Nonlocal versus local elastoplastic behaviour of heterogeneous materials |
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Institution: | 1. Université de Metz Laboratoire de Physique et Mécaanique des Matériaux URA CNRS 1215 ISGMP, Ile du Saulcy 57045 Metz, France;2. Institute of Physics Czechoslovak Academy of Sciences Na Slovance 2 18040 Prague 8 Czechoslovakia;1. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China;2. Shenzhen Institute of Research and Innovation, The University of Hong Kong, Shenzhen, China;3. ArcelorMittal Research, Voie Romaine-BP30320, 57283 Maizières-lès-Metz cédex, France;1. Institute of Histology and Embryology “Aleksandar Đ. Kostić”, School of Medicine, University of Belgrade, Serbia;2. Department of Biophysics, School of Medicine, University of Belgrade, Serbia;1. Dept. of Mathematics, University of Haifa-Oranim, Tivon 36006, Israel;2. Instituto de Matemáticas, UNAM Juriquilla, Querétaro, Mexico;3. UMDI, Facultad de Ciencias, UNAM Juriquilla, Querétaro, Mexico |
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Abstract: | The scale transition methods have been developed for many years in order to obtain the overall behavior of polycrystalline materials from their microscopic behavior and their microstructure. Nevertheless, some basic aspects are absent from such formalisms. The most significant one seems to be the heterogeneization by plastic straining which involves nonlocality of hardening. In this article, a nonlocal theory based upon crystalline plasticity is developed from which a nonlocal constitutive equation at the grain level is derived. With regard to the polycrystal, in order to deduce the behavior of a local equivalent homogeneous medium, an integral equation is proposed and solved for nonlocal inhomogeneous materials by the self-consistent approximation. This scheme is developed in case of a two-phase nonlocal material representing the dislocation cell structure induced during plastic straining. Numerical simulations based on a simplified model show significant effects on the intragranular heterogeneization. |
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