冷延軟鋼板における集合組織とヤング率の異方性

抄録

In order to study the possibility of calculating the Young's modulus, E, for a cold rolled mild steel sheet on the basis of its texture represented by the three-dimensional orientation distribution function, w(ψ, θ, φ), the E value calculated was compared with the experimental value. ψ, θ, and φ denote a set of Eulerian angles between the coordinate system of crystallite and the reference system of specimen. From the E value calculated, E(ψ, θ, φ), which was specified by means of Eulerian angles in the same definition as used in describing the orientation of a crystallite in a polycrystalline sheet, the E value for a polycrystalline sheet, E_cal, was computed by
E_cal=4/π²∫^π/2₀∫^π/2₀∫^π/2₀E(ψ, θ, φ)w(ψ', θ, φ) sin θdθdψ'dφ
where ψ'=ψ+ω and ω is an angle between the folling direction and stretching direction.
Experiments were made on rimmed steel, aluminium killed steel and decarburized rimmed steel, and their Young's modulus were measured by using the resonant vibration method.
The results obtained are summarized as follows:
(1) As for planar anisotropy of the calculated Young's modulus, E_cal at the transverse direction, E_T, was smaller than that making an angle of 45° with the rolling direction, E_D, and larger than that along the rolling direction, E_L. The planar anisotropy of the observed one, E_obs, showed the same tendency as that of E_cal for all samples.
(2) The observed Young's modulus E_obs, coincided with E_cal within the relative error of 1% for the sample having a strong preferred orientation. For the rimmed steel sample, which has the weakest preferred orientation, the ratio of E_obs and E_cal was 1.07. (where E=(E_L+E_T+2E_D)/4)
It was concluded from these results that the Young's modulus of a polycrystalline material can be, quantitatively, estimated from its texture analysed three-dimensionally.