The Flow of Metals under Various Stress Conditions

Abstract

The phenomena associated with the permanent deformations of the metals have attracted the attention of investigators during the last 100 to 150 years, and have inspired mathematically-minded observers in their endeavour to formulate mechanical rules or laws by which ductile metals flow under prescribed conditions. While the theory of elasticity is mostly concerned with very small strains, a theoretical treatment of the permanent or plastic deformations of metals must also frequently take account of strains of an order of ten to a hundred—and even more—times larger than the strains that can be sustained by them elastically.The engineering means for dealing with finite strains of this order will be reviewed in the lecture, and certain new types of strains that seem to offer possibilities for expressing the stress-strain relations required for developing the theories of the flow of metals under various conditions will be introduced. Several ideal substances, representing behaviour of metals or of other materials under different conditions, may be considered. For a perfectly plastic substance a special solution is quoted for a plane problem and for plastic shells with rotational symmetry. A case of the creep of metals at eleyated temperatures will be mentioned.Experiments made during the war years on the propagation of the plastic zone along mild-steel bars tested under tension, on the flow of copper and of medium carbon steel under combined stresses in the strain hardening range (including observations regarding the ensuing types of fractures which were observed), and experiments on the effect of the speed of deformation in these metals under normal and at elevated temperatures over a wide range of the rates of strain, will be reported.