scholarly journals Grain shape effect on the biaxial elastic–inelastic behavior of polycrystals with a self-consistent approach

2009 ◽  
Vol 1 (1) ◽  
pp. 13-16 ◽  
Author(s):  
M. Radi ◽  
A. Abdul-Latif
Keyword(s):  
Grain Shape ◽  
Shape Effect ◽  
Inelastic Behavior ◽  
Self Consistent ◽  
Consistent Approach

Modeling of the Grain Shape Effect on the Elastic-Inelastic Behavior of Polycrystals With Self-Consistent Scheme

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
A. Abdul-Latif ◽  
M. Radi
Keyword(s):  
Grain Shape ◽  
Spherical Inclusion ◽  
Shape Effect ◽  
Inelastic Behavior ◽  
Consistent Model ◽  
Self Consistent ◽  
Eshelby’S Tensor ◽  
Anisotropic Elastic ◽  
Nonlinear Elastic ◽  
Interaction Law

Based on a well established nonincremental interaction law for fully anisotropic elastic-inelastic behavior of polycrystals, tangent formulation-based and simplified interaction laws of softened nature are derived to describe the nonlinear elastic-inelastic behavior of fcc polycrystals. Using the Eshelby’s tensor, the developed approach considers that the inclusion (grain) form is ellipsoidal. It has been clearly demonstrated by Abdul-Latif et al. (2002, “Elastic-Inelastic Self-Consistent Model for Polycrystals,” ASME J. Appl. Mech., 69, pp. 309–316) for spherical inclusion that the tangent formulation-based model requires more calculation time, and is incapable to describe correctly the multiaxial elastic-inelastic behavior of polycrystals in comparison with the simplified model. Hence, the simplified nonincremental interaction is studied considering the grain shape effect. A parametric study is conducted showing principally the influence of the some important parameters (the grain shape (α) and the new viscous parameter γ) and the effect of their interaction on the hardening evolution of polycrystals. Quantitatively, it is recognized that the model describes suitably the grain shape effect together with the new viscous parameter γ on the strain-stress behavior of aluminum and Waspaloy under tensile test.

Grain Shape Effect and the Viscoplastic Parameter on the Evolution of Isotropic and Kinematic Hardening of Metallic Materials under Cyclic Loading

2019 ◽  
Vol 820 ◽  
pp. 48-59
Author(s):  
Abdelhamid Kerkour-El Miad ◽  
A. Kerour-El Miad ◽  
Redouane Kouddane
Keyword(s):  
Grain Shape ◽  
Kinematic Hardening ◽  
Inelastic Strain ◽  
System Level ◽  
Elastic Behavior ◽  
Isotropic Hardening ◽  
Shape Effect ◽  
Metallic Materials ◽  
Crystallographic Slip ◽  
Self Consistent

The main objective of this work is to study the grain shape effect (aspect ratio α = a / b) and the viscoplastic parameter γ on the evolution of the kinematic and isotropic hardening of FCC type metallic materials, under uniaxial cyclic Tension-Compression ‘‘TC’ and to interpret these results. These parameters of shape and viscoplastic were developed and introduced by Abdul-Latif and Radi, indeed in this study we use their model. Expressed within the framework of a self-consistent approach, the rate-dependent inelastic strain is examined at the crystallographic slip system level describing a constitutive model for FCC metallic polycrystals, whereas the elastic strain is determined at the granular level. Based on the Eshelby’s tensor, the elastic behavior is assumed to be compressible. For a polycrystalline structure, the grains deform plastically by crystallographic slip located at the most favorably oriented systems supporting a high resolved shear stress . The approach considers that the inclusion (grain) form is ellipsoidal of half axes defining by a, b and c such as a ≠b= c. Several numerical tests are carried out highlighting the role of shape and viscoplastic parameter on the evolution of kinematic and isotropic hardening. A general comparison between the and effect on the overall hardening of the polycrystal shows that this work hardening is more sensitive to the parameter (for given ) compared to (for given). Keywords: Grain shape effect, Ellipsoidal inclusion, Viscoplastic parameter effect, Kinematic and isotropic hardening, Uniaxial cyclic ‘‘TC‘‘, Self-consistent model.

Modeling of Grain Shape Effect on Multiaxial Plasticity of Metallic Polycrystals

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
A. Abdul-Latif
Keyword(s):  
Grain Shape ◽  
Inelastic Strain ◽  
Cyclic Behavior ◽  
Loading Path ◽  
Model Parameters ◽  
Shape Effect ◽  
Inelastic Behavior ◽  
Aspect Ratios ◽  
Ellipsoidal Shape ◽  
Aluminum Alloy 2024

A simplified nonincremental interaction law is used describing the nonlinear elastic-inelastic behavior of FCC polycrystals proposed recently (Abdul-Latif and Radi, 2010, “Modeling of the Grain Shape Effect on the Elastic-Inelastic Behavior of Polycrystals with Self-Consistent Scheme,” ASME J. Eng. Mater. Technol., 132(1), p. 011008). In this scheme, the elastic strain defined at the granular level based on the Eshelby's tensor is assumed to be isotropic, uniform and compressible. Hence, the approach considers that the inclusion (grain) has an ellipsoidal shape of half axes defining by a, b and c such as a ≠ b = c. The granular heterogeneous inelastic strain is locally determined using the slip theory. Both elastic and inelastic granular strains depend on the granular aspect ratio (α = a/b). An aggregate of grains of ellipsoidal shape is supposed to be randomly distributed with a distribution of aspect ratios having a log-normal statistical function. The effect of this distribution on the mechanical behavior is investigated. A host of cyclic inelastic behavior of polycrystalline metals is predicted under uniaxial and multiaxial loading paths. Using the aluminum alloy 2024, an original complex cyclic loading path type is proposed and carried out experimentally. After the model parameters calibration, the elastic-inelastic cyclic behavior of this alloy is quantitatively described by the model. As a conclusion, the model can successfully describe the elasto-inelastic at the overall and local levels.

Erratum to: On a self-consistent approach to a bose model near the criticality

1981 ◽  
Vol 32 (2) ◽  
pp. 39-44 ◽  
Author(s):  
L. S. Campana ◽  
M. D’Ambrosio ◽  
L. De Cesaee
Keyword(s):  
Self Consistent ◽  
Consistent Approach

scholarly journals The Rules for the Lattice Rotation Accompanying Slip as Derived From a Self-Consistent Model

1999 ◽  
Vol 31 (4) ◽  
pp. 217-230 ◽  
Author(s):  
R. A. Lebensohn ◽  
T. Leffers
Keyword(s):  
Solid Mechanics ◽  
Grain Shape ◽  
Rolling Plane ◽  
Lattice Rotation ◽  
Consistent Model ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
The One ◽  
Equiaxed Grains ◽  
Very High

The rules for the lattice rotation during rolling (plane strain) deformation of fcc polycrystals are studied with a viscoplastic self-consistent model. Very high values of the ratesensitivity exponent are used in order to establish Sachs-type conditions with large local deviations from the macroscopic strain. The lattice rotation depends on the grain shape. For equiaxed grains the lattice rotation follows the MA rule, which is the one normally used in solid mechanics. For elongated and flat grains the lattice rotation follows a different rule, the PSA rule. In the standard version the model performs a transition from MA to PSA with increasing strain. There is avery clear difference between the textures resulting from the two different rules. MA leads to a copper-type texture, and PSA leads to a brass-type texture.

Micromagnetic simulations on the grain shape effect in Nd-Fe-B magnets

2016 ◽  
Vol 120 (3) ◽  
pp. 033903 ◽  
Author(s):  
Min Yi ◽  
Oliver Gutfleisch ◽  
Bai-Xiang Xu
Keyword(s):  
Grain Shape ◽  
Shape Effect ◽  
Micromagnetic Simulations

scholarly journals The two-particle self-consistent approach and its application to real materials

2021 ◽  
Author(s):  
◽  
Karim Zantout
Keyword(s):  
Self Consistent ◽  
Consistent Approach

Diese Thesis befasst sich mit dem Problem korrelierter Elektronensysteme in realen Materialien. Ausgangspunkt hierbei ist die quantenmechanische Beschreibung dieser Systeme im Rahmen der sogenannten Kohn-Scham Dichtefunktionaltheorie, welche die Elektronen der Kristallsysteme als effektiv nicht-wechselwirkende Teilchen beschreibt. Während diese Modellierung im Falle vieler Materialklassen erfolgreich ist, unterscheiden sich die korrelierten Elektronensysteme dadurch, dass der kollektive Charakter der Elektronendynamik nicht zu vernachlässigen ist. Um diese Korrelationseffekte genauer zu untersuchen, verwenden wir in dieser Arbeit das Hubbard-Modell, welches mit der projektiven Wannierfunktionsmethode aus der Kohn-Scham Dichtefunktionaltheorie konstruiert werden kann. Das Hubbard-Modell umfasst hierbei nur die lokale Elektron-Elektron-Wechselwirkung auf einem Gitter. Auch wenn das Modell augenscheinlich sehr simpel ist, existieren exakte Lösungen nur in bestimmten Grenzfällen. Dies macht die Entwicklung approximativer Ansätze erforderlich, wobei die Weiterentwicklung der sogenannten Two-Particle Self-Consistent Methode (TPSC) eine zentrale Rolle dieser Arbeit einnimmt. Bei TPSC handelt es sich um eine Vielteilchenmethode, die in der Sprache funktionaler Ableitungen und sogenannter conserving approximations hergeleitet werden kann. Der zentrale Gedanke dabei ist, den effektiven Wechselwirkungsvertex als statisch und lokal zu approximieren. Dies wiederum erlaubt die Bewegungsgleichung des Systems erheblich zu vereinfachen, sodass eine numerische approximative Lösung des Hubbard-Modells möglich wird. Vorsetzung hierbei ist nur, dass sich das System in der normalleitenden Phase befindet und die bei Phasenübergängen entstehenden Fluktuationen nicht zu groß sind. Während diese Methode ursprünglich von Y. M. Vilk und A.-M. Tremblay für das Ein-Orbital Hubbard-Modell entwickelt wurde, stellen wir in dieser Arbeit eine Erweiterung auf Viel-Orbital-Systeme vor. Im Falle mehrerer Orbitale treten in der TPSC-Herleitung einzelne Komplikationen auf, die mit weiteren Approximationen behandelt werden müssen. Diese werden anhand eines einfachen Zwei-Orbital Modell-Systems diskutiert und die TPSC-Ergebnisse werden darüber hinaus mit den Ergebnissen der etablierten dynamischen Molekularfeldnährung verglichen. In diesem Zusammenhang werden auch mögliche zukünftige Erweiterungen bzw. Verbesserungen von TPSC diskutiert. Ein weiterer wichtiger Aspekt ist die Anwendung von TPSC auf reale Materialien. In diesem Zusammenhang werden in dieser Arbeit die supraleitenden Eigenschaften der organischen K-(ET)2X Systeme untersucht. Hierbei lassen die TPSC-Resultate darauf schließen, dass das populäre Dimer-Modell, welches zur Beschreibung dieser Materialien herangezogen wird, nicht genügt um die experimentell bestimmten kritischen Temperaturen zu erklären und dass das komplexere Molekülmodell weitere exotische supraleitende Lösungen zulässt. Schließlich untersuchen wir außerdem die elektronischen Eigenschaften des eisenbasierten Supraleiters LiFeAs und diskutieren inwieweit nicht-lokale Korrelationseffekte, welche durch TPSC aufgelöst werden können, die experimentellen Daten reproduzieren.

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