Skip to main content
Top
Published in: International Journal of Material Forming 6/2020

03-12-2019 | Original Research

Analytical modelling of buckling in stringer sheet forming

Authors: Stefan Köhler, Henning Husmann, Daniel Corbean, Peter Groche

Published in: International Journal of Material Forming | Issue 6/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Stringer sheet forming enables an efficient production of branched sheet metal structures. Compared to conventional sheet metal components, stringer sheets show a significant increase in stiffness and therefore offer new possibilities for lightweight design. A challenge in stringer sheet forming is the failure due to instability, which appears in the buckling of the stringer in concave curvatures. The prediction of this failure mode is so far only possible by complex numerical simulations. This work introduces an analytical model for the prediction of the buckling failure during forming of concave stringer sheet curvatures under different process boundary conditions. It is derived from Kirchhoff’s plate theory. A detailed sensitivity analysis of all influencing parameters is shown and extends the process understanding. The model is validated by means of a 4-point bending test and a stamping process. It can be used for a conservative estimation of the buckling failure limit in stringer sheet forming.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Bar-Cohen Y (2006) Biomimetics - using nature to inspire human innovation. Bioinspiration Biomim 1(1):1–12CrossRef Bar-Cohen Y (2006) Biomimetics - using nature to inspire human innovation. Bioinspiration Biomim 1(1):1–12CrossRef
2.
go back to reference Zhao L, Ma J, Wang T, Xing D (2010) Lightweight design of mechanical structures based on structural bionic methodology. J Bionic Eng 7(4):S224–S231CrossRef Zhao L, Ma J, Wang T, Xing D (2010) Lightweight design of mechanical structures based on structural bionic methodology. J Bionic Eng 7(4):S224–S231CrossRef
3.
go back to reference Köhler S, Rohnert C, Groche P (2018) Extension of geometric limits in drawing of stringer sheets. Procedia Manuf 15:693–700CrossRef Köhler S, Rohnert C, Groche P (2018) Extension of geometric limits in drawing of stringer sheets. Procedia Manuf 15:693–700CrossRef
4.
go back to reference Groche P, Bruder E, Gramlich S (eds) (2017) Manufacturing Integrated Design - Sheet Metal Product and Process Innovation. Springer international Publishing AG, Cham (Switzerland) Groche P, Bruder E, Gramlich S (eds) (2017) Manufacturing Integrated Design - Sheet Metal Product and Process Innovation. Springer international Publishing AG, Cham (Switzerland)
5.
go back to reference Ertugrul M, Groche P (2009) Hydroforming of laser welded sheet stringers. Key Eng Mater 410-411:69–76CrossRef Ertugrul M, Groche P (2009) Hydroforming of laser welded sheet stringers. Key Eng Mater 410-411:69–76CrossRef
6.
go back to reference Bäcker F (2015) Forming of multi-axially strongly curved steel sheets with load-adapted stiffening ribs. In German: Formgebung mehrachsig stark gekrümmter Stahlbleche mit lastangepassten Versteifungsrippen. Dissertation, Technische Universität Darmstadt (Institut für Produktionstechnik und Umformmaschinen), Bäcker F (2015) Forming of multi-axially strongly curved steel sheets with load-adapted stiffening ribs. In German: Formgebung mehrachsig stark gekrümmter Stahlbleche mit lastangepassten Versteifungsrippen. Dissertation, Technische Universität Darmstadt (Institut für Produktionstechnik und Umformmaschinen),
7.
go back to reference Ertugrul M (2011) Active media-based deep drawing of ribbed sheets. In German: Wirkmedienbasiertes Tiefziehen von verrippten Blechen. Dissertation, Technische Universität Darmstadt (Institut für Produktionstechnik und Umformmaschinen), Ertugrul M (2011) Active media-based deep drawing of ribbed sheets. In German: Wirkmedienbasiertes Tiefziehen von verrippten Blechen. Dissertation, Technische Universität Darmstadt (Institut für Produktionstechnik und Umformmaschinen),
8.
go back to reference Volk W, Groche P, Brosius A, Ghiotti A, Kinsey BL, Liewald M, Madej L, Min J, Yanagimoto J (2019) Models and modelling for process limits in metal forming. CIRP Ann Manuf Technol 62(2):775–798CrossRef Volk W, Groche P, Brosius A, Ghiotti A, Kinsey BL, Liewald M, Madej L, Min J, Yanagimoto J (2019) Models and modelling for process limits in metal forming. CIRP Ann Manuf Technol 62(2):775–798CrossRef
9.
go back to reference Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis, and applications. CRC press Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis, and applications. CRC press
14.
go back to reference Bleich F (1952) Buckling strength of metal structures. McGraw-hill, New York Bleich F (1952) Buckling strength of metal structures. McGraw-hill, New York
15.
go back to reference Groche P, Zettler A, Berner S, Schneider G (2011) Development and verification of a one-step-model for the design of flexible roll formed parts. Int J Mater Form 4(4):371–377CrossRef Groche P, Zettler A, Berner S, Schneider G (2011) Development and verification of a one-step-model for the design of flexible roll formed parts. Int J Mater Form 4(4):371–377CrossRef
16.
go back to reference Magrinho JPG, Silva CMA, Silva MB, Martins PAF (2018) Formability limits by wrinkling in sheet metal forming. Proc Inst Mech Eng Part L: J Mater Design Appl 232(8):681–692 Magrinho JPG, Silva CMA, Silva MB, Martins PAF (2018) Formability limits by wrinkling in sheet metal forming. Proc Inst Mech Eng Part L: J Mater Design Appl 232(8):681–692
20.
go back to reference Bäcker F, Groche P (2014) An algorithm for positioning functional and structural elements on semi-finished products for forming technology. In German: Ein Algorithmus zur Positionierung von Funktions- und Strukturelementen auf Halbzeugen für die Umformtechnik. Zwischenkolloquium SFB 666 Tagungsband 5 Bäcker F, Groche P (2014) An algorithm for positioning functional and structural elements on semi-finished products for forming technology. In German: Ein Algorithmus zur Positionierung von Funktions- und Strukturelementen auf Halbzeugen für die Umformtechnik. Zwischenkolloquium SFB 666 Tagungsband 5
21.
go back to reference Bäcker F, Groche P, Abedini S (2012) Stringer Sheet Forming. Paper presented at the Proceedings of NAMRI/SME, Notre Dame (Indiana) Bäcker F, Groche P, Abedini S (2012) Stringer Sheet Forming. Paper presented at the Proceedings of NAMRI/SME, Notre Dame (Indiana)
23.
go back to reference Köhler S, Groche P, Baron A, Schuchard M (2016) Forming of stringer sheets with solid tools. Adv Mater Res 1140:3–10CrossRef Köhler S, Groche P, Baron A, Schuchard M (2016) Forming of stringer sheets with solid tools. Adv Mater Res 1140:3–10CrossRef
27.
go back to reference Timoshenko SP, Gere JM (1961) Theory of elastic stability. Dover Publications, New York Timoshenko SP, Gere JM (1961) Theory of elastic stability. Dover Publications, New York
29.
go back to reference Hutchinson J, Neale K (1985) Wrinkling of curved thin sheet metal. Plastic instability: 71–78 Hutchinson J, Neale K (1985) Wrinkling of curved thin sheet metal. Plastic instability: 71–78
32.
go back to reference Kirchoff G (1850) About the balance and movement of an elastic disc. In German: Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal fur die reine und angewandte Mathematik (Crelle's Journal) 40:51–88 Kirchoff G (1850) About the balance and movement of an elastic disc. In German: Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal fur die reine und angewandte Mathematik (Crelle's Journal) 40:51–88
33.
go back to reference Liu N, Yang H, Li H, Yan S (2016) Plastic wrinkling prediction in thin-walled part forming process: a review. Chin J Aeronaut 29(1):1–14CrossRef Liu N, Yang H, Li H, Yan S (2016) Plastic wrinkling prediction in thin-walled part forming process: a review. Chin J Aeronaut 29(1):1–14CrossRef
35.
go back to reference Kim J, Yoon JW, Yang D (2003) Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory. Int J Numer Methods Eng 56(12):1673–1705CrossRef Kim J, Yoon JW, Yang D (2003) Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory. Int J Numer Methods Eng 56(12):1673–1705CrossRef
36.
go back to reference Kawka M, Olejnik L, Rosochowski A, Sunaga H, Makinouchi A (2001) Simulation of wrinkling in sheet metal forming. J Mater Process Technol 109(3):283–289CrossRef Kawka M, Olejnik L, Rosochowski A, Sunaga H, Makinouchi A (2001) Simulation of wrinkling in sheet metal forming. J Mater Process Technol 109(3):283–289CrossRef
37.
go back to reference Correia JDM, Ferron G (2004) Wrinkling of anisotropic metal sheets under deep-drawing: analytical and numerical study. J Mater Process Technol 155:1604–1610CrossRef Correia JDM, Ferron G (2004) Wrinkling of anisotropic metal sheets under deep-drawing: analytical and numerical study. J Mater Process Technol 155:1604–1610CrossRef
41.
go back to reference Ludwik P (1909) Elements of technological mechanics. In German: Elemente der technologischen Mechanik. Springer-Verlag, Berlin Ludwik P (1909) Elements of technological mechanics. In German: Elemente der technologischen Mechanik. Springer-Verlag, Berlin
42.
go back to reference Reihle M (1961) A simple method for recording the flow curves of steel at room temperature. In German: Ein einfaches Verfahren zur Aufnahme der Fließkurven von Stahl bei Raumtemperatur, in arch. Eisenhüttenwes. 32:331–336CrossRef Reihle M (1961) A simple method for recording the flow curves of steel at room temperature. In German: Ein einfaches Verfahren zur Aufnahme der Fließkurven von Stahl bei Raumtemperatur, in arch. Eisenhüttenwes. 32:331–336CrossRef
43.
go back to reference Dietrich J (2018) Forming practice: forming and cutting processes, tools, machines. In German: Praxis der Umformtechnik : Umform- und Zerteilverfahren, Werkzeuge, Maschinen. 12. Aufl. 2018 edn., Wiesbaden Dietrich J (2018) Forming practice: forming and cutting processes, tools, machines. In German: Praxis der Umformtechnik : Umform- und Zerteilverfahren, Werkzeuge, Maschinen. 12. Aufl. 2018 edn., Wiesbaden
44.
go back to reference Doege E and Behrens BA (2010) Handbook forming. In German: Handbuch Umformtechnik. Springer, Berlin, Heidelberg Doege E and Behrens BA (2010) Handbook forming. In German: Handbuch Umformtechnik. Springer, Berlin, Heidelberg
45.
go back to reference DIfNe V (1998) EN ISO 14125 - Faserverstärkte Kunststoffe - Bestimmung der Biegeeigenschaften. Beuth Verlag GmbH, Berlin DIfNe V (1998) EN ISO 14125 - Faserverstärkte Kunststoffe - Bestimmung der Biegeeigenschaften. Beuth Verlag GmbH, Berlin
47.
go back to reference Abaqus analysis user's manual (2010), vol IV. Dassault Systèmes (Abaqus), Providence, RI, USA Abaqus analysis user's manual (2010), vol IV. Dassault Systèmes (Abaqus), Providence, RI, USA
49.
go back to reference DIfNe V (2017) DIN EN 1993-1-5 - design of steel structures - part 1–5; plated structural elements. Beuth Verlag GmbH, Berlin DIfNe V (2017) DIN EN 1993-1-5 - design of steel structures - part 1–5; plated structural elements. Beuth Verlag GmbH, Berlin
50.
go back to reference Kang J-H, Leissa AW (2005) Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges. Int J Solids Struct 42(14):4220–4238CrossRef Kang J-H, Leissa AW (2005) Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges. Int J Solids Struct 42(14):4220–4238CrossRef
51.
go back to reference Siebel E, Beisswänger H (1955) Deep drawing. In German: Tiefziehen. C. Hanser, München Siebel E, Beisswänger H (1955) Deep drawing. In German: Tiefziehen. C. Hanser, München
52.
go back to reference Darendeliler H, Akkök M, Yücesoy CA (2002) Effect of variable friction coefficient on sheet metal drawing. Tribol Int 35(2):97–104CrossRef Darendeliler H, Akkök M, Yücesoy CA (2002) Effect of variable friction coefficient on sheet metal drawing. Tribol Int 35(2):97–104CrossRef
53.
go back to reference Lange K (1985) Handbook of metal forming. McGraw-Hill Book Company, New York Lange K (1985) Handbook of metal forming. McGraw-Hill Book Company, New York
55.
go back to reference Recklin V, Dietrich F, Groche P (2018) Influence of test stand and contact size sensitivity on the friction coefficient in sheet metal forming. Lubricants 6(2):41CrossRef Recklin V, Dietrich F, Groche P (2018) Influence of test stand and contact size sensitivity on the friction coefficient in sheet metal forming. Lubricants 6(2):41CrossRef
Metadata
Title
Analytical modelling of buckling in stringer sheet forming
Authors
Stefan Köhler
Henning Husmann
Daniel Corbean
Peter Groche
Publication date
03-12-2019
Publisher
Springer Paris
Published in
International Journal of Material Forming / Issue 6/2020
Print ISSN: 1960-6206
Electronic ISSN: 1960-6214
DOI
https://doi.org/10.1007/s12289-019-01518-y

Other articles of this Issue 6/2020

International Journal of Material Forming 6/2020 Go to the issue

Premium Partners