Tresca’s Yield Condition and the Rotating Disk

1983 ◽  
Vol 50 (3) ◽  
pp. 676-678 ◽  
Author(s):  
U. Gamer
Keyword(s):  
Stress Field ◽  
Plastic Strain ◽  
Tensile Stress ◽  
Displacement Field ◽  
Yield Condition ◽  
Rotating Disk ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Solid Disk ◽  
Associated Flow Rule

The displacement field belonging to the elastic-plastic stress field in a rotating solid disk that can be found with the help of Tresca’s yield condition, in textbooks on plasticity, is discontinuous at the elastic-plastic interface. Tresca’s yield condition cannot be applied to this problem since its associated flow rule predicts a negative plastic strain caused by a tensile stress.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

Elastic-Plastic Analysis of Some Pressure Vessel Heads

1970 ◽  
Vol 92 (2) ◽  
pp. 309-316 ◽  
Author(s):  
E. P. Popov ◽  
M. Khojasteh-Bakht ◽  
P. Sharifi
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Good Accuracy ◽  
Yield Condition ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Thin Walled ◽  
Associated Flow Rule

Sixteen ASME standard torispherical heads attached to cylinders and subjected to internal pressure are analyzed as elastic and/or elastic-plastic shells using a new finite element. As basic elements, thin-walled frusta with curved meridians having common tangents and radii at the nodal circles are employed assuring good accuracy of the results. In the plastic analysis each wall-thickness was subdivided into concentric lamina in order to monitor the behavior of the material. The incremental law of plasticity in conjunction with the Mises yield condition and the associated flow rule were used in the inelastic range. The results of the analysis are presented in detail and are compared with the provisions of the ASME Pressure Vessel Code.

Gradient of Soil Constitutive Model

2010 ◽  
Vol 168-170 ◽  
pp. 1126-1129
Author(s):  
Wen Xu Ma ◽  
Ying Guang Fang
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Soil Analysis ◽  
Natural Material ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Gradient Effect ◽  
Non Local ◽  
Associated Flow Rule ◽  
Plastic Strain Gradient

For the soil is a very complex natural material, significant strain gradient effect exist in soil analysis. Based on the "gradient" phenomenon, we add the plastic strain gradient hardening item into the traditional Cambridge yield surface. By using the consistency conditions and associated flow rule, we get the explicit expression of plastic strain gradient stiffness matrix. And the finite element method of plastic strain gradient is also shown in this article. Plastic strain gradient is actually a phenomenological non-local model containing microstructure information of the material. It may overcome the difficulties in simulating the gradient phenomenon by traditional mechanical model.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

An Anisotropic Hardening Rule With Non-Associated Flow Rule for Pressure-Sensitive Materials

2009 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Plastic Strain ◽  
Hysteresis Loops ◽  
Flow Rule ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Strength Differential ◽  
Hardening Rule ◽  
Pressure Sensitive ◽  
Associated Flow Rule

In this paper, cyclic plastic behaviors of pressure-sensitive materials based on an anisotropic hardening rule with two non-associated flow rules are examined. The Drucker-Prager pressure-sensitive yield function and the Mises plastic potential function are adopted to explore the cyclic plastic behaviors of pressure-sensitive materials or strength-differential materials. The constitutive relations are formulated for the initial loading and unloading/reloading processes based on the anisotropic hardening rule of Choi and Pan [1]. Non-associated flow rules are employed to derive closed-form stress-plastic strain relations under uniaxial cyclic loading conditions. The stress-plastic strain curves based on a conventional non-associated flow rule do not close, and show a significant ratcheting under uniaxial cyclic loading conditions. A new non-conventional non-associated flow rule is then formulated based on observed nearly closed hysteresis loops of pressure-sensitive materials. The stress-plastic strain curves based on the non-conventional non-associated flow rule show closed hysteresis loops under uniaxial cyclic loading conditions. The results indicate that the anisotropic hardening rule with the non-conventional non-associated flow rule describes well the strength-differential effect and the asymmetric closed hysteresis loops as observed in the uniaxial cyclic loading tests of pressure-sensitive materials.

Limits of Economy of Material in Plates

1955 ◽  
Vol 22 (3) ◽  
pp. 372-374
Author(s):  
H. G. Hopkins ◽  
W. Prager
Keyword(s):  
Yield Condition ◽  
Transverse Load ◽  
Constant Thickness ◽  
Flow Rule ◽  
Plate Material ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Varying Thickness ◽  
Limiting Case ◽  
Associated Flow Rule

Abstract The paper is concerned with the limits of economy of material in a simply supported circular plate under a uniformly distributed transverse load. The plate material is supposed to be plastic-rigid and to obey Tresca’s yield condition and the associated flow rule. The criterion of failure adopted is that used in limit analysis. It is shown that the plate of uniform thickness has a weight efficiency of about 82 per cent. Stepped plates of segmentwise constant thickness are discussed, and the plate of continuously varying thickness is treated as the limiting case obtained by letting the number of steps go to infinity.

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.

The Yield Condition and Flow Rule for a Metal Subjected to Finite Elastic Volume Change

1971 ◽  
Vol 93 (4) ◽  
pp. 708-712 ◽  
Author(s):  
J. B. Haddow ◽  
T. M. Hrudey
Keyword(s):  
Plastic Deformation ◽  
Hydrostatic Pressure ◽  
Plastic Flow ◽  
Volume Change ◽  
High Hydrostatic Pressure ◽  
Elastic Strain ◽  
Yield Condition ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Plastic Flow Rule

A theory for elastic-plastic deformation with finite elastic strain is outlined. The results of this theory are specialized to consider a metal subjected to high hydrostatic pressure which produces finite elastic volume change. Drucker’s postulate is used to obtain the form of the yield condition and the associated plastic flow rule.

Experimental Solution of Elastic-Plastic Plane-Stress Problems

1962 ◽  
Vol 29 (4) ◽  
pp. 735-743 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Plane Stress ◽  
Yield Condition ◽  
Strain Curve ◽  
Loading Path ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain ◽  
Plane State ◽  
Elastic Plastic ◽  
Principal Strains

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.

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