Abstract
On estimating physical or mechanical properties of polycrystal by a three-dimensional orientation distribution function, two averaging procedures may be used. It has been found that the Young's modulus of polycrystal, Ecal, is better approximated, if the averaging procedure ignoring the interaction between crystals is used.
With this averaging procedure, Ecal was calculated for aluminum-killed steel and rimmed steel by the following equation.
Ecal=4/π2∫π/20∫π/20∫π/20E(ψ, θ, φ)w(ψ', θ, φ)sinθdθdψ'dφ
where ψ, θ and φ denote a set of Eulerian angles between the coordinate system of crystallite and the reference system of specimen. ψ'=ψ+ω, and ω stands for an angle between the rolling direction and the stretching direction.
Ecal was compared with the other averaging value, EV, calculated from the Voigt model by taking the interaction into account and the experimentally obtained one, Eobs.
The results obtained were:
(1) In both steel, Ecal was less than the others. That is Ecal<Eobs<EV.
(2) With respect to planar anisotropy, the both models gave the values close to the observed one, although E varied depending upon direction as EL<ET<ED, where L, T and D refer to the rolling direction, the transverse direction and the direction with 45° to the rolling direction, respectively.
The fact of Ecal<Eobs<EV was considered to result from the difference between the two procedures in dealing with the interaction. k(=(Eobs-Ecal)/Ecal) was quantitatively related to the following orientation-dependence factor, σ, with the assumption that the interaction depends upon the degree of intensity of preferred orientation of texture.
σ2=4/π2∫π/20∫π/20∫π/20{w(ψ, θ, φ, )-wRand}2sinθdθdψdφ
where wRAND is given by the three-dimensional orientation distribution function of randomly oriented polycrystals.
