塑性変形による異方性

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A new theory of plasticity was advanced to account for various experimental facts, and it was explained in the previous paper that the experiments on the stress relation between tension and pure shear agreed very well with this theory, and that the relation between the yielding of mild steel and the plastic deformation after that could be also accounted for. In this paper, the theory was compared with experiments on the anisotropy due to plastic deformation. The author's theory is as follows : 1. The plastic deformation is to be divided into shears in 3 directions, and each shear is to be considered individually. 2. Let the resistances to the strain increases in the 3 directions be R_1,R_2 and R_3 respectively, then[numerical formula] provided that the directions of principal stresses and those of principal strains coincide. 3. When the direction of shear strain is reversed, the stress range of elastic deformation is R concerning each direction. 4. R_1,R_2 and R_3 do not correspond to the shearing stresses τ_1,τ_2 and τ_3,but they correspond to such shearing stresses S_1,S_2 and S_3 as [numerical formula] where, σ_x, σ_y and σ_z are principal stresses, and σ_m is the mean stress. Concerning each direction, this theory is a shearing stress theory ; the shearing stress in this case is not τ but S. Anisotropy due to plastic deformations can also be accounted for by this theory. Experiments were carried out for comparison. Thin hollow cylinders of brass were at first deformed plastically under (a) internal pressure, (b) combined tension and internal pressure, the ratio being such that the plastic strain was a pure shear of longitudinal elongation, (c) tension, and (d) combined tension and internal pressure, the ratio being such that the plastic strain was a compression in the direction of thickness, and unloaded. Then the cylinders were again subjected to internal pressure, and longitudinal and circumferential elongations were measured. The stress-strain relation conformed very closely to the theory.
一般社団法人日本機械学会の論文
1959-07-25

塑性変形による異方性

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