Abstract
Wrinkling is a significant challenge associated with the forming of tubes via diameter reduction. The work reported herein employed elastoplastic principles to assess the external pressure diameter reduction forming process by generating a strain diagram showing the occurrence of critical instability. This diagram can be used to effectively predict the appearance of wrinkling defects during forming. The Donnell linear buckling theory together with a bilinear material model was used to derive an expression for the critical external pressure leading to wrinkling instability, employing constant tube end conditions and a uniform external pressure, and the effects of forming conditions and material parameters on wrinkling were explored. During experimental trials, AA6061 tubes were formed via diameter reduction in conjunction with varying heat treatment conditions using the solid granule medium forming process. A Vialux portable mesh strain tester was employed to collect relevant data to verify the critical instability points, and the effects of various factors on resistance to wrinkling were investigated. An analysis of the experimental results demonstrates that the conclusions of the theoretical analysis are correct.
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Abbreviations
- C :
-
Micro unit
- MN :
-
Tube-free deformation zone
- \( \overline{\sigma} \) :
-
Equivalent stress
- σ s :
-
Yield stress
- K :
-
Linear enhancement coefficient
- \( \overline{\varepsilon} \) :
-
Equivalent strain
- q :
-
External pressure
- δ :
-
Tube wall thickness
- σ θ, σ z :
-
Hoop, axial stress
- r θ,r z :
-
Hoop, longitudinal curvature radius of the micro unit C
- r z :
-
Longitudinal curvature radius of the micro unit C
- L :
-
Tube blank deformation zone
- α:
-
Half of the centering angle of the tube blank free deformation area
- r t :
-
Fillet of the mold
- k :
-
Stress ratio (k = σz/σθ)
- ε θ,ε z :
-
Hoop, axial strain
- δ i :
-
Thickness of the deformed tube
- δ 0 :
-
Thickness of the initial tube
- λ :
-
Strain ratio (λ = εz/εθ)
- E :
-
Elastic modulus
- E t :
-
Plastic tangent modulus
- r, θ, x :
-
Radial, ring, and axial coordinate respectively
- w, u, v :
-
Radial, axial, and hoop displacement
- q cr :
-
Critical buckling pressure
- μ :
-
Poisson ratio
- R :
-
Radius of the tube blank neutral layer
- Z :
-
S.B. Bathorf parameter \( Z=\sqrt{1-{\mu}^2}\frac{L^2}{Rt} \)
- n :
-
Circumferential buckling wave number
- q s :
-
Initial yield outer pressure
- σ θ−s :
-
Yielding hoop stress
- k s :
-
Yielding stress component ratio
- r θ−cr, r z−cr :
-
Hoop, longitudinal curvature radius of the buckling moment
- σ θ−cr :
-
Instability hoop stress
- δ i :
-
Wall thickness of deformed tube blank
- S i :
-
Superficial area of tube blank neutral layer at some moment
- ε δ−cr, ε z−cr, ε θ−cr :
-
Buckling strain of normal, longitudinal and hoop direction
- δ 0 :
-
Test tube blank thickness
- D 0 :
-
Test tube blank diameter
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Funding
The present work is financed by the National Natural Science Foundation of China (contract no. 51605420, 51775480, 51775481). We thank Liwen Bianji, Edanz Editing China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript .
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Zhao, C., Han, Z., Du, B. et al. Wrinkling prediction of aluminum alloy tubes during reduced diameter compression forming. Int J Adv Manuf Technol 106, 65–75 (2020). https://doi.org/10.1007/s00170-019-04432-4
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DOI: https://doi.org/10.1007/s00170-019-04432-4