On the numerical integration of rate independent single crystal behavior at large strain

Autor: Clément Keller, Abdelwaheb Dogui, Olivier Débordes, Laurent Duchene, Mohamed Ben Bettaieb
Přispěvatelé: ArGEnCo Department, MS2F Division (ArGEnCo), Université de Liège, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Génie Mécanique [Monastir] (LGM / ENIM), École Nationale d’Ingénieurs de Monastir (ENIM), ERMECA (ERMECA), Groupe de physique des matériaux (GPM), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), Université de Monastir - University of Monastir (UM)-Université de Monastir - University of Monastir (UM), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Matériaux Avancés (IRMA), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2012
Předmět:
Zdroj: International Journal of Plasticity
International Journal of Plasticity, Elsevier, 2012, 32-33, pp.184-217. ⟨10.1016/j.ijplas.2011.10.010⟩
International Journal of Plasticity, 2012, 32-33, pp.184-217. ⟨10.1016/j.ijplas.2011.10.010⟩
ISSN: 0749-6419
DOI: 10.1016/j.ijplas.2011.10.010⟩
Popis: International audience; This paper presents a new numerical algorithm for the integration of the constitutive equations of a single crystal for finite rate-independent elastoplastic strains. The algorithm addressed in this paper is dedicated to face-centered-cubic (FCC) crystal structures. Its first feature is a much more efficient and more accurate integration scheme of the constitutive equations compared to previous attempts. This scheme is based on a fully implicit integration procedure, yet it may be transformed easily into an explicit scheme. Determining the set of active slip systems is performed by the use of a combinatorial search procedure, and the determination of the slip rates of the different active slip systems is based on the fixed point method. The second feature of this algorithm stems from the original method used to solve the ambiguity of the possible non-uniqueness of the set of active slip systems. A robust method, based on a small positive perturbation of the critical shear stresses, is proposed to overcome this difficulty. It is worth mentioning that the algorithm developed in this paper is not limited to one particular hardening law or to FCC crystal structures. Rather, it can be used and extended to various hardening laws and crystal structures (e.g. BCC or HCP...) in a straightforward manner. The authors demonstrate the performance of the proposed algorithm and illustrate its accuracy and efficiency through various numerical simulations at the single crystal and polycrystal scales. The predicted results obtained from those simulations were compared with those obtained using other numerical techniques and algorithms (i.e., a pseudo-inversion technique and an explicit algorithm). Our numerical predictions are also compared with some numerical and experimental results from other papers. The response of the polycrystal was computed by using the proposed algorithm combined with Taylor's homogenization scheme, which is used to compute the overall polycrystalline behavior. The paper ends with a statistical study of the influence of the perturbation technique on the response prediction for a single crystal and a polycrystal.
Databáze: OpenAIRE
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