Abstract:Polycrystalline structure is of paramount importance to materials science and engineering. It provides an important example of a space-filling irregular network structure that also occurs in foams as well as in certain biological tissues. Therefore, seeking an accurate description of the characteristics of polycrystals is of fundamental importance. Recently, one of the authors (MEG) published a paper in which a method was devised of representation of irregular networks by regular polyhedra with curved faces. I… Show more
“…Therefore deformation of various idealized grain shapes can be investigated. For instance crystals can be modeled by regular polyhedron -tetrakaidecahedron [2]. One method is based on dependence of the ratio of relative surface area of grain boundaries in deformed state S V and undeformed state S V0 to strain [3].…”
Section: Local Strain Estimationmentioning
confidence: 99%
“…In case of anisotropic plastically deformed structure the grains have anisometric dimension, it is necessary to describe their anisotropy [1]. The anisotropic microstructure is decomposed into isotropic, planar and/or linear oriented components -specific surface area of grain boundaries and these parameters are measured using stereology [2]. Degree of grain boundary orientation is estimated as ratio of oriented specific surface area to total specific surface area.…”
In most of cases, technological processing leads to microstructure anisotropy of material. Results obtained from the analysis of anisotropy can be used for evaluation of material properties and parameters of technology processes. Stereological metallography was used for describing of structure anisotropy. In case of plastically deformed material, degree of orientation of grain boundaries was determined. Grain boundaries are decomposed into isotropic, planar and linear oriented components -specific surface area of grain boundaries and these parameters were measured using oriented test lines stereology method. These results were used for estimation of local plastic deformation using conversion model of orientation grain boundaries to deformation of grains. Our proposed conversion method enables estimation of local plastic deformation in arbitrary place of body with arbitrary state of initial deformation. In case of short fibre reinforced thermoplastics oriented test plane stereology method was used for estimation of experimental orientation of fibres. Degree of orientation was estimated from the number of intersections of fibres with test planes and from these results components of an orientation tensor are estimated. This method is very simple in comparison with a current method which is based on measurement of dimensions and orientation of lot of fibre intersections in analyzed plane.
“…Therefore deformation of various idealized grain shapes can be investigated. For instance crystals can be modeled by regular polyhedron -tetrakaidecahedron [2]. One method is based on dependence of the ratio of relative surface area of grain boundaries in deformed state S V and undeformed state S V0 to strain [3].…”
Section: Local Strain Estimationmentioning
confidence: 99%
“…In case of anisotropic plastically deformed structure the grains have anisometric dimension, it is necessary to describe their anisotropy [1]. The anisotropic microstructure is decomposed into isotropic, planar and/or linear oriented components -specific surface area of grain boundaries and these parameters are measured using stereology [2]. Degree of grain boundary orientation is estimated as ratio of oriented specific surface area to total specific surface area.…”
In most of cases, technological processing leads to microstructure anisotropy of material. Results obtained from the analysis of anisotropy can be used for evaluation of material properties and parameters of technology processes. Stereological metallography was used for describing of structure anisotropy. In case of plastically deformed material, degree of orientation of grain boundaries was determined. Grain boundaries are decomposed into isotropic, planar and linear oriented components -specific surface area of grain boundaries and these parameters were measured using oriented test lines stereology method. These results were used for estimation of local plastic deformation using conversion model of orientation grain boundaries to deformation of grains. Our proposed conversion method enables estimation of local plastic deformation in arbitrary place of body with arbitrary state of initial deformation. In case of short fibre reinforced thermoplastics oriented test plane stereology method was used for estimation of experimental orientation of fibres. Degree of orientation was estimated from the number of intersections of fibres with test planes and from these results components of an orientation tensor are estimated. This method is very simple in comparison with a current method which is based on measurement of dimensions and orientation of lot of fibre intersections in analyzed plane.
“…The construction of ANHs has been described in detail in earlier publications [2][3][4][5][6][7] . Two ANHs, one with four faces, the 4-hedron, and another with six faces, the 6-hedron, are illustrated in Figure 1.…”
Section: Construction and Properties Of Anhsmentioning
confidence: 99%
“…Expressions for topological factors corresponding to the (dimensionless) curvature, h, area, a, and volume, v, are not given here for space reasons. But full details of the structure and mathematical properties of ANHs may be found elsewhere [2][3][4][5] .…”
Section: Construction and Properties Of Anhsmentioning
confidence: 99%
“…This approach greatly simplifies the analysis of materials configured as real irregular networks, such as polycrystals, as all the geometric properties of ANHs can be calculated exactly. ANHs may, therefore, be used as 'proxies' for analyzing real irregular network grains, allowing the rigorous treatment of related problems pertaining to such network structures [2][3][4][5][6][7] .…”
Grain growth theories normally describe a grain using the concept of ‘grain radius’. However, this assumption bypasses all topological information relating to the grain, viz., the number of its faces, edges, etc. This study, by contrast, introduces a new methodology, treating normal and abnormal grain growth in three dimensions in terms of both metrical and topological properties of the grains
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