A Comparison of Flow and Deformation Theories in a Radially Stressed Annular Plate

1973 ◽  
Vol 40 (1) ◽  
pp. 283-287 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Internal Pressure ◽  
Closed Form ◽  
Deformation Theory ◽  
Annular Plate ◽  
Yield Condition ◽  
Flow Theory ◽  
Quantitative Comparison ◽  
The Other ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Two mathematically consistent solutions to the strains and displacement in a partly plastic, annular plate stressed by internal pressure are obtained according to the deformation theory of Hencky and to the flow theory of Prandtl-Reuss. In both cases, the material is assumed to be elastic, perfectly plastic and obeying the Mises yield condition. It is shown that one solution is expressed in closed form and the other, in terms of simple integrals. A quantitative comparison of two theories is given and the effect of compressibility is discussed.

Elastic, Plastic Stresses in Free Plate With Periodically Varying Surface Temperature

1958 ◽  
Vol 25 (4) ◽  
pp. 603-606
Author(s):  
Halil Yüksel
Keyword(s):  
Steady State ◽  
Surface Temperature ◽  
Constant Temperature ◽  
Thermal Stresses ◽  
Plastic Material ◽  
The Other ◽  
Perfectly Plastic ◽  
Temperature Oscillations ◽  
Steady State Temperature ◽  
Elastic Perfectly Plastic

Abstract The paper is concerned with a free plate that consists of an elastic, perfectly plastic material and is subjected to a harmonically varying temperature at one face, while the other face is kept at a constant temperature and the edge is perfectly insulated. The thermal stresses associated with the steady-state temperature oscillations are analyzed, and the development of plastic regions is discussed.

A Quantitative Comparison of Flow and Deformation Theories of Plasticity

1950 ◽  
Vol 17 (2) ◽  
pp. 180-184
Author(s):  
P. G. Hodge ◽  
G. N. White
Keyword(s):  
Hollow Cylinder ◽  
Yield Condition ◽  
Quantitative Comparison ◽  
The Other ◽  
Stress Strain ◽  
Flow Type ◽  
Deformation Law

Abstract The stresses and displacements in a partly plastic, infinitely long, hollow cylinder are obtained according to the flow type of stress-strain law of Prandtl-Reuss and to the deformation law of Hencky. In both cases the Mises yield condition is used and the compressibility of the material is taken into account. It is shown that under these assumptions the two theories yield substantially the same results for this particular problem, but that one theory or the other may be preferable for computing purposes in certain cases. The results are compared with those of other investigations in which different combinations of stress-strain law, yield condition, compressibility, and end loading were assumed.

Closed-form aftershock reliability of damage-cumulating elastic-perfectly-plastic systems

2013 ◽  
Vol 43 (4) ◽  
pp. 613-625 ◽  
Author(s):  
Iunio Iervolino ◽  
Massimiliano Giorgio ◽  
Eugenio Chioccarelli
Keyword(s):  
Closed Form ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Closed-Form Plastic Collapse Loads of Pipe Bends Under Combined Pressure and In-Plane Bending

2006 ◽  
Author(s):  
Chang-Sik Oh ◽  
Yun-Jae Kim
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Plastic Collapse ◽  
Plastic Limit ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Bending Mode ◽  
Wide Range ◽  
Plane Bending ◽  
Elastic Perfectly Plastic

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

Use of API 579-1/ASME FFS-1 Limit-Load Criteria for Establishing Load Limits for Pressure Vessel Internals

2010 ◽  
Author(s):  
Brian R. Macejko
Keyword(s):  
Closed Form ◽  
Pressure Vessel ◽  
Limit Load ◽  
Process Equipment ◽  
Maximum Pressure ◽  
Plastic Collapse ◽  
Closed Form Solutions ◽  
Perfectly Plastic ◽  
Section Viii ◽  
Elastic Perfectly Plastic

The 2007 edition of ASME Boiler & Pressure Vessel Code Section VIII Division 2 and the 2007 edition of Fitness-For-Service API 579-1/ASME FFS-1 provide the option to use the limit-load method to assess protection against plastic collapse for components of pressurized process equipment. Per the methodology presented therein, the allowable load on a component is established by applying design factors to the elastic-perfectly plastic limit-load such that the onset of gross plastic deformation (plastic collapse) will not occur. Typically, the design limitations of pressure vessel internal components have been assessed through closed form solutions with conservative assumptions. It has been found that the maximum pressure delta across vessel internals established through closed form solutions can become limiting in determination of time between equipment shutdowns. This paper will outline a practical example of industry applied use of the limit-load method to qualify extended limits on mechanical loads applied to pressure vessel internals.

Closed-Form Collapse Moment Equations of Throughwall Circumferentially Cracked Elbows Subjected to In-Plane Bending Moment

2004 ◽  
Vol 126 (3) ◽  
pp. 307-317 ◽  
Author(s):  
J. Chattopadhyay ◽  
A. K. S. Tomar ◽  
B. K. Dutta ◽  
H. S. Kushwaha
Keyword(s):  
Closed Form ◽  
Bending Moment ◽  
Moment Equations ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Circumferential Crack ◽  
Opening Mode ◽  
Plane Bending ◽  
Elastic Perfectly Plastic ◽  
Bending Modes

A large throughwall circumferential crack in an elbow subjected to in-plane bending moment can significantly reduce its collapse load. Therefore, it is very important to know the collapse moment of an elbow in the presence of a throughwall circumferential crack. The existing closed-form collapse moment equations of throughwall circumferentially cracked elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack, especially for opening mode of bending moment. Therefore, the present study has been carried out to investigate through elastic-plastic finite element analysis the effect of a throughwall circumferential crack on the collapse moment of an elbow under in-plane bending moment. A total of 72 cases of elbows with various sizes of circumferential cracks (2θ=0–150 deg), different wall thickness (R/t=5–20), different elbow bend radii Rb/R=2,3 and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form expressions have been proposed to evaluate collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations have been compared with 8 published elbow test data and are found to be within ±11% variation except for one case.

scholarly journals The yield condition strongly influences the formation of Dugdale plastic strips ahead of crack tips under tensile plane stress loading conditions

2012 ◽  
Vol 21 (1-2) ◽  
pp. 37-39
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Yield Condition ◽  
Loading Conditions ◽  
Element Analysis ◽  
Plastic Strip ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractA finite element analysis indicates a good correlation between the Dugdale plastic strip model and a linear elastic/perfectly plastic material under plane stress loading conditions for a flow theory of plasticity based on the Tresca yield condition. A similar analysis under the von Mises yield condition reveals no plastic strip formation.

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