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

采用有限元方法对多晶材料的成形极限进行了宏观和微观影响分析。得到的结果如下：1。轧制生产过程中不可避免地引起的材料各向异性对应变局部化的发生和发展具有重要影响。特别是在拉伸载荷作用下颈缩方向垂直于滚动方向产生，而在平衡双轴拉伸作用下颈缩方向向平行方向延伸。两种加载模式的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，该方案将每个Voronoi多边形分配给具有随机滑移面的晶体，而边界对应于晶界。分析结果表明，由于滑移系统的不同，多晶的变形是不均匀的，而晶界的刚度对不均匀性的演变起着重要的作用。并对特制的微网格压痕试样进行了实验研究。观察到，表面粗糙度随两个或三个晶粒尺寸的变化具有周期性，这是由晶界处的差异引起的。进一步的全三维模拟将使我们能够从微观不均匀性的角度来评估金属的成形极限。

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.