Evaluation for Nonlocal Damaged State in terms of Voronoi Porygon

对于材料的韧性断裂，孔洞损伤对材料力学性能的影响是非常重要的，有必要明确损伤定量评价与孔洞生长之间的关系。在本项目中，我们提出了一种利用voronoi镶嵌和立体学来评估由于空洞引起的局部损伤状态的新方法。将穿孔板作为损伤材料的平面模型，在单轴拉伸条件下进行检测，测量圆孔的变形。实验结果表明，该方法能很好地描述相邻孔间的距离和方向。在严重损伤区域，圆孔的变形变大。将模型开始断裂的部分评定为严重损伤部分。结果表明，孔板的断裂和局部塑性变形与用voronoi镶嵌和体视学方法估计的损伤较大的部位很好地对应。采用引入周期边界条件的有限元方法，数值分析了平面应力条件下圆孔有规则分布的多孔板的弹塑性变形。结果表明：多孔板的变形行为很大程度上取决于孔洞的分布，孔洞的排列导致了板屈服应力的各向异性，这与孔洞附近的应力集中有关。结果还表明，穿孔板的高度变形区域对应于voronoi多边形，其中局部损伤张量分量的值特别大。

For ductile fracture of materials, the influence of damage due to voids on the mechanical property of materials is very important, and it is necessary to clarify the relation between quantitative evaluation of damage and void growth.In this project, we propose a new method to evaluate the local damage state due to voids using the voronoi tessellation and the stereology. Perforated sheets were set up as the plane models of damaged materials and were examined under the condition of uniaxial tension, where the deformation of circular holes is measured. The experimental results show that the distance and the direction between adjacent holes are well described in this method. The deformation of circular holes becomes larger in severely damaged domain. The part where fracture of models starts is evaluated as severely damaged part. It is shown that the fracture of perforated sheets and local plastic deformation is well corresponding to the part with large damage estimated by means of the voronoi tessellation and the stereology.Elastic - Plastic deformation of perforated sheet, where circular holes are distributed regularly, were also analyzed numerically under the plane stress condition by means of finite element method introducing the periodic boundary conditions. It is shown that the deformation behavior depends highly on the distribution of holes and the arrangement of holes results in the anisotropy of yield stresses of perforated sheets, which is related to the stress concentration near the holes. It is also shown that the highly deformed regions in perforated sheets corresponds with the voronoi porygon where the value of local damage tensor componets are especially large.