Plane strain distribution in perfectly plastic regions around circular holes due to unequal biaxial loads

1966 ◽  
Vol 1 (5) ◽  
pp. 394-397 ◽  
Author(s):  
I S Tuba
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Strain Distribution ◽  
Plastic Region ◽  
Secant Modulus ◽  
Compatibility Equation ◽  
Perfectly Plastic ◽  
Biaxial Loads ◽  
Circular Holes ◽  
Elastic Perfectly Plastic

The elastic-perfectly plastic solution of Galin provides only the stress distribution for the plastic region. The theory is extended and the compatibility equation is solved for the secant modulus. The unfinished problem of Galin is thus completed and the strain distribution is obtained for the perfectly plastic region around a circular hole due to unequal biaxial loads.

Computerized Relaxation Applied to the Plane-Strain Indenter

1969 ◽  
Vol 91 (4) ◽  
pp. 816-821
Author(s):  
J. W. Wesner ◽  
A. S. Weinstein
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Slip Line ◽  
Relaxation Method ◽  
Strip Thickness ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Distribution Problems ◽  
Plastic Stress

A computer adaptation of Southwell’s Relaxation Method was developed for the solution of elastic-perfectly plastic stress distribution problems. This method was employed to study some aspects of the problem of the plane-strain indenter. For two ratios of strip thickness to indenter width, the load for, and location of, initial yielding and the load for the onset of indentation were found. The results are compared with slip-line solutions.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

A Finite Element Based Study on the Elastic-Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Shankar ◽  
M. M. Mayuram
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Plastic Material ◽  
Plastic Region ◽  
Real Contact Area ◽  
Real Contact ◽  
Perfectly Plastic ◽  
The Difference ◽  
Elastic Perfectly Plastic ◽  
Green Model

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios (ω∕ωc) for the evolution of the elastic core and the plastic region within the asperity for different Y∕E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y∕E ratio of the material.

Plastic Strain Concentrations in Ligaments

1977 ◽  
Vol 99 (2) ◽  
pp. 328-336 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Plastic Strain ◽  
Numerical Solutions ◽  
Pure Shear ◽  
Solid Material ◽  
Shear Loading ◽  
Plastic Strains ◽  
Perfectly Plastic ◽  
Circular Holes ◽  
Elastic Perfectly Plastic ◽  
Conservative Values

The sheet perforated with a uniform array of circular holes arranged in a square pattern is investigated. The plastic strains are derived for progressive in-plane loading which eventually results in gross yielding. The finite element method is used to obtain numerical solutions. Plane stress conditions and elastic perfectly plastic solid material properties are assumed. Thus the results provide conservative values of plastic strain concentrations for a considerable range of perforated materials. The plastic strain multipliers for equibiaxial and pure shear loading are given for three ligament efficiencies of the penetration pattern. The tendency of forming highly localized plastic strains with progressive yielding is observed, and the implications of the results in plastic design are discussed.

Elastic-Plastic Plane Strain Analysis of Compressible Materials

1987 ◽  
Vol 109 (3) ◽  
pp. 357-358
Author(s):  
Hui Fan ◽  
G. E. O. Widera
Keyword(s):  
Plane Strain ◽  
Order Approximation ◽  
Strain Analysis ◽  
Perturbation Parameter ◽  
Incompressible Material ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
First Order Approximation ◽  
Compressible Materials ◽  
Walled Cylinder

The analysis of elastic, perfectly plastic compressible materials under the assumption of plane strain is a statically indeterminate problem. In the present paper, by introducing a perturbation parameter ε = 1/2−ν, the problem can be changed into a series of statically determinate ones. The first-order approximation yields the solution for the incompressible material. In order to show the details of this method, the second-order approximation for the problem of the thick-walled cylinder under internal pressure is obtained.

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