**64**, 3, pp. 311-350, 2016

**10.24423/engtrans.374.2016**

### Analysis of the Nonstability States During Bending Processes of Metallic Tubes at Bending Machines Part I. Derivation of the basic expressions and relationships; Part II. Examples of calculations and analysis of some unstability states

**Keywords**: allowable strains and stresses; bending angles; neutral layer; wall thickness of elbows

#### References

PART I

Marciniak Z., Limit Deformations in Sheet Metal Stamping, [in Polish], WNT, Warszawa, 1971.

Śloderbach Z., A Model of Deformation Geometry in Pipe Bending Processes, Engineering Transactions, 47(1): 3–20, 1999.

Śloderbach Z., Strauchold Sz., Approximate Methods for EvaluatingStrains In Pipe Bending Processes [in Polish], Dozór Techniczny, 1/99, pp. 1–6, 1999.

Beskin L., Bending of thin curved tubes, Journal of Applied Mechanics, Transactions of the ASME, 12, 1945.

Boyle M., Bending thin wall stainless tubing, Machinery, 77/71, 1–36, 1971.

Dzidowski E. S., Reliability and Solving Problems in Thin-Walled Pipe Bending Processes for the Case of Great Manufacturing Tolerance [in Polish], Materials of Fourth Conference PIRE 2001, ISBN 83-909539-3-5, Lądek Zdrój, 91–101, 2001.

Dzidowski E. S., Strauchold Sz., Effect of Technological Factors in Pipe Bending on Damage Characteristics and Reliability of Power Pipelines [in Polish], Scientific Books of the Opole University of Technology, Series Electricity 6, pp. 119–125, Opole, 1998.

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

Gruner P., Über Rohrbiegeverfahren. Maschinenmarkt, 30/31: 120–129, 1960.

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

Korzemski J. W., Thin-Walled Pipe Bending with use of the Mandrels [in Polish], Mechanik, 4/68, pp. 207–210, 1968.

Korzemski J. W., Thin-Walled Pipe Bending [in Polish], WNT, Warszawa, 1971.

Pesak F., Bending thin wall tubing. Machinery, 60: 147–151, 1963.

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, Pajak J. : Determination of the thicknesses of pipe elbows on the basis of equations resulting from EU-Directive, Archive of Applied Mechanics, 85(5): 629–640, 2014.

Śloderbach Z., Some problems of mechanics in pipeline bending processes [in Polish], Publishing House of the Wrocław University of Technology, Wrocław, pp. 1–218, 2002.

Śloderbach Z., Derivations of relations and analysis of tube bending processes using discontinuous fields of plastic strains. Part. I. Derivation of geometric-analytic relationships, Part. II. Discussion and analysis of the obtained results, International Journal of Applied Mechanics and Engineering, 20(2): 417–426, 427–435, 2015.

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

Tang N. C., Plastic-deformation analysis in tube bending, International Journal of Pressure Vessels and Piping, vol. 77, No. 12, Publisher Elsevier UK, 751-759, 2000.

UDT Conditions (WUDT-UC-WO-O/02:10), Pressure Installations. General Requirements. Bending Elbows. Strength Calculations [in Polish], 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 technicans, Vol. II, Forming, 4th ed., Society of Manufacturing Engineers, One ASME Drive, Dearbon, Michigan, USA, 2001.

Zhang Z., Yang H., Li H., Ren N. And Tian Y., Bending behaviors of large diameter thinwalled 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.

Zdankiewicz M., Investigations of the cold tubes bending processes [in Polish], Mechanik, No 7/70, pp. 609–519, 1970.

Zdankiewicz M., European Directive Concern a Pressure Installations. Design Recommendations for Pressure Vessels – Manufacturing [in Polish], Dozór Techniczny, 2/98, pp. 25–33 and 48, 1998.

Dobosiewicz J., Wojczyk K., Life Prediction for Steam Pipeline Bends [in Polish], Energetyka, nr 3/88, pp. 88–90, 1998.

Seyna F., Ginalski J., Diagnosis Methods for Safe Service of Master Steam Pipelines [in Polish], Dozór Techniczny, 2/99, pp. 31–33, 1999.

Seyna F., Ginalski J., Numerical Methods for Long-Term Evaluating Residua Life of Steram Pipelines [in Polish], Dozór Techniczny, 3 /89, 6–13, 1989.

Seyna F., Ginalski J., Conditions for Long-Term Safe Service of Steam Pipelines [in Polish], Energetyka, 6, pp. 214–217, 1987.

Życzkowski M., Skrzypek J., Influence of Bending, Torsion and Tension on the Stationary Creep of a Pipe Line, Archives of Mechanics, 23(4): 465–494, 1971.

EN 13445-4: Unfired Pressure Vessels – Part 4: Fabrication (p. 9. 2. 4 Tube Bents, expression 9. 2-4), 2009, or earlier: Draft Standart EN UFPV Unfired Pressure Vessels – Part 4. Manufacture, CEN/TC54/267 JWGB N277, rev. 5, May, 1996.

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: 535–556, 1972.

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

Hill R., Mathematical Theory of plasticity, Oxford, Clarendon Press, London, 1985.

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, 1964/1965.

Śloderbach Z., Sawicki T., Evaluation of the Spherical Cap Height in a Test of Hydraulic Forming for Certain Instability Conditions, IFTR-Reports-PAN, No 4/84, Warszawa, (984.

Erbel S., Kuczyński K., Marciniak Z., Plastic Metal-Working Processes [in Polish], PWN, Warszawa, 1986.

Marciniak Z., Kołodziejski J., Fundamentals of Metal-Working Processes [in Polish], Warsaw University of Technology, Warszawa, 1983.

Olszak W., Perzyna P., Sawczuk A., Theory of Plasticity [in Polish], PWN, Warszawa, 1965.

Swift H. W., Plastic Instability Under Plane Stress, Journal of the Mechanics and Physics of Solids, 1(1): 1–76, 1962.

Szczepiński W., Theory of Plastic Working of Metals [in Polish], WN PWN, Warszawa, 1993.

Raniecki B., Sawczuk A., Thermal Effects In Plasticity. Part I. Coupled Theory, Zeitschrift fur Angewandte Mathematik und Mechanik, ZAMM, 55: 333–341, 1975.

Raniecki B., Sawczuk A., Thermal Effects In Plasticity. Part II. Uniqueness and Aplications, Zeitschrift fur Angewandte Mathematik und Mechanik, ZAMM, 55: 363–371, 1975.

Marciniak Z. (editor), Plastic Metal-Working Processes. Which Methods of Forming? On Cold, Hot or Half-Hot? [in Polish], Mechanik, SIMP, No 2, Warszawa, 1987.

Nowacki W. K., Thermal effects in dynamic plasticity, numerical solution and experimental investigations (thermographic-infrared detection). Journal de Physique, 48(8): 113–119, 1985.

PART II

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., The Conditions of instabilitiy in the plastic deformations analysis [in Polish], Publishing House of the Opole University of Technology, ISBN 978-83-60691-85-4, Opole, pp. 1–188, 2010.

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: 535–556, 1972.

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

Marciniak Z., Kołodziejski J., Fundamentals of metal-working processes [in Polish], Warsaw University of Technology, Warszawa, 1983.

Swift H. W., Plastic instability under plane stress, 1952, Journal of the Mechanics and Physics of Solids, 1(1): 176–187, 1952.

Śloderbach Z., Some problems of mechanics in pipeline bending processes [in Polish], Publishing House of the Wrocław University of Technology, ISBN 83-7085-665-9, Wrocław, pp. 1–218, 2002.

Śloderbach Z., Derivations of relations and analysis of tube bending processes using discontinuous fields of plastic strains. Part. I. Derivation of geometric-analytic relationships, Part. II. Discussion and analysis of the obtained results, International Journal of Applied Mechanics and Engineering, 20(2): 417–426, 427–435, 2015.

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

Hill R., Mathematical Theory of plasticity, Oxford, Clarendon Press, London, 1985.

Olszak W., Perzyna P., Sawczuk A., Theory of plasticity, PWN, Warszawa, 1965.

Szczepiński W., Theory of plastic working of metals [in Polish], PWN, WN Warszawa, 1993.

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

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

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, 1964/1965.

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

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

Śloderbach Z., Sawicki T., Evaluation of the Spherical Cap Height in a Test of Hydraulic Forming for Certain Instability Conditions [in Polish], Institute of Fundamental Technological Research Reports (IFTR-Reports), No 4/84, Warszawa, 1984.

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

Erbel S., Kuczyński K., Marciniak Z., Plastic metal-working processes [in Polish], PWN, Warszawa, 1986.

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

Dobosiewicz J., Wojczyk K., Life prediction for steam pipeline bends [in Polish], Energetyka, No 3/88, 88–90, 1988.

Dzidowski E. S., Influence of the manufacturing and repair technology criteria on the materiale properties applied in power industry [in Polish], Materials of First Conference PIRE ’98, ISBN 83-909539-5-1, Kudowa Zdrój, pp. 51–56, 1998.

Dzidowski E. S., The mezomechanical aspects of reliability of the pipelines elements manufactured by the cold bending processes [in Polish], Materials Four Conference PIRE 2001, ISBN 83-909539-3-5, Lądek Zdrój, pp. 103–110, 2001.

Dzidowski E. S., Strauchold Sz., Effect of technological factors in pipe bending on damage characteristics and reliability of power pipelines [in Polish], Scientific Booklets of the Opole University of Technology, Elektrical Series 6, Opole, 119–125, 1998.

Seyna F., Ginalski J., Diagnosis methods for safe service of master steam pipelines [in Polish], Dozór Techniczny, No 2/99, 31–33, 1999.

Seyna F., Ginalski J., Numerical methods for long-term evaluating residua life of steam pipelines [in Polish], Dozór Techniczny, No 3 /89, 6–13, 1989.

Seyna F., Ginalski J., Conditions for long-term safe Sservice of steam pipelines [in Polish], Energetyka, No. 6, 214–217, 1987.

Marciniak Z. (ed. ), Plastic metal-working processes. Which methods of forming? On cold, hot or half-hot? [in Polish], Mechanik, SIMP, No 2, Warszawa, 1987.

Zdankiewicz M., European Direktive concern a pressure installations. Design recommendations for pressure vessels. Manufacturing [in Polish], Dozór Techniczny, 2/98, 25–33 and 48, 1998.

EN 13445-4 Unfired Pressure Vessels – Part 4: Fabrication (p. 9. 2. 4 Tube Bents, expression 9. 2-4), 2009 or earlier: Draft Standart EN UFPV Unfired Pressure Vessels – Part 4. Manufacture, CEN/TC54/267 JWGB N277, rev. 5, May, 1996.

DOI: 10.24423/engtrans.374.2016