Finite Twisting and Expansion of a Hole in a Rigid/Plastic Plate

1963 ◽  
Vol 30 (4) ◽  
pp. 605-612 ◽  
Author(s):  
R. P. Nordgren ◽  
P. M. Naghdi
Keyword(s):  
Plane Stress ◽  
Work Hardening ◽  
Infinite Plate ◽  
Yield Function ◽  
The State ◽  
Numerical Results ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Combined Action ◽  
Concentric Circles

This paper is concerned with the finite twisting and expansion of an annular rigid/plastic plate in the state of plane stress. The plate, bounded by two concentric circles one of which may extend to infinity, is subjected in its plane to the combined action of pressure on the inner boundary and a couple due to circumferential shear. A detailed solution which includes the effect of isotropic work hardening is obtained with the use of Tresca’s yield function and its associated flow rules and the corresponding solution with the use of Mises’ yield function and its associated flow rules is also discussed. Numerical results are given which illustrate the influence of twisting on the expansion of a hole in an infinite plate.

scholarly journals Plane Stress Yield Function Described by 3rd-degree Spline Curves Considering Differential Work Hardening

2016 ◽  
Vol 57 (662) ◽  
pp. 245-251 ◽  
Author(s):  
Hideo TSUTAMORI ◽  
Eiji IIZUKA ◽  
Toshiro AMAISHI ◽  
Kentaro SATO ◽  
Yuki OGIHARA ◽  
...  
Keyword(s):  
Plane Stress ◽  
Work Hardening ◽  
Yield Function ◽  
Spline Curves

On Plane Stress Solution of an Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (3) ◽  
pp. 407-410
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Stress ◽  
Yield Surface ◽  
Complete Solution ◽  
Yield Function ◽  
The State ◽  
Perfectly Plastic ◽  
State Of Stress ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic ◽  
Flow Laws

Abstract With the use of Tresca’s yield function and its associated flow laws, the complete solution is obtained for an isotropic elastic, perfectly plastic wedge (with an included angle β < π/2) subjected to a uniform traction in the state of plane stress. Unlike its corresponding plane strain solution, the state of stress in a portion of the plastic domain of the wedge is at a corner of Tresca’s yield hexagon where, in general, the normal to the yield surface is not defined uniquely.

scholarly journals General bi-harmonic analysis for a plate containing circular holes

1940 ◽  
Vol 176 (964) ◽  
pp. 121-139 ◽  
Keyword(s):  
Stress Distribution ◽  
General Solution ◽  
Harmonic Analysis ◽  
Plane Stress ◽  
Infinite Plate ◽  
Numerical Results ◽  
General Character ◽  
Stress Distributions ◽  
Finite Plate ◽  
Circular Holes

A general solution is given for problems of generalized plane stress distributions in an infinite plate which contains circular holes of varying sizes in any positions, subject only to certain conditions of convergence of the solution. The method for extending the results to allow for the effect of one or two straight boundaries is indicated. As a particular case of the general solution the problem of the stress distribution in an infinite plate under tension containing three holes in a row, is discussed, and a few numerical results are given. These results are compared with experiments which were carried out by Mr P. L. Capper. The comparison is incomplete as the experiments were done for a finite plate and the influence of the edges of the plate on the numerical values of the stresses is considerable. Agreement, however, is found for the general character of some of the stresses.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

On the Plastic Flow of Coulomb Solids Beyond Original Failure

1959 ◽  
Vol 26 (4) ◽  
pp. 599-602
Author(s):  
A. W. Jenike ◽  
R. T. Shield
Keyword(s):  
Velocity Field ◽  
Stress Field ◽  
Plastic Flow ◽  
Yield Function ◽  
Two Dimensions ◽  
Rigid Plastic ◽  
Variable Yield ◽  
Angle Of Friction ◽  
Effective Angle

Abstract Principles developed for rigid-plastic solids exhibiting Coulomb’s properties are adapted to the analysis of flow beyond original failure. A variable yield function is proposed to account for the changes of cohesion during flow and equations are evolved for the stress field in two dimensions. It is shown that, while in the stress field an effective angle of friction larger than the actual angle of friction is mandatory for these materials, in the velocity field the materials can be assumed incompressible.

Wellbore Integrity: An Integrated Experimental and Numerical Study to Investigate Pore Pressure Variation during Cement Hardening under Downhole Conditions

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
Weicheng Zhang ◽  
Andreas Eckert ◽  
Steven Hilgedick ◽  
Harvey Goodman ◽  
Meng Meng
Keyword(s):  
Pore Pressure ◽  
Numerical Study ◽  
Pressure Variation ◽  
The State ◽  
Numerical Results ◽  
Von Mises Stress ◽  
Fluid Loss ◽  
Wellbore Integrity ◽  
State Of Stress ◽  
Pressure Decrease

Summary Understanding the cement hardening process and determining the development of the state of stress in the cement under specific downhole conditions are challenging but fundamental requirements to perform an accurate prediction of wellbore integrity. As an essential component of the state of stress, the temporal variation of cement pore pressure is a critical factor that affects the occurrence of cement failure. In this study, we present a novel laboratory setup to measure the cement pore pressure variation during hardening under representative downhole conditions, including the pressure, temperature, and water exchange between the cement and formation. The pore pressure measurements are further incorporated with a staged finite element analysis (FEA) approach to investigate the state of stress development during cement hardening and to evaluate cement failure under different operations and after different wait-on-cement (WOC) periods. The laboratory measurements show that the external water supply from the formation significantly impedes the pore pressure drop in the cement. The numerical results indicate that the accelerated pore pressure decrease obtained without considering downhole conditions elevates the contact pressure at the cement-formation interfaces significantly and moderately increases the von Mises stress in the cement. The numerical results further predict that the accelerated pore pressure decrease leads to an overestimation of shear failure during pressure testing and steamflooding operations but an underestimation of debonding failure during severe fluid loss and injection-related cooling processes. Based on the results of the integrated laboratory and numerical approach, qualitative and quantitative suggestions are provided for field operations to inhibit wellbore integrity risk during the wellbore life cycle.

A Yield Function for Anisotropic Sheet Material Described by 3rd-Degree Spline Curve and its Applications

2016 ◽  
Vol 725 ◽  
pp. 653-658 ◽  
Author(s):  
Toshiro Aamaishi ◽  
Hideo Tsutamori ◽  
Eiji Iizuka ◽  
Kentaro Sato ◽  
Yuki Ogihara ◽  
...  
Keyword(s):  
Aluminum Alloy ◽  
Mild Steel ◽  
Plane Stress ◽  
Sheet Material ◽  
Yield Function ◽  
Sheet Metals ◽  
Anisotropic Behavior ◽  
Spline Curve ◽  
Series Aluminum Alloy

A new plane stress yield function using the 3rd-degree spline curve is proposed for the anisotropic behavior of sheet metals. This yield function considers the evolution of anisotropy in terms of both r values and stresses. In order to demonstrate the applicability of the proposed yield function, hole expanding tests with mild steel and 6000 series aluminum alloy sheets were simulated.

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