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.

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.

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.

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.

Evaluation of Associated and Non-Associated Flow Metal Plasticity; Application for DC06 Deep Drawing Steel

2012 ◽  
Vol 504-506 ◽  
pp. 661-666 ◽  
Author(s):  
Mohsen Safaei ◽  
Wim De Waele ◽  
Shun Lai Zang
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Strain Rate ◽  
Yield Stress ◽  
Deep Drawing ◽  
Kinematic Hardening ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

A Corotational Elastoplastic Formulation With Subloading Surface Model for Hardening Materials

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Reza Saidi ◽  
Koichi Hashiguchi
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Simple Shear ◽  
Deformation Theory ◽  
Elastoplastic Deformation ◽  
Strain Tensor ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Hencky Strain ◽  
Stress Components

In this paper a corotational constitutive model for the large elastoplastic deformation of hardening materials using subloading surface model is formulated. This formulation is obtained by refining the large deformation theory of Naghdabadi and Saidi (2002) adopting the corotational logarithmic (Hencky) strain rate tensor and incorporating it into the subloading surface model of Hashiguchi (1980, 2003) falling within the framework of the unconventional plasticity. As an application of the proposed constitutive model, the large Elastoplastic deformation of simple shear example has been solved and the results have been compared with classical elasto-plastic model using the Hencky strain tensor. Also the effect of the choice of corotational rates on stress components has been studied.

Analysis of Casting Materials under Thermal Fatigue

2015 ◽  
Vol 784 ◽  
pp. 95-103
Author(s):  
Holm Altenbach ◽  
Frank Laengler ◽  
Konstantin Naumenko ◽  
Mykola Ievdokymov
Keyword(s):  
Strain Rate ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Inelastic Strain ◽  
Material Model ◽  
Material Behavior ◽  
Strain Rate Tensor ◽  
Inelastic Behavior ◽  
Damage Evolution Equation ◽  
High Temperature Components

High-temperature components, for example turbochargers, are often subject to complex thermal and mechanical loading paths. Non-uniform temperature distribution and constraints by neighboring components result in complex timely varying stress and strain states during operation. In this paper the inelastic behavior of a casting material Ni-resist D-5S in a wide stress, strain rate and temperature ranges is analyzed. The material model including a constitutive equation for the inelastic strain rate tensor, a non-linear kinematic hardening rule and a damage evolution equation is developed. To calibrate the model, experimental databases from creep and low cycle fatigue (LCF) tests are applied. For the verification of the model, simulations of the material behavior under uni-axial thermo-mechanical fatigue (TMF) loading conditions are performed. The results for the stress response and lifetime are compared with experimental data.

The Study of Elastic-Plastic Fatigue Behavior of Nigerian-Rolled NST 37-2 Steel

2010 ◽  
Vol 3 ◽  
pp. 28-41
Author(s):  
B.O. Malomo ◽  
S.A. Ibitoye ◽  
L.O. Adekoya
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Fatigue Behavior ◽  
Numerical Results ◽  
Test Material ◽  
Flow Rule ◽  
Static Fatigue ◽  
Elastic Plastic

The NST 37-2 steel represents about 75% volume of Nigerian-produced steel which is yet to be fully characterized for its fatigue behavior. Thus, its suitability for many applications is questionable. This paper presents a framework based on the theory of elasto-plasticity in order to make appropriate recommendations in this regard. Experimentally, tensile tests were carried out on test specimens to establish the baseline material properties of the steel in annealed, as-rolled, normalized and hardened/tempered conditions. Fatigue tests were then conducted at 60% Su; 70% Su and 80% Su of the test material and fractographic examinations on the test specimens were subsequently carried out. The frequency harmonic fatigue analysis was implemented in the ANSYS software environment for the numerical study. The elastic-plastic material property was described by the von Mises yield criterion, the flow rule of Prandtl-Reuss, and the kinematic hardening rule of Prager. The numerical results indicate with respect to rate-dependence fatigue behavior that the annealed test specimen is most resilient under cyclic deformation as compared with the normalized, hardened/tempered and as-rolled specimens respectively. The experimental and numerical results were found to be in close agreement and based on the general performance, the steel material is recommended for use in low cycle, quasi-static fatigue applications.

Simulation of Dense Solid-Liquid Two-Phase Flow in a Pump Impeller

2004 ◽  
Author(s):  
Shuhong Liu ◽  
Xuelin Tang ◽  
Yulin Wu ◽  
Michihiro Nishi
Keyword(s):  
Strain Rate ◽  
Dynamic Model ◽  
Rotation Rate ◽  
Second Order ◽  
Staggered Grid ◽  
Strain Rate Tensor ◽  
Governing Equations ◽  
Two Phase ◽  
Pump Impeller ◽  
Solid Liquid

In the present study, simulation with the second-order dynamic model for sub-grid stress is used to solve the governing equations of dense solid-liquid two-phase (DSLTP) flow numerically, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the current second-order dynamic model with double dynamic coefficients, the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor. This model considers the symmetry of the sub-grid-scale stresses, dimensional consistency with the Cauchy-Helmholtz theorem, the Smagorinsky model and the invariants of the strain-rate tensor and the rotation-rate tensor in large eddy simulation (LES). In the numerical calculation, the SIMPLEC algorithm and a staggered grid system were applied for the solution of the discretized particle-liquid turbulent flow equations, and Body-fitted Coordinates were used to simulate the flow over the complex geometry field. In this paper, the second-order dynamic model for turbulent dense solid-liquid two-phase flows was applied to a centrifugal pump impeller.

Stress update algorithm for non-associated flow metal plasticity

2012 ◽  
Vol 3 (2) ◽  
pp. 106-110
Author(s):  
Mohsen Safaei ◽  
Wim De Waele
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Kinematic Hardening ◽  
Quadratic Function ◽  
Yield Function ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

. In this paper we present the continuum plasticity model based on non-Associated Flow Rule (nonAFR) for Hill’s48 quadratic yield function. In case of non-AFR, Hill’s quadratic function used as plasticpotential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate.In addition, the yield function uses direction dependent yield stress data. Therefore more accuratepredictions are expected in terms of both yield stress and strain ratios at different orientations. Weimplemented a modified version of the non-associative flow rule originally developed by Stoughton [1] intothe commercial finite element code ABAQUS by means of a user material subroutine UMAT. The mainalgorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumesproportional loading cases and therefore only isotropic hardening effect is considered. In our model theincremental change of plastic strain rate tensor is not equal to the incremental change of the compliancefactor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finiteelement simulations with experimentally determined values for deep drawing steel DC06. A criticalcomparison is made between numerical results obtained from AFR and non-AFR based models.

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