A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

2003 ◽  
Vol 70 (5) ◽  
pp. 649-654 ◽  
Author(s):  
Y.-Q. Zhang ◽  
H. Hao ◽  
M.-H. Yu
Keyword(s):  
Plane Stress ◽  
Yield Criterion ◽  
Strength Criterion ◽  
Rigid Plastic ◽  
Strength Criteria ◽  
Special Cases ◽  
Characteristic Theory ◽  
Characteristic Methods ◽  
Von Mises ◽  
Suitable Characteristic

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.

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–Brittle–Plastic Analysis of Double-Layered Combined Thick-Walled Cylinder Under Internal Pressure

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Qian Zhu ◽  
Junhai Zhao ◽  
Changguang Zhang ◽  
Yan Li ◽  
Su Wang
Keyword(s):  
Internal Pressure ◽  
Principal Stress ◽  
Yield Criterion ◽  
Engineering Application ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Material Behavior ◽  
Strength Theory ◽  
Special Cases ◽  
Walled Cylinder

The elastic–brittle–plastic unified solutions of limit internal pressure are presented for double-layered combined thick-walled cylinder by the triple-shear unified strength criterion. The unified solutions obtained in this paper are especially versatile that can take into account of material brittle softening and intermediate principal stress quantitatively. The conventional existing elastic-perfectly plastic solutions, based on the Tresca yield criterion, Mises yield criterion, or twin-shear strength theory, can be categorized as special cases of the present unified solutions which can overcome their shortages. Parametric studies were carried out to evaluate the influences of various factors such as brittle softening parameter, strength theory parameter, cohesion, internal friction angle, and intermediate principal stress coefficient on the unified solutions. It is shown that proper choices of failure criterion, material behavior model, and brittle softening are significant in combined cylinder design. The new solutions can be naturally degraded to the existing formula and agree well with the results of the prevailing failure criteria. It is concluded that the unified solutions have an important practical value for the optimum design and engineering application of combined thick-walled cylinder.

A Corotational Flow Rule for Rigid Plastic Hardening Materials Based on Logarithmic Strain Tensor

2002 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mehdi Yeganeh ◽  
Alireza Saidi
Keyword(s):  
Yield Criterion ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Cauchy Stress ◽  
Logarithmic Strain ◽  
Rigid Plastic ◽  
Corotational Rate ◽  
Plastic Hardening ◽  
Von Mises

In this paper a flow rule for rigid plastic hardening materials based on von Mises yield criterion is introduced. This flow rule relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. Using different corotational rates in the proposed flow rule, the deviatoric Cauchy stress tensor is calculated for rigid plastic isotropic, kinematic and combined hardening materials in the simple shear problem at large deformations. For the purpose of verification, the results for different corotational rates are compared with the results presented in referenced articles.

Limit pressures for spherical vessels with radial branches of differing protrusion lengths

1987 ◽  
Vol 22 (4) ◽  
pp. 209-214 ◽  
Author(s):  
M Robinson ◽  
R Kitching ◽  
C S Lim
Keyword(s):  
Yield Criterion ◽  
Branch Pipe ◽  
Plastic Limit ◽  
Linear Programming Method ◽  
Rigid Plastic ◽  
Design Rules ◽  
Non Linear Programming ◽  
Von Mises ◽  
Plastic Limit Pressure ◽  
Spherical Pressure

The effectiveness of the length by which a radial branch pipe extends within a spherical pressure vessel is discussed with reference to the plastic limit pressure of the vessel and the design rules of BS 5500. Lower bound limit pressures are calculated using a non-linear programming method, the stress resultants being expressed in polynomial form. The material was assumed to be rigid-plastic and to obey the von Mises yield criterion.

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.

scholarly journals A Study of Yielding and Plasticity of Rapid Prototyped ABS

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1495
Author(s):  
Dan-Andrei Șerban ◽  
Cosmin Marșavina ◽  
Alexandru Viorel Coșa ◽  
George Belgiu ◽  
Radu Negru
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Plastic Flow ◽  
Plane Stress ◽  
Yield Criterion ◽  
Numerical Analyses ◽  
Flow Potential ◽  
Stress States ◽  
State Configuration

In this article, the yielding and plastic flow of a rapid-prototyped ABS compound was investigated for various plane stress states. The experimental procedures consisted of multiaxial tests performed on an Arcan device on specimens manufactured through photopolymerization. Numerical analyses were employed in order to determine the yield points for each stress state configuration. The results were used for the calibration of the Hosford yield criterion and flow potential. Numerical analyses performed on identical specimen models and test configurations yielded results that are in accordance with the experimental data.

scholarly journals A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions

2020 ◽  
Vol 37 ◽  
pp. 100-107
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng
Keyword(s):  
Coordinate System ◽  
Plane Strain ◽  
Principal Stress ◽  
Plane Stress ◽  
Plastic Material ◽  
Yield Criterion ◽  
Boundary Value ◽  
Equilibrium Equations ◽  
Geometric Problem ◽  
Principal Lines

Abstract A general plastic material under plane strain and plane stress is classified by a yield criterion that depends on both the first and second invariants of the stress tensor. The yield criterion together with the stress equilibrium equations forms a statically determinate system. This system is investigated in the principal lines coordinate system (i.e. the coordinate curves of this coordinate system coincide with trajectories of the principal stress directions). It is shown that the scale factors of the principal lines coordinate system satisfy a simple equation. Using this equation, a method for constructing the principal stress trajectories is developed. Therefore, the boundary value problem of plasticity theory reduces to a purely geometric problem. It is believed that the method developed is useful for solving a wide class of boundary value problems in plasticity.

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