Research ArticleHydroforming Process for an Ultrasmall Bending Radius Elbow

Shangwen Ruan ,1 Lihui Lang,1 and Yulong Ge2

1School of Mechanical Engineering and Automation, Beihang University, Beijing, China2State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University,Beijing, China

Correspondence should be addressed to Shangwen Ruan; ruanshangwen@buaa.edu.cn

Received 1 November 2017; Revised 9 January 2018; Accepted 12 February 2018; Published 1 April 2018

Academic Editor: Giovanni Berselli

Copyright © 2018 Shangwen Ruan et al. *is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Bent pipes are widely used in automotive, aviation, and aerospace industries for delivering fluids. Parts having small relativebending radiuses are called elbows. However, fabricating a thin-walled elbow part using the simple bending process poses manychallenges. One possible way to manufacture elbows is with the stamping-welding process. *e major drawbacks of this methodinclude the decline in sealing performance and the addition in weight attributed to the lap welding process. Tube hydroforming(THF) is considered as a feasible solution to these problems. However, the forming process could be quite complex, and multistepforming is necessary. *is study investigates the effects of preliminary processes on elbow forming such as bending, partitionforming, and heat treatment and presents a high-performance optimized process design to achieve an ultrasmall radius elbow.*eeffects of multistep forming on the thickness distribution and the heat treatment on the microstructure have been evaluated. *eresults obtained from simulations show a reasonable agreement with those from the experiments.

1. Introduction

With an increasing demand on lightweight products, manythin-walled hollow structural parts have been widely appliedin the fields of transport instead of casted ones. Bent pipesand elbows are common components found in pipingsystems for their flexibility compared to straight pipes [1].Tube NC bending is the major process to manufacture bentpipes, but it is too hard to obtain an elbow with relativebending radius less than 1.0 with this method [2], even withlocal heating [3]. *e stamping-welding process can be usedas an option in industry [4]. Similarly, the use of flanges isunavoidable in the lap welding process, which adds excessiveweight to components and introduces the risk of fluidleakage.

Tube hydroforming (THF) technology is attractingmuch attention as a superior option to traditionalmanufacturing methods. *e so-called bending-bulgingforming is very appropriate to form elbow parts [5]. *eblank can be either a seamless tube or a brazed tube. Highhydraulic pressure and axial feeding are applied to the

internal wall of the tube to force the blank to attach the diecavity. To obtain an elbow part without failure, thickness,stress, and strain distributions through steps should beevaluated. Furthermore, the process design, which includessequence and parameters such as feeds and forming pres-sure, should be optimized. Bending, hydroforming, and heattreatment combinations have been employed to achieve thebending-bulging, and their influences on the componentquality have been investigated. Yuan et al. [6] put fortha hydroforming process for the manufacturing of large el-bow pipes based on integral hydrobulging forming tech-nology of spherical and ellipsoidal shells. In this process,a toroidal component with a polygonal cross section pre-welded by sheets is filled with a liquid medium and thenpressurized by a pump. It can be cut into four 90° elbows sothat a large diameter elbow pipe can be manufacturedwithout special equipment or dies. However, assembling andwelding are required. Shr [7] reviewed and analyzed thebending process for hydroforming and gave an un-derstanding of the relationship between design parametersand bending characteristics. Kong et al. [8] studied the

HindawiAdvances in Materials Science and EngineeringVolume 2018, Article ID 7634708, 15 pageshttps://doi.org/10.1155/2018/7634708

deformation behavior and the failure in bending-bulgingforming. is study showed that the bending operationmight consume most of the formability of the tube, thefracture failure sometimes occurred outside of the bending,and the maximum work hardening e�ect takes place aroundthe rear end of the bend section. anakijkasem et al. [9]considered e�ects of bright annealing in the tube hydro-forming process. For 304 stainless steel, during the formingdeformation, the induced martensitic transformation takesplace at the deformed area in an anisotropic way, leading tothe development of texture and working hardening. It isfound that, at the temperature of 1050°C, holding for 30min,and rapidly cooling by purging nitrogen gas, best tensile testresults were achieved. Ma et al. [10] carried out the e�ect ofprocesses on tube hydroforming and achieved a soundcomplex 3D pipe. e results showed that considerablethickness variations and phase transformation at the curvezones after the bending process were present. Heat treatmentmust be provided to improve the formability of the tube. Onthe other hand, considering the process parameters, An et al.[11] and Ge et al. [12] used a multiobjective optimizationalgorithm to achieve better loading path solutions forbending-bulging processes separately.

Although previous studies have given examples ofbending-bulging processes, obtaining a well-performanceelbow part is still di�cult in several aspects, including thee�ects of welding, risk of defection, and massive computing.In this paper, the component under consideration is anultrasmall bending radius elbow made of 304 stainless steel. e preliminary processes are investigated using both nu-merical and experimental methods. e simulations areimplemented using LS-DYNA software.

2. Part Description

2.1. Part Speci�cations. In the present study, the manufac-ture of an ultrasmall bending radius elbow used in an au-tomobile engine was studied. e model of this componentis depicted in Figure 1. e desired outer diameter D is50.0mm and the bending radius R is 27.5mm, respectively. us, the relative bending radius R/D is about 0.56, which is

very small in comparison to the commonly observed value of0.8. e initial thickness of the blank is 2.0mm and thepermissible thinning ratio is 30%, which means that theminimum allowable thickness of the part must be larger than1.4mm. e material of this part is 304 austenitic stainlesssteel manufactured by BAOSTEEL. Young’s modulus andPoisson’s ratio are 207GPa and 0.28, respectively. e stress(σ)–strain (ε) relationship can be represented in the Swiftharden law as follows:

σ � K · (ε + ε)n

� 1426.5 ×(0.029 + ε)0.5,(1)

where K is the strength coe�cient, ε is the initial strain, andn is the harden exponent.

2.2. Part Analysis. Considering the required part shape, thetube initially needs to be bent. During the bending process,the inside of the bend is thickened by the tension-compression stress and the outside is thinned due to thetension-tension stress, which can be seen in Figure 2.

e thicknesses of outside to and inside ti of bending canbe evaluated using the following equation [7]:

to�2R

2R +D0 − t0t0 � 1−

1− t0/D0

2R/D0 + 1− t0/D0( )t0,

ti �2R/D0

2R/D0 − 1 + t0/D0t0 � 1 +

1− t0/D0

2R/D0 − 1 + t0/D0( )t0,

(2)

where D0 and t0 represent the initial outer diameter andthickness, respectively, and R is the bending radius.When thethickening and thinning are inaptly controlled, the instabilityof the material may lead to defects including wrinkles andcracks in the tube. According to the geometry relationships ofbending, the limited bending radius R/D0 (LBR) must besatis¥ed. LBR describes an extreme condition, where theelongation on the outside reaches the tension fracture strainof the material. At this point, the relationship of the outerdiameter must satisfy the following constraint [7]:

(a)

15

ϕ50

90°

15

2

R 27.5

(b)

0.0 0.1 0.2 0.3True strain

Stre

ss (M

Pa)

0.4 0.5 0.6 0.70

100200300400500600700800900

10001100

Experiment pointFitting line

(c)

Figure 1: Model of the targeted component and material. (a) Isometric view, (b) sectional view, and (c) material harden law.

2 Advances in Materials Science and Engineering

R

D0>

12 eεf − 1( )

, (3)

where εf is the fracture strain. e actual R should be muchlarger than the minimum value. In practice, the limitedrelative bending radius is about 1.5. us, it is too hard toobtain an elbow component only using the bending process. e bent tube must be bulged up to satisfy the requirementshape with a very high expansion ratio η, whichmay result inoverthinning of the material in the forming process. eexpansion ratio can be expressed as [13]

η �D

D0, (4)

where D is the maximum section diameter.Compared to the bulging process of the straight tube, the

bending-bulging process is much more complicated. Asimpli¥ed torus model has been used to analyze this process.In a torus model, the homogeneous internal pressure p isplaced on the inner surface as illustrated in Figure 3.

According to the equilibrium equations, the axial stress σθand the hoop stress σφ can be expressed as [8]

σθ �pD

4t2−

sinφ2R/D− sinφ

( ), (5)

σφ �pD

4t, (6)

where φ is the angle between the bending line and the sectionnormal direction and t is the current thickness. From (6), itcan be found that the stress distributes uniformly along thehoop direction, and from (5), the ratio of axial and hoopstress σθ/σφ would be very high when the relative bendingradius is small. Meanwhile, the axial stress on the inside ofbending could be much larger than the one on the outside,potentially resulting in serious problems in elbow formingexplained as follows.

In the elbow-forming process, however, the boundaryconditions of bending-bulging are quite di�erent to the

R

ddθ

Ry

rm

rm

σθ

σθ

dφ

dφσt

σt + dσt σt + dσt

σφ + dσφ

σφ + dσφ

σφ + dσφ

σφ + dσφσt + dσt

εt + dεt

εt + dεt

εθ + dεθ

εθ + dεθ

σθ + dσθ

σθ + dσθ

σθ + dσθ

σt + dσt

σθ + dσθ

dRy

ρD

φ

φ

r

σθ

σφ

σφ

σθ

εθ

εθ

εt

εt

σt

σt

Figure 2: Stress and strain state of the bending process.

62.06

44.06

R18

Figure 3: Torus model analysis under internal pressure.

Advances in Materials Science and Engineering 3

quarter symmetry section of a torus. Since the ends of anelbow are not ¥xed and potential axial feedings in thehydroforming process, they are not capable of o�ering theaxial tension forces on the cross section. e axial stresses onthe tube ends will be zero, or for most cases, they will benegative. So, the equilibrium equation (5) in the torus modelalong axial direction cannot be matched in the elbow-forming process. As a result, when the internal pressure isimposed on the tube, because of a larger area, the force onthe outside bend is higher than that on the inside and there isan unbalanced condition. It will make the tube deviate fromthe bending center to outward until it reaches the die surface,as detailed in Figure 4. Here, due to the thickness changingon the tube, the hoop stress distribution is no longer uni-form. e thickened area is less likely to further deform. ismay cause overthinning in bulging, as shown in Figure 5(a).

On the other hand, there is a tendency for the tube endsto shrink, especially on the inside. For this reason, axial feedingof the material to the bulging zone is very di�cult to achievebecause the wrinkle or buckle cannot be ¦attened. A largeexpansion ratio is di�cult to realize, as seen in Figure 5(b).

To summarize, the major challenges for a small relativebending radius elbow-forming process are the following: (a)small relative bending radius is hard to obtain using bendingitself, (b) the inner pressure loading could lead to a wrinkleon the inside of the bend, and (c) inhomogeneous thicknessdistribution could aggravate the wrinkle and also result incrack on thinning areas.

However, if the process is well designed, the charac-teristic of the bent tube can be helpful to obtaining a qual-i¥ed elbow component.

3. Multistep Forming Process

e aim of the present forming process is to reduce therelative bending radius from 1.5 in rotary bending to 0.56 inthe target component. Two major methods are adopted toachieve this goal: further bending to decrease the bendingradius and bulging to increase the outer diameter of the tube. us, a multistep partition-forming process is proposed inthis study.

3.1. Process Solutions to Elbow Forming. In Figure 6, thegeometry relationships of the prebent tube and targetcomponent are illustrated. ey have a signi¥cant in¦uenceon the thickness distribution and the ¥nal part quality.Figure 6(a) demonstrates the most dangerous zones in theforming process. e pink area represents the target com-ponent, and the blue area is the tube blank. Section A is thecenter section in bending where the most thinning andthickening are located. Section B is the transition betweenthe origin tube and the formed area, so the stress state here issimilar to a uniaxial tension and is likely to fracture.

So, the prebent tube is divided into four subregions (seethe cut view of section A in Figure 6(b)). Bent thinning

(a)

Internalpressure

(b)

Figure 4: Movement of the bent tube under internal pressure: (a) bent tube and (b) pressure imposed.

Crack

(a)

Wrinkle

(b)

Figure 5: Defections in the forming process: (a) crack and (b) wrinkle.

4 Advances in Materials Science and Engineering

region (I) is on the outside bend where the thickness isreduced by 15% through estimation. Cracking is highlyprobable to happen here when there is excess deformationinduced by the hydroforming process.

Bent thickening region (II) is on the inside bend, wherethe thickness is increased by about 20%. Here, there is a highrisk of wrinkle due to the bending and the potential com-pression stresses under internal pressure mentioned pre-viously. But it is interesting that there is enough materialaccumulated in this region after bending, leading to thepossibility of avoiding feeding in bulging and prevention ofthe elbow from wrinkle.

e middle layer region (III), as the name suggests, is themiddle layer area in the bending deforming region, andbending straight region (IV) (Figure 6(c)) is the inside regionout of the deformed region. ese two regions deform littlein the bending process and almost retain almost fullformability and retain full formability for next steps.

Above that, it indicates that the further thinning on thebent thinning region should be inhibited and more bulgingdeformation could be induced into the bent thickening area.In this way, the crack and wrinkle can be eliminated in theforming process. us, four steps are employed in thisprocess: a rotary bending and three-step partition forming tocontrol the tube deforming in sequence andmake best use ofthe material. Figure 7 demonstrates the processes and mainideas in each step.

e ¥rst forming step (THF1) is a combination of crushbending and bulging to reduce the bending radius withoutspringback.

e second step in the partition bulging process (THF2)aims to further increase the outer diameter by bulging theinside region of the tube. In the ¥nal hydroforming step(THF3), the middle layer and straight regions are dilated upand the whole part is calibrated to attach the target shape.

To enhance the formability of the material, in this study,the bright annealing process is also used after tube bending.304 austenitic stainless steel, one of the most widely usedmaterials, has good mechanical properties and corrosionresistance. However, the strain-induced martensitic trans-formation that occurs during the forming process will de-crease the formability of the tubular material [14]. e yieldstrength σs increases during the deformation. At the sametime, the elongation decreases signi¥cantly. As the de-formation is quite high in the bulging process, the risk offracture will be increased. Bright annealing can re¥ne theproperty of this austenitic stainless steel.

First, a series of simulations are performed using LS-DYNA ¥nite element code to predict the processes beforeexperimentation. Considering the 2mm thickness, the tubeblank is meshed with shell elements in the Belytschko–Tsaytype with a size of 3mm and 5 integration points. Additionally,the tools are viewed as rigid bodies in simulations, and thefriction coe�cient between blank and tools is set to 0.125.

Rotationdirection

A

BB

Feedingdirection

(a)

Zone IIZone I

Zone III

A-A

Zone III

(b)

Zone IV

A

BB

(c)

Figure 6: Geometry relationships of the prebent tube and target component. (a) Cross section indications. (b) Cross section A. (c) Crosssection along the axial line.

Advances in Materials Science and Engineering 5

At the end of an analysis, LS-DYNA code will writea “dynain” ¥le. A “dynain” ¥le contains a set of keyword datathat can be inserted into an input deck to initialize de-formation, shell thickness, and element history variables forthe next analyze step. Otherwise, the annealing process canbe simulated by removing the stress and strain informationfrom the “dynain” ¥le [15] which includes stresses, backs-tresses, plastic strains, and velocities.

3.2. Fine Design of the Partition-Forming Processes. In thebending process, the relative radius should be as small aspossible while the thinning and thickening are considered.Although there are several types of bending methods thatcan be applied as preforming in the process, the NC rotarybending was selected for its stability and predictability ofspringback, as seen in Figure 8. e front of the blank is ¥xed

in the cavity between the clamp die and bend die, andthemiddle section is bent by the rotation of the bend die. erear goes forward with the push die and constrained by thepressure die and wiper die. In the inner cavity of the tube,there are mandrels and balls to prevent the tube fromwrinkling or distorting.

ree major parameters need to be determined such asinitial diameters of the blank D0, bending radius R, andbending angle α. In most tube hydroforming processes, theminimum outer diameter on the ¥nal parts can be taken asthe initial diametersD0 of blanks. In elbow forming, becauseof the limited relative bending radius, D0 should be muchsmaller than usual. e deformation on the tube must becarefully controlled. To obtain a reasonable prebent tube,D0is selected as 42mm which is a common dimension used intube blanks to lower computational cost. R is 63mm, so therelative bending radius is 1.5, which is a commonly

Tubeblank

Upper die moverment

Further bulging the straight-line area

Crushing bending and bulging

(1) Pushing the blank to the upper surface(2) Bulging the blank to the lower surface

Bending

Brightannealing

THF1:crush bending

THF3:straight-line region

THF2:bending thickening

region

PartitionHydroforming

Brightannealing

Cutting

Brightannealing

Lower die stationary

Figure 7: Flowchart of the partition-forming process.

6 Advances in Materials Science and Engineering

acceptable value in rotary bending. Considering the generalspringback coe�cients, the bending angle α is selected tobe 92°.

In addition, there are several other parameters that a�ectthe bending quality especially the wrinkle, such as thenumber of mandrel balls and the interval between the ballsand ball width. e wrinkle on the thickening region can bedivided into two sections: before and after the tangent point. e wrinkle before the tangent point is mainly caused by thecompressive stresses during the bending, and the other iscaused by the hindering e�ect of the balls on the blankmovement. As a result, a smaller gap between the mandreland blank is preferred, and a larger gap between balls and

blanks is better. e gap here indicates the distance from themandrel and ball’s outer surfaces to the inner surface of thetube blank. e main dimensions of rotary bending tools arelisted in Table 1. e thickness distribution in ¥nite simu-lation can be seen in Figure 9. e minimum thickness isabout 1.73mm on the outside, and the maximum thicknessis 2.37mmon the inside. e corresponding thinning ratio is13.33% and −18.65%, and there is no obvious wrinkle foundafter bending.

en, a bright annealing is performed to improve theformability of the tube. It is heated gradually from roomtemperature to 1050°C in a protective atmosphere, held for30 minutes, and then cooled down in air [9], as seen in

Push TubeMandrel

Pressure die Wiper die

W

Bending die

Insert die

Clamp die

Balls

Figure 8: Schematics of the rotary bending process.

Table 1: Dimensions of rotary bending tools (mm).

Tool Insert die Clamp die Pressure die Wiper die Mandrel shaft Balls Ball interval Ball widthLength 126 126 126 126 126 3 20 10Gap 0.12 0.12 0.12 0.12 0.3 0.3 0.3 0.3

Trianglepoint

Gap between the tube and the mandrel

Figure 9: ickness distribution after rotary bending.

Advances in Materials Science and Engineering 7

Figure 10. us, the most optimal mechanical properties ofthe SS304 tube for the hydroforming process are provided. e yielding strength is about 170MPa, and a total elon-gation of about 70% can be obtained. It is worth mentioningthat the BA treatment introduces little changes in thebending angle but does not a�ect the bulging process.

e average grain size is estimated according to ASTME112 [15] to verify the validity of using bright annealingthrough observation of the microstructure evolution, as seenin Figure 11. e martensitic fraction is measured using thegrid method. e sample before bending is homogeneousaustenite. e grains are moderate in size, and boundariesare mostly straight edges. No martensite is found here.

e grains are squashed after bending. Some austenitegrains exhibit characteristics of slip lines, which are pre-sumed to be martensite produced by deformation. Othergrains retain the twin characteristics of austenite. e vol-ume fraction of martensite is between 14% and 22%, and theaverage grain size is about 6.50.

e microstructure recovers, and an obvious re-crystallization occurs during the bright annealing treatment. e martensite totally transforms back to austenite. Besides,the grains are with smaller size due to the heat temperatureand holding time. e average grain size here is about 8.18.

After heat treatment, a three-step partition-formingprocess is employed. As mentioned above, THF1 is a com-bination of crush bending and bulging. Crushing operationis a common process within hydroforming during dieclosing employed to re¥ne the thickness distribution andmake additional deformations in the tubular part [5]. In thisstudy, the closing movement of the upper die is in theprebending plane and the direction is the center line inprebending, so it can be deemed to be crush bending, as seenin Figure 12(a). To reduce springback [16], the internalpressure should be imposed subsequently to release residualstress on the tube.

e expansion ratio is limited to prevent the bentthinning region from serious thinning in this step. Mean-while, since it is not necessary to feeding material into thedeforming zone here, only the internal pressure needs to beconsidered in the loading path design. e maximum valuep can be expressed as

p � 2tσtD− t

, (7)

where σt is the tensile strength of the material.Figure 12(c) demonstrates the strain paths of these two

regions of the tube in this step. In the crush-bending stage,

0 10 20 30 40 500

200

400

600

800

1000

1200

Time (min)

Tem

pera

ture

(°C)

1050°C 30 min in N2 protection

Cooling in air

Figure 10: Temperature-time pro¥le used for the BA process.

(a) (b) (c)

Figure 11: Crystalline phase (100x). (a) Before bending. (b) After bending. (c) After bright annealing.

8 Advances in Materials Science and Engineering

the bent thinning region is under a tensile-compress stateand the thickness retains stability. e thickening region isunder the compress-compress state, so the material ¦ows inand cumulates here. In the bulging process, there is notobvious deformation until the internal pressure about45MPa. en, the strain state of the thinning region be-comes tensile-tensile, which leads to a large deformation,and the thickness decreases rapidly. e thickening region isunder the tensile-compress state, and no more thickeningoccurs. e least thickness of this region is 1.52mm with thethinning ratio less than 25%, which is a quite ideal result, asseen in Figure 12(b). e largest thickness in the bentthickening region is 2.43mm with the thinning ratio as−21.5%, and no wrinkle happens. In this step, the relativeradius of the elbow decreases from 1.5 to about 1.2.

e second step in the partition bulging process (THF2)aims to further increase the outer diameter by bulging thebent thickening region to obtain a better thickness distri-bution. To achieve this goal, there is a sight pushing on boththe ends that the thinning region to attach the die surfacebefore the internal pressure is increasing, so friction betweenthe tube and die can help to reduce the sustained thinninghere, as shown in Figures 13(a) and 13(b). ere are a small

radius ¥llet to be formed in this step with the value of 4mmon the thickening region and another two ¥llets with thevalue of 5mm on the straight-line regions. In this condition,the maximum forming pressure is called calibration pressurepcal. It can be given by the following formula:

pcal �2�3

√ tiσtRmin − ti/2

, (8)

where Rmin is the minimum ¥llet radius for the target part.It can be found that the minimum thickness of the bent

thinning region is kept as 1.52mm, and the thickeningregion is further thickened slightly during pushing. en,during the increasing of internal pressure, the thickeningregion starts deforming. e tube is stretched in hoop di-rection and shrinks in the axial direction, due to which thethickness in this area decreases. e area on the intersectionof thickening and straight-line regions should be empha-sized as it is the most thinning (MT) region on the tube.Meanwhile, this area needs to be formed into the ¥llets, asshown in Figure 13(c). e thickness here changes from2.3mm to 2.0mm with the thinning ratio as 15%. ey havesimilar strain paths to the thickening region here, as shownin Figure 13(d). MT begins to deform earlier, and the ef-fective strain is smaller. It is because that the initial thickness

Upper die moving direction Thickness

1.5581.6021.6471.6911.7351.7791.8231.8671.9111.9551.9992.0442.0882.1322.1762.2202.2642.3082.3522.3962.441

0

Major principalstrain middle

layer

(a) (b)

(c)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0–0.10–0.08–0.06–0.04–0.02

0.000.020.040.060.080.10

Time (s)

0

10

20

30

40

50

Major principal strain in the bent thinning regionMinimum principal strain in the bent thinning regionMajor principal strain in the bent thickening regionMinimum principal strain in the bent thickening regionPressure

Pres

sure

(MPa

)

Stra

in

Figure 12: e ¥rst forming step: (a) die movement, (b) thickness distribution, and (c) strain paths of subregions I and II.

Advances in Materials Science and Engineering 9

here is lower and MT areas ¥rst attach the die surface.Additionally, the strain paths of the thinning region are stillstable in bulging. It indicates that although a tension-compression deformation occurs on the thickening re-gion, there is no more material accumulation.

In the third bulging step, the tube needs to be furtherexpanded, while the ¥llet needs to be further calibrated.Similar to the last step, a sight prepushing is adopted toprevent thinning region deforming, as seen in Figures 14(a)and 14(b). en, the internal pressure raises up to 160MPasince the minimum ¥llet radius is 3mm. e middle layerregion dilates up along with further deforming on thethickening region so that section A-A transforms from anellipse into a circle with the diameter of 50mm, as shown inFigure 14(c). As there is su�cient material formability here,no risk of crack exists. e strain path here is more likely inan axial tension state. In addition, the straight-line regionand MT area are expanded in similar tension-compressionstrain states, but the magnitude of straight-line region ismuch higher, as demonstrated in Figure 14(d). It can also be

seen that the deformation of the thinning region can beignored and MT area continues to deform in this step butmuch lower than the last step. It indicates that the strategy ofpartition forming can e�ectively control the deformation onthe tube in the process.

e springback of the ¥nal bulging process is shown inFigure 15. Single point constraint is applied on one side ofthe end in simulation. e most springback displacement isless than 0.35mm on the other end which is ignorable in theforming process. Finally, end cutting and, at this point, theultrasmall bending radius elbow part are obtained.

4. Results and Discussion

In this study, a multistep forming process is employed toobtain an ultrasmall bending radius elbow. Each of these stepsaims to make a special region of the tube deformed to makethe thickness distribution uniform. As shown in Figure 14, thedeformation in bent thinning regions is quite low, and thebent thickening regions reduce their thickness sequentially

End pushing End pushing

MIN:1.52

MAX:2.43

(a)

MIN:1.52

MIN:2.56

(b)

Internal pressure

MT

MIN:1.51

MAX:2.22

(c)

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3–0.5–0.4–0.3–0.2–0.1

0.00.10.20.30.40.50.60.7

Time (s)

0

20

40

60

80

100

120

Major strain in the thinning regionMinimum strain in the thinning regionMajor strain in the thickening regionMinimum strain in the thickening regionMajor strain in the MT areaMinimum strain in the MT areaPressure

Pres

sure

(MPa

)

Stra

in

(d)

Figure 13: e second forming step: (a) pushing starts, (b) pushing ends, (c) bulging, and (d) strain paths.

10 Advances in Materials Science and Engineering

Thickness A

A

(a)

InternalpressureStraight-line

region

MT

3 mm

(b)

A-A

1.511.541.581.611.641.671.711.741.771.811.841.871.911.941.972.012.042.072.102.142.17

1.481.511.541.571.601.631.651.681.711.741.771.801.831.861.881.911.941.972.002.032.06

0

∗

0

∗

(c)

0.0 0.5 1.0 1.5 2.0 2.5

–0.4

–0.2

0.0

0.2

0.4

0.6

Time (s)

0

50

100

150

Major strain in the thinning regionMinimum strain in the thinning regionMajor strain in the thickening regionMinimum strain in the thickening regionMajor strain in the middle layer regionMinimum strain in the middle layer regionMajor strain in the straight-line regionMinimum strain in the straight-line regionMajor strain in the MT areaMinimum strain in the sub-MT areaPressure

Pres

sure

(MPa

)

Stra

in

(d)

Figure 14: e ¥nal forming step: (a) part location, (b) bulging, (c) cross-section deformation, and (d) strain paths.

0.3430.3260.3080.2910.2740.2570.2400.2230.2060.1880.1710.1540.1370.1200.1030.0860.0690.0510.0340.0170.000

0

∗

Figure 15: Springback in the ¥nal forming step.

Advances in Materials Science and Engineering 11

chiming in the partition-forming process. e ¥nal formedcomponent is shown in Figure 16. ere are three thinningareas which are present in the bent thinning region andstraight-line region and one thickening area which appears onthe bent thickening region. e least thickness is 1.48mmwith the thinning ratio of 26%, which is a reasonable resultcompared to the design requirement. e most thickness isonly 2.09mm, which reduces during the hydroforming pro-cesses after bending.

Figure 16(b) instructs the forming limit diagram of thehydroforming process. Although the strain path of the tubeis not linear in di�erent steps, it is believable that the ma-terial has a large safe margin to the limit lines. e strainpaths of most bending thinning, thickening, and MTregionsare shown in Figure 16(c). No crack nor wrinkle will occur inthe elbow component. is is due to the reasonable con-trolling of the deformation extent and order by the partition-forming process. In Figure 17, the deformation processes ofcross sections A and B in Figure 6, which are the most typicalfeatures on the component, are clearly demonstrated. Sec-tion A has the most thinning and thickening area afterbending. Bent thinning, thickening, and middle layerregions are formed in a controllable sequence in stepsusing the boundary conditions of die design. As thestraight-line region rarely changed in the bending processand is located out of the wrinkle zone, the major formingprocess of this region is in the ¥nal calibrating step during

the increase of internal pressure. It is worth mentioningthat because there is no material feeding during thebulging processes, design of the loading path can besu�ciently simpli¥ed.

e process design then is validated by experiments, asshown in Figures 18(b) and 18(c). ere is no defect foundon the component. e crystalline phase experiment is alsoimplemented after the ¥nal forming process. e martensitecontent is about 30%. Finally, an extra bright annealingprocess is used to release the stress and strain on the formedcomponent to restore themicrostructure of thematerial. etypical austenite structure with small grain size, planarboundary, and twins is found in Figure 18(d).

5. Conclusion

In this study, both numerical and experimental in-vestigations are performed on a multistep tube hydro-forming process considering the rotary bending, heattreatment, and a partition-forming method to obtain anultrasmall bending radius elbow component.

Because there is a phase transformation from austeniteto martensite at the curve zones during the rotary bendingprocess, bright annealing must be provided before bulging toimprove the formability.

As the foundation of the process design, the reason ofwrinkle that could happen in forming is analyzed. Due to the

2.090

2.062.032.001.971.941.911.881.851.821.791.761.731.691.661.631.601.571.541.511.48

∗

(a)

1.00

Crack

Safe

Wrinkle

Riskof crack

Wrinkletendency

SeverewrinkleInsufficientstretch

0.80

0.60

0.40

0.20

0.00

(b)

–0.4 –0.3Minimum strain

Maj

or st

rain

–0.2 –0.1 0.0 0.10.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Most thinning regionMost thickening regionMT region

(c)

Figure 16: Quality of the target component. (a) ickness distribution. (b) Forming limit diagram. (c) Strain paths of crucial regions.

12 Advances in Materials Science and Engineering

analysis, it is found that the material feeding during bulgingshould be abolished in small radius elbow forming. eloading paths can be simpli¥ed into achieving the highestvalue of internal pressure in each step, which shows excellentagreement between the experiments and simulations.

Partition-forming process is introduced to take fulladvantage of the material features after bending. e resultsshow that the considerable thickness variations at the curvezone can help to achieve a better thickness distribution afterhydroforming. e process of partition forming utilizes the

2.410

2.382.352.312.282.242.212.182.142.112.072.042.001.971.941.901.871.831.801.771.73

2.420

2.372.332.282.242.192.152.102.062.021.971.931.881.841.791.751.701.661.611.571.52

2.420

2.372.332.282.242.192.152.112.062.021.971.931.881.841.791.751.701.661.611.571.52

2.170

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2.050

2.032.001.971.941.911.881.861.831.801.771.741.711.691.661.631.601.571.541.521.49

∗

∗

∗

∗

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(a)

THF1

THF2

THF3

2.040

2.032.022.022.012.012.001.991.991.981.981.971.961.961.951.951.941.941.931.921.92

1.990

1.991.981.981.981.971.971.971.961.961.961.951.951.941.941.941.931.931.931.921.92

2.400

2.372.332.292.262.222.192.152.122.082.042.011.971.941.901.861.831.791.761.721.68

2.110

2.102.082.062.052.032.022.001.981.971.951.941.921.901.891.871.851.841.821.811.79

1.820

1.811.801.791.781.771.751.741.731.721.711.691.681.671.661.651.631.621.611.601.59

∗

∗

∗

∗

∗

(b)

Figure 17: Deformation processes in (a) section A and (b) section B.

Advances in Materials Science and Engineering 13

boundary conditions provided by the die surface to e�-ciently control the deformation path of each subregion forhydroforming a quali¥ed component without crack andwrinkle defects.

Conflicts of Interest

e authors declare that there are no con¦icts of interestregarding the publication of this paper.

References

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2.090

2.062.032.001.971.941.911.881.851.821.791.761.731.691.661.631.601.571.541.511.48

∗

(a) (b)

(c) (d)

Figure 18: Ultrasmall bending radius elbow. (a) Trimmed simulation component. (b) Trimmed experimental component. (c) Tool set forthe ¥nal forming step. (d) Microstructure after ¥nal annealing.

14 Advances in Materials Science and Engineering

Advanced Manufacturing Technology, vol. 91, no. 5–8,pp. 2369–2381, 2017.

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[12] Y.-L. Ge, X.-X. Li, L.-H. Lang, and S.-W. Ruan, “Optimizeddesign of tube hydroforming loading path using multi-objective differential evolution,” International Journal ofAdvanced Manufacturing Technology, vol. 88, no. 1–4,pp. 837–846, 2017.

[13] S. Yuan,Modern Hydroforming Technology, National DefenceIndustry Press, Beijing, China, 2009.

[14] Z.-Y. Xue, S. Zhou, and X.-C. Wei, “Influence of pre-transformed martensite on work-hardening behavior ofSUS 304 metastable austenitic stainless steel,” Journal of Ironand Steel Research, International, vol. 17, no. 3, pp. 51–55,2010.

[15] ASTM, Standard Test Methods for Determining Average GrainSize, ASTM International, West Conshohocken, PA, USA,2013.

[16] C.-P. Jiang and C.-C. Chen, “Grain size effect on thespringback behavior of the microtube in the press bendingprocess,” Materials and Manufacturing Processes, vol. 27,no. 5, pp. 512–518, 2012.

Advances in Materials Science and Engineering 15

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