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.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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
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
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
Hadoush A, van den Boogaard AH (2012) Efficient implicit simulation of incremental sheet forming. Int J Numer Methods Eng 90:597–612
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
Hwan CL (1997) An upper bound finite element procedure for solving large plane strain deformation. Int J Numer Methods Eng 40:1909–1922
Hwan CL (1997) Plane strain extrusion by sequential limit analysis. Int J Mech Sci 39:807–817
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
Corradi L, Panzeri N (2004) A triangular finite element for sequential limit analysis of shells. Adv Eng Softw 35:633–643
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
Echrif SBM, Hrairi M (2011) Research and Progress in Incremental Sheet Forming Processes. Mater Manuf Processes 26:1404–1414
Fei H, Jian-hua M (2008) Numerical simulation and experimental investigation of incremental sheet forming process. J Cent S Univ Technol 15:581–587
Manco GL, Ambrogio G (2010) Influence of thickness on formability in 6082-T6. Int J Mater Form 3(suppl 1):983–986
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
Jhonson W, Mellor PB (1983) Engineering plasticity. Ellis Horwood, UK
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
Abrinia A, Ghorbani M (2012) Theoretical and Experimental Analyses for the Forward Extrusion of Nonsymmetric Sections. Mater Manuf Processes 27:420–429
Long YQ, Cen S, Long ZF (2009) Advanced finite element method in structural engineering. Springer, Berlin
MOSEK ApS (2012) The MOSEK optimization toolbox for Matlab manual, Version 6.0 (Revision 135). MOSEK ApS, Denmark
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
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
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
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
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
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
Bambach M (2008) Process strategies and modeling approaches for asymmetric incremental sheet forming. Umformtechnische Schriften Band 139. Shaker Verlag, Aachen
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
- Single point incremental forming (SPIF)
- Sequential limit analysis
- Second-order cone programming (SOCP)