• Smart Structures and Systems
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• 제15권6호
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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.

• 비파괴검사학회지
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• 제33권2호
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• pp.138-146
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• 2013

본 논문에서는 두꺼운 배관에 존재하는 비 이상화된 원주방향 관통균열의 탄성 응력확대계수 해를 제시하였다. 이를 위해 3차원 탄성 유한요소해석을 수행하였으며, 배관의 형상 및 비 이상화된 원주방향 관통균열의 영향을 고려하기 위해 배관의 두께, 기준균열길이 및 관통균열길이 비를 체계적으로 변화시켰다. 하중 조건으로는 인장하중, 굽힘모멘트 및 내압을 고려하였다. 또한 본 논문에서는 이상화된 원주방향 관통 균열로부터 비 이상화된 원주방향 관통균열의 응력확대계수를 쉽게 계산하기 위해 관통균열 보정계수를 제시하였다. 본 논문의 결과는 실제 균열성장거동을 고려하여 원자력 배관의 배관파단확률을 보다 정확하게 계산하기 위해 적용될 수 있다.

• 대한기계학회논문집A
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• 제33권4호
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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.

• 대한기계학회논문집
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• 제19권2호
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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.

• Steel and Composite Structures
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• 제51권2호
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• pp.139-151
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• 2024

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.

• 한국압력기기공학회 논문집
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• 제8권3호
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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.

• 대한기계학회논문집A
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• 제22권2호
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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.

• 대한기계학회논문집A
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• 제27권9호
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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.

• Structural Engineering and Mechanics
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• 제56권1호
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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.

• Steel and Composite Structures
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• 제26권5호
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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.