An Anisotropic Generalization of the Bridgman Analysis of Tensile Necking

Tensile necking in anisotropic bars is analyzed in the spirit of P. W. Bridgman’s treatment of the isotropic case. Anisotropic plastic flow causes an initially axisymmetric bar to develop an elliptical neck. Using physical approximations analogous to Bridgman’s, an approximate analytical solution for the stress distribution is obtained. The solution is shown to be asymptotically correct in two important limiting cases: (a) the fully developed anisotropic neck, and (b) the isotropic limit. In the latter case it is shown that the solution is a member of a one-parameter family of solutions, which includes the Bridgman and the Davidenkov and Spiridonova solutions.