An Estimating the Local Deformation Parameters in Grained Structures via Stereological Methods

A lot of sophisticated methods have been developed to study grained structures by 2D imaging such as image correlation method, triple points technique, electron backscatter diffraction (EBSD), computer tomography (CT), etc. With applying 3D volume data mentioned methods can significantly help in precise investigation of grained structures. However these methods have several limitations. They are neither always economically efficient nor can be applied for different situations. In this paper we present relationship between change of grain's shape caused by deformation and deformation parameters. Next we investigate a ratio ξ between total surface area of images of all grains in structure displayed in orthogonal 2D projection and their total surface area in the 3D (that means entire surface of grain boundaries). During an applied mechanical loading the grained structure is deformed and this ratio ξ varies. One specific conclusion of our work is that in cases of giant random grained structures mentioned ratio is a definite smooth function of deformation parameters. This result suggests that deformation of grained structure can be intuitively estimated on the basis of grains surface distortion in given area of bulk sample which is visible on metallographic cut. Unfortunately 2D images of real grains in orthogonal projection overlap each other and stereological methods must be used in precise deformation analysis. (paper)