Prediction of necking in HCP sheet metals using a two-surface plasticity model

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In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.