• Title, Summary, Keyword: Thick Walled Cylinder

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A novel solution for thick-walled cylinders made of functionally graded materials

  • Chen, Y.Z.
    • Smart Structures and Systems
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    • v.15 no.6
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    • pp.1503-1520
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    • 2015
  • This paper provides a novel solution for thick-walled cylinders made of functionally graded materials (FGMs). In the formulation, the cylinder is divided into N layers. On the individual layer, the Young's modulus is assumed to be a constant. For an individual layer, two undetermined constants are involved in the elastic solution. Those undetermined coefficients can be evaluated from the continuation condition along interfaces of layers and the boundary conditions at the inner surface and outer surface of cylinder. Finally, the solution for thick-walled cylinders made of functionally graded materials is obtainable. This paper provides several numerical examples which are useful for engineer to design a cylinder made of FGMs.

Evaluation of Crack Growth Estimation Parameters of Thick-Walled Cylinder with Non-Idealized Circumferential Through-Wall Cracks (비 이상화된 원주방향 관통균열이 존재하는 두꺼운 배관의 균열 성장 매개변수 계산)

  • Han, Tae-Song;Huh, Nam-Su;Park, Chi-Yong
    • Journal of the Korean Society for Nondestructive Testing
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    • v.33 no.2
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    • pp.138-146
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    • 2013
  • The present paper provides the elastic stress intensity factors(SIFs) of thick-walled cylinder with non-idealized circumferential through-wall cracks. For estimating these elastic SIFs, the systematic three-dimensional(3D) elastic finite element(FE) analyses were performed. In order to consider practical shape of thick-walled cylinder and non-idealized circumferential through-wall crack, the values of thickness of cylinder, reference crack length and crack length ratio were systematically varied. As for loading conditions, axial tension, global bending and internal pressure were considered. In particular, in order to calculate the SIFs of thick-walled cylinder with non-idealized circumferential through-wall crack from those of thick-walled cylinder with idealized circumferential through-wall crack, the correction factor representing the effect of non-idealized crack on the SIFs were proposed in this paper. The present results can be applied to accurately evaluate the rupture probabilities of nuclear piping considering actual crack growth behaviors.

A Study on the Fatigue Life of Autofrettaged Compound Cylinder (자긴가공된 이중후육실린더의 피로수명에 관한 연구)

  • Lee, Eun-Yup;Lee, Young-Shin;Yang, Qui-Ming;Kim, Jae-Hoon;Cha, Ki-Up;Hong, Suk-Kyun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.4
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    • pp.296-309
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    • 2009
  • Thick-walled cylinder with high pressure have had wide application in the armament industry. In the thick-walled cylinder, fatigue crack is generated at inner radius and developed toward the outer radius. To prevent generation of fatigue crack, the autofrettage process had been used. The compressive residual stress induced by the autofrettage process extends loading pressure and fatigue life of the thick-walled cylinder. In this study, the residual stress of single and compound cylinder by the autofrettage process was evaluated. The analytical compressive residual stress of single cylinder was good agreement with experimental result at inner radius. The analysis on the residual stress of compound cylinder was conducted. The compressive residual stress at inner radius was increased with the overstrain level. And fatigue life of the compound cylinder with initial crack was evaluated. The considered initial crack shape was straight and semi-elliptical. The fatigue life was extended with the overstrain level. The fatigue life of the compound cylinder with semi-elliptical crack was longer than straight crack. The suitable way to extend fatigue life of the compound cylinder was proposed.

Determination of Thermal Shock Stress Intensity Factor for Elliptical Crack by Modified Vainshtok Weight Function Method (수정 Vainshtok 가중함수법에 의한 타원균열의 열충격 응력세기계수의 결정)

  • 이강용;김종성
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.2
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    • pp.463-474
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    • 1995
  • Modified Vainshtok weight function method is developed. The thermal shock stress intensity factors for elliptical surface cracks existed in the thin and thick walled cylinders are determined. The present results are compared with previous solutions and shown to be good agreement with them.

Elastic Crack Opening Displacement of Slanted Circumferential Through-Wall Cracks in Thick-Walled Cylinder (원주방향 경사관통균열이 존재하는 두꺼운 배관의 탄성 균열열림변위)

  • Han, Tae-Song;Huh, Nam-Su;Shim, Do-Jun;Kim, Jin-Su;Lee, Jin-Ho
    • Transactions of the Korean Society of Pressure Vessels and Piping
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    • v.8 no.3
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    • pp.13-22
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    • 2012
  • According to recent research on leak-rate estimates to assess rupture probabilities of nuclear piping which contains a circumferential surface/through-wall cracks due to PWSCC, i.e., xLPR (Extremely Low Probability of Rupture) program, it has been revealed that the use of crack shape with an idealized circumferential through-wall crack during actual crack growth can lead to overestimate of the leak-rate. Thus, for accurate estimation of the leak-rate during crack growth, the more realistic crack shape that can simulate the crack shape transition from surface crack to through-wall crack should be used. In this context, in the present study, the elastic crack opening displacement of slanted circumferential through-wall crack in thick-walled cylinder was proposed based on 3-dimensional elastic finite element fracture mechanics analyses. To propose the elastic crack opening displacement of slanted circumferential through-wall crack in thick-walled cylinder, the geometric variables affecting crack opening displacement, i.e., thickness of cylinder, reference inner crack length and slant crack ratio were systematically varied. In terms of loading conditions, axial tension, global bending moment and internal pressure were considered. The present results can be applied to calculate the leak-rate considering more realistic crack shape transition from surface crack to idealized through-wall crack, and can be expected to enhance current leak-rate estimation scheme, for instance, in xLPR program etc.

Analysis of Apparent Fracture Toughness of a Thick-Walled Cylinder with an FGM Coating at the Inner Surface Containing a Radial Edge Crack (반경방향의 모서리 균열을 갖고 내면이 경사기능재료(FGM)로 코팅된 두꺼운 실린더의 겉보기 파괴인성해석)

  • Afsar, A.M.;Rasel, S.M.;Song, J.I.
    • Composites Research
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    • v.23 no.2
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    • pp.1-9
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    • 2010
  • This study analyzes the apparent fracture toughness of a thick-walled cylinder with a functionally graded material (FGM) coating at the inner surface of the cylinder. The cylinder is assumed to have a single radial edge crack emanating from its inner surface. The crack surfaces and the inner surface of the cylinder are subjected to an internal pressure. The incompatible eigenstrain developed in the cylinder due to nonuniform coefficient of thermal expansion as a result of cooling from sintering temperature is taken into account. Based on a method of evaluating stress intensity factor introduced in our previous study, an approach is developed to calculate apparent fracture toughness. The approach is demonstrated for a cylinder with a TiC/$Al_{2}O_{3}$ FGM coating and some numerical results of apparent fracture toughness are presented graphically. The effects of material distribution profile, cylinder wall thickness, application temperature, and coating thickness on the apparent fracture toughness are investigated in details. It is found that all of these factors play an important role in controlling the apparent fracture toughness of the cylinder.

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.

Magneto-thermo-elastic response of a rotating functionally graded cylinder

  • Hosseini, Mohammad;Dini, Ali
    • Structural Engineering and Mechanics
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    • v.56 no.1
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    • pp.137-156
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    • 2015
  • In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

Fatigue crack propagation life evaluation of an autofrettaged thick-walled cylinder (자긴가공된 두꺼운 실린더의 피로균열 전파수명평가)

  • Lee, Song-In;Kim, Jin-Yong;Jeong, Se-Hui;Go, Seung-Gi
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.2
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    • pp.321-329
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    • 1998
  • To ensure the structural integrity of the autofrettaged thick-walled cylinder subjected to cyclic internal pressure loading, the fatigue crack propagation life of the cylinder was evaluated. Stress intensity factors of the external cracked cylinder due to internal pressure and autofrettage loadings were calculated using the finite element method. The fatigue crack propagation lives of the cylinder based on the fracture mechanics concepts were predicted and compared to the experimental fatigue lives evaluated from the C-shaped simulation specimens. There were good correlations between the predicted and experimental fatigue lives within a factor of 3 for the single and double grooved C-shaped simulation specimens. Predicted fatigue crack propagation lives of the double grooved cylinders were about 1.5-5 times longer than those of the single grooved cylinders depending on the levels of autofrettage.

Two dimensional time-dependent creep analysis of a thick-walled FG cylinder based on first order shear deformation theory

  • Loghman, Abbas;Faegh, Reza K.;Arefi, Mohammad
    • Steel and Composite Structures
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    • v.26 no.5
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    • pp.533-547
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    • 2018
  • In this paper the time-dependent creep analysis of a thick-walled FG cylinder with finite length subjected to axisymmetric mechanical and thermal loads are presented. First order shear deformation theory (FSDT) is used for description of displacement components. Inner and outer temperatures and outer pressure are considered as thermo-mechanical loadings. Both thermal and mechanical loadings are assumed variable along the axial direction using the sinusoidal distribution. To find temperature distribution, two dimensional heat transfer equation is solved using the required boundary conditions. The energy method and Euler equations are employed to reach final governing equations of the cylinder. After determination of elastic stresses and strains, the creep analysis can be performed based on the Yang method. The results of this research indicate that the boundaries have important effects on the responses of the cylinder. The effect of important parameters of this analysis such as variable loading, non-homogeneous index of functionally graded materials and time of creep is studied on the behaviors of the cylinder.