An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation

Autor: Farid Abed-Meraim, J. Paux, Houssem Badreddine, Carl Labergere, M. Ben Bettaieb, Khemais Saanouni
Přispěvatelé: Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Institut de recherche technologique Matériaux Métallurgie et Procédés (IRT M2P), Laboratoire des Systèmes Mécaniques et d'Ingénierie Simultanée (LASMIS), Institut Charles Delaunay (ICD), Université de Technologie de Troyes (UTT)-Centre National de la Recherche Scientifique (CNRS)-Université de Technologie de Troyes (UTT)-Centre National de la Recherche Scientifique (CNRS), Institut de Thermique, Mécanique, Matériaux (ITheMM), Université de Reims Champagne-Ardenne (URCA), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Damaged single crystal
Computation
Constitutive equation
Computational Mechanics
General Physics and Astronomy
[PHYS.MECA.GEME]Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph]
010103 numerical & computational mathematics
Sciences de l'ingénieur
01 natural sciences
[SPI.MAT]Engineering Sciences [physics]/Materials
[PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph]
[SPI]Engineering Sciences [physics]
[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
Applied mathematics
Elasto-plasticity
0101 mathematics
Physics
Mechanical Engineering
Scalar (physics)
Forming processes
Metal forming
[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]
Finite element method
Computer Science Applications
010101 applied mathematics
Objectivity (frame invariance)
Mechanics of Materials
Self-consistent scheme
Finite strain theory
Finite strain
Tangent modulus
Schmid criterion
Zdroj: Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 368, pp.113138. ⟨10.1016/j.cma.2020.113138⟩
Computer Methods in Applied Mechanics and Engineering, 2020, 368, pp.113138. ⟨10.1016/j.cma.2020.113138⟩
ISSN: 0045-7825
DOI: 10.1016/j.cma.2020.113138⟩
Popis: International audience; Elasto-plastic multiscale approaches are known to be suitable to model the mechanical behavior of metallic materials during forming processes. These approaches are classically adopted to explicitly link relevant microstructural effects to the macroscopic behavior. This paper presents a finite strain elastoplastic self-consistent model for damaged polycrystalline aggregates and its implementation into ABAQUS/Standard finite element (FE) code. Material degradation is modeled by the introduction of a scalar damage variable at each crystallographic slip system for each individual grain. The single crystal plastic flow is described by both the classical and a regularized version of the Schmid criterion. To integrate the single crystal constitutive equations, two new numerical algorithms are developed (one for each plastic flow rule). Then, the proposed single crystal modeling is embedded into the self-consistent scheme to predict the mechanical behavior of elasto-plastic polycrystalline aggregates in the finite strain range. This strategy is implemented into ABAQUS/Standard FE code through a user-defined material (UMAT) subroutine. Special attention is paid to the satisfaction of the incremental objectivity and the efficiency of the convergence of the global resolution scheme, related to the computation of the consistent tangent modulus. The capability of the new constitutive modeling to capture the interaction between the damage evolution and the microstructural properties is highlighted through several simulations at both single crystal and polycrystalline scales. It appears from the numerical tests that the use of the classical Schmid criterion leads to a poor numerical convergence of the self-consistent scheme (due to the abrupt changes in the activity of the slip systems), which sometimes causes the computations to be prematurely stopped. By contrast, the use of the regularized version of the Schmid law allows a better convergence of the self-consistent approach, but induces an important increase in the computation time devoted to the integration of the single crystal constitutive equations (because of the high value of the power-law exponent used to regularize the Schmid yield function). To avoid these difficulties, a numerical strategy is built to combine the benefits of the two approaches: the classical Schmid criterion is used to integrate the single crystal constitutive equations, while its regularized version is used to compute the microscopic tangent modulus required for solving the self-consistent equations. The robustness and the accuracy of this novel numerical strategy are particularly analyzed through several numerical simulations (prediction of the mechanical behavior of polycrystalline aggregates and simulation of a circular cup-drawing forming process).
Databáze: OpenAIRE
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