Plane-strain indentation on a smooth foundation: A range of solutions for rigid-perfectly plastic strip

1974 ◽  
Vol 16 (12) ◽  
pp. 923-930 ◽  
Author(s):  
P. Dewhurst
Keyword(s):  
Plane Strain ◽  
Plastic Strip ◽  
Perfectly Plastic

Plane Strain Compression of Rigid-Perfectly Plastic Strip Between Parallel Dies With Slipping Friction

1979 ◽  
Vol 46 (2) ◽  
pp. 317-321 ◽  
Author(s):  
N. S. Das ◽  
J. Banerjee ◽  
I. F. Collins
Keyword(s):  
Yield Stress ◽  
Plane Strain ◽  
Upper Bound ◽  
Metal Interface ◽  
Plastic Strip ◽  
Perfectly Plastic ◽  
Slipping Friction ◽  
Computer Calculations ◽  
Linear Integral ◽  
Linear Integral Equations

This paper presents the results of computer calculations of a class of slipline solutions for compression between parallel dies with slipping friction at the die-metal interface such that the frictional shear traction is a constant proportion of the yield stress. The slipline fields considered here have previously only been suggested qualitatively. The fields are of “indirect type”, requiring the solution of linear integral equations. They have been analyzed and computed here using the recently developed matrix operator procedure. The numerical results obtained are compared with those obtained from approximate upper bound and other “technological” theories.

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.

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.

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