Authors: Ivan Saxl, Petr Ponížil, Katarína Sülleiová

Abstract: The estimators proportional to (NA(x,y)NA(x,z)NA(y,z))1/2 and (NL(x)NL(y)NL(z)) obtained by profile and intercept counts are recommended by ASTM Standards E 112 for 3D grain intensity l of anisotropic grain structures (NA(•) are estimated in three mutually perpendicular planes suitably
oriented with respect to the prevailing anisotropy direction and NL(•) are intercept intensities along three suitably selected mutually perpendicular directions). However, l is also related to the profile and intercept intensities l', l', namely l= c'(l')3/2= c'(l')3. The induced intensities are estimated by
arithmetic means NA = (NA(x,y)+NA(x,z)+NA(y,z))/3, NL = (NL(x)+NL(y)+NL(z))/3. A simple model isdeveloped, in which the role of geometric and arithmetic means of profile and intercept counts in the grain size estimation is elucidated. Its results are compared with computer simulated random tessellations with prevailing rod-like and plate-like cells and applied to anisotropic grain structures
of pure Al produced by ECAP and to platinum based composite Pt - 0.5 Y2O3.

239

Authors: Jaroslav Procházka, Petr Ponížil, Ivan Saxl

Abstract: The estimation of grain size (volume) by using computer database of tessellations is
explained and demonstrated. As model material was selected an anisotropic material formed by
compression-moulded pellets of PVC. The pellets were first covered with carbon paste to highlight
borders of grains in final specimen and then moulded; their volumes were exactly known. Standard
profile and intercept counts were carried out on the planar sections of the specimen and used to
estimate the grain size by means of computer database. The obtained estimates were then compared
with the known pellet characteristics.
The estimation of grain volume and of other suitable characteristics by inspection of section planes
is necessary in opaque materials (e.g. metal alloys, crystalline polymers, ceramics), where their
values are inaccessible by direct measurements. The aim of this work is show that the standard
approaches can be improved with the help of a suitably prepared computer database.

285

Authors: Ivan Saxl, Vaclav Sklenička

Abstract: The results of intercept and profile counts are commonly interpreted as a suitable estimates of the mean grain size as represented e.g. by the grain density V. The term grain size is not explicitly defined even when some relation to grain volume and/or mean grain breadth (the mean Ferret diameter) is tacitly assumed. However, the intercept count L is directly related to the mean value of grain boundary area per unit volume SV and the profile count A is, under relatively general assumptions, directly related to the mean value of grain junctions per unit volume LV. Their relation to V can be generally written as V = c¢(A)3/2 = c²(L)3, but the coefficients c¢ and c² strongly depend on the structural characteristics like grain size dispersion, anisotropy etc. and their evaluation is far from being simple. Consequently, whereas the reliable estimates of SV and LV result from intercept and profile counts, the estimate of grain density based on them requires a careful consideration.

403

Authors: Khalil Farhangdoost, S. Rahnama

Abstract: The concept of random tessellation is extensively used in wide area of natural sciences, especially material sciences. In this paper a simple but complete explanation of the random tessellation and mathematical tools requirements is presented. Then introducing the algorithm and the program for display random tessellation diagram was written. This program, with high speed and simple algorithm for random tessellation has the ability to change the level of statistical parameters such as number, mean, variance of the area of the grain. The ability to model microstructures of metals and grains for mechanical application, such as estimation of mechanical properties and crack propagation model in microstructure scale is very important. Finally, the microstructure produced by this program show good fitness of random generation with real microstructure.

529

Authors: Hai Na Lu, Dong Bin Wei, Zheng Yi Jiang

Abstract: Grain size, shape and orientation play an important role on the deformability of micro workpiece as the geometrical dimensions approach to a characteristic scale in micro-forming process. This paper addresses the three-dimensional (3D) finite element (FE) model with weighed centroidal voronoi diagram (WCVD). Steady-state grains are generated when the voronoi generating points approach the grain centroid utilising a simplex integration algorithm. As a result of the centroidal process, the topological features of grains advance the uniform and steady state gradually, which may cause a decrease of interfacial energy. The grain size distribution is compared between the 3D domain and random cross-sectional plan. The effects of centroidal process on the distributions of grain size and number of grain corners, facet and edge are analysed.

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