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The stress-strain relations for the cold working of the ductile metals are described for a group of cases assuming that the stresses under which they yield plastically depend only on the permanent parts of the strains, leaving out of the consideration the influence of the elasticity and of the speed of the plastic deformation. The behavior of the metals in the strain-hardening range is expressed by means of a strain-hardening function which connects the octahedral shearing stress with the octahedral unit shear. These variables are defined for strains of finite magnitude.

In this paper equations are set up which describe the behavior of a solid under the action of combined stresses when a steady state of creep is assumed to exist. A material is said to be in a steady state of creep if it yields with a constant speed under a given constant stress. In an ordinary creep test the steady state exists when the deformation has reached the point where the ``creep curve'' becomes a straight line. In mathematical language this can be expressed by saying that the stress is a function of the rate of strain and is independent of the amount of strain. Cases are worked out in which this stress vs. strain rate relation is a simple power function. Various types of flow including purely plastic flow and viscous flow can be discussed by changing the value of the exponent in the power function relation. Several specific examples which include the case of the thick walled cylinder with closed ends loaded by internal pressure and the case of a disk having a circular hole and loaded in its plane are worked out. Equations are developed which show the steady state stresses in such cases. Expressions for the stress concentration factors in creep are also obtained.

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