Recursive bifurcation of tensile steel specimens

Abstract

Failure modes of steel specimens subjected to uniaxial tension are investigated. These modes are well known to display complex geometrical characteristics of deformation accompanied by the plastic instability behavior. As an underlying mechanism of such complexity, we here focus on the recursive occurrence of bifurcations. In the theory, the rule of recursive bifurcation of a rectangular parallelepiped domain is obtained by the group-theoretic bifurcation theory so as to exhaust all the mathematically possible courses of bifurcation. In the experiment, we examine the representative failure modes with reference to the rules to identify actual courses of recursive bifurcation. Three-dimensional finite element analysis of a thin specimen is conducted to observe the recursive bifurcation, in which diffuse necking is formed by the direct bifurcation and the single shear band by the secondary bifurcation. The recursive bifurcation has thus been identified as the mechanism to create the complex failure modes.