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Application of two conditions of loss of stability in analysis of the tube bending process

Śloderbach Z.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 4

200--223

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 y0, during cold bending metal thin-walled tubes at bending machines for bending angles […].

Analysis of the nonstability states during bending processes of metallic tubes at bending machines. P. 1, Derivation of the basic expressions and relationships

Śloderbach Z.

Engineering Transactions

2016

Vol. 64, iss. 3

311--330

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.