A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

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.

Temporal Instabilities (Dissipative Structures) In Cyclically Deformed Metallic Alloys

1995 ◽  
Vol 409 ◽  
Author(s):  
Michael V. Glazov ◽  
David R. Williams ◽  
Campbell Laird
Keyword(s):  
Cyclic Loading ◽  
Point Defects ◽  
Cyclic Deformation ◽  
Temporal Evolution ◽  
Dissipative Structures ◽  
Metallic Alloys ◽  
Dislocation Densities ◽  
Creep Fatigue ◽  
Chatelier Effect ◽  
First Time

AbstractThe existing models for the “classical” Portevin-Le-Chatelier effect have been analyzed, and the non-linear dynamical model has been proposed in order to quantify the nature of temporal instabilities in fatigued metallic alloys. The model employs the concept of a positive feed-back among the populations of mobile, immobile and Cottrell-type dislocations with atmospheres of point defects. Three major types of loading have been numerically simulated: pure sinusoidal, creep fatigue (“the Lorenzo-Laird bursts”) and ramp loading (“the Neumann bursts”, when the amplitude of otherwise cyclic loading grows linearly with time). Computer movies of the temporal evolution of stress and dislocation densities have been prepared as an aide for analysis and illustration. The model successfully reproduces stress serrations in terms of the underlying dislocation mechanisms and thus for the first time establishes a fundamental link between the micro-and macromechanics of cyclic deformation.

Parameter Evaluation for a Unified Constitutive Model

1993 ◽  
Vol 115 (2) ◽  
pp. 157-162 ◽  
Author(s):  
P. E. Senseny ◽  
N. S. Brodsky ◽  
K. L. DeVries
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Least Squares ◽  
Constitutive Equations ◽  
Laboratory Data ◽  
Constant Strain Rate ◽  
Nonlinear Least Squares ◽  
Evolutionary Equation ◽  
Internal Variables ◽  
Isotropic Hardening

Parameters for the unified constitutive model MATMOD [1] were evaluated for rock salt (NaCl) by using nonlinear least squares to fit the model to isothermal laboratory data. MATMOD incorporates two internal variables that represent the effects of both kinematic and isotropic hardening. The constitutive equations contain nine parameters that must be evaluated to model isothermal deformation. Laboratory data from stress relaxation, constant strain rate, and long-term creep tests were used. The latter two test types included staged tests in which the strain rate or stress was changed step-wise during the test. The test conditions were precisely controlled by a computer and the constitutive equations were integrated to simulate the laboratory conditions closely. The MATMOD parameters were then evaluated by fitting the integrated equations to the laboratory data using nonlinear least squares. The model fits the data well, but the fit may be improved by changing the evolutionary equation for the internal variable that accounts for isotropic hardening.

SIMULATION TO THE CYCLIC DEFORMATION OF POLYCRYSTALLINE ALUMINUM ALLOY USING CRYSTAL PLASTICITY FINITE ELEMENT METHOD

2013 ◽  
Vol 02 (03n04) ◽  
pp. 1350019 ◽  
Author(s):  
JUAN LUO ◽  
GUOZHENG KANG ◽  
MINGXING SHI
Keyword(s):  
Finite Element ◽  
Aluminum Alloy ◽  
Cyclic Loading ◽  
Constitutive Model ◽  
Single Crystal ◽  
Crystal Plasticity ◽  
Cyclic Deformation ◽  
Face Centered Cubic ◽  
Loading Conditions ◽  
Polycrystalline Aluminum

A crystal plasticity based finite element model (i.e., FE model) is used in this paper to simulate the cyclic deformation of polycrystalline aluminum alloy plates. The Armstrong–Frederick nonlinear kinematic hardening rule is employed in the single crystal constitutive model to capture the Bauschinger effect and ratcheting of aluminum single crystal presented under the cyclic loading conditions. A simple model of latent hardening is used to consider the interaction of dislocations between different slipping systems. The proposed single crystal constitutive model is implemented numerically into a FE code, i.e., ABAQUS. Then, the proposed model is verified by comparing the simulated results of cyclic deformation with the corresponding experimental ones of a face-centered cubic polycrystalline metal, i.e., rolled 5083 aluminum alloy. In the meantime, it is shown that the model is capable of predicting local heterogeneous deformation in single crystal scale, which plays an important role in the macroscopic deformation of polycrystalline aggregates. Under the cyclic loading conditions, the effect of applied strain amplitude on the responded stress amplitude and the dependence of ratcheting strain on the applied stress level are reproduced reasonably.

scholarly journals A dislocation density-based model for the work hardening and softening behaviors upon stress reversal

2021 ◽  
Vol 21 (2) ◽  
Author(s):  
Paulina Lisiecka-Graca ◽  
Krzysztof Bzowski ◽  
Janusz Majta ◽  
Krzysztof Muszka
Keyword(s):  
Dislocation Density ◽  
Electron Backscatter Diffraction ◽  
Microstructural Analysis ◽  
Back Stress ◽  
Carbon Steels ◽  
Internal Variables ◽  
Low Carbon ◽  
Average Dislocation Density ◽  
Calculation Results ◽  
Mechanical Behaviours

AbstractThe mechanical behaviours of microalloyed and low-carbon steels under strain reversal were modelled based on the average dislocation density taking into account its allocation between the cell walls and cell interiors. The proposed model reflects the effects of the dislocations displacement, generation of new dislocations and their annihilation during the metal-forming processes. The back stress is assumed as one of the internal variables. The value of the initial dislocation density was calculated using two different computational methods, i.e. the first one based on the dislocation density tensor and the second one based on the strain gradient model. The proposed methods of calculating the dislocation density were subjected to a comparative analysis. For the microstructural analysis, the high-resolution electron backscatter diffraction (EBSD) microscopy was utilized. The calculation results were compared with the results of forward/reverse torsion tests. As a result, good effectiveness of the applied computational methodology was demonstrated. Finally, the analysis of dislocation distributions as an effect of the strain path change was performed.

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