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.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

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.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 1: Analysis of Single Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 67-74 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Rolling Contact ◽  
Stress And Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Contact Width ◽  
Elastic Perfectly Plastic

This paper describes a two-dimensional (plane strain) elastic-plastic finite element model of rolling contact that embodies the elastic-perfectly plastic, cycle and amplitude-independent material of the Merwin and Johnson theory, but is rigorous with respect to equilibrium and continuity requirements. The rolling contact is simulated by translating a semielliptical pressure distribution. Both Hertzian and modified Hertzian pressure distributions are used to estimate the effect of plasticity on contact width and the continuity of the indentor-indentation interface. The model is tested for its ability to reproduce various features of the elastic-plastic indentation problem and the stress and strain states of single rolling contacts. This paper compares the results derived from the finite element analysis of a single, frictionless rolling contact at p0/k = 5 with those obtained from the Merwin and Johnson analysis. The finite element calculations validate basic assumptions made by Merwin and Johnson and are consistent with the development of “forward” flow. However, the comparison also reveals significant differences in the distribution of residual stress and strain components after a single contact cycle.

Elasto-Plastic Finite Element Analysis of Repeated, Two-Dimensional Rolling-Sliding Contacts

1988 ◽  
Vol 110 (1) ◽  
pp. 44-49 ◽  
Author(s):  
G. Ham ◽  
C. A. Rubin ◽  
G. T. Hahn ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Tangential Force ◽  
Element Model ◽  
Sliding Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Pure Rolling ◽  
Tangential Surface ◽  
Elastic Perfectly Plastic

The stresses, strains, and deformations produced by repeated, two-dimensional rolling-sliding contact are analyzed using a modified finite element model developed by Bhargava et al. [1]. Rolling and sliding are simulated by translating an appropriate set of normal and tangential surface tractions across an elastic-perfectly plastic half space. The study examines a peak-pressure-to-shear strength ratio of po/k = 4.5 and normal to tangential force ratios of T/N = 0.20 and T/N = 0.17. The calculations describe the residual stresses, displacements and the continuing cyclic radial, shear and equivalent strains generated at various depths in the rim. The results are compared with previous calculations by Johnson and Jefferis [2] of rolling-sliding contact and with pure rolling. The present work predicts much higher deformations than previously calculated.

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

2004 ◽  
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 formulae. The only significant limitation is that the shape of the moment-curvature relation must not change. I.e. the moment-curvature relation for the problem to be solved 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 formulae 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.

Spherical Indentation of an Elastic–Perfectly Plastic Half-Space: Deformation Map and Evolution of Plasticity

2009 ◽  
Author(s):  
Z. Song ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Material Properties ◽  
Deformation Behavior ◽  
Spherical Indentation ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Wide Range ◽  
Elastic Perfectly Plastic

A finite element analysis of the indentation of an elastic-perfectly plastic half-space by a rigid sphere was performed for a wide range of material properties. The post-yield deformation behavior was found to consist of four deformation regimes, namely linear elastic-plastic, non-linear elastic-plastic, transient fully-plastic, and steady-state fully-plastic deformation. The boundaries of these deformation regimes were determined numerically in terms of elastic-plastic material properties. The deformation behavior in different regimes was examined in the context of finite element results showing the evolution of subsurface plasticity for different material properties.

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.

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.

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