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.

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.

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.

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.

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.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

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