A theory of the yielding and plastic flow of anisotropic metals

The Royal Society - Tập 193 Số 1033 - Trang 281-297 - 1948
Rodney Hill

Tóm tắt

A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises’ concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Körber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thinwalled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

Từ khóa


Tài liệu tham khảo

Barrett C. S. 1943

Cook M., 1937, J, Inst. Met., 60, 159

Cook M., 1943, J, Inst. Met., 69, 201

Cook M., 1947, J, Inst. Met. Paper, 1061, 541

Geiringer H. 1937 Memor. Sci. Math. 86.

Hill R., 1947, Proc. Roy, Soc. A, 191, 278

Korber F., 1928, Mitt, K.-With.-Inst., 10, 175

Korber F., 1928, Mitt, K.-With.-Inst. Eisenforsch., 10, 189

Swift H. W. 1947 Engineering 163 253.

10.1098/rsta.1932.0009

von Mises R., 1928, Z. angew, Math. Mech., 8, 161

Wilson F. H. & Brick R. M. 1945 Metals Technol. 12.

Thông tin
Thông tin xuất bản

The Royal Society

Tập 193 Số 1033

281-297

Thông tin tác giả