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Effects of Cross-Sectional Ovalization on Springback and Strain Distribution of Circular Tubes Under Bending

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Abstract

Springback and cross-sectional ovalization are two important defects in the bending formation of tubular parts. In this article, an analytic model considering ovalization is presented to calculate the springback and tangential strain in tube bending. Compared with the calculation neglecting ovalization, the proposed model could better predict the trends of springback angle over bending radius ratio and wall thickness ratio. Moreover, calculation of the tangential strain indicates that the bending deformation is more severe in the middle than at the ends of a bent tube. Through comparison of the results of this model and the calculations neglecting ovalization, it is shown that the effects of ovalization on springback are negligible only if the bending radius ratio and the wall thickness ratio are large enough. Also, the influence of ovalization differs a lot from one material to another.

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Abbreviations

R :

bending radius (curvature radius of neutral surface before unloading)

R′:

curvature radius of neutral surface after unloading

d :

outer diameter

r :

outer radius

t :

wall thickness

R/d :

bending radius ratio

t/d :

wall thickness ratio

φ:

bending angle (angle before unloading)

φ′:

angle after unloading

Δφ:

springback angle

θ:

tangential position on the bent tube

α1, α2 :

circumferential positions on the cross sections of the tube

ρ:

curvature radius before unloading

ρ′:

curvature radius after unloading

a :

length of the major axis of the distorted cross section

b :

length of the minor axis of the distorted cross section

E :

Young’s modulus

C :

strength coefficient

n :

strain hardening exponent

ε:

tangential strain

σ:

tangential stress

εmax :

maximum tangential strain (tangential strain at the extrados)

D :

calculation deviation rate of springback angle

B :

breadth of the cross section

I :

cross-sectional moment of inertia

M :

bending moment

UDR:

uniformly distorted region

NUDR:

non-uniformly distorted region

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Authors and Affiliations

  1. School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Yafei Liu & Daxin E

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  1. Yafei Liu
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  2. Daxin E
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Correspondence to Daxin E.

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Liu, Y., E, D. Effects of Cross-Sectional Ovalization on Springback and Strain Distribution of Circular Tubes Under Bending. J. of Materi Eng and Perform 20, 1591–1599 (2011). https://doi.org/10.1007/s11665-010-9813-z

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  • DOI: https://doi.org/10.1007/s11665-010-9813-z

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