Engineering Transactions, 63, 3, pp. 361–376, 2015
10.24423/engtrans.306.2015

Calculations of the Strains and Thicknesses of Pipe Elbows on the Basis of Expressions Resulting from the EU Directive for the Case of Large Strains

Zdzisław ŚLODERBACH
Opole University of Technology, Opole,
Poland

The relations to calculate the maximum value of relative strains, which occur in a process of bending of tubes on benders, in stretched layers of tubes, are presented in this work on the basis of the EU Directive concerning production of pressure equipment. It has been shown that for large deformations that occur during bending of the pipes on knees, logarithmic strain measures (real) and relative strain measures give different values of strain and equal wall thicknesses in the bending zone. Reverse expressions were also derived to calculate the required initial wall thickness of the tube to be bent, in order to obtain the desired wall thickness of a knee after bending.
Keywords: EU Directive; required thicknesses of pipe elbows; pipe bending processes; relative and logarithmic measures of deformation; required initial thickness of a bent tube.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

EN 13445-4 “Unfired Pressure Vessels” – Part 4: Fabrication, (point 9.2.4 Tube Bents, expression 9.2-4), 2009 (earlier: Draft Standard EN UFPV “Unfired Pressure Vessels” – Part 4. “Manufacture”, CEN/TC54/267 JWGB N277, rev. 5, May, 1996).

Zdankiewicz M., The European Directive concerning pressure installations. Requirements concerning manufacturing [in Polish], Technical Inspection (Dozór Techniczny), 2, 25–33 and 48, 1998.

Gabryszewski Z., Theory of elasticity and plasticity [in Polish], Publishing House of Wrocław University of Technology, Wrocław, 2001.

Hill R., Mathematical theory of plasticity, Clarendon Press, Oxford, 1985.

Johnson W., Mellor P.B., Engineering plasticity, Van Nostrand Reinhold Company, London, 1975.

Lubliner J., Plasticity theory, Macmillan Publishers, New York, 1990.

Mendelson A., Plasticity – theory and applications, Macmillan Publishers, New York, 1988.

Olszak W., Perzyna P., Sawczuk A. [Eds.], Theory of plasticity [in Polish], PWN, Warszawa, 1981.

Życzkowski M., Combined loading in the theory of plasticity, PWN-Nijhoff, Warszawa Alpen aan den Rijn, 1981.

Śloderbach Z., Strauchold Sz., Approximate methods for evaluating strains in pipe bending processes [in Polish], Technical Inspection (Dozór Techniczny), 1, 1–6, 1999.

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

Śloderbach Z., Genaralized model of strains during bending of metal tubes in bending machines, Journal of Theoretical and Applied Mechanics, 52, 1, 1093–1106, 2014.

Śloderbach Z., A model of deformation geometry in pipe bending processes, Engineering Transactions, 47, 1, 3–20, 1999.

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

Team Work, Technical requirement. Calculations and checking of wall thickness of bent tubes [in Polish], Steam Boilers Factory “RAFAKO” S.A., WT-1/0/R, Racibórz, Poland 1991.

Team Work, Pressure installations. General requirements. Strength calculations [in Pol ish], UDT Conditions, (WUDT-UC-WO-O/02:10), Issue I, Warszawa, 2003.

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

Franz W.D., Numerisch gesteuerte Rohrkaltbiegemaschinen, Werkstatt und Betrieb, 9, 129–145, 1969.

Grunow O., Praktisches Rohrbiegen, Springer-Verlag, Berlin, 1985.

Korzemski J.W., Thin-walled pipe bending [in Polish], WNT, Warszawa, 1971.

Wick Ch., Benedict J.T., Veilleux R.F., Tool and manufacturing engineers hand book. A reference book for manufacturing engineers, managers and technicians, Volume 2, Fourth Edition – forming, Society of Manufacturing Engineers, Dearbon, Michigan, USA 2001.

Zhang Z., Yang H., Li, H., Ren N., Tian Y., Bending behaviors of large diameter thin walled CP-Ti tube in rotary draw bending, Progress in Natural Science: Materials International, 21, 401–412, 2011.

Zhiqiang J., Mei Z., He Y., Xudong X., Guangjun L., Deformation behavior of medium strength TA18 high-pressure tubes during NC bending with different bending radii, Chinese Journal of Aeronautics, 24, 657–664, 2011.

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

Szczepiński W., Theory of plasticity in metalworking [in Polish], PWN, Warszawa, 1987.

Gabryszewski Z., Gronostajski J., Fundamentals of metal-working processes [in Polish], PWN, Warszawa, 1991.

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

Haupt P., Continuum mechanics and theory of materials, Springer-Verlag, Berlin – Heidelberg, 2002.

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

Śloderbach Z., Pajak J., Generalized coupled thermoplasticity taking into account large strains: part I. Conditions of uniqueness of the solution of boundaryvalue 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 de formations, Journal Mécanique Theoretique et Applique, 1, Numero special, 175–186, 1982.




DOI: 10.24423/engtrans.306.2015