Engineering Transactions, 63, 4, pp. 481-507, 2015

Determination of the Initial Thickness of a Tubes to Bending. Part I. Derivation of the Basic Expressions and Relationships. Part II. Discussion and Analysis of Obtained Results

Zdzisław Śloderbach
Politechnika Opolska

Abstract I. Part one of the paper presents the derived equations for calculations of the initial wall thick-ness g0 of a tube to bending for elbows, and a proper bending angle 0. The expressions for calculating g0 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. At any case, a value of g0 depends on a radius and an angle of bending, an external diameter of the tube, and a per-missible elbow thickness according to the European-Polish Standards and recommendations of the European-Polish Technical Inspection Office, on the coordinates of the point where the thickness g1all was determined, and the coefficient of the bending zone range k (defined during tests). In this paper, the external or internal diameter of the tube subjected to bending is applied as a parameter.
Abstract II. In this second part of the paper, applying epressions derived in Part I, the exemplary calcu-lations of initial thickness of a metallic tube to bending at bending machines are presented. The ex-pressions for calculating of 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 calculations the external or internal diameter of the tube subjected to bend-ing 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 are lower than those calculated depending on the internal diameter. For example expression for calculation of deformations included in UE Directive [1], contain dependence on dext not on dint.The calculations results are pre-sented on the graphs and tabele enclosed.
Keywords: bending tubes; three simplifications; strains; initial wall thickness; discontinuous strain fields
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EN 13445-4. (2009), Unfired Pressure Vessels – Part 4: Fabrication, Tube Bents, or earlier: Draft Standard EN UFPV, (1996): Unfired Pressure Vessels – Part 4, Manufacture. CEN/TC54/267 JWGB N277, rev. 5.

Śloderbach Z., Strauchold Sz., Approximate methods of strain calculations in the tube bending process [in Polish]. Technical Inspection, No 1, pp. 1–6, Warszawa, 1999.

Śloderbach Z., A Model for strain geometry evaluation in pipe bending processes. Engineering Transactions, 47, 1, 3–20, 1999.

Śloderbach Z., Rechul Z., Effect of strain hardening and normal anisotropy on allowable values of strain and stress in pipe-bending processes. Journal of Theoretical and Applied Mechanics, 4, 38, 843–859, 2000.

Śloderbach Z., Some problems of mechanics in pipeline bending processes [in Polish]. Publishing House of Wrocław University of Technology, Wrocław, 2002.

Śloderbach Z., Generalized model of strains during bending of metal tubes in bending machines. Journal of Theoretical and Applied Mechanics, 52, 4, 1093–1106, 2014.

Śloderbach Z., Derivation of relations and analysis of tube bending processes using discontinuous fields of plastic strains. Part I. Derivation of the geometric-analytic relationships. Part II. Discussion and analysis of the obtained results. International Journal of Applied Mechanics and Engineering, 20, 2, 417–435, 2015 (in print).

Śloderbach Z., Pajak J., Determination of the required thicknesses of pipe elbows on the basis of expressions resulting from EU-Directive, Archives of Applied Mechanics, 85, 5, 629–640, 2015.

Franz W.D., Das Kalt-Biegen von Rohren. Berlin, Springer-Verlag, 1961.

Grunow O., Praktisches Rohrbiege. Berlin: Springer-Verlag, 1985.

Korzemski J.W., Bending of thin-walled pipes [in Polish]. Warszawa, WNT, 1971.

UDT DT-UT-90/WO-W/06, General requirements. Manufacturing. Bending pipes of pressure elements [in Polish], Job Publishing Company Legal, Warszawa, 1991.

UDT Conditions (WUDT-UC-WO-O/02:10), Pressure Installations. General Requirements. Bending Elbows. Strength Calculations [in Polish]. Company Legal, Issue I, Warszawa 2003.

Wick Ch., Benedict J.T., Veilleux R.F., Tool and manufacturing engineers handbook. A reference book for manufacturing engineers, managers and technicians, Forming, 4th ed., Society of Manufacturing Engineers, One SME Drive, USA, vol. II, Dearbon, Michigan, 2001.

Dobosiewicz J., Wojczyk K., Life assessment in steam pipeline bends [in Polish]. Power Industry, 3, 88–90, 1998.

Dzidowski E.S., Strauchold Sz., Effect of technological factors in pipe bending on damage characteristics and reliability of power pipelines [in Polish], Scientifics Papers of the Opole Technical University, Series Electric, 46, 119–125, 1998.

Życzkowski M., Tran L.B., Interaction curves corresponding to the decohesive carrying capacity of a cylindrical shell under combined loading, International Journal of Plasticity, 13, 6–7, 551–570, 1997.

Tang N.C., Plastic-deformation analysis in tube bending processes, International Journal of Pressure Vessels and Piping, 77, 12, 751–759, 2000.

Moore G.G., Wallace J.F., The effect of anisotropy on instability in sheet-metal forming. Journal of the Institute of Metals, 93, 2, 33–38, 1964/65.

El-Sebaie M.G., Mellor P.B., Plastic instability conditions in the deep-drawing of a circular blank of sheet metal. International Journal of Mechanical Science, 14, 9, 91–101, 1972.

Marciniak Z., Limit deformations in sheet metal forming [in Polish]. WNT, Warszawa, 1971.

Gabryszewski Z., Gronostajski J., Fundamentals of Metal-Working Processes [in Polish]. Warszawa, WNT, 1991.

Haupt P., Continuum Mechanics and Theory of Materials, Springer-Verlag, Berlin, Heidelberg, 2002.

Hüttel C., Matzenmiller A., Extension of generalized plasticity to finite deformations and structures, International Journal of Plasticity, 36, 34, 5255–5276, 1999.

Pęcherski R.B., Finite deformation plasticity with strain induced anisotropy and shear banding, Journal of Materials Processing Technology, 60, 1–4, 35–44, 1996.

Śloderbach Z., Pajak J.: Generalized coupled thermoplasticity taking into account large strains. Part I. Conditions of uniqueness of the solution of boundary-value problem and bifurcation criteria, Mathematics and Mechanics of Solids, 15, 3, 308−327, 2010.

Życzkowski M., Szuwalski K., On the termination of the process of finite plastic deformations, Journal Mécanique Theoretique et Applique, 1, Numero Special, 175–186, 1982.

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