三次元結晶方位分布関数を用いた冷延鋼板のγ値の計算

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To investigate the possibility of calculating the Lankford value, γ, for a low carbon steel sheet on the basis of three-dimensional orientation distribution function, ω(ψ, θ, φ, ), comparison was made between the calculated γ-value and experimental one. ψ, θ, and φ denote a set of Eulerian angles between the coordinate system of crystallite and the reference system of specimen. The γ-values, γ(ψ, θ, φ), that were specified by means of Eulerian angles in the same definition as used in describing the orientation of a crystallite in a polycrystalline sheet were computed at 5° intervals for 0°≤ψ, θ and φ≤90°, by taking into account all fourty-eight slip systems in alpha iron and by assuming that an amount of slip in each slip system was proportional to its Schmid factor. For a polycrystalline sheet the γ-value was calculated by (γ(ω))/(1+γ(ω))=4/π^2∫^<π/2>_0∫^<π/2>_0∫^<π/2>_0 (γ(ψ, θ, φ))/(1+γ(ψ, θ, φ))ω(ψ, θ, φ) sin θdθdψ′dθ where ψ′=ψ+ω, and ω is an angle between rolling direction and stretching direction. In practical computation of γ(ψ, θ, φ), the following cases were examined : (1) All slip systems whose Schmid factors were not less than a certain value, a, (0≤a<0.5), were assumed to be activated and (2) slip systems of a constant number, ss, were assumed to be activated in all the orientations. Calculated γ-values, γ(cal), were in good agreement with the observed ones, γ(obs), if no crystal rotation was assumed to take place during deformation. Above all, the values of γ(cal) were in accord with those of γ(obs) within ±0.15 in the case where either a=0.10 or ss=32 was assumed.
社団法人日本鉄鋼協会の論文
1976-09-01

三次元結晶方位分布関数を用いた冷延鋼板のγ値の計算

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