Elastic-Plastic Modeling of Hardening Materials Using a Corotational Rate Based on the Plastic Spin Tensor

2007 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Isotropic Hardening ◽  
Strain Rate Tensor ◽  
Spin Tensor ◽  
Plastic Spin ◽  
Elastic Plastic ◽  
Proposed Model ◽  
Corotational Rate ◽  
Shear Problem

In this paper based on the multiplicative decomposition of the deformation gradient, the plastic spin tensor and the plastic spin corotational rate are introduced. Using this rate (and also log-rate), an elastic-plastic constitutive model for hardening materials are proposed. In this model, the Armstrong-Frederick kinematic hardening and the isotropic hardening equations are used. The proposed model is solved for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the results of proposed theoretical model and the experimental data. As another example, the Prager kinematic hardening equation is used. In this case, the stress results are compared with those obtained by Bruhns et al. [2], in which they used the additive decomposition of the strain rate tensor.

Corotational Analysis of Elastic-Plastic Hardening Materials Based on Different Kinematic Decompositions

2006 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Theoretical Models ◽  
Isotropic Hardening ◽  
Strain Rate Tensor ◽  
Elastic Plastic ◽  
Mixed Hardening ◽  
Hardening Models ◽  
Shear Problem ◽  
Plastic Hardening

In this paper, two corotational modeling for elastic-plastic, mixed hardening materials at finite deformations are introduced. In these models, the additive decomposition of the strain rate tensor as well as the multiplicative decomposition of the deformation gradient tensor is used. For this purpose, corotational constitutive equations are derived for elastic-plastic hardening materials with the non-linear Armstrong-Frederick kinematic hardening and isotropic hardening models. As an application of the proposed constitutive modeling, the governing equations are solved numerically for the simple shear problem with different corotational rates and the stress components are plotted versus the shear displacement. The results for stress, using the additive and the multiplicative decompositions are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the proposed theoretical models and the experimental data. As another example, the Prager kinematic hardening equation is used instead of the Armstrong-Frederick model. In this case the results for stress are compared with the theoretical results of Bruhns et al. [2].

Elastic-Plastic Modeling of Kinematic Hardening Materials Based on F=FeFp Decomposition and the Logarithmic Strain Tensor

Volume 1 ◽  
2004 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Flow Rule ◽  
Deformation Gradient Tensor ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Corotational Rate ◽  
Stress Components ◽  
Shear Problem

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material.

Nonlinear Plastic Modeling of Materials Based on the Generalized Strain Rate Tensor

2008 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Strain Rate ◽  
Simple Shear ◽  
Large Deformations ◽  
Kinematic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Governing Equations ◽  
Elastic Plastic ◽  
Shear Problem ◽  
Plastic Hardening

In this paper, a method for modeling of elastic-plastic hardening materials under large deformations is proposed. In this model the generalized strain rate tensor is used. Such a tensor is obtained on the basis of the method which was introduced by the authors. Based on the generalized strain rate tensor, a flow rule, a Prager-type kinematic hardening equation and a kinematic decomposition is proposed and the governing equations for such materials are obtained. As an application, the governing equations for the simple shear problem are solved and some results are compared with those in the literature.

3-D Elastic-Plastic Constitutive Relationship of Mixed Hardening

2012 ◽  
Vol 249-250 ◽  
pp. 927-930
Author(s):  
Ze Yu Wu ◽  
Xin Li Bai ◽  
Bing Ma
Keyword(s):  
Finite Element ◽  
Constitutive Relation ◽  
Kinematic Hardening ◽  
Constitutive Relationship ◽  
Isotropic Hardening ◽  
Element Analysis ◽  
Hardening Model ◽  
Elastic Plastic ◽  
Mixed Hardening ◽  
Advantages And Disadvantages

In finite element calculation of plastic mechanics, isotropic hardening model, kinematic hardening model and mixed hardening model have their advantages and disadvantages as well as applicability area. In this paper, by use of the tensor analysis method and mixed hardening theory in plastic mechanics, the constitutive relation of 3-D mixed hardening problem is derived in detail based on the plane mixed hardening. Numerical results show that, the proposed 3-D mixed hardening constitutive relation agrees well with the test results in existing references, and can be used in the 3-D elastic-plastic finite element analysis.

The influence of non-dissipative quantities in kinematic hardening plasticity

2004 ◽  
Vol 218 (6) ◽  
pp. 615-622 ◽  
Author(s):  
M Wallin ◽  
M Ristinmaa ◽  
N S Ottosen
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Material Behaviour ◽  
Dissipative Part ◽  
Real Material ◽  
Shear Problem ◽  
Evolution Laws ◽  
Thin Walled ◽  
Plastic Parts ◽  
Walled Cylinder

A kinematic hardening plasticity model valid for finite strains is presented. The model is based on the well-known multiplicative split of the deformation gradient into elastic and plastic parts. The basic ingredient in the formulation is the introduction of a locally defined configuration—a centre configuration—which is associated with a deformation gradient that is used to characterize the kinematic hardening behaviour. The non-dissipative quantities allowed in the model are found when the plastic and kinematic hardening evolution laws are split into two parts: a dissipative part, which is restricted by the dissipation inequality, and a non-dissipative part, which can be chosen without any thermodynamic considerations. To investigate the predictive capabilities of the proposed kinematic hardening formulation, necking of a bar is considered. Moreover, to show the influence of the non-dissipative quantities, the simple shear problem and torsion of a thin-walled cylinder are considered. The numerical examples reveal that the non-dissipative quantities can affect the response to a large extent and are consequently valuable and important ingredients in the formulation when representing real material behaviour.

scholarly journals Effect of Strain Hardening on Elastic-Plastic Contact of a Deformable Sphere against a Rigid Flat under Full Stick Contact Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Biplab Chatterjee ◽  
Prasanta Sahoo
Keyword(s):  
Strain Hardening ◽  
Kinematic Hardening ◽  
Contact Condition ◽  
Isotropic Hardening ◽  
Contact Conditions ◽  
Elastic Plastic ◽  
Finite Element Software ◽  
Hardening Models ◽  
Load Carrying ◽  
Contact Parameters

The present study considers the effect of strain hardening on elastic-plastic contact of a deformable sphere with a rigid flat under full stick contact condition using commercial finite element software ANSYS. Different values of tangent modulus are considered to study the effect of strain hardening. It is found that under a full stick contact condition, strain hardening greatly influences the contact parameters. Comparison has also been made between perfect slip and full stick contact conditions. It is observed that the contact conditions have negligible effect on contact parameters. Studies on isotropic and kinematic hardening models reveal that the material with isotropic hardening has the higher load carrying capacity than that of kinematic hardening particularly for higher strain hardening.

A Dislocation Density-Based Viscoplasticity Model for Cyclic Deformation: Application to P91 Steel

2018 ◽  
Vol 10 (05) ◽  
pp. 1850055 ◽  
Author(s):  
Xu He ◽  
Yao Yao
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Yield Strength ◽  
Cyclic Deformation ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Isotropic Hardening ◽  
P91 Steel ◽  
Numerical Predictions ◽  
Proposed Model

To describe the viscoplastic behavior of materials under cyclic loading, a dislocation density-based constitutive model is developed based on the unified constitutive theory in which both the creep and plastic strain are integrated into an inelastic strain tensor. The stress evolution during cyclic deformation is caused by the mutual competition and interaction between hardening and recovery. To incorporate the physical mechanisms of cyclic deformation, the change of mobile dislocation density is associated with inelastic stain in the proposed model. The evolution of immobile dislocation density induced by strain hardening, dynamic recovery, static recovery and strain-induced recovery are simulated separately. The deterioration of yield strength following the hardening in tension (or compression) and subsequently in compression (or tension) is described by the Bauschinger effect and reduction of immobile dislocation density, the latter is induced by static- and strain-induced recovery. A kinematic hardening law based on dislocation density is proposed, both isotropic hardening and softening are described by determining the evolution of hardening parameters. The experimental data of P91 steel under different strain rates and temperatures are adopted to verify the proposed model. In general, the numerical predictions agree well with the experimental results. It is demonstrated that the developed model can accurately describe the hardening rate change, the yield strength deterioration and the softening under cyclic loading.

Elastic-plastic finite element analysis of hollow tubes with axially loaded axisymmetric internal projections

1993 ◽  
Vol 28 (3) ◽  
pp. 187-196 ◽  
Author(s):  
S J Hardy ◽  
A R Gowhari-Anaraki
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Elastic Stress ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Published Data ◽  
Elastic Plastic ◽  
Concentration Factors ◽  
Stress Concentration Factors

The finite element method is used to study the monotonic and cyclic elastic-plastic stress and strain characteristics of hollow tubes with axisymmetric internal projections subjected to monotonic and repeated axial loading. Two geometries having low and high elastic stress concentration factors are considered in this investigation, and the results are complementary to previously published data. For cyclic loading, three simple material behaviour models, e.g., elastic-perfectly-plastic, isotropic hardening, and kinematic hardening are assumed. All results have been normalized with respect to material properties so that they can be applied to all geometrically similar components from other materials which may be represented by the same material models. Finally, normalized maximum monotonic strain and steady state strain range, predicted in the present investigation and from previously published data, are plotted as a function of the nominal load for different material hardening assumptions and different elastic stress concentration factors. These plots can be used in the low cycle fatigue design of such geometrically similar components.

Elastic-Plastic Modeling of the Hardening Materials Based on an Eulerian Strain Tensor and a Proper Corotational Rate

2005 ◽  
Author(s):  
Reza Naghdabadi ◽  
Kamyar Ghavam
Keyword(s):  
Kinematic Hardening ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Governing Equations ◽  
Plastic Part ◽  
Elastic Plastic ◽  
Eulerian Strain ◽  
Corotational Rate ◽  
Conjugate Stress

In this paper a model for analyzing elastic-plastic kinematic hardening materials is introduced, based on the additive decomposition of the corotational rate of an Eulerian strain tensor In this model, the elastic constitutive equation as well as the flow rule and the hardening equation is expressed in terms of the elastic and plastic parts of the corotational rate of the mentioned Eulerian stain tensor and its conjugate stress tensor. In the flow rule, the plastic part of the corotational rate of the Eulerian strain tensor is related to the difference of the deviatoric part of the conjugate stress and the back stress tensors. A proportionality factor is used in this flow rule which must be obtained from a consistency condition based on the von Mises yield criterion. A Prager type kinematic hardening model is used which relates the corotational rate of the back stress tensor to the plastic part of the corotational rate of the Eulerian strain tensor. Also in this paper a proper corotational rate corresponding to the Eulerian strain tensor is introduced. Finally the governing equations for the analysis of elastic-plastic kinematic hardening materials are obtained. As an application, these governing equations are solved numerically for the simple shear problem and the stress and back stress components are plotted versus the shear displacement. The results are compared with those, which are available in the literature.

Simulation of Electromagnetic Forming of a Cross-Shaped Cup by Means of a Viscoplasticity Model Coupled with Damage at Finite Strains

2013 ◽  
Vol 554-557 ◽  
pp. 2363-2368 ◽  
Author(s):  
Yalin Kiliclar ◽  
O. Koray Demir ◽  
Ivaylo N. Vladimirov ◽  
Lukas Kwiatkowski ◽  
Stefanie Reese ◽  
...  
Keyword(s):  
Finite Element ◽  
Deep Drawing ◽  
High Speed ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Deformation Gradient ◽  
Electromagnetic Forming ◽  
Isotropic Hardening ◽  
Order Structure ◽  
Forming Process

In the field of sheet metal forming traditional forming processes are used. However, a quasi-static forming process combined with a high speed forming process can enhance the forming limits of a single one. In this paper, the investigation of the process chain quasi-static deep drawing – electromagnetic forming by means of a new coupled damage-viscoplasticity model for large deformations is performed. The finite strain constitutive model, used in the finite element simulation combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. The anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. Hill-type plastic anisotropy is modelled by expressing the yield surface as a function of second-order structure tensors as additional tensor-valued arguments. The coupling of damage and plasticity is carried out in a constitutive manner according to the effective stress concept. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package of LS-Dyna with the electromagnetical modul. Aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming process.

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