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Formability prediction using bifurcation criteria and GTN damage model

Article dans une revue avec comité de lecture
Author
NASIR, Muhammad Waqar
484601 University of Central Punjab
ccCHALAL, Hocine
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
243747 Labex DAMAS
ccABED-MERAIM, Farid 

URI
http://hdl.handle.net/10985/20267
DOI
10.1016/j.ijmecsci.2020.106083
Date
2021
Journal
International Journal of Mechanical Sciences

Abstract

In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.

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