A Graphic Representation of Traction for a 3D Elastic/Plastic Stress State

Abstract

The stress ellipsoid is often used to describe the variation scope of total stress of one stress state. But the direction of one vector from the original point to the ellipsoid surface is not always the one of the corresponding acting plane. A 3D graphic representation of total stress for an elastic/plastic stress state is given in this paper for the first time. The magnitude of the total stress on one plane can be described by the projection along the corresponding normal direction. The real direction of the total stress can be given directly. In a principal axes system, the figure is symmetric about the three principal axes. As for a plastic stress state, the stereograph of total stress has its own characters because the yield criterion must be obeyed. From the total stress figure, it is easy to get the magnitude of total stress acting on a certain plane. It is very helpful in understanding the concept of the stress ellipsoid and the variation of total stress across different acting planes.