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2 Śloderbach Z.

2 2015

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Derivation of relations and analysis of tube bending processes using discontinuous fields of plastic strains. Part I. Derivation of geometric-analytic relationships

Śloderbach Z.

International Journal of Applied Mechanics and Engineering

2015

Vol. 20, no. 2

417--426

The generalized strain scheme in bending metal tubes at bending machines with the use of a mandrel presented in Śloderbach (1999; 2002; 20131,2; 2014) satisfies initial and boundary kinematic conditions of bending, conditions of continuity and inseparability of strains. This paper introduces three formal simplifications gradually imposed into forms of principal components of the generalized strain model giving suitable simplifications of the 1st, 2nd and 3rd types. Such mathematical simplifications cause that the obtained strain fields do not satisfy the condition of consistency of displacements and strain continuity. The simplified methods determine safer values of the wall thickness than those from the generalized continuous strain scheme. The condition of plastic incompressibility was used for the derivation of an expression for distribution of Wall thickness of the bent elbow in the layers subjected to tension and compression for three examples of discontinuous kinematic strain fields.

Determination of the initial thickness of tubes subjected to bending. Part II. Discussion and analysis of obtained results

Śloderbach Z.

Engineering Transactions

2015

Vol. 63, iss. 4

497--507

In this second part of the paper, applying epressions derived in Part I, the exemplary calculations of the initial thickness of a metallic tube subject to bending at bending machines are presented. The expressions for calculating of the initial thickness were presented for a suitable measure of the big actual radius Ri in the bending zone for an exact (general) solution and for three formal simplifications of the 1st, 2nd, and 3rd order. In the calculations the external or internal diameter of the tube subjected to bending is applied as a parameter. In this paper, the author shows that the calculated initial thickness of the tube (for the same parameters of bending) depending on the external diameter is lower than that calculated depending on the internal diameter. For example, the expression for calculation of deformations included in the UE Directive [1], contains dependence on dext not on dint. The results of the calculations are presented in the graphs and tables enclosed.