Finite element analysis of dual hydroforming processes

Journal of Materials Processing Technology 145 (2004) 59–65

Finite element analysis of dual hydroforming processes

Nishant Jaina, Jyhwen Wangb,∗, Richard Alexandera,ba Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA

b Department of Engineering Technology and Industrial Distribution, Texas A&M University, College Station, TX 77843, USA

Received 3 January 2003; accepted 26 June 2003

Abstract

The tube hydroforming process has gained increasing attention in recent years. With the hydroforming process, manufacturers canrealize substantial cost savings as it provides reduced part count, increased part strength and stiffness, and reduced weight. Coordinationof the pressurization and feeding curves is critical to generate successful parts without fracture or wrinkling failure. Herein a new processparameter, counter pressure, is introduced to achieve favorable tri-axial stress state during deformation process. This paper will establishthe merits of applying external counter pressure in tube hydroforming. It is observed that the counter pressure will provide back supportto the tube material. Excessive thinning and premature wrinkling could be prevented. Thus, larger tube expansion could be achieved. Theprocess will be referred as dual hydroforming.© 2003 Elsevier B.V. All rights reserved.

Keywords: Tube expansion; Counter pressure; Dual hydroforming

1. Introduction

Tube hydroforming has gained increasing attentionand has become one of the indispensable manufacturingtechniques in recent years. Hydroformed tube parts haveincreased strength and stiffness, retain their structural in-tegrity, offers reduced part count, thus reduces overallmanufacturing cost. The success of tube hydroforming pro-cess is dependent on an appropriate combination of internalpressure and axial feed at the tube ends. One of the keyconcerns is to control the deformation process so as tomaximize the expansion such that more complex shapes invarious applications can be achieved. Analogously, for agiven shape, a higher strength, lighter weight, less formable,or lower cost material can be adopted.

Generally tube deformation is controlled by ‘gradually’increasing the internal pressure during the application of ax-ial load. In reality, the result of forming process deviates de-pending on the load paths. Thus, process design and controlplays a key role in the success or failure of the tube hydro-forming operation. The objective of this study is to extendthe boundary of current tube hydroforming process capabil-ity through application of the counter pressure. The process

∗ Corresponding author.E-mail address: [email protected] (J. Wang).

will be referred to as dual hydroforming. Dual hydroformingwill impart better stability to the process, leading to theopportunities of optimizing the deformation process.

The motivation to apply the counter pressure in THF pro-cess comes from the fact that counter pressure has been usedeffectively in many manufacturing processes to enhance themanufacturing capabilities. The most notable work relatedto the counter pressure approach is in sheet hydroformingresearch[1–4]. It was suggested that counter pressure couldsuppress wrinkling and prevent fracture. Analytical modelswere developed by Yossifon and coworkers[5,6] to predictthe results in deep drawing. It was shown that a pressureload path lying between the derived upper (causes fracture)and lower (causes wrinkling) limits can be identified andrecommended for practical use. Similarly, Lo et al.[7] usedthe upper bound–lower bound approach to develop loadpaths for hemispherical stretch forming. The punch deformsthe workpiece by forcing it against a controlled pressurizedfluid. It can be observed that deformation geometry of thehemispherical stretch forming is comparable to that of thepole on the free bulging of tubes. As a part of the hydro-forming research at the NSF Engineering Research Centerat The Ohio State University, Liu et al.[8] evaluated sheetmetal formability using viscous pressure forming (VPF)dome test. Based on the proposed critical damage valuecriterion and the experimental results, it was found that theformability of the sheet stretched with viscous pressure is

0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0924-0136(03)00862-8

60 N. Jain et al. / Journal of Materials Processing Technology 145 (2004) 59–65

Fig. 1. Application of counter force for T-shaped protrusion in tubehydroforming.

higher than that obtained with a solid hemispherical punch.In their paper, the feasibility of applying counter pressurewas discussed but not implemented. Ahmed and Hashmi[9] simulated bulge forming of a circular plate by applyingrestrained load on three central elements at the top surface.The restrained forming resulted in better configuration.The papers presented by Nakagawa et al.[10] and Aminoet al.[11] summarize the various merits and applications ofhydraulic counter-pressure deep drawing. Industrial appli-cations of the process were also demonstrated.

Successful tube hydroforming requires the bulging to takeplace without causing any type of instability like bursting,necking, wrinkling or buckling. Excessive pressure withoutsufficient axial feed will cause the tube to fracture while ex-cessive application of axial force will lead to wrinkling ofthe tube. Thus, as shown inFig. 1, the counter force has beenused on significant regions in T-shaped and Y-shaped pro-trusion that allow the internal pressure to be increased be-yond the critical value[12]. It was reported by Tonghai et al.[13] that use of counter force in elastomer forming processincreased the obtainable protrusion height to 1.5 times of theoriginal diameter for low carbon steel tubes whereas expan-sion ratio without counter force was found to be 1.2. Koc andAltan [12] presented various application of counter force.Counter punches are used in some cases where the requiredexpansion is more than what tube material can normally sus-tain. Therefore, counter load that restrain the expansion ina controlled manner is applied at critical region rather thanusing axial loading, which may cause wrinkling. It becomesnecessary to apply counter force where the chance of feed-ing material into section is less and the amount of expansionis large. The paper also presented the analytical model tocalculate counter force necessary to maintain a tri-axial stateof stress at the bulged region as a function of stress ratio, in-ternal pressure, flow stress, protruding radius and thickness.

As mentioned earlier, the crucial goal in THF is to obtainbetter part without causing any type of instability. The pointis fracture failure can be prevented by controlling the defor-mation rather than providing the axial force that may causewrinkling. But in some cases like axisymmetric bulging,counter force cannot be applied due to inherent constraint.The part geometry precludes the case of counter punch. It isnot possible to design a counter punch tooling for a simple

Fig. 2. Application of counter pressure (dual hydroforming) in axisym-metric bulge forming.

axisymmetrical bulge forming process. Thus, the applica-tion of a dual pressure system as shown inFig. 2to increasethe bulge height, is a logical alternative.

Finite element simulation provides an opportunity tostudy the effect of counter pressure on free bulging in anaxisymmetric case. In this paper, finite element analyseshave been carried out to simulate different hydroformingconditions. Finite element analysis (FEA) model has beendeveloped using LS DYNA3D and utilizing Hypermesh aspre-processor and Hyperview as post-processor. Results ofthe dual hydroforming simulations with discussion havebeen presented. Lastly, the conclusion and further scope ofwork in dual hydroforming has been discussed.

2. Modeling of tube hydroforming processes

Finite element modeling provides a powerful tool fordesign engineers. Since the main interest is to demonstratethe merits of dual tube hydroforming, simulation of tubehydroforming with no external counter pressure was firstconducted to establish a baseline for comparison. The de-velopment of validated FEA is required to access accurateresult, the simulation technique is validated based on exper-imental data presented by Hutchinson[14] and MacDonaldand Hashmi[15].

In this simulation, a model of a cylindrical tube with24.12 mm diameter, 107.00 mm length, and 1.37 mm thick-ness was constructed to simulate axisymmetric bulge form-ing. The material properties used are shown inTable 1. Asmost of the commercial tube hydroforming processes, axialstroke and internal pressure are prescribed in the simulation.Since Hutchinson performed the experiments with axial

Table 1Material properties

Material properties

Young’s modulus (MPa) 124× 103

Yield strength (MPa) 160Tangent modulus (MPa) 925Poisson’s ratio 0.3Density (kg/mm3) 8.9 × 10−6

Ultimate tensile stress (MPa) 330

N. Jain et al. / Journal of Materials Processing Technology 145 (2004) 59–65 61

Fig. 3. Comparison of bulge heights obtained for various simulations withexperimental results.

force (instead of axial stroke) for various internal pressures,it was necessary to convert the axial force to approximateaxial feed. For this purpose, the graph of ratio of final to ini-tial tube length (in %) versus compressive axial load (in kN)as presented by Hutchinson was used. The axial force of85 kN in the experiment was found to be close to 15.00 mmaxial stroke. Based on this condition, the bulge heights wereobtained for various internal pressures. The simulation runs1–4 represent internal pressures of 27.60, 34.50, 41.40, and48.30 MPa given by Hutchinson. As shown inFig. 3, thebulge heights obtained from the simulations agree reason-ably well with the experimental results. While recordingthe minimum tube thickness versus bulge height in one ofthe runs, the simulation result is also close to that of theexperiment as shown inFig. 4. The possible reasons forslight disagreement could be because of the material model(the tubular material properties used in the simulations weretaken from the compression test by MacDonald and Hashmi[15]), the size of mesh, and the coefficient of friction.

Fig. 4. Comparison of deformation for axisymmetric bulge forming.

Fig. 5. Finite element model showing tube, die and punch for tubehydroforming.

3. Simulation of dual hydroforming processes

In the simulations carried out in this section, the samefinite element model of the cylindrical tube (24.12 mm di-ameter and 107 mm length) with quadrilateral shell elementwas constructed to simulate axisymmetric free bulge form-ing. The discretized quarter model is as shown inFig. 5.The die and the punch were considered to be rigid by theanalysis and are modeled as rigid surface. A master–slavecontact approach was used in the analysis where the diewas considered as the slave surface, and the surface of thetube was considered as the master surface. While the dieand punch were assigned rigid material properties, the tube


Fig. 6. Variation of pressure and stroke with time for Load Pattern 1.




was assigned a piecewise linear elastic–plastic materialmodel.

Three types of loading were considered in the simulations.The internal hydraulic pressure was applied as a uniformlydistributed load to the tube inner surface and was introducedas a linearly increasing function of time. The axial feedwas applied as a prescribed displacement of the punch atthe edge of the tube, also as a linearly increasing functionof time. The external counter pressure was applied usingLOAD MASK option in LS DYNA [16], which facilitatesto apply a distributed load to a subset of elements of tubewithin a fixed global box.

Three different loading conditions were analyzed. The ini-tial run was without applying external counter pressure asLoad Pattern 1 shown inFig. 6. Keeping the same internalpressure and axial feed curves, the two analyses followedwere for different external counter pressure curves. InFig. 7(Load Pattern 2), the external pressure is applied as a linearlyincreasing function. To understand the counter pressure ef-fects in stress and strain distribution, the application of exter-nal pressure is delayed for 3.0 ms in Load Pattern 3 (Fig. 8).

4. Simulation results and discussion

To demonstrate the effects of different loading conditions,the stress, strain, bulge height, and tube thickness data werecollected.Fig. 9 shows the distribution of von Mises stressdeveloped at the top of the bulge during the simulations.The stress state at a given time and location varies with theprocess history and the design and control of the load paths.The von Mises stress for the Load Pattern 1 (without counterpressure) is higher than that of Load Pattern 2 (with counterpressure). It can be found that the curves for Load Patterns1 and 3 closely follow each other till the application ofcounter pressure (at 3.0 ms). Due to back support, increase invon Mises stress in Load Pattern 3 becomes less significant.As tabulated inTable 2, the maximum von Mises stress

Fig. 9. von Mises stress plot for various load patterns.

Table 2Maximum von Mises stress for bulge height of approximately 10 mm fordifferent load patterns

Load pattern Bulge height(mm)

Maximum von Misesstress (MPa)

No counter pressure(Load Pattern 1)

10.094 191.455

Counter pressure(Load Pattern 2)

10.055 165.275


10.130 176.090

Fig. 10. von Mises stress contour plot for tube hydroforming with noexternal pressure.

for similar bulge height is lower for the dual hydroformingprocesses.

The von Mises stress contour plot of the bulged tube withno external pressure and dual hydroforming is shown inFigs. 10 and 11, respectively. With the external pressureadded as a process parameter, stress states in the deformationprocess can be better controlled. Dual hydroforming haswell distributed von Mises stress in comparison to the onewithout counter pressure.


Fig. 11. von Mises stress contour plot for dual hydroforming.

Fig. 12. Thickness contour plot for tube hydroforming with no externalpressure.

The thickness contour plot of the bulged tube with no ex-ternal pressure and dual hydroforming is shown inFigs. 12and 13, respectively. The top bulge part of the tube is sen-sitive to thinning. There is large variation of thickness for

Fig. 14. Comparison of bulge height and minimum thickness for various load patterns.

Fig. 13. Thickness contour plot for dual hydroforming.

the hydroforming without counter pressure relative to dualhydroforming. It is clear from the thickness contour plotsthat, dual hydroforming results in well distributed and moreuniform thickness. Similarly, the minimum thickness of theelement traces the same path for Load Patterns 1 and 3 ini-tially. With the application of counter pressure (after 3.0 ms),more uniform strain distribution occurs (rather than beingconfined to a small area) thereafter.

Monitoring the elements that end up with the minimumthickness in these runs,Fig. 14shows the thickness historyof these elements versus bulge height. The simulations re-sulted in different bulge heights. However, the simulationsshowed that at the same bulge height, different counterpressure load paths could lead to different minimum thick-ness on the tube. On the other hand, for a given minimumthickness, different counter pressure could result in differentdegree of tube expansion. As shown inTable 3, at the min-imum thickness of around 1.20 mm, the dual hydroformingprocess (Load Patterns 2 and 3) can result in more than20% increase in bulge height. Thus, it can be concluded that


Table 3Bulge height for minimum thickness of approximately 1.20 mm for dif-ferent load patterns

Load pattern Minimumthickness (mm)

Bulge height(mm)

No counter pressure(Load Pattern 1)

1.206 6.865


1.203 8.338


1.203 7.592

different and favorable strain distributions can be obtainedfrom well-coordinated dual hydroforming processes.

5. Conclusion

The simulations established that better final bulged con-figuration could be obtained by the application of counterpressure. The new process parameter has enabled favorabletri-axial stress state during deformation. The counter pres-sure provided back support to the tube material and henceexcessive thinning and premature wrinkling could be pre-vented. Thus, larger tube expansion could be achieved. Asknown, the stress state at a given time and location varieswith the process history, design and control of the loadpaths become a critical task in hydroforming operation.With the use of the dual pressure system and end feeding,stress state of the tube can be carefully prescribed. Further,the ability of controlling the stress state will lead to betterdeformation paths and thus provide the basis for processoptimization. Additionally, analytical model can be devel-oped to facilitate the understanding of stress propagation indual tube hydroforming. As the loading condition in dualhydroforming is different from that of the previous work, ananalytical model could be developed to calculate the effec-tive stress and determine the yielding of the tube under dualhydroforming. As part of further investigation, effect ofdifferent parameters like hardening coefficient, anisotropicvalue, etc. in dual tube hydroforming could be established.

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Finite element analysis of dual hydroforming processes

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