Transient and Residual Thermal Stresses in an Elastic-Plastic Cylinder

1960 ◽  
Vol 27 (3) ◽  
pp. 481-488 ◽  
Author(s):  
H. G. Landau ◽  
E. E. Zwicky
Keyword(s):  
Thermal Stresses ◽  
Plastic Material ◽  
Numerical Procedure ◽  
Yield Condition ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Perfectly Plastic ◽  
Plastic Cylinder ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Equations are given for the stress rates in solid cylinders subject to transient temperature distributions, based on the assumption of an elastic, perfectly plastic material obeying a von Mises temperature-dependent yield condition. A numerical procedure for integrating the equations is developed and applied to a temperature distribution approximating a phase transformation and to a quenched cylinder. The effect of various factors on the residual stresses is noted.

Thermal Stress in a Viscoelastic-Plastic Plate With Temperature-Dependent Yield Stress

1960 ◽  
Vol 27 (2) ◽  
pp. 297-302 ◽  
Author(s):  
H. G. Landau ◽  
J. H. Weiner ◽  
E. E. Zwicky
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Yield Stress ◽  
Plastic Material ◽  
Numerical Procedure ◽  
Yield Condition ◽  
Residual Stress Distribution ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Perfectly Plastic

Equations are given for the determination of transient and residual stresses in plates subject to transient temperature distributions, based on the assumption of a viscoelastic, perfectly plastic material obeying a von Mises temperature-dependent yield condition. A numerical procedure for integrating the equations is developed and applied to the case of a symmetrically cooled plate. It is found that, for steel, viscoelasticity has little effect on the residual stress distribution, but the temperature dependence of yield stress is important. The types of residual stress distribution after cooling are similar to those for an elastic-plastic material with constant yield stress, and for this case the residual stress is given approximately by formulas developed earlier for a slowly varying heat input.

Transient Thermal Stresses in Elasto-Plastic Discs

1969 ◽  
Vol 11 (4) ◽  
pp. 384-391 ◽  
Author(s):  
H. Odenö
Keyword(s):  
Temperature Distribution ◽  
Thermal Stresses ◽  
Plastic Material ◽  
Yield Condition ◽  
Transient Temperature ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Exterior Surface ◽  
Tresca Yield Condition ◽  
Perfectly Plastic

A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed. The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method. The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic. An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are calculated.

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.

Approximate Elastic-Plastic Analysis of Intersecting Equal Diameter Cylindrical Shells

1981 ◽  
Vol 103 (1) ◽  
pp. 111-115
Author(s):  
D. P. Updike
Keyword(s):  
Plastic Material ◽  
Cylindrical Shells ◽  
Yield Condition ◽  
Pressure Vessels ◽  
Ductile Materials ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Design of connections of pipes and pressure vessels on the basis of a calculated maximum elastic stress often proves to be too conservative in the case of ductile materials. Elastic-plastic analysis by the finite element method proves to be too costly. This paper presents an alternative method which reduces the calculations to those of a rotationally symmetric shell subjected to axisymmetric loading. Using this approach approximate elastic-plastic deformations on the meridian passing through the crotch of a tee branch connection of cylindrical shells of equal diameter and thickness are determined. The method is limited to cases of the normal intersection of very thin shells of identical diameter, thickness, and material and to internal pressure loading. Numerical results for the intersection of two shells of R/t equal to 100 are given for an elastic-perfectly plastic material satisfying the von Mises yield condition.

Transient and Residual Stresses in Heat-Treated Cylinders

1959 ◽  
Vol 26 (1) ◽  
pp. 31-39
Author(s):  
J. H. Weiner ◽  
J. V. Huddleston
Keyword(s):  
Residual Stresses ◽  
Plastic Material ◽  
Poisson Ratio ◽  
Yield Condition ◽  
Transient Temperature ◽  
Fixed Temperature ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Temperature Distributions ◽  
Elastic Perfectly Plastic

Abstract General equations for the computation of stress rates in solid and hollow cylinders subjected to transient temperature distributions are developed, based on the assumptions of an elastic, perfectly plastic material obeying the Tresca yield condition with Poisson ratio of one half. For most temperature distributions, it appears that these equations can be integrated only by numerical means. However, for one particular temperature distribution, equivalent to a phase transformation which occurs at a fixed temperature, it is found possible to integrate them analytically, and expressions for the transient and residual stresses are obtained in closed form. The latter results are compared with experiment and qualitative agreement noted.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field

2005 ◽  
Vol 72 (1) ◽  
pp. 62-67 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Admissible Solution ◽  
Mode I ◽  
Mode I Crack ◽  
Perfectly Plastic ◽  
Compressive Stresses ◽  
Von Mises

A statically admissible solution for a perfectly plastic material in plane stress is presented for the mode I crack problem. The yield condition employed is an alternative type first proposed by von Mises in order to approximate his original yield condition for plane stress while eliminating most of the elliptic region as pertaining to partial differential equations. This yield condition is composed of two intersecting parabolas rather than a single ellipse in the principal stress space. The attributes of this particular solution of the mode I problem over that previously obtained are that it contains neither stress discontinuities nor compressive stresses anywhere in the field.

scholarly journals Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

2016 ◽  
Vol 838-839 ◽  
pp. 196-201
Author(s):  
Maxime Rollin ◽  
Vincent Velay ◽  
Luc Penazzi ◽  
Thomas Pottier ◽  
Thierry Sentenac ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Stresses ◽  
Superplastic Forming ◽  
Model Material ◽  
Material Behavior ◽  
Mechanical Modeling ◽  
Temperature Dependent ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In AIRBUS, most of the complex shaped titanium fairing parts of pylon and air inlets are produced by superplastic forming (SPF). These parts are cooled down after forming to ease their extraction and increase the production rate, but AIRBUS wastes a lot of time to go back over the geometric defects generated by the cooling step. This paper investigates the simulations of the SPF, cooling and clipping operations of a part on Abaqus® Finite element software. The different steps of the global process impact the final distortions. SPF impacts the thickness and the microstructure/behavior of material, cooling impacts also the microstructure/behavior of material and promotes distortions through thermal stresses and finally, clipping relaxes the residual stresses of the cut part. An elastic-viscoplastic power law is used to model material behavior during SPF and a temperature dependent elastic perfectly plastic model for the cooling and clipping operations.

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.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

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