An Analytical Study of Macro/Microscopic Effects on the Forming Limit of Polycrystalline Materials

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Finite element analyzes have been carried out in order to evaluate both macro-and micro-scopic effects on the forming limit of polycrystalline materials. Theobtained results are as follows :1. The material anisotropy which is inevitably induced through the production process of rolling has a predominant influence on the onset as well as the growth of strain localization. In particular the direction of necking is generated perpendicular to the rolling direction when subjected to a tensile loading, while it extends to the parallel direction under a balanced biaxial stretching. The analytical results show qualitative agreement with experiments for both cases of loading pattern.2. In order to simulate real polycrystalline metals, a sophisticated mesh generation scheme is proposed in such a way that each Voronoi polygon is assigned to a crystal with random slip plane while the boundary corresponds to a grain boundary. The analytical result shows that the deformation in the polycrystal is inhomogeneous due to the difference in slip system and that the stiffness of grain boundary plays an important role in the evolution of the inhomogeneity. An experimental study is also carried out on a specially prepared specimen with micro-grid indentation. It is observed that the surface roughness has a periodicity with two of three crystal grain size and that it is caused by the discrepancy at the grain boundary. Further simulation with more elements in fully three-dimensional state will enable us to evaluate the forming limit of metals in terms of the microscopic inhomogeneity.