Influence of size effect on the springback of sheet metal foils in micro-bending

J. G. Liu, Mingwang Fu, J. Lu, Wai Lok Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

84 Citations (Scopus)


To analyze the unloading springback of sheet metal foils after micro-bending process, a constitutive model is proposed based on the surface layer model by which the sheet foil is divided into surface layer and inner portions. For the inner portion, each grain is envisaged as a composite, comprised of grain interior and grain boundary work-hardened layer. The classical composite model is then used to calculate its flow stress. For the surface layer portion, a model without grain boundary strengthening is constructed to represent the flow stress in this zone. The developed method is verified through the comparison of the calculated strain-stress curves with the tensile test results of four kinds of pure copper sheet foils with different thicknesses ranging from 0.1 mm to 0.6 mm. To investigate the effect of thickness and grain size on the springback of pure copper sheet foils, three-point bending tests are carried out. A finite element (FE) model for predicting the springback in micro-bending process is further developed, which takes into account the deformation behavior and orientation of each grain. The influences of grain size and thickness on the springback of sheet foils are investigated. The research results show that the decrease of sheet foil thickness or the increase of grain size results in a big springback. The scatter of springback angle is mainly attributed to the elastic anisotropy of surface grains and increases with the reduction of grains along the thickness direction. A good agreement between the experimental results and the analytical calculations shows that the developed FE model can predict the springback of sheet metal foils well in micro-bending process.
Original languageEnglish
Pages (from-to)2604-2614
Number of pages11
JournalComputational Materials Science
Issue number9
Publication statusPublished - 1 Jul 2011


  • Constitutive model
  • FE model
  • Microforming
  • Sheet metal foil
  • Size effect
  • Springback

ASJC Scopus subject areas

  • Computer Science(all)
  • Chemistry(all)
  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Computational Mathematics


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