Analysis of the Nonstability States During Bending Processes of Metallic Tubes at Bending Machines Part I. Derivation of the basic expressions and relationships; Part II. Examples of calculations and analysis of some unstability states - ŚLODERBACH, Zdzisław (Engineering Transactions, 2016)
ABSTRACT PART I. 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 and the cracking criterion based on the technological index A5 (five fold sample) 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. Occurrence of loss of stability (especially that in a localised form) during tube bending can strongly reduce the service life. Thus, it is recommended to avoid such states during tube bending for elbows for pipelines or pipe installations. ABSTRACT PART II. In this part of the paper, applying epressions derived in Part I, the exemplary calculations of some selected states of loss of stability during cold bending of thin-walled metal tubes at bending machines are presented. The conditions of the dispersed and localised loss of stability together with formation of the plane state of deformation (PSD) under the plane stress state (PSS) and the cracking criterion based on the technological index A5 as the criteria of unstability were assumed. The majority of calculations were performed for a generalised model of strain and simplification of the 3rd type. It appears that they are two extreme cases: one provides the greatest strains and greatest bending angles and the other provides the lowest strains and lowest bending angles [1]. For simplifications of types 1 and 2, values of the bendng angles are included between these extreme values. The calculations were performeded for the top points of the elbow where strains are the greatest and the wall thickness is the smallest. The calculation results were presented as suitable graphs being useful nomograms.