Application of Two Conditions of Loss of Stability in Analysis of the Tube Bending Process

Abstract

In this paper, the derivation of expressions for admissible values of strains and stresses for vertex points of layers subjected to tension during tube bending at bending machines is presented. The conditions of the dispersed and located loss of stability of the bent tube were assumed as criteria of instability. The original element of this paper is the extension of the criterion of strain location in a form of possible initiation of a neck or furrow (introduced by Marciniak for thin plates [1]) to bending thin- and thick-walled metal tubes at bending machines. The conditions of the dispersed and localized loss of stability together with formation of the plane state of deformation (PSD) in the plane stress state (PSS) were assumed as the criteria of instability. The calculation results were presented as graphs being useful nomograms. We present also simple examples of calculations of permissible and critical strains and values of bending angles including and not including displacement of the neutral axis y 0 , during cold bending metal thin-walled tubes at bending machines for bending angles .

Keywords

• allowable strains and stresses
• bending angles
• neutral layer
• wall thickness of elbows