An Anisotropic Model with Linear Perturbation Technique to Predict HCP Sheet Metal Ductility Limit

Mohamed Yassine Jedidi (1, 2) , Mohamed Ben Bettaieb (1, 3) , Farid Abed-Meraim (1, 3) , Mohamed Taoufik Khabou (2) , Anas Bouguecha (2) , Mohamed Haddar (2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 LA2MP - Laboratoire de recherche de Mécanique, Modélisation et Production
3 Labex DAMAS

In this paper, hexagonal closed packed (HCP) sheet metal ductility for a viscoplastic material is analyzed by using a linear perturbation technique. It can be used for the analysis of local-ized necking. This technique is used to perturbate the material behavior in a rate dependent formulation by superimposing a perturbation to the basic flow which its stability or instability is characterized by the increasing or decreasing of the perturbation. Hardening and initial ani-sotropic parameters are fitted by experimental results from the literature. In this investigation, Cazacu yield function is used to predict the forming limit diagrams (FLDs) of HCP sheet metals. The coupling between analytic perturbation method and the behavior modelling is provided by an efficient implicit algorithm to solve the constitutive equations. After verifica-tions and validations of the numerical simulations from the literature, the ductility limit of a particular HCP magnesium alloy is numerically predicted. A parametric study is presented to analyze the effect of instability and mechanical parameters, viscosity and distortion on the FLDs. Moreover, a comparative study between Marciniak and Kuckzynski ductility approach and linear perturbation technique is done in this contribution.

Mots clés: Behavior modelling; Forming limit diagrams; Hexagonal closed packed material; Linear perturbation technique; Necking criteria; Plastic instabilities

Domaines: Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Modélisation et simulation; Génie des procédés; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Mohamed Yassine Jedidi, Mohamed Ben Bettaieb, Farid Abed-Meraim, Mohamed Taoufik Khabou, Anas Bouguecha, et al.. An Anisotropic Model with Linear Perturbation Technique to Predict HCP Sheet Metal Ductility Limit. Advances in Materials, Mechanics and Manufacturing, Springer International Publishing, pp.164-176, 2021, 978-303084957-3. ⟨10.1007/978-3-030-84958-0_18⟩. ⟨hal-03454441⟩