Tensile Deformation

IN recent papers, O'Neill,1 Vivian,2 and Zener and Hollomon3 have reviewed some of the information concerning the relations between stress and strain during plastic deformation. Since further information has been obtained since these reviews were published, this paper attempts to further coordinate and amplify the knowledge concerning the plastic deformation of metals in simple tension. Ordinarily the results of tensile tests of metals are presented as graphs in which the load divided by the original area is plotted as a function of the percentage of elongation measured over some specified gauge length. The interpretation of graphs of this sort is limited, since the stress required to deform the metal at any stage of the deformation is actually the load divided by the instantaneous rather than the original area. Furthermore, each increment of the deformation is performed on metal that has been previously deformed, and, as pointed out by Ludwik,4 the strain could be more effectively defined: [e = In A t][I] where a is the strain and Ao and A are, respectively, the original and instantaneous areas. The results of the tensile tests can be more effectively presented and interpreted if the stress* (load divided by actual area) is plotted as a function of the strain as defined above. A schematic curve of this type is presented as Fig. I. In a previous paper,6 the concept of Ludwik7 concerning the flow and fracture of metals was successfully employed to explain some of the puzzling results of notched-bar impact tests of steel. It appears that the use of this concept is very fruitful and should be kept in mind in any study of the deformation characteristics of metals. Ludwik considered that a flow stress-strain curve of a metal was essentially a locus of points that described the stress required for plastic flow of an infinite number of specimens, each with a different strain history determined by the preceding part of the flow curve. Each of these specimens can also be considered to have a fracture strength. Unfortunately (or fortunately depending upon the point of view), all the specimens, except the one deformed to the fracture strain, flow and do not fracture. Even though the metals do not fracture, the concept of a fracture-strength curve seems