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Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms

Article dans une revue avec comité de lecture
Auteur
AKPAMA, Holanyo K.
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
BEN BETTAIEB, Mohamed
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
ABED-MERAIM, Farid
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]

URI
http://hdl.handle.net/10985/10654
DOI
10.1002/nme.5215
Date
2016
Journal
International Journal for Numerical Methods in Engineering

Résumé

In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).

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Documents liés

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  • Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach 
    Article dans une revue avec comité de lecture
    AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid (Argentinean Association of Computational Mechanics, Brazilian Association of Computational Mechanics, Mexican Association of Numerical Methods in Engineering and Applied Sciences, 2017)
    The prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed ...
  • Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms 
    Article dans une revue avec comité de lecture
    AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid (Wiley, 2016)
    In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially ...
  • Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach 
    Article dans une revue avec comité de lecture
    AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid (Elsevier, 2017)
    The present study focuses on the development of a relevant numerical tool for predicting the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In ...
  • Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory 
    Article dans une revue avec comité de lecture
    AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid (Argentinean Association of Computational Mechanics, Brazilian Association of Computational Mechanics, Mexican Association of Numerical Methods in Engineering and Applied Sciences, 2016)
    The aim of this paper is to investigate the impact of the microscopic yield surface (i.e., at the single crystal scale) on the forming limit diagrams (FLDs) of face centred cubic (FCC) materials. To predict these FLDs, ...
  • A comparative study of Forming Limit Diagrams predicted by two different plasticity theories involving vertex effects 
    Article dans une revue avec comité de lecture
    AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid (Trans Tech Publications, 2015)
    The main objective of this contribution is to compare the Forming Limit Diagrams (FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the ...

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