Plane strain necking of V-notched and un-notched tensile bars

Abstract

An analytical nonsteady solution for plane strain necking of V-notched, rigid/perfectly-plastic tensile bars was obtained by E.H. Lee in 1952. In his solution the plastic zone remains geometrically similar, a velocity discontinuity occurs on the rigid-plastic boundary, and when carried to the point of separation, the plastic flow results in a wedge-shaped neck. In this paper a new analytical solution is given for the same problem. However, the plastic zone does not remain geometrically similar, velocity discontinuities are absent, and plastic flow results in a convexshaped neck. Comparisons with measurements of neck profiles obtained under conditions approximating plane strain indicate that the new solution is a good representation of the physical situation n metals. Thus, it appears to be useful for estimating basic stress-strain relations from tensile tests after necking, and for estimating the stresses and strains required for fracture from notched bar tests.