1948/05/27 by Rodney Hill · 3,989 citations
Engineering · Materials Science · Mathematics · #Anisotropy #Composite material #Cylinder #Finite element method #Geometry #Isotropy #Material Properties and Failure Mechanisms #Materials science #Mathematics #Mechanics #Metal Forming Simulation Techniques #Metallurgy and Material Forming #Necking #Optics #Physics #Plasticity #STRIPS #Thermodynamics #Torsion (gastropod) #Yield (engineering) #von Mises yield criterion
paper · doi:10.1098/rspa.1948.0045
published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 193(1033), 281-297 (Royal Society)
openalex publication_date 1948/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Abstract 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.