Evaluation for Nonlocal Damaged State in terms of Voronoi Porygon

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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.