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Research on the axial elongation and springback law of thick-walled tubes in cold bending forming

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Abstract

The axial elongation and springback problems of tube bending need to be solved respectively, to realize the “no allowance bending” and “flange welding prior to bending” processes for ship thick-walled tubes. The axial elongation and springback analytical models of the tube bending process are established respectively based on the force balance condition, comprehensively considering the influence law and mechanism of geometric and material intrinsic parameters. The relationships between the axial elongation and forming angle, the bending angle, and forming angle are found respectively. A formula for calculating the start bending point position of the tube is obtained according to the geometric relationship after springback. The finite element (FE) model of the thick-walled tube is established based on the ABAQUS platform; the processes of tube bending and springback are simulated. The accuracy of the established FE model and theoretical analysis models is verified through tube bending experiments. The influence of main process parameters on the axial elongation and springback of the tube bending is analyzed. The results show that for tubes with the same materials, in the scope of engineering application, both the axial elongation and the bending angle have linear relations with the forming angle, and they are not through the origin of the coordinate; the axial elongation of the tube bending increases with the increasing of the forming angle; the springback angle increases with the increasing of the bending angle. At last, the applications of axial elongation and springback law are proposed.

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Abbreviations

\(E\) :

Elastic modulus

\(\mu\) :

Poisson’s ratio

\(\sigma_{s}\) :

Yield stress

\(\sigma\) :

Real stress

\(\sigma_{ij}\) :

Shear stress

\(\sigma_{{{\text{ro}}}} ,\sigma_{{{\text{ri}}}}\) :

Radial stress of the outer/inner arc portion

\(\sigma_{\theta \mathrm o} ,\sigma_{\theta \mathrm i}\)  :

Tangential stress of the outer/inner arc portion

\(\varepsilon_{{\text{r}}}\) :

Radial strain

\(R\) :

Bending radius

\(\rho\) :

Radius of stress and strain NL

\(R_{{\text{i}}}\) :

Radius of inner ridge

\(t\) :

Tube initial wall thickness

\(t_{{{\text{om}}}}\),\(t_{{{\text{im}}}}\) :

Minimum/maximum wall thickness

\(D\) :

Tube outer diameter

\(y_{{\text{o}}} ,y_{{\text{i}}}\) :

Boundary distance of elastic and outer/inner plastic deformation zone

\(\alpha_{\sigma }\) :

Position angle of stress and strain NL

\(M\) :

Total bending moment

\(M_{{\text{e}}}\) :

Bending moment of elastic deformation zone

\(M_{{{\text{pi}}}}\) :

Bending moment of inner plastic deformation zone

\(\theta\) :

Tube bending angle

\(\Delta \theta\) :

Springback angle

\(l_{{\text{s}}}\) :

Start bending length

\(n\) :

Strain hardening exponent

\(K\) :

Strength coefficient

\(\varepsilon_{s}\) :

Yield strain

\(\varepsilon\) :

Real strain

\(\varepsilon_{ij}\) :

Shear strain

\(\sigma_{\alpha }\) :

Circumferential stress

\(\varepsilon_{\alpha }\) :

Circumferential strain

\(\varepsilon_{\theta }\) :

Tangential strain

\(R^{\prime}\) :

Forming radius

\(R_{{\text{o}}}\) :

Radius of outer ridge

\(e_{{\text{n}}}\) :

Stress and strain NL shifting displacement

\(t^{\prime}\) :

Tube forming wall thickness

\(\Delta t_{{\text{o}}}\),\(\Delta t_{{\text{i}}}\) :

Wall thickness changing of outer/inner ridge line

\(r\) :

Tube inner radius

\(\alpha ,\beta\) :

Position angle of boundary of elastic and outer/inner plastic deformation zone

\(\varphi\) :

Position angle in cross section

\(\overline{t}_{{\text{o}}} ,\overline{t}_{{\text{i}}}\) :

Average thickness of inner/outer arc portion

\(M_{{{\text{po}}}}\) :

Bending moment of outer plastic deformation zone

\(I\) :

Cross-sectional moment of inertia

\(\theta^{\prime}\) :

Tube forming angle

\(\Delta l\) :

Axial elongation

\(\varepsilon_{{\text{p}}}\) :

Plastic strain

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Funding

This work was supported by the National Natural Science Foundation of China (No. 51779200).

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Authors and Affiliations

  1. Ministry of Education, Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Wuhan, 430063, China

    Huan Zhang & Yong Hu

  2. School of Transportation, Wuhan University of Technology, Wuhan, 430063, China

    Huan Zhang & Yong Hu

Authors
  1. Huan Zhang
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  2. Yong Hu
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Contributions

Huan Zhang: study conception and design, theoretical derivation, acquisition of data, analysis and interpretation of data, drafting of manuscript. Yong Hu: critical revision, study conception and design, funding acquisition.

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Correspondence to Yong Hu.

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Zhang, H., Hu, Y. Research on the axial elongation and springback law of thick-walled tubes in cold bending forming. Int J Adv Manuf Technol 120, 669–689 (2022). https://doi.org/10.1007/s00170-022-08794-0

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