Studies of Plastic Flow of Steel, Especially in Two-Dimensional Compression

Abstract

The experimental methods are described by which rectangular blocks are subjected to two-dimensional compressional stresses and at the same time flow is maintained two-dimensional with deviations of less than one percent. Within this range of flow a rather wide range of stress conditions is possible, so that the equations of plastic flow can be examined over a correspondingly wide range of conditions. It is found that two-dimensional flow is much more sensitive than three-dimensional flow to shearing instabilities initiated at the edges where there are singularities in the mathematical solution. By proper lubrication it is, however, possible to produce approximately homogeneous deformations in two-dimensional compression at least up to shortenings to two-thirds the initial length. It is found that the transverse stress Xx required to maintain two-dimensional flow is consistently higher than the theoretical value ½Zz; for some materials the excess above the theoretical value may rise to as much as 20 percent. This excess tends to be less in the early stages of flow, and does not tend to increase beyond strains of 10 percent. The failure of Xx to be equal to ½Zz indicates a failure of the fundamental condition of isotropy of flow; this failure may be demonstrated in other ways. The time rate of primary flow is studied at various points on the strain-hardening curve. The rate of flow rises rapidly as the stress increases above the limiting strain-hardening curve. The rate of increase of the rate of flow for a given displacement from the limiting curve is much greater in the early stages of flow. It is this which makes possible the calculation of the rate of propagation of a plastic disturbance from the parameters of the static strain-hardening curve. Beyond the early stages of flow new time effects begin to appear. The flow loses its smoothness and becomes more and more inclined to be jerky. At high strains, flow may not start at once when the load is increased, but there may be an initiation period during which flow is built up. The application of the results to the generalized strain-hardening curve is discussed. In view of the failure of isotropy, strictly speaking, a generalized strain-hardening curve does not exist. Within the strain limits of this paper it is found that both the maximum shearing stress criterion and the ``significant'' stress-strain criterion apply with errors of the order of 10 percent, the maximum shearing stress criterion being on the whole perhaps somewhat better.