The method of the principal shear stress tracing line and its application in the flaring and expanding of a thin-walled tube with a conical punch

In this paper, the method of the principal shear stress tracing line is presented. The changing rule of the normal stress along the principal shear stress tracing line is described first by the normal stress equation. This method is applied in solving the problem of the typical processes of thin-walled tube forming with a conical punch, its results being the same as the results given by the slab method. The essential point of this method is to extend the idea that slip-line field theory treats just a pair of orthogonal tracing lines of the maximum shear stress to one of the three pairs of orthogonal principal shear stress tracing lines. Thus, the method of principal shear stress tracing line has led to the development of the theory of slip-line fields.