ON THE REALISTIC STRESS SPACE OF SOLIDS (CONTINUED)

Abstract

A general theory on the realistic stress space of solids was formulated in a previous paper. In this paper, the bell stress spaces of several metals are compared, the concept of "efficiency of plastic deformation" is introduced and formulated, and the locus of deformation is discussed in connection with the theory of bell stress space. The main concepts of this paper are:Because the concept of strength of solids is associated with the stress state, it is difficult to bring out the concrete meaning of strength by a brief definition. Inasmuch as the volume of the closed stress space is a complete and concrete measure of the fracture strength and the limit of strain-hardened elastic strength in all stress states, we are inclined to define this volume as strength. This is not just a matter of definition; the important point is that the size and shape of the closed space actually reflect the physical and mechanical aspects of strength, and it gives one a clear impression about what is meant by strength.The concept of "efficiency of plastic deformation" arises from the fact that one may raise the internal potential energy of a solid infinitely without causing plastic deformation if the stress state is not favourable. This efficiency is the ratio of plastic distortion energy to the sum of elastic and plastic strain energies. It may be formulated, by simple arguments, as a function of octahedral shear strain and a stress state parameter c=θ/τ, where θ is the average normal stress and τ the octahedral shear stress. It increases with increasing strain and decreases with increasing hydrostatic stress, and it is actually measured by the length and the direction cotangent (c) of the position vector with respect to the hydrostatic axis.A process of deformation can hardly be well understood without knowing its locus of deformation in relation to the limiting surfaces of the stress space. By the theory of bell stress space and experimental measurements, such locus can be located. A locus for strip rolling is presented. It is interesting to note that there is a natural tendency for continuous processes of deformation to turn towards the [111] direction in order to make the total strain energy of the system a minimum.