An investigation into thickness distribution in single point incremental forming using sequential limit analysis

Abstract

Single point incremental forming (SPIF), needing no dedicated tools, is the simplest variant of incremental sheet metal forming processes. In the present work, a simplified model of SPIF of a truncated cone, capable of predicting the thickness distribution, has been developed using sequential limit analysis (SLA). The obtained results were validated experimentally and compared with thickness predictions obtained from an explicit shell FE model implemented in Abaqus. It is shown that SLA is capable to solve the thickness prediction problem more accurately and efficiently than the equivalent FEA approach. As an application of the proposed model, the effect of the diameter of the hemispherical tool tip and the step down on the thickness distribution and the minimum thickness in a 50° cone is studied using SLA. By introducing bending and stretching zones in the wall of the cone, variations of the minimum thickness by changing the tool diameter and the step down are discussed.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. 1.

    Robert C, Ben Ayed L, Delamézière A, Dal Santo P, Batoz JL (2010) Development of A Simplified Approach of Contact For Incremental Sheet Forming. Int J Mater Form 3(suppl 1):987–990

    Article  Google Scholar 

  2. 2.

    Robert C, Ben Ayed L, Delamézière A, Dal Santo P, Batoz JL (2009) On a Simplified Model for the Tool and the Sheet Contact Conditions for the SPIF Process Simulation. Key Eng Mater 410–411:373–379

    Article  Google Scholar 

  3. 3.

    Bambach M (2010) A geometrical model of the kinematics of incremental sheet forming for the prediction of membrane strains and sheet thickness. J Mater Process Technol 210:1562–1573

    Article  Google Scholar 

  4. 4.

    Hadoush A, van den Boogaard AH (2012) Efficient implicit simulation of incremental sheet forming. Int J Numer Methods Eng 90:597–612

    Article  MATH  Google Scholar 

  5. 5.

    Raithatha A, Duncan SR (2009) Rigid plastic model of incremental sheet deformation using second-order cone programming. Int J Numer Methods Eng 78:955–979

    Article  MATH  MathSciNet  Google Scholar 

  6. 6.

    Hwan CL (1997) An upper bound finite element procedure for solving large plane strain deformation. Int J Numer Methods Eng 40:1909–1922

    Article  Google Scholar 

  7. 7.

    Hwan CL (1997) Plane strain extrusion by sequential limit analysis. Int J Mech Sci 39:807–817

    Article  MATH  Google Scholar 

  8. 8.

    Huh H, Kim KP, Kim HS (2001) Collapse simulation of tubular structures using a finite element limit analysis approach and shell elements. Int J Mech Sci 43:2171–2187

    Article  MATH  Google Scholar 

  9. 9.

    Corradi L, Panzeri N (2004) A triangular finite element for sequential limit analysis of shells. Adv Eng Softw 35:633–643

    Article  MATH  Google Scholar 

  10. 10.

    Jeswiet J, Micari F, Hirt G, Bramley A, Duflou J, Allwood J (2005) Asymmetric Single Point Incremental Forming of Sheet Metal. CIRP Ann 54:88–114

    Article  Google Scholar 

  11. 11.

    Echrif SBM, Hrairi M (2011) Research and Progress in Incremental Sheet Forming Processes. Mater Manuf Processes 26:1404–1414

    Article  Google Scholar 

  12. 12.

    Fei H, Jian-hua M (2008) Numerical simulation and experimental investigation of incremental sheet forming process. J Cent S Univ Technol 15:581–587

    Article  Google Scholar 

  13. 13.

    Manco GL, Ambrogio G (2010) Influence of thickness on formability in 6082-T6. Int J Mater Form 3(suppl 1):983–986

    Article  Google Scholar 

  14. 14.

    Li J, Li C, Zhou T (2012) Thickness distribution and mechanical property of sheet metal incremental forming based on numerical simulation. Trans Nonferrous Metals Soc China 22:s54–s60

    Article  Google Scholar 

  15. 15.

    Jhonson W, Mellor PB (1983) Engineering plasticity. Ellis Horwood, UK

    Google Scholar 

  16. 16.

    Mirnia MJ, Mollaei Dariani B (2012) Analysis of incremental sheet metal forming using the upper-bound approach. Proc Inst Mech Eng B: J Eng Manuf 226:1309–1320

    Article  Google Scholar 

  17. 17.

    Abrinia A, Ghorbani M (2012) Theoretical and Experimental Analyses for the Forward Extrusion of Nonsymmetric Sections. Mater Manuf Processes 27:420–429

    Article  Google Scholar 

  18. 18.

    Long YQ, Cen S, Long ZF (2009) Advanced finite element method in structural engineering. Springer, Berlin

    Google Scholar 

  19. 19.

    MOSEK ApS (2012) The MOSEK optimization toolbox for Matlab manual, Version 6.0 (Revision 135). MOSEK ApS, Denmark

  20. 20.

    Makrodimopoulos A, Martin CM (2007) Upper bound limit analysis using simplex strain elements and second-order cone programming. Int J Numer Anal MethodsGeomech 31:835–865

    Article  MATH  Google Scholar 

  21. 21.

    Le CV, Nguyen-Xuan H, Nguyen-Dang H (2010) Upper and lower bound limit analysis of plates using FEM and second-order cone programming. Comput Struct 88:65–73

    Article  Google Scholar 

  22. 22.

    Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge

    Google Scholar 

  23. 23.

    Ma LW, Mo JH (2008) Three-dimensional finite element method simulation of sheet metal single-point incremental forming and the deformation pattern analysis. Proc Inst Mech Eng B: J Eng Manuf 222:373–380

    Article  Google Scholar 

  24. 24.

    Eyckens P, Belkassem B, Henrard C, Gu J, Sol H, Habraken AM, Duflou JR, Van Bael A, Van Houtte P (2011) Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction. Int J Mater Form 4:55–71

    Article  Google Scholar 

  25. 25.

    Duflou J, Tunckol Y, Szekeres A, Vanherck P (2007) Experimental study on force measurements for single point incremental forming. J Mater Process Technol 189:65–72

    Article  Google Scholar 

  26. 26.

    Bambach M (2008) Process strategies and modeling approaches for asymmetric incremental sheet forming. Umformtechnische Schriften Band 139. Shaker Verlag, Aachen

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to B. Mollaei Dariani.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mirnia, M.J., Mollaei Dariani, B., Vanhove, H. et al. An investigation into thickness distribution in single point incremental forming using sequential limit analysis. Int J Mater Form 7, 469–477 (2014). https://doi.org/10.1007/s12289-013-1143-x

Download citation

Keywords

  • Single point incremental forming (SPIF)
  • Sequential limit analysis
  • Thickness
  • Second-order cone programming (SOCP)