Exploring Stress-Strain Relations of Isotropic Plastic Solids

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Abstract
Combined torsion and tension of thin‐walled tubes constitutes one of the few testing arrangements in which a fairly general state of uniform stress can be realized without too great experimental difficulties. A manner of representing graphically the results of such tests is used to discuss, in geometrical terms, some stress‐strain relations of the mathematical theory of plasticity. It is shown that the theories of B. de Saint‐Venant, M. Lévy, and R. v. Mises lead to physically unacceptable conclusions unless the material is supposed to be rigid as long as the stresses have not reached the yield limit. The predictions of the theories of L. Prandtl, E. Reuss, H. Hencky, and A. Nádai are compared with the results of experiments on mild steel; the possible effects of viscosity and strain hardening are discussed.

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