.H.
• Transactions of Materials Processing
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• v.1 no.1
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• pp.95-103
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• 1992
• The plane strain analysis for simulating the stretch/draw forming operation with an arbitrarily-shaped tool profile is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The linear line elements are used for depicting the formed sheet, based on membrane approximation. The FEM formulation is tested in the sections of automotive inner panel and two-side draw-in. Not only the excellent agreement between measured and computed strains is obtained in the stretched section, but also the numerical stability of formulation is verified in the draw-in section.

### Analysis of Densification Behavior of Nano Cu Powders during Cold Isostatic Pressing (나노 구리 분말의 냉간정수압 공정에 대한 치밀화 거동 해석)

• 윤승채;김형섭;이창규
• Journal of Korean Powder Metallurgy Institute
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• v.11 no.4
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• pp.341-347
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• 2004
• In the study, a hybrid constitutive model for densification of metallic powders was applied to cold isostatic pressing. The model is based on a pressure-dependent plasticity model for porous materials combined with a dislocation density-based viscoplastic constitutive model considering microstructural features such as grain size and inter-particle spacing. Comparison of experiment and calculated results of microscale and nanoscale Cu powders was made. This theoretical approach is useful for powder densification analysis of various powder sizes, deformation routes and powder processing methods.

### Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables (상태변수를 갖는 비탄성 구성식 적분법의 일반화)

• Yun, Sam-Son;Lee, Sun-Bok;Kim, Jong-Beom;Lee, Hyeong-Yeon;Yu, Bong
• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5
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• pp.1075-1083
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• 2000
• The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

### Comparison of Semi-Implicit Integration Schemes for Rate-Dependent Plasticity (점소성 구성식의 적분에 미치는 선형화 방법의 영향)

• Yoon, Sam-Son;Lee, Soon-Bok
• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.11
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• pp.1907-1916
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• 2003
• During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.

### Creep Behavior Analysis of High Cr Steel Using the Constitutive Model Based on Microstructure (미세조직기반 구성모델을 이용한 고크롬강의 크리프 거동 해석)

• 윤승채;서민홍;백경호;김성호;류우석;김형섭
• Transactions of Materials Processing
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• v.13 no.2
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• pp.160-167
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• 2004
• In order to theoretically analyze the creep behavior of high Cr steel at $600^{\circ}C$, a unified elasto-viscoplastic constitutive model based on the consideration of dislocation density is proposed. A combination of a kinetic equation describing the mechanical response of a material at a given microstructure in terms of dislocation glide and evolution equations for internal variables characterizing the microstructure provides the constitutive equations of the model. Microstructural features of the material such as the grain size and spacing between second phase particles are directly implemented in the constitutive equations. The internal variables are associated with the total dislocation density in a simple model. The model has a modular structure and can be adjusted to describe a creep behavior using the material parameters obtained from uniaxial tensile tests.

### 연약지반 변형해석을 위한 다목적 Program개발

• 박병기;정진섭
• Proceedings of the Korean Geotechical Society Conference
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• pp.362-375
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• 1991
• Background and Necessity of the study : For more than 20 years, the soil engineering reserach group of Chonnam National University has been performing the deformation analysis of soft clayey foundation, since the University is located near the south-western coast of Korean Peninsulla, along which tide reclamation works have been under proaressing. Associsted with the fact mentioned above, the researchers have been developing a computer program in order to carry out deformation analysis of soft foundation since early 1980. Case-studies : In this research, the Biot's equation was selected as the governing equation coupled with several constitutive models including original and modified Cam-clay models, elasto-viscoplastic model, Lade's model etc. The anisotropy of soi1 can be considered in this program. To validate the accuracy of the computer program developed a couple of case-studies were performed. These include the pilot banking, sand drain considering smear effect and compound foundation reinforced with sheet pile into soft foundation.i) The pilot banking Good results could be acquired by assuming banking load as the body force composed of finite element mesh rather than equivalent concentrated load.ii) The sand drain Due to smear, the delay of consolidation was remarkable at the early stsge. so safety for the failure of foundation should be checked for the initial step of consolidation. iii) The compound foundation Accurate results were obtained by introducing the joint element method for the soft foundation reinforced with sheet pile into soiㅣ.

### Analysis of Material Response Based on Chaboche Unified Viscoplastic Constitutive Equation; (CHABOCHE 통합 점소성 구성방정식을 이용한 재료거동해석)

• Kwak, D.Y.;Im, Y.T.;Kim, J.B.;Lee, H.Y.;Yu, B.
• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3516-3524
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• 1996
• Service conditions for structures at elevated temperatures in nuclear power plant involve transient thermal and mechanical load levels that are severe enough to caeuse inelastic deformations due to creep and plasticity. Therefore, a systematic mehtod of inelastic analysis is needed for the design of structural components in nuclear poser plants subjected to such loading conditions. In the present investigation, the Chabodhe model, one of the unified viscoplastic constitutive equations, was selected for systematic inelastic analysis. The material response was integrated based on GMR ( generallized mid-point rule) time integral scheme and provided to ABAQUS as a material subroutine, UMAT program. By comparing results obtaned from uniaxial analysis using the developed UMAT program with those from Runge-Kutta solutions and experimentaiton, the validity of the adopted Chaboche model and the numerical stability and accuracy of the developed UMAT program were verified. In addition, the developed material subroutine was applied for uniaxial creep and tension analyses for the plate with a hole in the center. The application further demonstrates usefulness of the developed program.

### Finite element analysis of inelastic thermal stress and damage estimation of Y-structure in liquid metal fast breeder reactor (액체금속로 Y-구조물의 비탄성 열응력 해석 및 손상평가에 관한 유한요소해석)

• Kwak, D.Y.;Im, Y.T.;Kim, J.B.;Lee, H.Y.;Yoo, B.
• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.7
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• pp.1042-1049
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• 1997
• LMFBR(Liquid Metal Fast Breeder Reactor) vessel is operated under the high temperatures of 500-550.deg. C. Thus, transient thermal loads were severe enough to cause inelastic deformation due to creep-fatigue and plasticity. For reduction of such inelastic deformations, Y-piece structure in the form of a thermal sleeve is used in LMFBR vessel under repeated start-up, service and shut-down conditions. Therefore, a systematic method for inelastic analysis is needed for design of the Y-piece structure subjected to such loading conditions. In the present investigation, finite element analysis of heat transfer and inelastic thermal stress were carried out for the Y-piece structure in LMFBR vessel under service conditions. For such analysis, ABAQUS program was employed based on the elasto-plastic and Chaboche viscoplastic constitutive equations. Based on numerical data obtained from the analysis, creep-fatigue damage estimation according to ASME Code Case N-47 was made and compared to each other. Finally, it was found out that the numerical predictio of damage level due to creep based on Chaboche unified viscoplastic constitutive equation was relatively better compared to elasto-plastic constitutive formulation.