1 23

Journal of Materials Engineering andPerformance ISSN 1059-9495Volume 22Number 12 J. of Materi Eng and Perform (2013)22:3601-3611DOI 10.1007/s11665-013-0636-6

The Effect of Geometric Parameters ofConical Cups on the Preform Shape inTwo-Stage Superplastic Forming Process

Asghar Shamsi-Sarband, Seyed JamalHosseinipour, Mohammad Bakhshi-Jooybari & Mohsen Shakeri

1 23

Your article is protected by copyright and

all rights are held exclusively by ASM

International. This e-offprint is for personal

use only and shall not be self-archived in

electronic repositories. If you wish to self-

archive your article, please use the accepted

manuscript version for posting on your own

website. You may further deposit the accepted

manuscript version in any repository,

provided it is only made publicly available 12

months after official publication or later and

provided acknowledgement is given to the

original source of publication and a link is

inserted to the published article on Springer's

website. The link must be accompanied by

the following text: "The final publication is

available at link.springer.com”.

The Effect of Geometric Parameters of Conical Cupson the Preform Shape in Two-Stage Superplastic

Forming ProcessAsghar Shamsi-Sarband, Seyed Jamal Hosseinipour, Mohammad Bakhshi-Jooybari, and Mohsen Shakeri

(Submitted October 22, 2012; in revised form May 12, 2013; published online August 14, 2013)

A combination of sensitivity analysis and finite element simulation has been developed for the preformdesign in two-stage superplastic forming process. The aim is to present a simple approach to generate anestimate for the preform shape. In this respect, the commercial finite element software ABAQUS/Standard6.8 was used as a computational tool and sensitivity analysis was used for preform design by minimizing themean fractional deviation from the target thickness as an objective function. The predicted preform wasverified through comparison with experimental results by investigating the deformation of AA5083 sheet attemperature of 500 �C. The effect of the geometric parameters of conical cups on the preform shape wasexamined. The results showed that the geometric parameters have a significant effect on the preform shape.By increasing the height and the cone angle of the final cup, the depth of the preform in the inner cavitydecreases and the dome region is approached to the center of the preform cup. By increasing the cornerradius of the final-die, only the height of the dome region decreases.

Keywords AA5083 sheet, conical cups, preform design, super-plastic forming

1. Introduction

Superplastic forming (SPF) is a manufacturing processwhereby gas pressure is applied to deform hot sheet metal intothe die cavity. Complex shapes can be formed in this processthat is mostly used to produce light and strong aerospacecomponents. In order to provide appropriate strain rates, the gaspressure should be controllable according to the pressure-timeschedule of the process. Thus, SPF is more difficult than theconventional manufacturing processes (Ref 1-3).

During the last few years several researchers have workedon different aspects of SPF. Jarrar et al. (Ref 4, 5) simulatedhigh-temperature bulge forming of AA5083 sheet and inves-tigated different approaches for gas pressure profile predictionin bulge forming under quick plastic forming (QPF) conditions.Ding et al. (Ref 6) analyzed the SPF process of thin sheets andobtained an optimal stable deformation path that reducesproduction time. Nazzal et al. (Ref 7) optimized the SPFprocess using a microstructure-based constitutive model and amultiscale deformation stability criterion. Hojjati et al. (Ref 8)simulated the SPF of AA5083 in a conical die at constantpressure and constant strain rate. Kim et al. (Ref 9) proposed a

method for blank design of SPF process by combiningnumerical simulation and optimization technique in order toobtain uniform thickness distribution after forming. Huanget al. (Ref 10) concentrated on the experimental validation ofsheet thickness optimization in the SPF process.

In order to obtain a more uniform thickness distribution, atwo-stage SPF has been developed by Xing et al. (Ref 11). Inthe first stage, gas pressure is applied to form the sheet metalinto a preform-die; in the second stage, the direction of gaspressure is reversed to deform the preformed workpiece in thefinal-die. They proposed a method based on a rigid-viscoplas-tic finite element program for preform design of conical parts.Luckey et al. (Ref 12) used the finite element analysis todesign a preform cavity for a complex component. Luo et al.(Ref 13, 14) used a hot draw mechanical process forpreforming rectangular parts and compared the advantages oftwo-stage gas forming (TSGF) and hot draw mechanicalpreforming (HDMP) on the forming of a complex dash panelpart.

Forming conical parts is one of the complex and difficultfields in sheet metal forming processes. Because of bursting,wrinkling, and non-uniformity in thickness distribution, theseparts are normally formed in industry by multi-stage deepdrawing processes (Ref 15). Shamsi-Sarband et al. (Ref 16, 17)developed a combination of sensitivity analysis and finiteelement method for preform design in a two-stage SPF processand studied the effect of friction coefficient on the preformshape of conical cups.

In this paper, the effect of geometric parameters of theconical cup on the preform shape and also on the thicknessdistribution and strain variation is studied. The aim of thisresearch is to present a simple approach to generate an estimatefor the shape of perform die. The deformation of AA5083 sheetat temperature of 500 �C is investigated experimentally forverification.

Asghar Shamsi-Sarband, Seyed Jamal Hosseinipour, MohammadBakhshi-Jooybari, and Mohsen Shakeri, Metal Forming ResearchGroup, Babol University of Technology, P.O. Box 484, Shariati Avenue,Babol, Iran. Contact e-mail: j.hosseini@nit.ac.ir.

JMEPEG (2013) 22:3601–3611 �ASM InternationalDOI: 10.1007/s11665-013-0636-6 1059-9495/$19.00

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3601

Author's personal copy

2. Experimental Procedure

A commercial aluminum alloy 5083 sheet with 1 mmthickness was examined in as-received condition. The chemicalcomposition of the material is given in Table 1. Figure 1 showsthe schematic of equipment used for the SPF process. Figure 2illustrates the schematic of the conical die set with a diameter ofDu = 115 mm, height of H = 35 mm, and cone angle ofb = 30�. Blanks with 150 mm diameter were cut from thesheet. The blank was clamped between the blank holders, andsufficient force was applied to prevent gas permeation from theforming zone. Argon gas was used to form the specimens. Thedie and the blank were heated to a specific temperature and thenthe gas pressure was applied. The temperature remainedconstant during the tests. The pressure was controlled by apressure sensor and a proportional valve. Lab View softwarewas utilized for applying the pressure-time profile to theproportional valve. The experiments were carried out at 500 �Cwithout applying any lubrication. After the tests, the cups weresection cut and the corresponding thickness was measured by amechanical thickness measurement set with an accuracy of0.01 mm.

3. Finite Element Simulation

The commercial finite element software ABAQUS/Standard6.8 was used to simulate the SPF process. An axisymmetricmodel was used for the simulation due to symmetry. Figure 3shows the FE models of the die and the blank. The die wasmodeled as a discrete rigid part and the sheet was considered tobe deformable. The element type of CAX4R was used formeshing with the size of 0.25 mm in both directions. Anextended load was applied to the sheet to model the gaspressure and an algorithm was used for controlling thepressure-time profile. The material flow equation was assumedas r ¼ 116 _e0:35 MPa (Ref 18, 19) that was implemented intothe software using an isotropic creep material model.

4. Sensitivity Analysis

Figure 4 shows the schematic of forming a conical cup in thetwo-stage process. As illustrated, the corner of the cup is the lastregion of deformation (region A) where the maximum thinningtakes place. To obtain uniform thickness in the final cup, thethickness in region A must be greater than that of the otherregions in the preform stage. Therefore, the preform-die musthave a dome A¢ to limit the sheet stretching in this region. Thethickness distribution in the base (OA) and the wall (AB) regionsof the final cup are controlled by the sheet stretching in the inner(O¢A¢) and outer (A¢C¢B¢) cavities of the preform-die, respec-tively. To design the preform-die, the position of the dome A¢and the cavities of O¢A¢ and A¢C¢B¢ must be determined.

Figure 5 illustrates the schematic of the position of nodes onthe sheet surface and the perform die surface. As it is shown,Xout(m) and Xin(m) represent the position vector of nodes on theoutside and inside surfaces of the sheet at iteration m. Similarly,Xdie(m) represents the position vector of nodes on the die surfaceand is used as the design variable. If the thickness of the cup atits final stage in each element h(m) is larger than the targetthickness of the final cup, Xdie(m+1) should be changed in orderto increase the sheet stretching in the preform stage until thethickness coincides with the target thickness. By assuming thatthe perform die shape changes in the direction of the unitnormal vector of the outside surface of the sheet, Xdie(m+1) canbe obtained as

Xdieðmþ1Þ ¼ XoutðmÞ þ NðmÞ � a; ðEq 1Þ

where N(m) is the unit normal vector, and a is the search-stepsize and is defined as

Table 1 The chemical composition of commercial AA5083

Si Fe Cu Mn Mg Cr Zn Pb Sn V Al

0.09 0.19 0.01 0.53 4.30 0.05 0.01 0.01 0.01 0.01 Base

Fig. 1 Schematic of the equipment used for SPF process

Fig. 2 Schematic of the conical die set

3602—Volume 22(12) December 2013 Journal of Materials Engineering and Performance

Author's personal copy

a ¼ bðmÞ � eðmÞ � SðmÞ; ðEq 2Þ

where b(m) is a weighting parameter and e(m) is an error func-tion that is defined as the difference between the final thicknessof the elements and the target thickness. S(m) is a sensitivityparameter for the deformation process and can be defined as

SðmÞ ¼Xðm�1Þ � Xm�2��

��

hðm�1Þ � hðm�2Þ��

��: ðEq 3Þ

The objective function is the mean fractional deviation fromthe target thickness, which must be minimized. At eachiteration, simulations are run with different values of b(m), andthe best result is used for the next iteration. The designprocedure is repeated with different initial estimates to achievethe best result.

Fig. 3 FE model of the conical die and the initial estimate of preform-die

Fig. 4 Schematic illustration of forming a conical cup in two-stage process: (a-c) preform stage, (d-f) final stage

Fig. 5 Schematic position of nodes on the sheet surface and pre-form-die surface

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3603

Author's personal copy

5. Results and Discussion

5.1 One-Stage SPF Process

Figure 6 shows the conical cups obtained from experimentand simulation in one-stage SPF process. It can be seen that themaximum equivalent creep strain (CEEQ) occurs in the cornerregion of the cup which is the last region of the sheet stretching.The experimental and simulation results of thickness distribu-tion of the cup are compared in Fig. 7. As it can be seen, thereis a good agreement between the results. Due to the friction

effect on the die surface and also the effect of clamping at theedges of the sheet, the sheet stretching and the thicknessdistribution are non-uniform. For low friction coefficient, themaximum thinning occurs in the base region O, while byincreasing the friction coefficient the maximum thinning isshifted to the corner region A of the cup. The simulation resultunder high friction coefficient is closer to that of theexperimental finding, because no lubricant was used in theexperiments. Therefore, for all the simulations, the frictioncoefficient between the sheet and the die were assumed to beclose to the sticking condition (l = 0.5). This was alsoperformed by Xing et al. (Ref 11).

5.2 Preform Design Results

Figure 8 shows the preform shape obtained from simulationand sensitivity analysis after 10 iterations. It can be observedthat the preform contains two regions: inner cavity O¢A¢ andouter cavity A¢C¢B¢ which are related to the base OA and thewall AB regions of the final cup, respectively. The preform andthe final cup produced in the experiment are shown in Fig. 9.Figure 10 shows the thickness distribution of the preform andthe final cup obtained from simulation and experiment. It canbe observed that the simulation result is in good agreement withthe experimental one. The results show that the thicknessdistribution of the preform cup is non-uniform and thethickness in the region A¢ is greater than those of the regionsO¢ and C¢. However, the thickness distribution of the final cupin the two-stage process is more uniform than that of the one-stage process (Fig. 7).

This technique for preform design of conical cups wascompared with the method proposed by Xing et al. (Ref 11) foran Al-2.05Li-2.06Cu-1.2Mg-0.12Zr alloy sheet with the initialthickness of 1.5 mm and a die with top and bottom diameters of63.5, 100 mm; a height of 45 mm; and a corner radius of9.0 mm. As can be seen in Fig. 11, this technique shows about10% improvement in the thickness distribution.

Figure 12 shows several steps of the forming process. It canbe seen that in the preform stage the deformation contains sheetstretching and bending. During the final stage the sheet iswrinkled at steps 5 and 6 in region D due to the bending andunbending effect. Then, the wrinkle disappears due to stretch-ing effect at steps 7 and 8. This means that during the final

Fig. 6 Conical cup produced in one-stage SPF process: (a) experi-ment, (b) simulation

Fig. 7 Experimental and simulation results of thickness distributionin one-stage process

Fig. 8 Predicted preform-die shape for the conical cup in two-stageprocess

3604—Volume 22(12) December 2013 Journal of Materials Engineering and Performance

Author's personal copy

deformation stage a limited sheet stretching is necessary foreliminating the sheet wrinkling.

5.3 Effect of Cup Height (H)

Figure 13 shows the preform shapes for different heights ofthe final cup obtained from simulation. It is seen that byincreasing the height, the depth of the center of the preformO¢ decreases and the dome A¢ approaches to the center of thepreform. Therefore, the length of O¢A¢ decreases, while that ofA¢C¢B¢ increases. This is because by increasing the height, thebase region of the final cup OA decreases and the wall regionAB increases.

The thickness distribution of the final cups with differentheights produced in one-stage and two-stage processes arecompared in Fig. 14. In the one-stage process, by increasing theheight, the thickness of the base region OA decreases morecompared to that of the wall region AB. In comparison, in thetwo-stage process, the thicknesses of the base OA and the wallAB regions decrease more uniformly. There are some fluctu-ation in the thickness distribution in the corner region A that isrelated to the effect of sheet wrinkling during the finaldeformation stage. It is seen that by increasing the height, thefluctuation in the thickness distribution decreases, because thesheet stretching in the final stage increases.

Figure 15 shows the minimum and average thickness of thefinal cups with different heights. As it is seen, these parametersdecrease linearly as the height increases. In the one-stageprocess, the difference between the minimum and average linesincreases by increasing the height of the final cup. In contrast, itis constant in the two-stage process, which indicates that the

Fig. 9 The preform (a) and final (b) cups produced by two-stageprocess

Fig. 10 Thickness distribution of (a) the preform cup and (b) thefinal cup

Fig. 11 A comparison between sensitivity analysis and Xing et al.method in thickness distribution of conical cup

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3605

Author's personal copy

two-stage process is more efficient for cups with a greaterheight.

For investigating the stretching ratio between the preformstage and the final stage, the area of the cups at the end of thepreform stage (SP) and final stage (SF) were considered. Table 2shows the value of SP and SF for various heights. It is seen thatby increasing the height of the cup, the ratio of SP to SFdecreases which means that the percent of the sheet stretchingin the final stage increases.

Figure 16 shows the CEEQ distribution for final cups withdifferent heights in the two-stage process. It can be observedthat by increasing the height of the cup, the maximum CEEQincreases because the percent of the sheet stretching in the finalstage increases. However, in comparison to the one-stageprocess (Fig. 6) for the cup with the height of 35 mm, themaximum CEEQ reduces. In addition, there are two regionswhere the value of CEEQ is higher than the others: the first is in

Fig. 12 Several steps of deformation in two-stage SPF process

Fig. 13 The predicted preform-die shape for conical cups with dif-ferent heights

Fig. 14 The thickness distribution of the final cups with differentheights in (a) one-stage process, (b) two-stage process

3606—Volume 22(12) December 2013 Journal of Materials Engineering and Performance

Author's personal copy

the corner of the cup due to maximum stretching and thesecond is in the wall of the cup due to the sheet wrinkling inregion D (Fig. 12) in the final stage.

5.4 Effect of the Cone Angle (b)

Figure 17 shows the preform-die shapes for different coneangles of the final cup. By increasing the cone angle, the baseregion of the final cup OA decreases and the wall region ABincreases. Therefore, it is seen that in the preform-die the regionO¢A¢ decreases and the region A¢C¢B¢ increases. Also, the depthof the center of the preform O¢ decreases and the dome A¢approaches to the center of the preform-die.

In Fig. 18 the thickness distribution of the final cups withvarious cone angles that were produced by one-stage and two-stage processes are compared. By increasing the cone angle ofthe final cup the corner thickness in the one-stage processdecreases and the thickness of the wall region AB decreasesmore compared to that of the base region OA. It can beobserved that in the two-stage process by increasing the coneangle, the thickness of the base OA and the wall AB regionsincrease uniformly, and the fluctuation in the thicknessdistribution decreases.

Figure 19 shows the minimum and average thickness of thefinal cups with different cone angles. The minimum andaverage thickness decrease linearly as the cone angle increases,because the sheet stretching increases. In the one-stage process,the difference between the minimum and average linesincreases by increasing the cone angle of the final cup, whereasthis difference is constant in the two-stage process, whichindicates that the two-stage process is more efficient for cupswith higher cone angle.

Table 3 illustrates that by increasing the cone angle, the ratioof SP to SF increases which means that by increasing the coneangle, the percent of the sheet stretching in the preform stageincreases. The area of the wall region with respect to the baseregion increases as the cone angle increases, and the sheettouches the wall region earlier than for the base region. Thefriction effect in the wall region limits the sheet stretching in thefinal stage and therefore the sheet stretching in the preformstage must be increased.

Figure 20 shows the CEEQ distribution for final cups withdifferent cone angles in the two-stage process. It can beobserved that by decreasing the cone angle of the cup, themaximum CEEQ increases because the percent of thesheet stretching increases. For the cone angle of 15�, the sheetwrinkling in the wall region was removed by the sheetstretching in the final stage, and therefore the CEEQ in the wallregion of the cup was reduced.

Fig. 15 The minimum and average thickness of the final cups withdifferent heights in one-stage and two-stage SPF processes

Table 2 The area of cups with various heights in thepreform and final stages

Cup heightArea of cup, mm2

SP/SFH, mm Preform (SP) Final (SF)

35 14,818 16,073 0.9240 14,276 16,608 0.8645 13,565 17,173 0.79

Fig. 16 CEEQ distribution in the final cups with different heights:(a) H = 35 mm, (b) H = 40 mm, and (c) H = 45 mm

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3607

Author's personal copy

5.5 Effect of the Corner Radius (re)

Figure 21 shows the preform-die shape for different cornerradiuses of the final cup. The height of dome region A¢

decreases by increasing the corner radius of the final cup andthe other regions exhibit a similar trend at each corner radius.

Figure 22 shows the thickness distribution of the final cupswith different corner radiuses that were produced by the one-stage and two-stage processes. In the one-stage process, thedifference between the thickness distribution curves is limitedto the corner region A of the cup and the thickness is reducedby decreasing the corner radius. It can be observed that in thetwo-stage process the thickness distribution is approximatelythe same for various corner radiuses, while the fluctuation in thethickness distribution increases by decreasing the corner radius.

Figure 23 shows the minimum and average thickness of thefinal cups with different corner radiuses. The minimumthickness increases linearly by increasing the corner radius ofthe final cup, while the average thickness is not changedsignificantly. In the one-stage process, the difference betweenthe minimum and average lines increases by decreasing thecorner radius of the final cup, whereas this difference isconstant in the two-stage process. It indicates that the two-stageprocess is more efficient for cups with small corner radius.

Table 4 illustrates that the value of SP and SF and thus thesheet stretching in the preform and final stages decreases byincreasing the corner radius of the final cup. However, the ratioof SP to SF is not changed significantly which means that thepercent of the sheet stretching between the preform and finalstages is similar in all the cases.

Figure 24 shows the CEEQ distribution in the final cupswith different corner radiuses in the two-stage process. It isseen that as the corner radius increases, the CEEQ in the cornerregion decreases because the sheet stretching decreases.However, the CEEQ in the wall region is not changed, because

Fig. 17 Predicted preform-die shape for conical cups with differentcone angles

Fig. 18 The thickness distribution of the final cups with differentcone angles in (a) one-stage process, (b) two-stage process

Fig. 19 The minimum and average thickness of the final cups withdifferent cone angles in one-stage and two-stage SPF processes

Table 3 The area of cups with various cone angles in thepreform and final stages

b

Area of cup, mm2

SP/SFPreform (SP) Final (SF)

15� 14,748 18,292 0.830� 14,818 16,073 0.9245� 13,555 13,936 0.97

3608—Volume 22(12) December 2013 Journal of Materials Engineering and Performance

Author's personal copy

Fig. 20 CEEQ distribution in the final cups with different cone an-gles: (a) b = 15�, (b) b = 30�, and (c) b = 45�

Fig. 21 The predicted preform-die shape for conical cups with dif-ferent corner radiuses

Fig. 22 The thickness distribution of the final cups with differentcorner radiuses in (a) one-stage process, (b) two-stage process

Fig. 23 The minimum and average thickness of the final cups withdifferent corner radiuses in one-stage and two-stage SPF processes

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3609

Author's personal copy

the percent of the sheet stretching between the preform andfinal stages is similar in all the cases.

6. Conclusion

The results obtained in this research showed that thesensitivity method is an efficient technique to design the

preform-die in the two-stage SPF process. By comparing theresults of the one-stage process with those of the two-stageprocess, it is shown that the maximum thinning decreasessignificantly using the designed preform. The uniformity of thethickness distribution is improved that causes to the maximumvalue of the creep strain decreases. Therefore, the likelihood ofcavitation that occurs due to creep strain is limited.

The geometric parameter of the final cup has a significanteffect on the preform-die shape. By increasing the height andthe cone angle of the final-die, the depth of the preform-die inthe inner cavity decreases and the dome region is approached tothe center of the preform-die. In contrast, by increasing thecorner radius of the final-die, only the height of the domeregion decreases. The results show that for conical cups withmore height and cone angle and less corner radius, preformdesign is more efficient. The percent of stretching in thepreform and final stages are very important parameters, whichhave significant effects on the uniformity of the thicknessdistribution and eliminating the sheet wrinkling.

Acknowledgments

The authors would like to appreciate the office of the VicePresident for Research of Babol University of Technology for thefinancial support.

References

1. A.J. Barnes, Superplastic Forming 40 Years and Still Growing,J. Mater. Eng. Perform., 2007, 16(4), p 440–454

2. L.D. Hefti, Commercial Airplane Applications of SuperplasticallyFormed AA5083 Aluminum Sheet, J. Mater. Eng. Perform., 2007,16(2), p 136–141

3. P.A. Friedman, S.G. Luckey, W.B. Copple, R. Allor, C.E. Miller, andC. Young, Overview of Superplastic Forming Research at Ford MotorCompany, J. Mater. Eng. Perform., 2004, 13(6), p 670–677

4. F.S. Jarrar, F.K. Abu-Farha, L.G. Hector, and M.K. Khraisheh,Simulation of High-Temperature AA5083 Bulge Forming with aHardening/Softening Material Model, J. Mater. Eng. Perform., 2009,18(7), p 863–870

5. F.S. Jarrar, L.G. Hector, M.K. Khraisheh, and K. Deshpande, GasPressure Profile Prediction from Variable Strain Rate DeformationPaths in AA5083 Bulge Forming, J. Mater. Eng. Perform., 2012,21(11), p 2263–2273

6. X.D. Ding, H.M. Zbib, C.H. Hamilton, and A.E. Bayoumi, On theOptimization of Superplastic Blow-Forming Processes, J. Mater. Eng.Perform., 1995, 4(4), p 474–485

7. M.A. Nazzal, M.K. Khraisheh, and B.M. Darras, Finite ElementModeling and Optimization of superplastic Forming Using VariableStrain Rate Approach, J. Mater. Eng. Perform., 2004, 13(6), p 691–699

8. M.H. Hojjati, M. Zoorabadi, and S.J. Hosseinipour, Optimization ofSuperplastic Hydroforming Process of Aluminium Alloy 5083,J. Mater. Process. Technol., 2008, 205, p 482–488

9. Y.H. Kim, J.S. Lee, and S. Hong, Optimal Design of SuperplasticForming Processes, J. Mater. Process. Technol., 2001, 112, p 166–173

10. A. Huang, A. Lowe, and M.J. Cardew-Hall, Experimental Validation ofSheet Thickness Optimisation for Superplastic Forming of EngineeringStructures, J. Mater. Process. Technol., 2001, 112, p 136–143

11. H.L. Xing, K.F. Zhang, and Z.R. Wang, A Preform Design Method forSheet Superplastic Bulging with Finite Element Modeling, J. Mater.Process. Technol., 2004, 151, p 284–288

12. G. Luckey, P. Friedman, and K. Weinmann, Design and ExperimentalValidation of a Two-Stage Superplastic Forming Die, J. Mater. Process.Technol., 2009, 209, p 2152–2160

13. Y. Luo, S.G. Luckey, P.A. Friedman, and Y. Peng, Development of anAdvanced Superplastic Forming Process Utilizing a Mechanical Pre-forming Operation, Int. J. Mach. Tools Manuf., 2008, 48, p 1509–1518

Table 4 The area of cups with various corner radiusesin the preform and final stages

re, mm

Area of cup, mm2

SP/SFPreform (SP) Final (SF)

5 14,818 16,073 0.9210 14,507 15,938 0.9115 14,627 15,776 0.92

Fig. 24 CEEQ distribution in the final cups with different cornerradiuses: (a) re = 5 mm, (b) re = 10 mm, and (c) re = 15 mm

3610—Volume 22(12) December 2013 Journal of Materials Engineering and Performance

Author's personal copy

14. Y. Luo, S.G. Luckey, W.B. Copple, and P.A. Friedman, Comparison ofAdvanced SPF Die Technologies in the Forming of a Production Panel,J. Mater. Eng. Perform., 2008, 17(2), p 142–152

15. A. Gorji, H. Alavi-Hashemi, M. Bakhshi-jooybari, S. Nourouzi, andS.J. Hosseinipour, Investigation of Hydrodynamic Deep Drawing forConical-Cylindrical Cups, Int. J. Adv. Manuf. Technol., 2011, 56,p 915–927

16. A. Shamsi-Sarband, S.J. Hosseinipour, and M. Bakhshi-Jooybari,Theoretical and FEM Investigation of Superplastic Blow Forming inConical Die, Steel Res. Int., 2010, 52(9), p 651–654

17. A. Shamsi-Sarband, S.J. Hosseinipour, M. Bakhshi-Jooybari, and M.Shakeri, Study on the Effect of Friction Coefficient on theOptimized Preform Die Shape in a Multi-Stage SuperplasticForming, Steel Res. Int., Special Edition-Metal Forming, 2012,p 1007–1010

18. S.J. Hosseinipour, An Investigation into Hot Deformation of Alumi-num Alloy 5083, Mater. Des., 2009, 30, p 319–322

19. E. Soleymani, S.J. Hosseinipour, and H. Baseri, Hot Forming LimitDiagram of Al-5083 Alloy by Gas Blow Forming Process, Steel Res.Int., Special Edition-Metal Forming, 2012, p 695–698

Journal of Materials Engineering and Performance Volume 22(12) December 2013—3611

Author's personal copy