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

为了评价宏观和微观因素对多晶材料成形极限的影响，进行了有限元分析。结果表明：1.在轧制生产过程中不可避免地产生的材料各向异性对应变局部化的开始和发展都有重要影响。特别是，当承受拉伸载荷时，颈缩方向垂直于轧制方向产生，而在平衡双向拉伸时，颈缩方向向平行方向延伸。对于两种加载方式，分析结果与实验结果定性一致。为了模拟真实的多晶金属，提出了一种复杂的网格生成方案，将每个Voronoi多边形分配给一个具有随机滑移面的晶体，而边界对应于一个晶界。分析结果表明，由于滑移系的不同，多晶中的变形是不均匀的，晶界的刚度对非均匀的演化起着重要的作用。还对一种特殊制备的微栅格压痕试件进行了实验研究。观察到表面粗糙度具有两个或三个晶粒度的周期性，这是由晶界差异引起的。在全三维状态下对更多元素进行进一步的模拟，将使我们能够根据微观不均匀性来评估金属的形成极限。

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.