Constitutive relation of an orthorhombic polycrystal with the shape coefficients

An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.

Effect of textural characteristics on engineering properties of some sedimentary rocks

As it is commonly known,the estimation of physical and mechanical characteristics of rocks is very important issue in various geotechnical projects.The characteristics are mainly influenced by the microfabric-texture features of rocks.In this research,dry unit weight,effective porosity,point load index,Schmidt rebound hardness,uniaxial compressive strength,and texture coefficient were measured with the aim of correlating the physical and mechanical properties to the texture coefficient.For this purpose,a comprehensive laboratory testing program was conducted after collecting twenty sedimentary block samples including nine limestones and eleven mudstones,taken from Kalidromo(central Greece)in accordance with ASTM and ISRM standards.Also,mineralogical and petrographic properties,textural characteristics as well as X-ray diffractions were studied and the obtained results were statistically described and analysed.The maximum and minimum values of the texture coefficient were 0.13 and 0.50,respectively.The highest value was obtained for the rocks with a large amount of grains.Regression analyses were used to investigate the relationships between the texture coefficient and the engineering properties.Thus,empirical equations were developed and because of the good determination coefficients,they showed that all of the engineering properties were well correlated to the texture coefficient.

Texture coefficient and band gap tailoring of Fe-doped SnO_(2) nanoparticles via thermal spray pyrolysis

An investigation of Fe-doping effect on SnO_(2) thin films was performed in this study using thermal spray pyrolysis(TSP) method.The surface morphology and structural,optical and electrical properties were studied by field energy scanning electron microscope(FESEM),X-ray diffraction(XRD),ultraviolet-visible(UV-Vis) spectroscopy and four-point probe method.FES EM images demonstrate that the surface morphology of the as-deposited films varies when Fe-doping content varies.XRD studies reveal that crystallite size and preferential growth orientations of the films are dependent on Fe-doping concentrations.The grain size is found to decrease with the increase in Fe content.These studies also specify that the films have tetragonal rutile-type structure with mixed secondary phases.The texture coefficient value of(110) plane increases with the concomitant in-plane(220) decrease in higher doping concentrations.The resistivity and the optical absorbance are found to increase with Fe concentration.The direct optical band gap decreases from 3.94 to3.52 eV with increasing Fe content.

Effect of Ti(C,N)Precipitation on Texture Evolution and Fish-Scale Resistance of Ultra-Low Carbon Ti-Bearing Enamel Steel

The Ti（C,N）precipitation and texture evolution in ultra-low carbon Ti-bearing enamel steel were studied to discover their correlation.Two different cooling paths of simulative coiling were adopted to gain different morphologies of Ti（C,N）precipitate in hot strips.It is found that the Ti（C,N）precipitate in hot strip using Path 2（put into asbestos box and air cooled）are finer and much more in quantity than that in hot strip using Path 1（held at 730℃ for 30min and furnace cooled）.The morphology of Ti（C,N）precipitate in hot strip has great effect on recrystallization texture in the subsequent cold-rolled annealed sheet.γ-fiber texture of strong recrystallization is gained in coldrolled and annealed sheet came from Path 1.On the contrary,in the one came from Path 2,theγ-fiber texture is weak.This may be due to the pinning force of numerous fine Ti（C,N）precipitate which retard the growth of preferential nucleated{111}orientated grains.Annealed steel sheets in the test came from both paths have excellent fishscale resistance.