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A different approach to estimate the process parameters in tube hydroforming

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Abstract

An enhanced unfolding inverse finite element method (IFEM) has been used together with an extended strain-based forming limit diagram (FLD) to develop a fast approach to predict the feasibility of tube hydroforming process of concept part and determine where the failure or defects can occur. In tube hydroforming, the inverse IFEM has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this study is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this article a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the extended strain-based forming limit diagram, the components of strain can lead us to measure the potentials for failures during the deformation. The extended strain-based FLD based on the Marciniak and Kuczynski (M-K) model has been computed and used to predict the onset of necking during tube hydroforming. The extended strain-based FLD is built based on equivalent plastic strains and material flow direction at the end of forming. This new forming limit diagram is much less strain path dependent than the conventional forming limit diagram. Furthermore, the use and interpretation of this new diagram is easier than the stress-based forming limit diagram. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software. The results indicate that the fluid pressure estimated by this method is 2.7 % greater than the results obtained by the experiment in the square bulging sample. In addition, the fluid pressure estimated in the free bulge sample is 5.6 % greater than the experimental results.

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Abbreviations

IFEM :

Inverse finite element

FLD :

Forming limit diagram

3D :

Three dimensional

CST :

Constant strain triangle

\( \widehat{n} \) :

Element normal vector

\( \overrightarrow{ AB},\overrightarrow{ AC} \) :

Sides of the element

\( {\overrightarrow{K}}_{rot} \) :

Rotation vector calculated for each element

\( \widehat{k} \) :

Unit vector in Z direction

θ :

Angle of rotation for each element calculated in unfolding step

\( R\left({\overrightarrow{K}}_{rot},\theta \right) \) :

Finite rotation operator

K 1, K 2, K 3 :

Components of \( {\overrightarrow{K}}_{rot} \)

2D :

Two dimensional

K :

Global stiffness matrix

F e :

Force vector of each element

K e :

Stiffness matrix of each element

Δu e :

Nodal displacement vector

U :

Global displacement vector

F :

Assembled force vector

σ 1, σ 2, σ 3 :

Stress components

ρ 1, ρ 2 :

Circumferential and longitudinal radii of curvature of deformation zone

P :

Fluid pressure

t :

final thickness of tube

ε 1, ε 2 :

Components of strain

ε e :

Equivalent strain

σ e :

Equivalent stress

λ′:

The ratio of equivalent strain to equivalent stress using in levy-Mises flow rule

F jack :

Part of the axial force causing the displacement of the tube

R 0 :

Initial tube radius

t 0 :

Initial tube thickness

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science & Technology, Tehran, Iran

    R. Hashemi

  2. Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    M. Bostan Shirin, M. Einolghozati & A. Assempour

Authors
  1. R. Hashemi
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  2. M. Bostan Shirin
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  3. M. Einolghozati
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  4. A. Assempour
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Correspondence to R. Hashemi.

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Hashemi, R., Shirin, M.B., Einolghozati, M. et al. A different approach to estimate the process parameters in tube hydroforming. Int J Mater Form 8, 355–366 (2015). https://doi.org/10.1007/s12289-014-1175-x

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  • DOI: https://doi.org/10.1007/s12289-014-1175-x

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