Papers - Relations between Stress and Reduction in Area for Tensile Tests of Metals

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain