Issue 53

R. Harbaoui et alii, Frattura ed Integrità Strutturale, 53 (2020) 295-305; DOI: 10.3221/IGF-ESIS.53.23 296 resulting from the rolling process [4, 5]. It also results in a strong tension / compression asymmetry based on the test data of Kelley and Hosford [6]. More experience with different loading conditions is required for magnesium alloy sheets to fully understand their complex mechanical behavior. Jia and Bai [7] carried out a complete series of experiments on the plasticity and fracture of AZ31B-H24 magnesium under various multiaxial loading conditions. The plasticity and fracture of magnesium is a significant challenge due to its closed HCP structure and its twinning deformation mechanism, which has not yet been properly detailed due to its complexity [7, 8]. To describe the plastic behavior of this material, it is necessary to specify the yield surface defined by an equivalent stress of a plasticity criterion and the hardening law. In previous works, Amna et al [9, 10] have shown the ability of the Barlat criterion [11] to successfully simulate the plastic behavior in simple tensile test of pure aluminum [10], aluminum alloy 2024 [12] and aluminum alloy 7075 [13] and on the other hand in simple and cyclic shear tests of aluminum alloy 2024 [14]. On the other hand, Amna et al [9] have shown that this criterion is insufficient to model the plastic behavior of AZ31B Magnesium alloy sheets under multiaxial loading according to the Lankford coefficient. To remedy this insufficiency, Rym et al [15] used the Casazu criterion [16] which is dedicated to the compact hexagonal structure HCP to identify the plastic behavior of titanium alloy subjected to tensile tests. In this work, the plastic behavior of the AZ31B-H24 alloy is modeled using an identification strategy that depends on a plastic Casazu criterion, an isotropic hardening law (Hollomon law, Voce law, swift law and ludwick law) and an evolution law. For this purpose, an experimental database [17] corresponds to various hardening curves for tensile and compression tests interpreted as homogeneous and their Lankford coefficients is used. Thereafter, by smoothing the experimental hardening curves in three loading directions relative to rolling direction, a selection is made in order to choose the most appropriate hardening law for the identification of the AZ31B-H24 behavior. Finally, our identification strategy with a Simplex method is validated from Lankford coefficients and it is used to conduct the evolution of the load surface for different tests. S TUDIED MATERIAL n this work, an AZ type magnesium alloy AZ31 has been studied. Its alloying elements are aluminum up to 3%, zinc with 1% and finally 0.4% manganese [18] . The AZ31B-H24 magnesium alloy has a nominal composition (in wt %) of 3% Al and 1% Zn. The H24 condition refers to strain hardening and partially annealing (recrystallization without grain growth). This material is treated as having an orthotropic plasticity in three directions: RD (rolling direction), TD (transverse direction) and ND (normal direction). Al Zn Mn Cu Ca Ni Fe Mg O 2.5-3.5 0.7-1.3 0.2 min 0.05 max 0.04 max 0.005 max 0.005 max balance none Table 1: Composition of AZ31B-H24 magnesium alloy (wt%) I DENTIFICATION MODEL n this study, it is essential to use an identification strategy taking into account: the anisotropic behavior of the material and the SD "strength-differential" effect, the evolution law and the equivalent stress. For the identification step, the following assumptions must be respected [9-15]: - Identification by "small deformations", - The used tests are considered as homogeneous tests, - The elastic deformation are neglected; the behavior is considered as rigid plastic incompressible. - The plasticity surface evolves homothetically (isotropic hardening) - All the tests are carried out in the plane of the sheet resulting in a plane stress condition. The performance criterion can be then written as follows:       , D D c s f         (1) I I