scholarly journals On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Oana Cazacu ◽  
Benoit Revil-Baudard ◽  
Ricardo A. Lebensohn ◽  
Mihail Gărăjeu
Keyword(s):  
Porous Solids ◽  
Stress Deviator ◽  
Full Field ◽  
Perfectly Plastic ◽  
Third Invariant ◽  
Spherical Cavities ◽  
Plastic Potential ◽  
Plastic Matrix ◽  
Von Mises ◽  
New Criterion

In this work it is shown that the exact plastic potential for porous solids with von Mises perfectly plastic matrix containing spherical cavities should involve a very specific coupling between the mean stress and the third invariant of the stress deviator. Furthermore, a new approximate plastic potential that preserves this key feature of the exact one is developed. Unlike all existing analytical criteria for porous solids with von Mises matrix, this new criterion displays a lack of symmetry with respect to both the hydrostatic and deviatoric axes. A full-field approach is also used to generate numerical gauge surfaces. These calculations confirm the aforementioned new features of the dilatational response.

Constitutive Modeling of Creep and Damage Behaviors of the Non-Mises Type for a Class of Polycrystalline Metals

2002 ◽  
Vol 11 (3) ◽  
pp. 223-245 ◽  
Author(s):  
M. Kawai
Keyword(s):  
Hydrostatic Stress ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Irreversible Thermodynamics ◽  
Polycrystalline Materials ◽  
Isotropic Hardening ◽  
Stress Deviator ◽  
Third Invariant ◽  
Scaling Parameters ◽  
Von Mises

Phenomenological constitutive models to describe the creep and damage behaviors that deviate from the von Mises type for a class of polycrystalline materials are developed. Theoretical and empirical approaches are taken to the formulation. The effective stresses that govern the rates of creep and damage are scaled to describe any deviation from the response of the von Mises type. A general form of scaling parameter is proposed which can consider the hydrostatic stress and/or the third invariant of the stress deviator. A kinematic hardening model is first formulated on the basis of irreversible thermodynamics using the scaling parameters for creep and damage. Then, two kinds of empirical basis models are presented for cases of kinematic hardening and isotropic hardening, respectively. The proposed models can describe the primary, secondary and tertiary creep behaviors and distinguish between the creep and damage behaviors under different modes of loading. To illustrate the features of the proposed models, numerical simulations of the unequal creep behaviors under tension, compression, and torsion are carried out and compared with experimental results.

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 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.

scholarly journals INCREMENTAL METHOD FOR UNLOADING PHENOMENON FIXATION AT SHAKEDOWN

2003 ◽  
Vol 9 (3) ◽  
pp. 178-191
Author(s):  
Dovilė Merkevičiūtė ◽  
Juozas Atkočiūnas
Keyword(s):  
Deformation Energy ◽  
Programming Approach ◽  
Problem Solution ◽  
Energy Principle ◽  
Incremental Method ◽  
Perfectly Plastic ◽  
Residual Strains ◽  
Residual Force ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

Elasto-Plastic Asperity Contacts of Layered Media

2005 ◽  
Author(s):  
Qin Xie ◽  
Geng Liu ◽  
Tianxiang Liu ◽  
Ruiting Tong ◽  
Quanren Zeng
Keyword(s):  
Yield Criterion ◽  
Layered Media ◽  
Asperity Contact ◽  
Initial Stiffness ◽  
Programming Technique ◽  
Perfectly Plastic ◽  
Real Area Of Contact ◽  
Asperity Contacts ◽  
Elastic Perfectly Plastic ◽  
Von Mises

An elasto-plastic asperity contact model for layered media is developed in the work reported in this paper to analyze the influences of coating-substrate materials on contact when yielding and the strain-hardening properties of materials are taken into account. The finite element method, the initial stiffness method and the mathematical programming technique are employed to solve the model. The von Mises yield criterion is used to determine the inception of plastic deformation. The effects of different layer thickness and different coating-substrate materials on the contact pressure, real area of contact, average gap of rough surface, and stresses in layer and substrate under the elastic-perfectly-plastic and the elasto-plastic contact conditions are numerically investigated and discussed.

A Generalized von Mises Criterion for Yield and Fracture

1980 ◽  
Vol 47 (2) ◽  
pp. 297-300 ◽  
Author(s):  
W. H. Yang
Keyword(s):  
Bauschinger Effect ◽  
Hydrostatic Stress ◽  
Fracture Criteria ◽  
Deformation History ◽  
Von Mises Criterion ◽  
Effect On Yield ◽  
Von Mises ◽  
New Criterion ◽  
Physical Phenomena ◽  
Special Case

Yield and fracture criteria for real materials are to a varying degree affected by a state of hydrostatic stress. Some materials, after certain deformation history, exhibit different yield point when the direction of the stress is reversed, a behavior known as the Bauschinger effect. These physical phenomena are not represented by the von Mises criterion. Based on a convexity theorem of matrices, a generalization of the von Mises criterion is presented. The new criterion satisfies the convexity requirement of plasticity theory and, with two scalar functions of deformation history α and β, produces a class of hardening behavior. The current values of α and β account for the effect of hydrostatic stress and an aspect of the Bauschinger effect on yield and fracture. The generalized criterion reduces to the form of the von Mises criterion as a special case.

Study on Character of Triaxial Extension Strength of Compacted Clay

2011 ◽  
Vol 243-249 ◽  
pp. 2183-2187
Author(s):  
Jun Xin Liu ◽  
Zhong Fu Chen ◽  
Wei Fang Xu
Keyword(s):  
Stress Tensor ◽  
Triaxial Compression ◽  
Deviatoric Stress ◽  
Stress Deviator ◽  
Strength Ratio ◽  
Compacted Clay ◽  
The Third ◽  
Third Invariant ◽  
Coulomb Criterion ◽  
Triaxial Extension

For soils, failure occurs with lower deviatoric stress under the same pressure (the first invariant of stress tensor) in TXE compared with the strength of the triaxial compression, which is indicated that the strength of soils strongly depends on the third invariant of stress deviator; Although in the traditional Mohr-Coulomb criterion it can be reflected in difference of strength between triaxial extension and compression under the same pressure, it’s nothing to do with the pressure for the strength ratio between triaxial extension and compression. By TXC and TXE, changes of deviatoric stress and the ratio with the pressure were studied

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