Marc Milesi

Using Cross Stamping to Test Zinc Sheets Formability

Sheet metal formability has been studied for a half century. The sheet formability is mostly described by the Forming Limit Diagram (FLD). A prediction of this FLD is a source of interest for industrial companies. Indeed knowing the FLD of a material allows optimization of the production processes which leads to money saving. Nevertheless, the formability tests (tensile, bulge and Nakazima tests) which give the experimental FLD do not really represent the process that the sheet will undergo in industrial conditions. The paper therefore focuses on a cross stamping test. The material of interest is a Zinc sheet. FLD prediction is reported for a wide variety of metals [1] but literature about Zinc is nearly non existent. The studied Zinc sheets exhibit a highly anisotropic mechanical behaviour due to the hcp lattice structure and the inherited rolling texture. This anisotropic behaviour results in an anisotropic formability. The Zinc sheet FLD is influenced by the orientation of the rolling direction during the process. Experimental cross stamping of this material allows describing the studied material behaviour in a large range of mechanical solicitations from tensile to biaxial tension. The experimental results are compared with the finite element simulation and permit to understand where and why failures appear, which leads to a better understanding of Zinc anisotropic formability.

Theoretical and experimental evaluation of the formability of anisotropic zinc sheets

. Formability of metal sheet has been widely studied for the past 40 years. This study leads to the well known Forming Limit Diagram (FLD) proposed by Keeler and Backhofen [1]. Such a diagram needs typical drawing and stretching experiments to be achieved. Lots of different metals have been considered as steel, aluminium, titanium or magnesium alloys [2]. Despite of the large amount of papers about sheet metal forming, few deal with Zinc sheets. The material has an anisotropic mechanical response due to its hexagonal crystallographic lattice and its microstructural texture. In the presented work, Nakazima and tensile tests have been performed for different mechanical orientations (0°, 45° and 90° angle to the rolling direction) in order to characterise this typical response. A high anisotropic behaviour has been noticed for the hardening and for the critical strains. The FLD is therefore a function of the orientation. Moreover thickness sensitivity is observed and leads to some criticisms about the plane stress assumption usually used in the FLD predictive models [3, 4]. The Modified Maximum Force Criterion (MMFC) is evaluated, and discussed. Then, this model is compared to a damage model used in [5] within an FEM formulation.

Digital microstructures matching statistical distributions of features in real materials - Example of forgings

Various analytical rules of mixture are commonly used to take into account heterogeneous features of a material and to derive global properties. But, with such models, one may not be able to fulfil the requirements for separating appropriately the different lengthscales. This might be the case for some issues such as strain localisation, surface effect, or topological distributions. At an intermediate lengthscale, which we refer to as the mesoscopic scale, one can still apply continuum mechanics. So why not perform calculations using the finite element method on volumes of material to obtain the response of Representative Elementary Volumes (R.E.V.). The construction of digital microstructures for such calculations is performed in two steps. First, a series of R.E.V.s with statistics of features of real materials should be defined. Then, finite element meshes should be produced for these R.E.V.s and updated when calculations involve large strains. Powerful automatic three-dimensional mesh generators and remeshing techniques prove necessary for this latter task. This strategy is applied to create digital R.E.V.s which match statistical features of forgings. Measurements provide micromechanical parameters of each subvolume. As an example of calculations, numerical simulations provide the anisotropic fatigue properties of forgings.