Three-Dimensional Necking Bifurcation in Tensile Steel Specimens

Abstract

Three-dimensional (3D) necking bifurcation in tensile steel specimens is simulated by a finite-element method. Although conventional necking analysis has tended to depend on material instability approaches with two-dimensional analysis assuming plane strain or axis symmetric state, 3D necking behavior is treated in the framework of only geometrical instability without material instability in this study. To explicate an essential bifurcation phenomenon, a branch-switching procedure is utilized after strictly detecting a bifurcation point in a perfect system. Ultimate localized modes of the tensile steel specimens with various rectangular cross sections are computed. In addition, actual tension experiments of the steel specimens, of which cross-sectional width–thickness ratios correspond to those in computations, are conducted, and excellent correlation with the computational results without the material instability is demonstrated. Thus, behavior from a uniformly deformed state to the ultimate localized mode, just before fracture, has been proved continuous geometrical instability instead of the material instability.