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

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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.