On the Plastic and Viscoplastic Constitutive Equations—Part II: Application of Internal Variable Concepts to the 316 Stainless Steel

1983 ◽  
Vol 105 (2) ◽  
pp. 159-164 ◽  
Author(s):  
J. L. Chaboche ◽  
G. Rousselier
Keyword(s):  
Constitutive Equations ◽  
Kinematic Hardening ◽  
Cyclic Hardening ◽  
Internal Variable ◽  
Cyclic Behavior ◽  
Strain Component ◽  
Aging Effects ◽  
Viscoplastic Strain ◽  
Complex Phenomena ◽  
Hardening Rules

The constitutive equations developed in Part I with a combination of isotropic and nonlinear kinematic hardening rules can describe the usual monotonic and cyclic behavior of metals and alloys. Some materials, especially type 316 stainless steels, show interaction of many complex phenomena such as viscoplasticity, cyclic hardening, time softening and aging effects. . . On the basis of experimental results obtained in Electricite de France or taken from the literature the descriptive ability of the developed constitutive equations is discussed and a new methodology is proposed which treats instantaneous plasticity and creep by using a viscoplastic strain component alone.

scholarly journals On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept

1983 ◽  
Vol 105 (2) ◽  
pp. 153-158 ◽  
Author(s):  
J. L. Chaboche ◽  
G. Rousselier
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Internal Variable ◽  
Cyclic Behavior ◽  
Internal Variables ◽  
Plastic Behavior ◽  
Hardening Rules ◽  
Plastic Strain Tensor ◽  
Natural Description

The description of monotonic and cyclic behavior of material is possible by generalizing the internal stress concept by means of a set of internal variables. In this paper the classical isotropic and kinematic hardening rules are briefly discussed, using present plastic strain tensor and cumulated plastic strain as hardening variables. Some additional internal variables are then proposed, giving rise to many possibilities. What is called the “nonlinear kinematic hardening” leads to a natural description of the nonlinear plastic behavior under cyclic loading, but is connected to other concepts such as the Mroz’s model, limited to only two surfaces, and similarities with other approaches are pointed out in the context of a generalization of this rule to viscoplasticity.

Creep and Plastic Strains of 304 Stainless Steel at 593°C Under Step Stress Changes, Considering Aging

1982 ◽  
Vol 49 (2) ◽  
pp. 297-304 ◽  
Author(s):  
U. W. Cho ◽  
W. N. Findley
Keyword(s):  
Stainless Steel ◽  
Constitutive Equations ◽  
Time Dependent ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Strain Component ◽  
Plastic Strains ◽  
Aging Effects ◽  
Stress Changes ◽  
Step Down

Nonlinear constitutive equations for varying stress histories are developed and used to predict the creep behavior of 304 stainless steel at 593°C (1100°F) under variable tension or torsion stresses including reloading, complete unloading, step-up, and step-down stress changes. The strain in the constitutive equations (a viscous-viscoelastic model) consists of: linear elastic, time-independent plastic, time-dependent-recoverable viscoelastic, and time-dependent-nonrecoverable viscous components. For variable stressing, the modified superposition principle, derived from the multiple integral representation, and the strain hardening theory were used to represent the recoverable and nonrecoverable components, respectively, of the time-dependent strain. Time-independent plastic strains were described by a flow rule of similar form to that for nonrecoverable, time-dependent strains. The material constants of the theory were determined from constant stress creep and creep recovery data. Considerable aging effects were found and the effects on the strain components were incorporated in each strain predicted by the theory. Some modifications of the theory for the viscoelastic strain component under step-down stress changes were made to improve the predictions. The final predictions combining the foregoing features made satisfactory agreements with the experimental creep data under step stress changes.

Predictions of microtorsional experiments by micropolar plasticity

2005 ◽  
Vol 461 (2053) ◽  
pp. 189-205 ◽  
Author(s):  
Paschalis Grammenoudis ◽  
Charalampos Tsakmakis
Keyword(s):  
Size Effects ◽  
Bauschinger Effect ◽  
Kinematic Hardening ◽  
Circular Cylinders ◽  
Isotropic Hardening ◽  
Gradient Plasticity ◽  
Material Response ◽  
Micropolar Plasticity ◽  
Classical Plasticity ◽  
Hardening Rules

Kinematic hardening rules are employed in classical plasticity to capture the so–called Bauschinger effect. They are important when describing the material response during reloading. In the framework of thermodynamically consistent gradient plasticity theories, kinematic hardening effects were first incorporated into a micropolar plasticity model by Grammenoudis and Tsakmakis. The aim of the present paper is to investigate this model by predicting size effects in torsional loading of circular cylinders. It is shown that kinematic hardening rules compared with isotropic hardening rules, as adopted in the paper, provide more possibilities for modelling size effects in the material response, even if only monotonous loading conditions are considered.

Damage-coupled ratcheting behaviors of SA508 Gr.3 steel at room and elevated temperatures: Experiments and simulations

2020 ◽  
Vol 29 (9) ◽  
pp. 1379-1396
Author(s):  
Jun Tian ◽  
Xiaolong Fu ◽  
Xuejiao Shao ◽  
Lu Jiang ◽  
Jian Li ◽  
...  
Keyword(s):  
Path Dependence ◽  
Elevated Temperatures ◽  
Kinematic Hardening ◽  
Cyclic Softening ◽  
Dynamic Strain ◽  
Loading Paths ◽  
Proposed Model ◽  
Series Of Experiments ◽  
Hardening Rules ◽  
Multiaxial Loadings

A series of experiments subjected to uniaxial and non-proportionally multiaxial cyclic loadings were performed to investigate the ratcheting responses of SA508 Gr.3 steel at room and elevated temperatures. The influences of different stress levels and nonproportional loading paths on the damage-coupled ratcheting responses were discussed. From experimental results, cyclic softening characteristic and dynamic strain aging can be observed under cyclic loadings. Moreover, the steel exhibits an obvious nonproportional path-dependence of the damage evolution under multiaxial loading paths. To numerically simulate the ratcheting responses under uniaxial and multiaxial loadings with the extended cyclic plastic model, the damage-coupled variable was introduced into the classic isotropic and nonlinear kinematic hardening rules. Corresponding material parameters could be calibrated from experimental data, and comparisons between experimental and simulated results were performed to validate the proposed model.

A Continuum Model for Single Crystal Cyclic Plasticity

2003 ◽  
Vol 779 ◽  
Author(s):  
Biqiang Xu ◽  
Yanyao Jiang
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Kinematic Hardening ◽  
Strain Curve ◽  
Cyclic Behavior ◽  
Cyclic Plasticity ◽  
Amplitude Dependence ◽  
Slip Systems ◽  
Stress Strain ◽  
Copper Single Crystals

AbstractA constitutive model was developed to bridge the cyclic plasticity behavior of single crystals and the corresponding characteristic dislocation structures. Yield and flow were built on the individual slip systems. The Armstrong-Frederick kinematic hardening rule was invoked to capture the Bauschinger effect. A material memory parameter was introduced to consider the amplitude dependence of cyclic hardening. Latent hardening considering the interactions among the slip systems was used to describe the anisotropic cyclic behavior. The experimental results of copper single crystals were used to validate the model developed. It was found that the model was able to adequately describe the well-known three distinctive regions in the cyclic stress-strain curve of the FCC single crystal oriented for single slip and the associated dislocation substructures. The model was capable of capturing the enhanced hardening observed in copper single crystals in multi-slip orientations. For a given loading history, the model can predict not only the saturated stress-strain response but also the detailed evolution of the transient cyclic behavior. The characteristic dislocation structures can be featured with the slip evolution.

Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

1978 ◽  
Vol 100 (1) ◽  
pp. 104-111 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Cyclic Loading ◽  
Material Property ◽  
Yield Surface ◽  
Strain Path ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Limit Surface ◽  
Hardening Rule ◽  
Hardening Models ◽  
Hardening Rules

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

Numerical Design of Extrusion Process Using Finite Thermo-Elastoviscoplasticity with Damage. Prediction of Chevron Shaped Cracks

2009 ◽  
Vol 424 ◽  
pp. 265-272 ◽  
Author(s):  
Carl Labergère ◽  
Khemais Saanouni ◽  
Philippe Lestriez
Keyword(s):  
Constitutive Equations ◽  
Thermal Effects ◽  
Initial Temperature ◽  
Kinematic Hardening ◽  
Extrusion Process ◽  
Main Process ◽  
Damage Prediction ◽  
User Subroutine ◽  
Micro Cracks ◽  
Fully Coupled

The influence of the initial temperature and its evolution with large plastic deformation on the formation of the fully coupled chevron shaped cracks in extrusion is numerically investigated. Fully coupled thermo-elasto-viscoplastic constitutive equations accounting for thermal effects, mixed and nonlinear isotropic and kinematic hardening, isotropic ductile damage with micro-cracks closure effects are used. These constitutive equations have been implemented in Abaqus/Explicit code thanks to the user subroutine vumat and used to perform various numerical simulations needed to investigate the problem. It has been shown that the proposed methodology is efficient to predict the chevron shaped cracks in extrusion function of the main process parameters including the temperature effect.

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