an adaptive simulation approach designed for tube hydroforming processes

Journal of Materials Processing Technology 159 (2005) 303–310

An adaptive simulation approach designed for tubehydroforming processes

A. Aydemira,∗, J.H.P. de Vreea, W.A.M. Brekelmansa, M.G.D. Geersa,W.H. Sillekensb, R.J. Werkhovenb

a Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlandsb TNO Industrial Technology, Department of Manufacturing Development, PO Box 6235, 5600 HE Eindhoven, The Netherlands

Received 15 July 2003; received in revised form 17 May 2004; accepted 20 May 2004

Abstract

The efficiency of a tube hydroforming process is largely dependent on the process control parameters (i.e. the internal pressure and theaxial feeding) since they determine the occurrence of forming limits such as wrinkling and bursting. Therefore, these parameters should becarefully selected. In this paper an adaptive method is presented to obtain a more efficient process control for tube hydroforming processes.This method avoids the onset of wrinkling and bursting via dedicated stability criteria. The wrinkling criterion uses an energy-basedindicator inspired on the plastic bifurcation theory. For necking, followed by bursting, a criterion based on the forming limit curve isemployed. Applying these two criteria, the process parameters are adjusted during the simulation via a fuzzy knowledge based controller(FKBC). A case study is carried out for the hydroforming of a T-shape part using the designed adaptive system in combination with thefinite element method. For the simulations ABAQUS/Explicit is used.© 2004 Elsevier B.V. All rights reserved.

Keywords: Tube hydroforming; Process optimization; Adaptive simulation approach

1. Introduction

Hydroforming is a manufacturing technology that wasdeveloped in the 1960’s already. Widespread application,however, did not set in immediately. Today, hydroformingis still considered as a promising technology in forming.This technology, compared to conventional processes, stilloffers new possibilities with various fields of application.However, the effective use of the hydroforming technologyin the manufacturing industry has triggered new challengesin terms of the boundary conditions specified for the formingprocess and the material properties.

A classical example of a hydroforming process is visu-alized inFig. 1. The process is controlled by two types ofloads: an internal pressurepint and an axial forceFend. Thehydroforming process and its limitations corresponding todifferent loading paths can schematically be represented, asdepicted inFig. 2. The shaded area in this figure is the pro-cess window. Any path lying within this window is expected

∗ Corresponding author. Tel.:+31 40 247 58 94;fax: +31 40 244 73 55.E-mail address: [email protected] (A. Aydemir).

to result in a product without defects due to buckling orfracture.

If the axial force is very high while the internal pressureis too low, buckling and wrinkling may occur. If the axialforce is too low and the internal pressure is very high, thetube may burst. The virtual process window shown inFig. 2is relatively wide, while linear boundaries on both sides areassumed. However, for many processes there is often justa small non-linear corridor for the acceptable loading pathsrequired to achieve a product without failure. Therefore, fora successful application of a hydroforming process, knowl-edge and control of the process limits is important, in addi-tion to the selection of suitable components, materials anda proper material preparation.

The conventional way of designing a hydroforming pro-cess starts with the definition of the basic parameters such asthe die and tube geometries and the selection of the material.Then, a loading path is estimated to test the feasibility ofthe planned forming process. Basic information to ensure astable production process and high-quality parts, as well asthe knowledge of possible parameter combinations resultingin good or rejected parts, can be obtained via finite element(FE) simulations or real experiments[1–3]. Various sce-narios can be attempted to obtain the required feeding and

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2004.05.018

304 A. Aydemir et al. / Journal of Materials Processing Technology 159 (2005) 303–310

Fig. 1. Tube expansion process.

pressure histories. Especially for complex processes manytrial-and-error cycles will be required to obtain an acceptableresult. Therefore, the development of a new hydroformingprocess often deals with a considerable experimental effortand associated costs. Sometimes, the experiments will in-dicate that it is not possible to produce the part along anyloading path. In that case, the load control parameters haveto be changed, after which the whole procedure has to berepeated.

Since learning via a trial-and-error method is costly interms of money and time (especially for experiments but alsofor non-optimized simulations), an enhanced process simu-lation may offer better possibilities. The enhancement canbe achieved by including a control algorithm in the processsimulation to detect and avoid premature failure cases suchas buckling, wrinkling or bursting and to adjust the processparameters, i.e. the internal pressure and the axial force, inan adequate way. A flow chart of this type of process de-sign is shown inFig. 3. This kind of process simulation iscalled an adaptive process simulation since the process pa-rameters are continuously updated according to the new cir-cumstances during the simulation.

Currently, there is no unique method applicable for everytype of geometry, to determine the appropriate process pa-rameters. There are some analytical solutions available, butonly for very simple geometries. However, several strategiescan be used together with a FE analysis to obtain a suitableprocess plan. Most common used strategies are given below:

Fig. 2. Process window allowing different loading paths (adopted from[6]).

Fig. 3. Process design with enhanced simulation capabilities.

• The conventional approach: The process parameter curveis estimated based on some simple metal forming equa-tions.

• The self feeding approach: The process parameter curveis selected from a qualified family of curves. The startingpoint is to run an initial FE simulation without any forcedaxial feeding on the tube edges and with zero friction.Then, the simulations are repeated with modified param-eters until a satisfactory result is achieved.

• The optimization approach: The process parameter curveis obtained from a series of simulations with an appro-priate goal or criterion to be optimized, for example thethickness distribution.

• The adaptive approach: The process parameter curve isdetermined as the result of one single simulation with thehelp of an on-line control strategy.

So far, optimization and adaptive approaches seem to bemost promising in tube hydroforming process design, seefor example[4,5]. In this paper an adaptive system is pro-posed to obtain adequate process parameters for hydroform-ing, with the incorporation of a wrinkle indicator, a neckingindicator and a fuzzy knowledge based controller (FKBC).A novel approach is presented towards (adaptive) simulationof hydroforming processes, where the focus lies on the usedmethodology and not on the outline of a ‘ready to use’ andfully validated optimization tool for industrial applications.The method will be applied to design the hydroforming pro-cess of a T-shaped component as an example. The resultsshow that, in qualitative sense, an agreement with observa-tions in practice has been achieved.

2. Adaptive simulation approach

An adaptive approach is based on the ability to early de-tect the onset and growth of defects, or the occurrence of

A. Aydemir et al. / Journal of Materials Processing Technology 159 (2005) 303–310 305

Fig. 4. Scheme of the adaptive simulation procedure.

unwanted situations during the process and promptly reactto them. Several applications of this approach can be foundin [6–8]. A simplified scheme of the approach is given inFig. 4. Since the finite element method is applied using anincremental procedure, at the end of each increment thereis a possibility to modify the load incrementations for thesubsequent step. In this study, the loads are modified via therate of the incremental internal pressure (α) and the rate ofthe incremental axial force (β). The ultimate goal is the se-lection of a feasible loading path using a minimum numberof simulations, or even within a single run.

Numerical simulation based on the finite element methodwith an implicit or explicit integration scheme has becomean important tool to simulate hydroforming processes in-volving a complicated geometry and complex boundary con-ditions, including friction[9]. When an implicit method isused to predict possible failure in a product, mostly, an ini-tial imperfection, for example a specific mode shape and/ora material imperfection, is assigned to the original model.Unlike the implicit solver, the explicit method can generatefailure, for example wrinkling, due to the accumulation ofnumerical errors without any physical origin.

There are several commercial software packages, widelyused in research centers as well as in industry, such as AUT-OFORM [10], PAMSTAMP [11], etc., which are dedicatedto analyze metal forming processes. Usually these packagesdo not present an extensive flexibility for the implementa-tion of user-supplied subroutines. Since the present researchaims to pursue a new approach rather than to discuss thepossibilities of dedicated commercial software, in this studythe simulations are carried out using ABAQUS/Explicit[12]. This selection is motivated by the accessibility of thiscode and the user-oriented features for own developments.ABAQUS/Explicit can be applied in combination with thesubroutines VUMAT and VDLOAD: in the subroutine VU-MAT the strain and the stress states are calculated, in thesubroutine VDLOAD the loads are modified.

In designing an adaptive system for tube hydroformingprocesses, two important aspects in the whole procedure canbe recognised: a reliable wrinkle predictor and an indica-tor for the probability of necking/fracture. The method pro-posed in this study readjusts the process parameters based

Fig. 5. Strategy for the adaptive finite element simulation.

on some criteria at the end of each incremental solution, inorder to avoid the growth of wrinkles and to delay possi-ble bursting. The general strategy of the proposed method isto maximize the axial feeding and to minimize the internalpressure, while preventing the development of irreversiblewrinkles and bursting. This ensures that the highest possiblewall thickness in the product is obtained. The objective isrealized by using the strategy given inFig. 5. This strategyincludes a wrinkle prediction method as well as a methodto detect the possibility of necking of the tube material. Thedeformation state defined by the deformation gradient ten-sor F is sent to the subroutine VUMAT with some addi-tional information necessary to evaluate the input for thecontroller. The input valueImin of the controller is the crit-ical value supplied by the wrinkle indicator and the otherinput parameterd is the critical value of the necking indi-cator in the product. Then, the controller determines whatthe values ofα andβ will be, based on the algorithms andadditional knowledge inserted in the controller.

2.1. Prediction of wrinkling

In metal forming the concept of a ‘wrinkle’ is used todenote short-waved out-of-plane deformations. Wheneverthe material is in a state of in-plane compression, thereis a potential risk for wrinkles. The initiation and growthof wrinkles are influenced by many factors such as thestress ratio, the mechanical properties, the geometry of theworkpiece and the contact conditions. The analysis of thewrinkling initiation and growth considering all these factorsis complicated because the associated effects are complexand the wrinkling behavior may show a wide scatter forsmall deviations of the conditions, as common in instabilityphenomena. Studying wrinkling, therefore, has been car-ried out case-by-case for a given process, and a generalisedwrinkling criterion that can be used effectively for variousprocesses has not been proposed and accepted yet[13].

There are several geometry-based wrinkle indicatorswhere a wrinkle is detected from predominantly geomet-rical considerations. Unfortunately, most of them are for aspecific product and they cannot be used directly for arbi-trary geometries. The most often used procedure for wrinkle


prediction in metals is based on the plastic bifurcation the-ory [14]. Although this theory is commonly used, the inte-gration into FE codes in its classic formulation is not trivial.Inspired by the plastic bifurcation theory, a computationally‘cheap’ and general-purpose wrinkling detection procedureis given by Nordlund[15]. This wrinkle indicator uses thestress state and the deformation to detect the wrinkle viathe local value of the second-order increment of internalwork. If the material point is under compression and ifadditionally the deformation is dominated by rotation thenmost likely a wrinkle will occur. However, there are somecases where these type of situations are dealt with withoutthe occurrence of any wrinkle. Therefore, this wrinkle in-dicator fails if a pure global rigid body rotation takes placein the process, which can hardly be expected in a real pro-cess, or if a large scale wrinkle starts to evolve[8,16]. Theassociated indicator quantityImin has, in spite of its disad-vantages, several beneficial properties for use in an adaptiveFE simulation. For example, it is generally applicable to allloading situations, including cases where contact forces andlarge elastoplastic deformations are involved. Furthermore,because its value is bounded in the interval of−1 and+1,the classification of a wrinkle is relatively easy comparedto other wrinkle indicators. Therefore, the wrinkle indica-tor defined by Nordlund is used in the present study in anadaptive framework. Note that other wrinkling criteria maybe used as well, not influencing the methodology presentedfurther on.

2.2. Prediction of necking

Bursting types of failure are related to the material forma-bility and these phenomena are difficult to quantify sincethey depend on the material used and the stress and strainconditions imposed on the workpiece. Especially for met-als, necking occurs first and is followed by bursting aftera continued forming process. Therefore, if necking can bedetected bursting might be prevented. For necking detectionseveral methods may be used[17,18]. The most popular oneis based on the actual strain state and the forming limit curve(FLC) using experimental data. FLCs are mostly assembledfrom the data obtained via several experiments with differentlinear strain paths. Since formability is strongly dependenton the deformation history, experimental determination ofthe FLCs is expensive. Therefore, also studies to determineFLCs from analytical expressions[19], or from FE simula-tions [20] are often considered in practice.

In this study, an input term for the controller is designedby calculating the shortest distanced of the strain state ofeach material point characterised byP to the material’s FLC,seeFig. 6.

2.3. The controller

Hydroforming is a rather complex deformation process.Therefore, the derivation of a direct analytical relation be-

Fig. 6. A typical forming limit diagram and the definition ofd.

tween the input and output variables is impossible for prac-tically realistic configurations. Since a lot of non-linearitiesare involved in a hydroforming process, even for simplegeometries, many assumptions are needed to arrive at ananalytical approximation. Additionally, there may be manyphysical features of the process that are not incorporated inthe analytical model used to design the controller, due to thecomplexity of the process or a lack of understanding of thephysics involved.

On the other hand, experienced process operators usu-ally possess a number of heuristic design rules which al-low them to control a process in a satisfactory manner. Asit is extremely difficult to develop techniques which casta heuristic control policy into analytical expressions, thereare other control techniques that circumvent the use of an-alytical models. A particular expert control technique em-ploying the heuristic knowledge available is known as theso-called fuzzy knowledge based controller. No further de-tails on FKBC’s will be presented here, but more informa-tion can be found, for example, in[21,22].

In this study, a FKBC is designed for tube hydroform-ing processes. When the subroutine VUMAT is called, thevalues of the wrinkle indicatorImin and the necking indica-tor d are determined. These two values constitute the inputto the controller. Then, the controller calculates the rates ofthe incremental internal pressureα and the incremental axialforceβ based on the expert knowledge inserted in it. Afterthat, when the subroutine VDLOAD is called, the load in-crements will be calculated using the recently determinedα

andβ.In the following, the designed FKBC for tube hydroform-

ing processes will be outlined. The controller prepares theoutput in order to modify the loads for the next increment.The deformation state is checked for wrinkles, as well asfor necking. In the example presented further on, the knowl-edge base used is primarily deterministic, since it includesrules relating the deformation state to the output. However,heuristic rules from practice can be added to it without anydifficulty.

2.3.1. Internal pressureAn internal pressurepint is applied to the inner surface of

the tube. For the internal pressure the update formula givenbelow is used:


pnewint = pold

int + α�pint (1)

where�pint is a predefined value,poldint the value from the

previous increment andα is considered as a fuzzy numberwith 0 ≤ α ≤ 1. Forα the following fuzzy sets are used inthe controller:

• α is ZERO (Z),• α is LOW (L),• α is HIGH (H).

Each fuzzy set is defined by a membership function. Amembership function may have different shapes, for exampletriangular, L-type, etc. In the present implementation onlytriangular, L- and�-types of membership functions are used.Necessary information on the membership functions can befound in almost any book written on fuzzy sets, for examplein [21].

2.3.2. Axial feedingFor modeling purposes, the axial feeding is obtained via

an axial forceFend applied to the rigid tools (so-called rams)at both ends of the tube, seeFig. 1. Contact conditions aredefined such that direct interaction between the die and therams is avoided. The contact between the tube end and theram is supposed to be frictionless. The axial force is modifiedaccording to:

Fnewend = Fold

end+ β�Fend (2)

where�Fend is a predefined value,Foldend the value from the

previous increment and−1 ≤ β ≤ 1. Accordingly, the axialforce is allowed to increase or decrease. Additionally,Fendis limited by a minimum force value to prevent leakage ofthe internal fluid. Here,β is considered as a fuzzy number.For β the fuzzy sets given below are used in the controller.

• β is NEGATIVE (N),• β is ZERO (Z),• β is POSITIVE (P).

2.3.3. The wrinkle indicatorFor the wrinkle indicator, three membership functions are

defined and used in the controller. Each membership func-tion classifies a wrinkle as given below:

• the wrinkle is very critical (veryCR),• the wrinkle is critical (CR),• the wrinkle is not critical (notCR).

2.3.4. The necking indicatorAssociated to the necking indicatord three membership

functions are specified, according to:

• the distanced is very close (veryCL),• the distanced is close (CL),• the distanced is not close (notCL).

In [19], a method is given to obtain the forming limits oftubular hydroforming based on plastic instability. In the im-

Fig. 7. The rule base for theα/β controller.

plementation, the FLC, which is needed to determined, isobtained using the definitions in[19]. The material proper-ties of the hydroformed tube will be given in the next sec-tions.

2.3.5. The rule baseThe rules to be implemented are usually derived from the

experience-based knowledge of the process operator and/orcontrol engineer. This is the first step to start with. This stephelps to provide an initial prototype version of the knowl-edge base. Consequent tuning of the membership functionsand rules is a necessary next step. In this study, the tuningis performed based on FE simulations.

The whole set of collected rules is given inFig. 7. Eachcell in Fig. 7 represents a rule. For example, the rule in theupper left cell can be formulated as: ‘IFthe wrinkle is verycritical (controlled by Imin) AND the deformation is veryclose to necking (controlled by d) THEN α is zero (Z) andβ is negative (N)’.

Accordingly, nine rules for bothα andβ can be distin-guished. The set of rules is complete since none of the cellsis empty. The rules ensure that as long as wrinkling is notcritical additional material is fed into the die cavity, withoutincreasing the internal pressure. As soon as a critical wrinkleis detected the internal pressure is increased by some value.To determine the output values both the wrinkle indicatorand the FLD-distance are taken into account.

3. A case study: hydroforming of T-shapes

The wrinkle indicator, the necking indicator and the con-troller are implemented into user subroutines additional tothe user subroutines VUMAT and VDLOAD. To evaluatethe indicators stress and strain states are necessary. In theused version of ABAQUS/Explicit, the user had no directaccess to the necessary stress information to evaluate thewrinkle indicator. The only way to obtain the required in-formation was application of the user subroutine VUMAT.Once VUMAT is invoked, the stresses can be calculated viaa constitutive law. Therefore, although the assumed materialbehavior is standard, it appeared to be necessary to imple-ment it inside the subroutine VUMAT.

3.1. Case description

As a well-known case study, hydroforming of a T-shapedcomponent, which is one of the most studied parts among


Fig. 8. An assembled view of the parts involved in the process.

T-branching tubes, is simulated. Different variants of thisT-shape can be distinguished. For example, the bulged partmay be inclined (Y-shaped, see[4]), bulgings may occur onthe top and bottom sides of the tube (cross-joint, see[23])and the bulging location may not be in the center of theblank (see[24]). In this paper, the simulated part containsa central bulging on the top side. In spite of the simplic-ity, it contains the basic features of tube hydroforming withtwo independent loading parameters. The ultimate goal isto manufacture the part with a maximum of material in thedie cavity. During the process, the occurrence of any kindof irreversible wrinkles should be prevented while neckingis delayed as much as possible.

The tube’s initial length, external diameter and wall thick-ness are 190, 42.2 and 1.4 mm, respectively. The final bulgeheight is fixed at 12 mm by using a stopper, seeFig. 8. Thefriction coefficient between the tube and the die is assumedto be 0.1. In the FE model, the double symmetry is takeninto account, so only a quarter part of the tube is actuallyanalyzed. The tube is modeled using three-dimensional lin-ear brick elements. In the tube thickness direction two layersof elements are used. The tools, i.e. the die and the rams,are modeled by an appropriate set of discrete rigid finite el-ements.

In tube hydroforming simulations, adequate materialproperties are of prominent importance for the reliabilityof the results. Principally, the material properties of theoriginal sheet of which the tube is rolled are not applicableanymore as the rolling process will induce some changes:the stress–strain behavior of the tubular blank will be differ-ent from the response of the original flat sheet. Neverthelessit is important to use a realistic material description inthe simulations. Further discussions on this subject can befound, for example, in[25–27].

For the present purpose, the material data have been as-sessed from several test specimens (strips) prepared fromthe blank tube, based on the performance in standard ten-sile experiments. The material properties measured for thetube material (steel, St 34) are specified below in the mod-eling context of a von Mises yield criterion combined withan isotropic power-law hardening description:

Young’s modulus E = 200 GPaPoisson’s ratio ν = 0.3Strength K = 603 MPaPre-strain ε0 = 0.0076Hardening exponent n = 0.226

Fig. 9. Obtained process plan.

The actual flow stress is defined by:

σf = K(ε0 + ε̄)n (3)

where ε̄ is the equivalent plastic strain. The FLC is evalu-ated using the material model and the material parametersspecified above, according to the procedure as discussed byXing and Makinouchi in[19].

3.2. Results

The computationally derived process plan is given inFig. 9. The process starts with a little axial feeding. Then,almost a linear path is followed until about 16 MPa internalpressure. Then, for a short period, the adaptive system is notable to feed more material into the die cavity and only theinternal pressure is increased. Thereafter, the axial feedingstarts to increase, and in combination with the internal pres-sure again following an almost linear path. The increase inthe internal pressure results in a strain state which becomesclose to necking. Once, the FLC is closely approached, theinternal pressure is not allowed to increase anymore. At themoment that the controller detects not to be able to increasethe internal pressure or the axial feeding the simulation isstopped.

Forming limit curves are commonly used to checkwhether the strains exceed the material’s forming capacity.For the simulated process, the forming limit diagram isshown inFig. 10. The line with triangular markers is theFLC for the tube material. The dots represent the strainstate of each material point at the end of simulation.Fig. 10demonstrates that at the end of the simulation the FLC isclosely approached indeed.

The deformed geometry of the tube is shown inFig. 11,together with the thickness distribution. Some minor thin-ning occurs in the bulged part of T-shape. In the other re-gions the loads result in thickening of the tube wall. Visualdefects on the product can be observed.


Fig. 10. The forming limit diagram at the end of the simulation.

Fig. 11. The deformed geometry and thickness distributions along the topand bottom sides.

4. Conclusions and future work

In this study, an adaptive method is designed for tubehydroforming. A criterion for wrinkling, as well as a crite-rion for necking, is included. Instead of exact statements as‘wrinkle yes/no’, the criteria are formulated in weak termsand rules resulting in a fuzzy knowledge based controller.The applicability of this controller to design a feasible hy-droforming process has been demonstrated.

Although the process plan has been obtained at the endof one single simulation, generally, in the first attemptit might be difficult to arrive at an acceptable solution.Therefore, a number of introductory simulations are gen-erally required before the final simulation run can be per-formed. This initialization is required because of the factthat the membership functions need to be fine-tuned. Thisfine-tuning can be realized via experiments, as well assimulations. In the present paper, the latter procedure waspursued.

The approach given in this paper has been elaborated fora simple case study. Evidently, validation of the method byperforming parallel experiments still needs to be done, whichis an issue to consider in the future. Nevertheless, the resultsshow a qualitative agreement with experiences in practice,see for example[7].

Acknowledgements

The results presented originate from a Dutch researchproject on hydro-mechanical forming that is carried out as aco-operation between Eindhoven University of Technologyand TNO Industrial Technology. The funding by the Ministryof Education, Culture and Sciences (OC&W) is gratefullyacknowledged.

References

[1] F. Dohmann, C.h. Hartl, Tube hydroforming-research and practicalapplication, J. Mater. Process. Technol. 71 (1997) 174–186.

[2] L. Gao, S. Motsch, M. Strano, Classification and analysis of tubehydroforming processes with respect to adaptive FEM simulations,J. Mater. Process. Technol. 129 (2002) 261–267.

[3] W.H. Sillekens, P.P.H. Veltmans, M.A. Guiterrez, J.I. Fernandez, Fac-torial experimentation and simulation of hydroforming processes fortubular parts, in: Proceedings of the Ninth International Conferenceon Sheet Metal, 2001, pp. 605–612.

[4] T. Altan, S. Jirathearanat, M. Strano, S.G. Shr, Adaptive FEM pro-cess simulation for hydroforming tubes, in: K. Siegert (Ed.), Hy-droforming of Tubes, Extrusions and Sheet Metals, vol. 2, 2001,pp. 363–384.

[5] M. Strano, S. Jirathearanat, S.-G. Shr, T. Altan, Virtual processdevelopment in tube hydroforming, J. Mater. Process. Technol. 146(2004) 130–136.

[6] E. Doege, R. Kosters, C. Ropers, Determination of optimised controlparameters for internal high pressure forming processes with theFEM, in: Proceedings of the Sixth International Conference on SheetMetal, vol. 2, 1998, pp. 119–128.

[7] W.H. Sillekens, R.J. Werkhoven, Hydroforming processes for tubularparts: optimisation by means of adaptive and iterative FEM simula-tion, Int. J. Forming Process. 4 (2001) 377–393.

[8] M. Strano, S. Jirathearanat, T. Altan, Adaptive FEM simulation fortube hydroforming: a geometry-based approach for wrinkle detection,Ann. CIRP 50/1 (2001) 185–190.

[9] J. Kim, Y.-H. Kang, H.-H. Choi, S.-M. Hwang, B.-S. Kang, Com-parison of implicit and explicit finite-element methods for the hy-droforming process of an automobile lower arm, Int. J. Adv. Manuf.Technol. 20 (2002) 407–413.


[10] W. Kubli, J. Reissner, Optimization of sheet-metal forming processesusing the special-purpose program AUTOFORM, J. Mater. Process.Technol. 50 (1995) 292–305.

[11] F. Heislitz, H. Livatyali, M.A. Ahmetoglu, G.L. Kinzel, T. Al-tan, Simulation of roll forming process with the 3-D FEM codePAM-STAMP, J. Mater. Process. Technol. 59 (1996) 59–67.

[12] ABAQUS Inc., ABAQUS/Explicit User’s Manual, Version 6.3, 2002.[13] J.B. Kim, J.W. Yoon, D.Y. Yang, F. Barlat, Investigation into wrin-

kling behaviour in the elliptical cup drawing process by finite ele-ment analysis using bifurcation theory, J. Mater. Process. Technol.111 (2001) 170–174.

[14] R. Hill, A general theory of uniqueness and stability in elastic–plasticsolids, J. Mech. Phys. Solids 6 (1958) 236–249.

[15] P. Nordlund, Adaptivity and Wrinkle Indication in Non-Linear ShellAnalysis, Doctoral Dissertation, Department of Solid Mechanics,Royal Institute of Technology, Stockholm, Sweden, 1997.

[16] A. Aydemir, A Numerical-Experimental Analysis of Tube Hydro-forming, MTD Thesis, Eindhoven University of Technology, ISBN90-444-0279-X, 2003.

[17] D. Banabic (Ed.), Formability of Metallic Materials: PlasticAnisotropy, Formability Testing, Forming Limits (Engineering Ma-terials), Springer-Verlag, 2000.

[18] M. Dutilly, J.C. Gelin, Design of sheet metal forming processesbased on quality functions, in: Proceedings of the Second Interna-

tional ESAFORM Conference on Material Forming, 1999, pp. 469–472.

[19] H.L. Xing, A. Makinouchi, Numerical analysis and design for tubularhydroforming, Int. J. Mech. Sci. 43 (2001) 1009–1026.

[20] E.M. Viatkina, W.A.M. Brekelmans, L.P. Evers, M.G.D. Geers, Form-ing limit diagrams for sheet deformation processes: a crystal plastic-ity approach, in: Proceedings of the Fourth International ESAFORMConference on Material Forming, 2001, pp. 465–468.

[21] D. Driankov, H. Hellendoorn, M. Reinfrank, An Introduction toFuzzy Control, Springer-Verlag, 1993.

[22] K.M. Passino, S. Yurkovich, Fuzzy Control, Addison-Wesley, Long-man Inc., 1998.

[23] B.J. Mac Donald, M.S.J. Hashmi, Finite element simulation of bulgeforming of a cross-joint from a tubular blank, J. Mater. Process.Technol. 103 (2000) 333–342.

[24] M. Ahmetoglu, K. Sutter, X.J. Li, T. Altan, Tube hydroforming:current research, J. Mater. Process. Technol. 98 (2000) 224–231.

[25] T. Altan (Ed.), Research papers on sheet forming, machining andtube hydroforming, J. Mater. Process. Technol. 146 (1) (2004) 1–143.

[26] M. Ahmetoglu, T. Altan, Tube hydroforming: state-of-the-art andfuture trends, J. Mater. Process. Technol. 98 (2000) 25–33.

[27] T. Altan, M. Koc, Y. Aue-u-lan, K. Tibari, Formability and designissues in tube hydroforming, in: K. Siegert (Ed.), Hydroforming ofTubes, Extrusions and Sheet Metals, vol. 1, 1999, pp. 105–121.

an adaptive simulation approach designed for tube hydroforming processes

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