Modelling of Springback in Tube Bending: A Generalized Analytical Approach

J. Ma, H. Li, M. W. Fu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)


Bending is widely used for manufacturing of lightweight tubular parts and structures in many industrial clusters. In tube bending, springback is an important deformation behavior since it causes crucial problems related to the accuracy, quality, and properties of the bent tubular parts. This research presents a generalized analytical solution for springback in tube bending, enabling accurate and efficient analysis of springback for bending of general tubular materials, in particular, for the tubes with tension-compression asymmetry. Via comprehensively considering the critical parameters related to material, geometry, and process, the neutral layer shifting was analytically modeled for an accurate solution of stress/strain distributions in bending deformation. In tandem with this, by introducing the deformation history affected nonlinear degradation of elastic modulus and the dimensional change of tube section into the analysis of unloading process, an analytical springback model was established. By taking the rotary draw bending of high-strength titanium tubes as a case study, the developed analytical modelwas carefully evaluated, showing its good efficiency for springback prediction—particularly for the large-angle (≥ 90 deg.) forming cases with an average relative error below 5.79%. Based on the model, the effects of the critical parameters related to material, geometry, and process on neutral layer shifting, moment, and springback were thoroughly studied for a better understanding of the sensitivity of springback to these influential factors.

Original languageEnglish
Article number106516
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - 15 Aug 2021


  • Analytical solution
  • Dimensional accuracy
  • Springback
  • Tension-compression asymmetry
  • Tube bending

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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