Young’s Modulus of Hot-Rolled “Alfer” Sheet

Abstract

The elastic anisotropy of hot-rolled “Alfer” sheets was studied. The young’s modulus of “Alfer” sheet was found closely dependent upon the roll direction, and the Young’s modulus vs. roll direction curve showed a maximum in cross direction, another maximum in 15°(165°) direction, and a minimum in 45°(135°) direction to the roll direction. In the case of a specimen with lower degree of roll reduction, the maximum in 15°(165°) direction became gradually smaller with rise of heating temperature, and finally disappeared at higher temperature. The Young’s modulus in each direction parabolically decreased with the rise of heating temperature. Furthermore, the general theoretical expression was presented for Young’s modulus of rolled b.c.c. magnetic substance, and Young’s modulus in θ direction of grain-oriented polycrystalline sheet E^θ was found to be expressed as follows.
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Where, \varphi and η are the angle between the principal direction ⟨100⟩ and roll direction in the {100} or {110} planes parallel to roll plane respectively, and h_{100}, h_{110} and h_{A} are the fractions of grain numbers having the principal plane {100}, {110} and the others parallel to roll plane respectively. {A} means random orientation. K_{100}i and K_{110}i are the fractions of above planes taking the angle of \varphi or η to the principal direction respectively. Using the above equation and the elastic coefficients S_iK obtained by the author, and assuming the same crystal orientation as in the case of magnetostriction, the theoretical young’s modulus was calculated. A good agreement existed between the theoretical and the experimental results.