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Three-Dimensional Nonlinear Finite Element Analysis of Hot RadialForging Process for Large Diameter TubesJ. Chena; K. Chandrashekharaa; V. L. Richardsb; S. N. Lekakhb

a Department of Mechanical and Aerospace Engineering, Missouri University of Science andTechnology, Rolla, Missouri, USA b Department of Materials Science and Engineering, MissouriUniversity of Science and Technology, Rolla, Missouri, USA

Online publication date: 05 August 2010

To cite this Article Chen, J. , Chandrashekhara, K. , Richards, V. L. and Lekakh, S. N.(2010) 'Three-Dimensional NonlinearFinite Element Analysis of Hot Radial Forging Process for Large Diameter Tubes', Materials and ManufacturingProcesses, 25: 7, 669 — 678To link to this Article: DOI: 10.1080/10426910903536790URL: http://dx.doi.org/10.1080/10426910903536790

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Materials and Manufacturing Processes, 25: 669–678, 2010Copyright © Taylor & Francis Group, LLCISSN: 1042-6914 print/1532-2475 onlineDOI: 10.1080/10426910903536790

Three-Dimensional Nonlinear Finite Element Analysisof Hot Radial Forging Process for Large Diameter Tubes

J. Chen1, K. Chandrashekhara

1, V. L. Richards

2, and S. N. Lekakh

2

1Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology,Rolla, Missouri, USA

2Department of Materials Science and Engineering, Missouri University of Science and Technology,Rolla, Missouri, USA

A nonlinear coupled finite element model is developed to predict the behavior of large diameter tubes subjected to mechanical and thermalloadings during hot radial forging process. The model is formulated in a three-dimensional (3D) framework to account for both axial andcircumferential effects. This model considers both material and geometric nonlinearities. A rate-dependent material model is used to describethe viscoplastic behavior of the workpiece subjected to high temperature and large strain. A tubular workpiece with the mandrel inside and fourforging dies outside is modeled in commercial finite element code. A subroutine is developed and implemented to simplify the modeling processfor radial forging simulation. Numerical results presented include residual stress, plastic strain, and temperature distribution along the axial andhoop directions in the deformed workpiece. Results are also presented for contact force to evaluate the performance of the die in the forgingprocess. Finite element model predictions are compared with experimental and two-dimensional (2D) axisymmetric simulation results available inliterature. A variety of case studies are conducted for hot radial forging process using the developed 3D model.

Keywords Large diameter tube; Mandrel; Radial forging; Three-dimensional finite element model.

Introduction

Hot radial forging is an open die metal forging processin which the tubular workpiece is deformed between themandrel and two pairs of simple shaped dies with aseries of compressive strokes. Due to the smooth surfacefinish, considerable material savings, minimum notch effect,preferred fiber structure, and increased material properties,radial forging process is an ideal manufacturing processto produce large cannon barrels, automobile axles andshafts, and other tubular components [1]. For many years,the design of forging process was based on trial-and-error methods. However, factors such as deformation, metalflow, friction between the dies and workpieces, and heattransfer and generation, which are crucial to obtain qualityparts, cannot be predicted by trial-and-error techniques.Assessment of process parameters, therefore, are necessaryfor better understanding the radial forging process andquantitative design and optimization of the process.Many researchers have studied the radial forging process.

Using the slab method, Lahoti and Altman [2] analyzedthe mechanical behavior of radial forging of tubes withcompound-angle dies. Ghaei et al. [3] studied the effectsof die geometry on deformation of a workpiece in theradial forging process. Using the upper bound method,Ghaei et al. [4] and Sanjari et al. [5] predicted the effects

Received October 26, 2009; Accepted December 7, 2009Address correspondence to K. Chandrashekhara, Department of

Mechanical and Aerospace Engineering, Missouri University of Scienceand Technology, MO 65409, USA; Fax: 573-341-6899; E-mail:chandra@mst.edu

of process parameters and the maximum required forgingload in the radial forging process. However, the highlysimplified slab and upper bound methods offer only arough means of investigation and cannot accurately predictprocess parameters. Recently, the finite element methodhas proved to be a powerful computational tool to analyzematerial forming processes. Many numerical studies havebeen performed on the radial forging process. Dombleskyet al. [6] and Altan et al. [7] used a two-dimensional(2D) axisymmetric finite element model to investigate themechanical and thermal behavior of the process. Thesemodels do not fully account for temperature-dependentmaterial properties and circumferential effects such asrotational feed and clearance between dies. Jang and Liou[8] studied the residual stress during the radial forgingprocess using a three-dimensional (3D) nonlinear finiteelement model without considering circumferential motionof the workpiece. Also, the material model considered doesnot include rate-dependant plasticity behavior and thermaleffect.In the present work, a nonlinear dynamic finite element

model has been developed to simulate the hot radialforging process. Circumferential motion of the workpieceand thermal effects on material properties are considered.The elasto-viscoplastic material model is used to accountfor strain rate dependent plastic behavior. The modeluses fully coupled thermal-stress technique to accountfor stress analysis and heat transfer during the forgingprocess. It is formulated in a 3D coordinate system thataccounts for both the axial and circumferential effects.Thermal properties of the material are used to investigateheat transfer during the process. Four hammer dies and

669

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670 J. CHEN ET AL.

an inner mandrel are modeled as rigid bodies throughoutthe simulation, thus reducing the computational cost. Theheat generated by plastic deformation, and the frictionbetween hammer dies, inner mandrel, and workpiece, areconsidered in the model. Heat dissipation due to radiationand convection are also considered in the analysis. Themodel is developed and implemented in the commercialfinite element code ABAQUS, and accounts for contact andmaterial nonlinearities. Due to the lack of experimental datafor hot radial forging process of large diameter tubes, the3D model simulation results for cold radial forging processare verified with the experimental results. Also, simulationresults for hot radial forging process are compared withavailable 2D axisymmetric model results in the literature.

Radial forging process

A typical schematic of the radial forging process is shownin Fig. 1. The tubular workpiece is clamped on the machineby grippers. The deformation of the workpiece is formedby the short-stroke of four hammer dies arranged radiallyaround the workpiece. During forging, the rotation of theworkpiece is intermittent and synergic with the die motion toprevent the workpiece from twisting [9]. When the hammersare in contact with the workpiece, the rotation is stopped.When the hammers move out of contact with the workpiece,the workpiece rotates by a specific angle to obtain a goodsurface finish. After each blow of the hammers, the tubularworkpiece is fed axially towards the die inlet at a specifiedrate. Consequently, at each stroke only a small portion ofthe workpiece is subjected to plastic deformation, therebya fairly low deformation load is required [10]. This processis repeated till the whole part is manufactured.The deformation of the workpiece (shown in Fig. 2)

can be divided into three typical zones: the sinking zone,

Figure 1.—Schematic of radial forging process.

Figure 2.—Three typical zones of radial forging process.

the forging zone, and the sizing zone. The diameter ofthe tubular workpiece is reduced in the sinking zone. Thedeformation takes place mainly in the forging zone. Thesizing zone creates the inner product shape and a goodsurface finish [11].

Modeling of hot radial forging process

Material ModelBecause the hot radial forging process produces large

deformations and high temperatures, both the mechanicaland thermal properties of the tubular workpiece should beconsidered in the analysis. AISI 4337 steel is used as thematerial for the tubular workpiece, and this material showselasto-viscoplastic behavior during the hot forging process.Since the viscoplastic material has a time-dependentbehavior, the effect of the strain rate cannot be ignored.Shida’s formula [12] is based on experimental data

obtained from compression tests at high temperatures andhigh strain rates. This formulation is specifically suitedfor flow stress measurement [13] and can be applied tocarbon steel for a carbon content range of 0.07–1.2%,a temperature range of 700–1200�C, strains up to 0.7, andstrain rates up to 100 s−1 [14]. The application of Shida’sformula is convenient in hot radial forging process becauseexperimental test data for plastic behavior of carbon steelat different strain rates and temperatures is not commonlyavailable. For the present study, Shida’s formula is used todescribe the flow stress (�) of AISI 4337 steel as a functionof strain (�), strain rate (�), and temperature (T ), and canbe expressed as

� = �d · fw��� · fr���� (1)

where fw��� and fr��� are functions dependent on strainand strain rate, respectively; �d is the deformation resistancefunction and is expressed as

�d = 0�28 exp(5�0T

− 0�01Ceq + 0�05

)for T � TP (2)

or

�d = 0�28 g�Ceq� T � exp(

Ceq + 0�32

0�19�Ceq + 0�41�− 0�01

Ceq + 0�05

)

for T ≤ TP� (3)

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THREE-DIMENSIONAL NONLINEAR FINITE ELEMENT ANALYSIS 671

where

Ceq = C + Mn6

+ Cu+ Ni15

+ Cr +Mo+ V5

�

T �K� = T��C�+ 2731000

�

TP = 0�95Ceq + 0�41

Ceq + 0�32�

and

g�Ceq� T � = 30�0 �Ceq + 0�9�(Teq − 0�95

Ceq + 0�49

Ceq + 0�42

)2

+ Ceq + 0�06

Ceq + 0�09�

The strain hardening function fw��� is expressed as follows:

fw��� = 1�3(

�

0�2

)n

− 0�3(

�

0�2

)� (4)

where n = 0�41− 0�07Ceq .The strain hardening function fr��� is expressed as

follows:

fr��� =(

�

10

)m

� (5)

where

m = �−0�019Ceq + 0�126�T + �0�0176Ceq − 0�05�

for T � Tp

and

m = �0�081Ceq − 0�154� T + �−0�019Ceq + 0�207�

+ 0�027Ceq + 0�32

for T ≤ TP�

Heat conductivity among workpiece, hammer dies, andmandrel, as well as convection and radiation between thehot workpiece and the environment are considered in thesimulation. Also, the heat generated by the plastic forgingand friction among workpiece, hammer dies, and mandrelis considered in the analysis. Thermal conductivity, thermalexpansion coefficient, specific heat, film coefficient, andinelastic heat fraction are required in the material modelto investigate the thermal behavior. The stress-strain curvesof AISI 4337 at different temperatures based on Shida’sformula are shown in Fig. 3 and the material parametersused in the simulation are listed in Table 1.

Figure 3.—Stress-strain curve of AISI 4337 (based on Shida’s formula).

Table 1.—Material parameters for hotradial forging process.

Density (kg/m3) 7850Young’s modulus (GPa) 200Poisson’s ratio 0.3Inelastic heat fraction 0.9Conductivity (W/m/�C) 15Thermal expansioncoefficient (1/�C)

1�2× 10−5

Specific heat (J/kg/�C) 750

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672 J. CHEN ET AL.

Finite Element ModelHot radial forging process includes significant heat

generation due to the large plastic deformation of thematerial which, in turn, changes material properties. Inaddition, the friction and contact conditions generate moreheat which depends on the pressure between the surfaces.Hence, a fully coupled temperature-displacement modelmust be used to solve the thermal and mechanical solutionssimultaneously.Explicit method is used to solve the hot radial forging

model. Compared to the implicit method which is moreefficient for smooth nonlinear problems, the explicit methodis the clear choice for hot radial forging problem whichincludes large deformation, thermal loading, contact, andmaterial complexity. Also, the explicit solution procedureis suitable for large models involving discontinuous loadingsteps.The 3D formulation for dynamic analysis can be

written as

�Me�{e

}+ �Ke�{e

} = F e�� (6)

where

�Me� =∫V��N �T �N �dV � �Ke� =

∫V�B�T �C��B�dV �

{e

} = u� v� w�T �

�Me� is the mass matrix, �Ke� is the stiffness matrix, F e�is mechanical loading, N is shape function, B is strain-displacement function, C is elasticity matrix, � is thedensity, and u� v� w�T are displacement components in arectangular coordinate system.The heat conduction can be expressed as

�CeT �{ e}+ �Ke

T � e� = Qe�� (7)

where

�CeT � =

∫V�cpN

TNdV � �KeT � =

∫VN TkNdV �

Qe� =∫SN TqdS +

∫VN T rdV �

�CeT � is the heat capacitance matrix, �Ke

T � is the conductivitymatrix, Qe� is the external flux vector. cp is the specificheat of the material, k is the thermal conductivity, q is thesurface heat flux, and r is the body heat flux generated byplastic deformation.Combining Eqs. (2) and (3), the coupled thermal-stress

equation can be written as

[M 00 0

]e {�0

}e

+[0 00 CT

]e {�

�

}e

+[K KT

KT KT

]e {� �

}e

={F�Q�

}e

� (8)

The equations of motion are integrated using the explicitcentral-difference integration rule

e��i� = �Me�−1�F e��i� − Ie��i�� (9)

e��i+ 12 �= e��i− 1

2 �+ t�i+1� + t�i�

2e��i� (10)

e��i+1� = e��i� + t�i+1�e��i+ 1

2 �� (11)

where Ie��i� is the internal force vector and is given byIe��i� = �Ke�e��i�.The subscript i refers to the increment number in an

explicit dynamics step. A lumped mass matrix is usedbecause its inverse is simple to compute.The heat transfer equations are integrated using the

explicit forward-difference time integration rule

e��i� = �CeT �

−1�Qe��i� − IeT ��i�� (12)

e��i+1� = e��i� + t�i+1� e��i�� (13)

where IeT ��i� is the internal heat flux vector, and is givenby IeT ��i� = �Ke

T � e��i�.

Hard contact is used to describe the normal contact tothe surfaces. The fraction of friction work converted to heatis defined in the contact model. A Coulomb friction modelis used to describe the tangential interaction of contactingsurfaces and is given by

�crit = �p� (14)

where �crit is the critical friction force, � is the coefficientof friction, and p is the contact pressure between the twosurfaces.

Numerical simulation

A 3D thermomechanical finite element model isdeveloped using ABAQUS/CAE. The dimensions of thetube and mandrel used in the present study are taken fromDomblesky et al. [6]. A circular die shape with multipledie angles is used to reduce the forging force and make theprocess more cost-effective [4]. The geometric parametersare summarized in Table 2. During the forging process, therotation of the tubular workpiece is intermittent and synergicwith the die motion. The stroking rate of the hammer diesis 200 per minute, and the stroking velocity is based on

Table 2.—Geometry of workpiece, mandrel and die.

Out diameter of the original workpiece (mm) 380Inner diameter of the original workpiece (mm) 180Out diameter of the forged part (mm) 344Inner diameter of the forged part (mm) 160Out diameter of mandrel (mm) 160Die total length (mm) 240Die land length (mm) 110Die inlet angle 10�Die outlet angle 8�

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THREE-DIMENSIONAL NONLINEAR FINITE ELEMENT ANALYSIS 673

Table 3.—Parameters for the motionof simulation.

Stroking rate (strokes per minute ) 200Rotational feed 15�Number of strokesperformed beforean axial feed

12

Axial feed rateafter each circlestroke (mm)

20

Number of axial feeds 3

the sinusoidal function. The chuck-heads remain stationarywhen the dies are in contact with the tube during the stroke.After each stroke, the tube is automatically rotated by 15�.The strokes continue until a good surface finish is obtainedin the circumferential direction. The tube is fed 30mmaxially towards the die inlet at a specified feed-rate to starta new stroke cycle. Parameters of the motion are shown inTable 3. The contact parameters are listed in Table 4. The8-node temperature-displacement coupled brick element isused to mesh the tubular workpiece. To avoid shear-lockingassociated with this element, a reduced integration strategywith hourglass control is used. The die and mandrel aremeshed using rigid elements since both undergo very littledeformation compared to the deforming workpiece. Thenumber of elements for each part is shown in Table 5.The mesh of different parts is shown in Fig. 4.

Table 4.—Contact parameters.

Friction factorbetween workpieceand die

0.6

Friction factorbetween workpieceand mandrel

0.5

Fraction of dissipatedenergy caused byfriction

0.9

Friction of convertedheat distributed toslave surface

0.5

Table 5.—Type and number of elements used for differentparts.

Type(ABAQUS)

Number ofelements

Tubularworkpiece

C3D8RT (8-nodethermally coupledbrick, trilineardisplacement andtemperature,reduced integration,hourglass control)

81,920

Die R3D4 (4-node3D bilinear rigidquadrilateral)

1,318

Mandrel R3D4 (4-node3D bilinear rigidquadrilateral)

4,480

Figure 4.—3D finite element model for tubular workpiece.

The implementation procedure of the developed modelis summarized as shown in Fig. 5. As the die stroke,workpiece rotation, and workpiece axial feed are alternatein the radial forging process, many simulation steps arenecessary to simulate the process. Also, the boundaryconditions change among the various simulation stepsresulting in extensive modeling work. To simplify themodeling procedure, a subroutine has been developed inMATLAB to generate the input file for ABAQUS. Thistechnique significantly reduces modeling time thus makingthe modeling process more efficient.

Results and discussion

Residual stress distribution is an important parameterbecause it directly affects the fatigue life of the workpieceand its dimensional stability. A large residual stress field

Figure 5.—Implementation procedure for simulation.

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674 J. CHEN ET AL.

Figure 6.—Residual stress distribution after three axial feeds.

can result in propagation of a crack, causing the workpieceto fail. Figure 6 shows the maximum principal stressdistribution after three axial feeds (36 strokes). The tensileresidual stress on the inner surface and the portion of theouter surface that are in contact with the hammer dies andthe mandrel, can help the propagation of possible crack andhence reduce the product life. The plastic strain distributionsshown in Fig. 7 are mainly at the forging and sizing zones.No plastic deformation is observed away from the forgingzone.

Comparison with Experimental Results of Cold RadialForging ProcessThe current 3D finite element model is verified with

experimental results of cold radial forging process presentedby Uhlig [15]. This problem is also studied by Ameli [10].The elastoplastic material properties for workpiece usedare E = 203GPa, � = 0�29, �Y = 200MPa. A power

law is used for strain hardening, and the parameters forthe power law are k = 750MPa, n = 0�2. Geometryof workpiece and the contact force from experimentalmeasurement are listed in Table 6. The contact forcesobtained from the current finite element model are comparedwith experimental results in Fig. 8. The simulation resultsagree well with experimental findings.

Comparison with 2D Axisymmetric Results for HotRadial Forging ProcessDue to the lack of available experimental data on hot

radial forging process, the accuracy of the present 3D modelis compared with the available 2D axisymmetric results.Table 7 shows comparison of 3D model results with the 2Daxisymmetric results for hot radial forging. The maximumforging temperature based on the current model is higherthan those predicted by the 2D axisymmetric model. This isbecause the heat generated by the friction between mandrel

Figure 7.—Plastic strain distribution after three axial feeds.

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THREE-DIMENSIONAL NONLINEAR FINITE ELEMENT ANALYSIS 675

Table 6.—Geometry of workpiece and contact force from experiment in thecold radial forging process [15].

SampleNo.

Outer radiusof preform

(mm)

Inner radiusof preform

(mm)

Out radiusof product(mm)

Inner radiusof product(mm)

Contactforce (kN)

1 15.97 5.8 13.18 3.915 172.002 15.97 5.8 13.25 3.915 167.003 15.03 5.8 13.11 3.915 124.004 13.99 5.8 13.03 3.915 74.00

and workpiece during circumferential movement is notconsidered in the 2D axisymmetric model. Having validatedthe developed model, results for residual stress, plasticstrain, contact force, and temperature distribution along theaxial and hoop directions in the deformed workpiece arepresented.

Axial DeformationAfter the first axial feed, the plastic strain distribution

along the axial direction in the inner, middle, and outer areasof the workpiece is shown in Fig. 9. Three deformationzones (sinking, forging, and sizing) exist during the forgingprocess. Only a small amount of deformation occurs in thesinking zone. In the forging zone, the deformation increases,and it reaches the maximum value in the sizing zone.Compared to the middle surface, the end of the tube on theouter and inner surfaces has significant deformation.Figure 10 shows the maximum principal stress

distribution of the inner, middle, and outer surfaces alongthe axial direction after the first axial feed. The outerand inner surfaces show higher residual stress than themiddle surfaces. The largest residual stress occurs in theouter surface. There is no significant variation of residualstress along the axial direction in the middle surface. Thecomparison of residual stresses among the three surfaces

Figure 8.—Comparison of contact force between experimental and simulationresults.

Table 7.—Comparison between the 2D axisymmetric and 3Dsimulation results.

3D nonlinearcoupled model

results

2Daxisymmetric

model results [6]

Effective strain at theforging zone

0.20–0.35 0.20–0.35

Effective strain at thesizing zone

0.35–0.40 0.35–0.45

Effective strain at thesinking zone

0.05–0.16 0.05–0.15

Maximum effective-strain-rate at the forging zone

1.50–2.50 2.00–3.00

Maximum effective-strain-rate at the sizing zone

0.00–1.00 0.00–1.00

Maximum effective-strain-rate at the sinking zone

0.50–1.50 1.00–2.00

Maximum temperature 1260�C 1020�CMinimum temperature 940�C 950�C

indicates that the outer surface may pull the material,causing it to crack and fail first.

Circumferential DeformationA 3D finite element model is required to simulate the

circumferential deformation of hot radial forging process.The cross-section of the deformed tubular workpiece atdifferent strokes is shown in Fig. 11. After the first stroke,the deformation is mainly concentrated at forging area ofthe tube where it is in contact with the hammer dies.Moreover, there are small gaps between the mandrel andthe inner surface of the tube. After the fourth stroke, no gapis found between the mandrel and the inner surface of thetube, and a good inner surface has been formed. However,some protuberances are found at the outer surface. After thetwelfth stroke, no gap is found, and a round outer surfaceis obtained. Both inner and outer surfaces are well finished.Figure 12 shows the plastic strain distribution on outer

surface along the hoop direction at various specific strokes.

Figure 9.—Plastic strain distribution along the axial direction.

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676 J. CHEN ET AL.

Figure 10.—Residual stress distribution along the axial direction.

It is obvious that the plastic strain increases as the number ofstrokes increases. Initially, the strain curve plotted againstthe hoop angle shows variation due to the deformation along

Figure 12.—The plastic strain distribution in outer surface at specific stokes.

the circumference of the tube caused by the four hammers.As the number of strokes increases, the variation reducessignificantly. After the ninth stroke, there is less variationin the strain distribution, resulting in a good finish on theouter surface.

Figure 11.—Deformation shape of cross-section at different stokes.

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THREE-DIMENSIONAL NONLINEAR FINITE ELEMENT ANALYSIS 677

Figure 13.—Residual stress distribution of different surfaces at the first stoke.

The residual maximum principal stress distributions onthe various surfaces after the first stroke are shown inFig. 13. The variation of the curve indicates the changesin deformation force in the circumference direction. Thisconforms to the variation of strain curve at the first stroke.In comparison to the middle and inner surfaces, the outersurface undergoes the highest residual stress. The maximumresidual stress occurs at the area in contact with the die onthe outer surface after the first stroke. Figure 14 shows thecontact force between the die and the tubular workpiecefor the first twelve strokes before the first axial feed. Thecontact force during the hot radial forging process is in therange of 2600 to 3200KN.

Figure 14.—Contact force versus stroke number.

Figure 15.—Temperature distribution after three axial feeds.

Temperature DistributionThe temperature distribution caused by plastic

deformation and friction after three axial feeds is shownin Fig. 15. The temperature on the outer surface doesnot change too much. This is because the heat generatedon outer surface by plastic forging and friction betweenthe tube and hammer dies is quickly transferred to theenvironment by convection and radiation. On the innersurface, however, the temperature increases to about 250�C,because the heat generated by friction between the mandreland the workpiece does not dissipate easily inside the tube.Hot radial forging experiments are expensive and time

consuming. Simulation results using a comprehensive 3Dmodel is a cost-effective tool to fully understand the variousaspects of hot radial forging process. The prediction ofresidual stress distribution indicates that the outer surfaceof the tube is most prone to fatigue failure. Also, theaxial plastic strain distribution shows the existence ofthree deformation zones during hot radial forging process.Furthermore, the circumferential deformation results fromthe 3D model can be used to determine the number ofstroke for good surface finish. The predicted contact forceand temperature distribution can also be used as importantparameters for the design of radial forging dies.

Conclusion

A comprehensive 3D finite element model has beendeveloped to analyze the behavior of the tubular workpiecesubjected to mechanical loading and heat transfer duringthe hot radial forging process. The model considers bothaxial and circumferential effects of the forging process.Shida’s constitutive equation is used to describe theflow stress of the workpiece material during hot radialforging deformation. A rate-dependent elasto-viscoplasticmaterial model has been implemented to accuratelypredict the plastic deformation of the tubular workpieceat high temperatures. The model is formulated in the3D coordinate system using the commercial softwareABAQUS. A subroutine is developed to generate theinput file to simplify the modeling work. The explicitmethod is used to solve the coupled thermo-mechanical

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678 J. CHEN ET AL.

model. Analysis of a typical case is conducted using thedeveloped model. Residual stress, plastic strain, contactforce, and temperature along the axial and hoop directionsare reported. Finite element model predictions are ingood agreement with experimental and 2D axisymmetricsimulation results available in literature. Results forcircumferential deformation are presented, which cannotbe predicted by using 2D axisymmetric model. The modeldeveloped here can be used to accommodate various casesof hot radial forging process. In addition, this model can beexpended for the cold radial forging process by changingthe mechanical loading, thermal condition, and materialproperties.

Acknowledgment

We would like to thank U.S. Army Benet Labsfor funding this research. The conclusions and opinionsexpressed are those of the authors and not of BenetLaboratories.

References

1. Altan, T.; Oh, S.I.; Gegel, H. Metal Forming Fundamentals andApplications; American Society for Metals: Materials Park, OH,1983.

2. Lahoti, G.D.; Altan, T. Analysis of the radial forging processfor manufacturing of rods and tubes. Journal of Engineering forIndustry 1976, 98, 265–271.

3. Ghaei, A.; Taheri, A.K.; Movahhedy, M.R. A new upper boundsolution for analysis of the radial forging process. InternationalJournal of Mechanical Sciences 2006, 48, 1264–1272.

4. Ghaei, A.; Movahhedy, M.R.; Taheri, A.K. Study of theeffects of die geometry on deformation in the radial forgingprocess. Journal of Material Processing Technology 2005, 170,156–163.

5. Sanjari, M.; Taheri, A.K.; Ghaei, A. Prediction of neural planeand effects of the process parameters in radial forging using an

upper bound solution. Journal of Material Processing Technology2007, 186, 147–153.

6. Domblesky, J.P.; Shivpuri, R.; Painter, B. Application of the finite-element method to the radial forging of large diameter tubes.Journal of Material Processing Technology 1995, 49, 57–74.

7. Altan, T.; Knoerr, M. Application of the 2D finite element methodto simulation of cold-forging process. Journal of Material ProcessTechnology 1992, 35, 275–302.

8. Jang, D.Y.; Liou, J.H. Study of stress development inaxisymmetric products processed by radial forging using a 3-D nonlinear finite element method. Journal of Material ProcessTechnology 1998, 74, 74–88.

9. Tszeng, T.C. Residual Stress Calculation by Finite ElementMethod in Manufacturing. Ph.D. thesis, Department of Mech-anical Engineering, University of California, Berkley, CA, 1987.

10. Ameli, A.; Movahhedy, M.R. A parametric study on residualstresses and forging load in cold radial forging process.International Journal of Advanced Manufacture Technology2007, 33, 7–17.

11. Nagpal, V.; Lahoti, G.D. “Application of the Radial ForgingProcess to Cold and Warm Forging of Cannon Tubes,” Vol. II– Selection of Die and Mandrel Materials, Battelle ColumbusLaboratories: Columbus, OH, pp. 62–63, 1980.

12. Shida, S. Empirical formula of flow stress of carbon steels –resistance to deformation of carbon steels at elevated temperature.Journal of Japanese Society for Technology of Plasticity 1969,10, 610–617.

13. Lee, Y.; Kim, B.M.; Park, K.J. A study for the constitutiveequation of carbon steel subjected to large strains, hightemperatures and high strain rates. Journal of Material ProcessingTechnology 2002, 130–131, 181–188.

14. Tang, J. A Study of Oxide Scale Deformation and SurfaceRoughness Transformation in Hot Strip Rolling. Ph.D. thesis,School of Mechanical, Materials and Mechatronic Engineering,University of Wollongong, Wallongong, Australia, 2006.

15. Uhlig, A. Deformation energy and tool forces in an idealizedradial forging process. Metal 1965, 19, 322.

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