Evaluation of Damaged state of Metallic Materials with Microsturctures in terms of Tesellation Analysis

在损伤材料的塑性变形中，孔洞分布对宏观力学性能的影响是一个重要的问题。本研究的目的是建立一种新的评价含孔洞金属材料损伤状态的方法。提出了一种基于Voronoi曲面细分和体视学的方法，将材料区域划分为多个Voronoi多边形，其中只包含一个空洞。该方法为含孔洞多边形的特定区域提供了代表性的单元格，便于计算损伤张量分量。对几种开孔试件进行了拉伸试验，试验结果表明，损伤张量沿加载方向的法向分量能很好地估计断裂模式。研究还表明，每个孔洞的变形与损伤张量密切相关。对于材料的韧性断裂，由于它是众所周知的，由于空洞的存在和它的形状起着重要的作用定性，它是必要的澄清损伤的定量评估，不仅考虑到空洞的体积分数，但空间配置的空洞。该理论为定量评价结构的损伤状态提供了一种简便的方法。对于三维空间中空洞变形引起的损伤扩展的评价还需要进一步的研究。

In plastic deformation of damaged materials, the influence of distribution of voids on macroscopic mechanical properites is an important issue. In this research project, it is our purpose to establish a new method in order to evaluate the damaged state of metalic materials with voids. We proposed a method using voronoi tessellation and stereology, where the material region is divided into many voronoi polygons in which only one void is inclueded. This method provides the representative unit cell for the specific region including polygons with a hole so that the damage tensor components can easily be calculated. Tensile tests of several kinds of perforated specimens were carried out and experimental results indicated that the fracture pattern was well estimated by the normal component of the damage tensor to the loading direction. It is also shown that the deformation of each hole is closely correlated with the damage tensor. For ductile fracture of materials, as it is well known that the existence of damage due to voids and its configuration play the important role qualitatively, it is necessary to clarify the quantitative evaluation of damage by taking account of not only the volume fraction of voids but the spatial configuration of voids. The theory presented here may provide the simple method to evaluate the damage state quantitatively. Further investigations are required to the evaluation of damage growth sue to deformation of voids in the 3 dimensional space.