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bending tubes ; three simplifications ; strains ; wall thickness ; discontinuous strain fields
Abstract:
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. ; Abstract Part II: This paper presents the calculation results obtained on the basis of three formal simplifications (derived in Part I) gradually led into the main components of the generalized model of strain where suitable simplifications of the 1st, 2nd and 3rd type have been obtained. The paper also presents the results of considerations on the wall thickness distribution in the vertex point of the elongated layers of the bent elbow, and values of main components of the strain state and intensity of the strain (equivalent strain) depending on the bending angle for the generalized strain scheme and three simplified methods. The results are shown in the form of graphs and table.
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Zielona Góra: Uniwersytet Zielonogórski
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IJAME, volume 20, number 2 (2015)