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.

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.

Elastic-plastic stress analysis of a cracked thick-walled cylinder

1983 ◽  
Vol 18 (4) ◽  
pp. 253-260 ◽  
Author(s):  
C L Tan ◽  
K H Lee
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Plastic Material ◽  
Boundary Integral ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Walled Cylinder ◽  
Plastic Stress

The boundary integral equation (BIE) method for two-dimensional elastic-plastic stress analysis is applied to an internally pressurized thick-walled cylinder containing a radial crack. Two different types of material are considered, namely, an elastic-perfectly plastic material and a work-hardening material. The loading conditions applied include the case when the internal pressure also acts on the crack faces, and the case when it does not. Results are presented showing the plastic zone development in the cylinder and the variations of the fracture mechanics parameter, the J line integral, with increasing internal pressure.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Input Parameter ◽  
Time Integration ◽  
Strain Increment ◽  
Total Strain ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Time Stepping ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham Π theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

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