IJMF 10TH ANNIVERSARY - ADVANCES IN MATERIAL FORMING Advances in anisotropy of plastic behaviour and formability of sheet metals Dorel Banabic 1 & Frédéric Barlat 2 & Oana Cazacu 3 & Toshihiko Kuwabara 4 Received: 30 September 2019 /Accepted: 9 July 2020 # Springer-Verlag France SAS, part of Springer Nature 2020 Abstract This paper reviews the most recent models for description of the anisotropic plastic behavior and formability of sheet metals. After a brief review of classic isotropic yield functions, recent advanced anisotropic criteria for polycrystalline materials of various crystal structures and their applications to cup drawing are presented. Next, the discussion focuses on novel formulations of anisotropic hardening. A brief review of the experimental methods used for characterizing and modeling the anisotropic plastic behavior of metallic sheets and tubes under biaxial loading is presented. The experimental methods and theoretical models used for measuring and predicting the limit strains, development of new tests for determining the Forming Limit Curves (FLC), as well as on studying the influence of various material or process parameters on the limit strains are presented. Keywords Anisotropic yield criteria . Anisotropic hardening . Polycrystals . Biaxial tensile tests . Forming limit . Sheet metals Introduction Given the current trends of globalization and active compe- tition on the world market, especially for automotive, the reduction of the lead time can be decisive. Virtual manufacturing using finite element analyses contribute to this reduction. The finite element analysis has been applied extensively to compare design options, understand the influ- ence of process conditions on both formability and structural performance and to reduce the trial and error of tools for optimum performance. For realistic simulations, the use of improved constitutive models for the description of the mechanical behaviour and accurate prediction of formability are essential. In particular, the use of yield conditions that capture the key features of the plastic behaviour during forming opera- tions are essential. Intrinsic anisotropy associated to a given crystal structure as well as the anisotropy induced by process- ing of polycrystalline metallic materials place severe restric- tions on the form of yield conditions. In Section Anisotropic yield criteria, after a brief review of the classical isotropic yield functions, we discuss the rigorous approaches that en- able the extension of isotropic yield criteria such as to account for specific material symmetries. Examples of very versatile anisotropic two-dimensional (2D) and three-dimensional yield criteria (3D) are provided for metallic materials with various crystal structures. For the case of 3-D yield orthotropic yield criteria based on Hershey-Hosford yield criterion involv- ing six anisotropy coefficients, equivalent expressions in terms of stresses and analytical identification procedures which enable to directly correlate the anisotropy parameters to mechanical properties, and consequently standardize their use in F.E. codes are discussed. The capabilities of anisotropic yield functions to describe the plastic behaviour for loading conditions other than those used for parameter identifications are also illustrated for FCC aluminium, HCP magnesium and titanium materials. Specifically, it is shown that currently it is possible to describe with great accuracy the earing profile of certain highly textured aluminium alloys. The importance of * Dorel Banabic banabic@tcm.utcluj.ro 1 CERTETA - Research Centre on Sheet Metal Forming Technology, Technical University of Cluj Napoca, 400140 Cluj Napoca, Romania 2 Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea 3 Department of Mechanical and Aerospace Engineering, University of Florida/REEF, Shalimar, FL 32579, USA 4 Division of Advanced Mechanical Systems Engineering, Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Nakacho, Koganei-shi, Tokyo 184-8588, Japan International Journal of Material Forming https://doi.org/10.1007/s12289-020-01580-x