Springback characterization and behaviors of high-strength Ti–3Al–2.5V tube in cold rotary draw bending

Journal of Materials Processing Technology 212 (2012) 1973–1987

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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec

Springback characterization and behaviors of high-strength Ti–3Al–2.5V tube in cold rotary draw bending H. Li a , H. Yang a,∗ , F.F. Song a , M. Zhan a , G.J. Li b a b

State Key Laboratory of Solidification Processing, School of Materials Science, Northwestern Polytechnical University, Xi’an 710072, China Chengdu Aircraft Industry (Group) Corporation Ltd., Chengdu 610092, China

a r t i c l e

i n f o

Article history: Received 28 November 2011 Received in revised form 27 April 2012 Accepted 29 April 2012 Available online 7 May 2012 Keywords: Springback High strength Titanium alloy Tube Bending

a b s t r a c t Stress-relieved Ti–3Al–2.5V bent tube in hydraulic bleeding systems improves the overall performance of advanced aircraft and spacecraft due to its unique high specific strength. However, the high ratio of yield strength to Young’s modulus may induce significant elastic recovery after unloading. The precision bending of the high strength Ti-tube (HSTT) depends on the understanding of the springback features and mechanisms. Using the plasticity deformation theory, the explicit/implicit 3D-FE and the physical experiments, the springback behaviors of the HSTT under multi-die constrained cold rotary draw bending (RDB) are addressed. The results show that: 1) The elastic recovery of the HSTT should be characterized by the significant angular springback, the radius growth and the sectional springback; Both the angular and radius springback should be compensated, while the sectional one decreases the cross-section flattening; 2) Among multiple parameters, both the material properties (Young’s modulus, strength coefficient and anisotropy exponent) and the geometrical dimensions (bending angle and bending radius) dominate the unloading; Both the angular and radius springback values decrease with the smaller bending radii; The angular springback increases linearly with the larger bending angles, while the radius growth fluctuates little with the increasing of the bending angles at the later bending stages; Both the springback values of the HSTT are far larger than the ones of the 5052O Al-alloy tube and the 1Cr18Ni9Ti tube; The maximum variations of the angular and radius springback with changing of the processing parameters are 78% and 62.5% less than the maximum ones under different material properties and geometrical ones, respectively. 3) A two level springback compensation methodology is proposed to achieve the precision bending in terms of both springback angle and radius. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction Due to high specific strength and corrosion resistance capability, the titanium alloy (Ti-alloy) tube currently has attracted increasing applications in hydraulic pmeumatic, fuel or environment control systems for advanced aircraft and spacecraft as bleeding components (Boyer, 1996). After stress relieving annealing, the strength of the Ti–3Al–2.5V tube reaches above 750 MPa and finds potential usage to satisfy the product requirements of the weight reduction, the fuel efficiency, the high-pressure resistance and thus the overall performance (SAE, 2010). Among various bending methods such as the compress bending, the stretch bending and the pushing bending, the rotary draw bending (RDB) is a feasible one for achieving stable bending of the high strength titanium tube (HSTT). However, under multi-tooling constraints as shown in

∗ Corresponding author. Tel.: +86 29 88495632; fax: +86 29 88495632. E-mail addresses: [email protected], [email protected] (H. Li), [email protected] (H. Yang).

Fig. 1, the tube bending is a tri-nonlinear physical process with various parameters and possible multiple defects. Among various defects such as wrinkling, over thinning, cross-section distortion, the elastic release phenomenon is inevitable (as shown in Fig. 1) and even behaves more obviously due to the high ratio of the yield strength to Young’s modulus of the HSTT. The springback reduces the dimensional accuracy of the bent tubular parts, and decreases the connection/sealing performance of tubes with other parts as well as the internal structure compact. Considering the closer tolerance needed in the aerospace industries, etc., there is a challenge for efficient controlling of HSTT springback and realization of precision bending. Whilst, the achieving of the above goal depends on the deeper epistemological understanding of the unloading mechanism of the HSTT tube in tube bending. Up to now, great efforts have been conducted on the springback of the sheet metal after plastic deformation by using experimental, analytical and numerical approaches. As to the unloading in tube bending, most studies focused on stainless steel or Al-alloy tube, and only the angular springback is considered with the radius growth frequently ignored. The experimental study (Lou

0924-0136/$ – see front matter. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.04.022

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H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

Fig. 1. Bending and unloading procedure of RDB for HSTT.

and Stelson, 2001) shows that the springback angle has linear relationship with the bending angle when the bending angle is larger, and the bend–rebend control is used to obtain the springback data and compensate for it online. Though the experiment-based springback prediction is relatively reliable, the obtained springback data is only suitable for the bending with the same forming conditions. Also, in this study, the tubes were thick-walled tube and the tooling structure did not include the flexible balls. Wu et al. (2008) experimentally obtained the effects of the temperature, bending velocity and grain size on the springback of the Mg-alloy tube in RDB. Tang (2000) employed the plastic-deformation theory to calculate the stress distributions and the bending moment, which is needed for springback analysis. Using the beam bending theory, Al-Qureshi and Russo (2002) derived an analytical formula for the prediction of the springback and residual stress distributions with assumptions of ideal elastic–plastic material, plane strain condition, absence of defects and “Bauschinger effect”. The coordinate experimental method was also used to analyze the springback and residual stress. The springback comparisons between the theoretical results and the experimental ones have shown the remarkable agreement. It is noted that, though many factors cannot be considered such as the contact conditions and unequal 3D stress/strain distributions, the analytical model surely provides insight into the underlying physical mechanism of the elastic recovery phenomenon. Over the past few years, combining with the experimental and analytical methods, the FE method has become the primary tool to deeply analyze the springback of tube bending. The study (E and Chen, 2010) obtained obvious effects of the mechanical properties on the springback angle. The study (E and Liu, 2010) analyzed the remarkable time-dependent springback of 1Cr18Ni9Ti stainless steel tubes in RDB. It was found that the time-dependent springback angle was more remarkable with the increase of the bending radii. Via the FE simulation and experiments, the study (Murata et al., 2008) investigated the springback of Al-alloy and stainless steel tubes in the draw bending and press bending. It was found that the

hardening exponent has little effect on the springback. The study (Hu, 2000) obtained the elastic–plastic solutions for the springback angle of the pipe bending with local induction heating. The literature (Zhan et al., 2006) proposed a numerical-analytic method to predict the springback angle of thin-walled tube bending, while the stress/strain states of bent-tube were obtained by the rigid-plastic FE simulation. Via the simulation of the whole process including tube bending, mandrel retracting and unloading (Gu et al., 2008), it was found that the total springback angle considering mandrel retracting was much smaller than that not considering mandrel retracting with maximum difference between them being 107.34%, and the total springback angle increases linearly with the increase of the bending angle when the bending angle is large. Recently, the numerical study (Jiang et al., 2010) was carried out on the coupling effects of the material properties such as Young’s modulus, yield stress, strain hardening exponent and normal anisotropic coefficient on the springback angle regarding middle strength TA18M tube bending of 14 × 1.35 mm (outer diameter D × wall thickness t). The above results and methods help for the realization of the precision bending of the HSTT. However, in practice, the efficient control of the HSTT springback is still solved by the know-how experience and “trial and error” experiments. Considering the unique material features of the extremely expensive HSTT as well as the complexity of tube bending, it is difficult to reveal the springback characteristics and the coupling effects of the forming parameters only using analytical or experimental methods. Thus, taking the geometrical specification 9.53 × 0.51 mm of the HSTT as the objective, the features of the material properties of the HSTT are firstly identified via the physical uniaxial tension tests. Then combining with the experiments and analytical analysis, a series of 3D-FE numerical studies are conducted to address the significant springback characteristics of the HSTT under different bending conditions, viz., changing of the bending radii, variations of the material properties and the processing parameters. The unequal deformation of both intrados and extrados of the high strength Titube is considered in terms of elastic/plastic strain distributions,

Table 1 Composition of high strength Ti–3Al–2.5V tube (in wt%) (SAE, 2010). Al

V

Fe

O

C

N

H

Y

Other

2.50–3.50

2.00–3.00

≤0.30

≤0.12

≤0.05

≤0.02

≤0.015

≤0.005

≤0.40

H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

1975

Table 2 Mechanical properties of different tubular materials. Materials

High strength Ti–3Al–2.5V tube

5052-O

1Cr18Ni9Ti

Geometrical specification (D × t) Young’s modulus, E [GPa] Fracture elongation [%] Initial yield stress [MPa] Strength coefficient, K [MPa] Strain hardening exponent, n Material constant, b Normal anisotropy exponent, r Yield stress/Young’s modulus

Ø9.53 × 0.51 104.9 18.75 817.5 1239.55 0.091 0.00035 1.508 0.78

Ø50 × 1.5 55 22 90 431 0.262 0 0.55 0.16

Ø38 × 1.0 200 60.3 213 1591 0.54 0 0.94 0.11

wall thinning variations and cross-section deformation. The analytical model is deduced to directly correlate the springback with the material properties and the geometrical dimensions. A series of validated explicit/implicit 3D-FE models are developed to provide the thorough and quantitative analysis platform. 2. Calibration of the material properties of the HSTT The accurate prediction and quantitative analysis of the springback phenomenon rely on the reliable calibration of the HSTT material properties including the stress–strain curve (hardening rules) and the anisotropic response. Table 1 shows the chemical composition of the HSTT (SAE, 2010). Fig. 2 shows the EBSD observed microstructure of the as-received HSTT along the longitudinal direction. The mean grain size of the HSTT is about 0.9 ␮m. The elongated wrought structure of the alpha phase dominates the microstructure of the HSTT, and some minor partially transformed beta phase also exists. The uniaxial tension test was conducted according to the GB/T228-2002, in which a piece of complete tube specimen (shown in Fig. 3) was directly cut from the raw tube by the wire cut. By inserting a tube plug, the tube is clamped and tensioned in a 200KN CMT5205 test machine. Both the longitudinal and vertical extensometers are used for accurate strain records with the specification of YSJ-50/25-ZC and YSJ-25/3-ZC. The velocity of cross-head is 3 mm/min since the bending is thought as a quasi-static process.

Fig. 2. EBSD obtained microstructure of the stress relieved near alpha HSTT.

Both the nominal stress and strain can be calculated by the  n = F/A0 and εn = l/L0 , in which F (N) is the tension force, A0 (mm2 ) is the original cross-sectional area, l (mm) is the displacement of the extensometer, and L0 (mm) is the original gauge length. The true stress and strain can be obtained by  t =  n (1 + εn ) and εt = ln(1 + εn ). The normal anisotropy is used to represent the anisotropic response of the HSTT tube. As for the normal anisotropic exponent, it is calculated by Eqs. (1) and (2) according to the volume conservation theory. The evolutionary of the normal exponent shows that the anisotropy increases gradually with the larger strain. The average normal anisotropic exponent is 1.508, which is used in the consequent FE modeling. 1 1 2 (D2 − d2 )L = (D1 2 − d1 )L1 4 4 r=

ln((D + d)/(D1 + d1 )) εD = ε ln(t/t1 )

(1) (2)

where D and d are the initial outside and inside diameters of tubular specimen, L and L1 the initial and transient length of tubular specimen, D1 and d1 the transient outside and inside diameters of tubular specimen. Fig. 3 shows the average nominal and true stress–strain curves for three specimens of the HSTT. The level of the equivalent strain during bending is higher than the maximum level of the equivalent strain obtained in the tension test, so the remaining part of the flow curve is extrapolated by the inverse method for the FE simulation. The exponent hardening law as  = K(ε0 + ε)n was used to calibrate the stress–strain curves. Table 2 shows the mechanical properties of the Ti-tube. It shows that the HSTT possesses a much higher ratio of the yield stress to Young’s modulus than the ones of 5052O Al-alloy tube and 1Cr18Ni9Ti stainless steel tube.

Fig. 3. Stress–strain curves for HSTT and other two materials.

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H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

Table 3 The variations of the material properties for high strength Ti–3Al–2.5V tube. Forming parameters

Value 1

Value 2

Value 3

Young’s modulus, E [GPa] Initial yield stress [MPa] Strength coefficient, K [MPa] Strain hardening exponent, n Normal anisotropy exponent, r

88.90(0.83) 787.5(0.88) 1139.55(0.85) 0.07136(0.51) 1.08(0.20)

104.86(0.91) 817.5(0.94) 1239.55(0.93) 0.0914(0.75) 1.51(0.60)

120.28(1.00) 847.5(1.00) 1339.55(1.00) 0.11136(1.00) 1. 98(1.00)

Note: The value in bold fonts is used in the simulation, the values in round brackets are the reference values for normalization in Figs. 22 and 23.

Due to the complex fabrication processing such as extrusion, multi-pass rolling and interval annealing and final stress-reliving, the material properties of the HSTT present an obvious scattering feature. Table 3 shows the variations of the material properties for the HSTT in the present study.

Table 4 Forming parameters used in the experiments and the numerical study.

3. Experimental procedure and theoretical modeling for springback prediction of HSTT in RDB

Values

Bending radius, R [mm] Bending speed [◦ /s] Relative pushing speed Vp /V

1.5D, 2.0D, 2.5D, 3.0D 66.5 0.9(0.83), 0.95(0.86), 1(0.91), 1.05(0.95), 1.1(1.00) 5, 10, 20, 30, 101.3, 120, 166.5

Bending angle [◦ ] Dimensions of mandrel Mandrel diameter, d [mm] Mandrel extension length, e [mm] Number of balls Thickness of balls [mm] Pitch of balls [mm] Ball diameter [mm] Length of mandrel shank [mm] Dimensions of other tools Length of clamp die [mm] Length of pressure die [mm] Length of wiper die [mm]

Based on the analysis of the experimental procedure, the theoretical models, viz., the analytical and 3D-FE ones, are developed to conduct the study on the HSTT springback. 3.1. Experimental procedure of the multi-die constrained RDB As shown in Fig. 1, in tube bending, both sides of the tube are subjected to the multi-tool constraints, such as bend die, clamp die, pressure die, wiper die and mandrel (with multiple flexible balls). The tube is clamped against the bend die by the clamp die and pressure die; then the clamp die and the bend die rotate simultaneously, and the tube is drawn past the tangent point and rotates along the bend die groove to obtain the desired bending angle and bending radius. Then the mandrel is withdrawn and the tube is unloaded by removing the tools. Thus the bending deformation is finished. Since the ratio of D/t of the HSTT equals nearly 20, various defects such as wrinkling, over thinning and cross-section distortion should occur with inappropriate die design and forming conditions. For present study, the feasible die sets and forming parameters should be preliminarily determined to ensure a defect free bending deformation. Thus, the wiper die and mandrel die with one flexible balls should be added besides the bend die, pressure die and clamp die. Table 4 shows the forming parameters for stable RDB modeling and experiments. The values in bold fonts are used in the experiment. For bending processes with different bending radii, the same forming parameters are applied without special declaration as shown in Table 4. As shown in Table 5, for the HSTT, the material type for each tooling should be assigned deliberately due to the different role of friction in tube bending (Yang et al., 2011). The lubricant is IRMCO GEL 980-301. The fully electronic servo drive control bending machine, viz., BLM DYNAMO-E LR150 is used to conduct the bending experiments. The non-contact laser probe is used to obtain the springback data with relatively high accuracy.

Items

8.35 0, 0.25, 0.5, 0.75, 1 1 3.5 2.0 8.32 120

28.6 132.7 300

Note: Vp —pushing speed of pressure die; V—bending speed of bend die. The value in bold fonts is used in the experiment, the value s in round brackets are the reference values for normalization in Fig. 24.

The springback behaviors depend on the bending histories such as wall thinning degree t and cross-section deformation D (shown in Fig. 4), which is expressed as

   t − t   × 100% t

(3)

D − D × 100% D

(4)

t =  D =

where t is tube initial wall thickness, t the minimum wall thickness after bending, D the initial tube outside diameter, D the section length in the vertical direction after bending. 3.2. Analytical modeling for springback prediction considering neutral layer shift Via the plasticity deformation theory, the analytical prediction model for springback is established considering tube specifications and material properties. On release of the external loads, the tensile stresses on the outside of the tube and the compressive stresses on the inner side create a net internal bending moment or residual stresses. The residual stresses cause a decreased change of the

Table 5 Friction conditions in various contact interfaces. Items

Contact interfaces

Tool materials

Coefficient of friction (CoF)

1 2 3 4 5 6

Tube wiper die Tube-pressure die Tube-clamp die Tube-bend die Tube-mandrel Tube-flexible balls

Al–bronze Cr18MoV Cr18MoV Cr18MoV Al–bronze Al–bronze

0.1 0.25(0.71), 0.275(0.79), 0.3(0.86), 0.325(0.93), 0.35(1.00) Rough 0.25 0.05(0.33), 0.075(0.5), 0.1(0.67), 0.125(0.83), 0.15(1.00) 0.1

Note: The value in bold fonts is used in the experiment, the values in round brackets are the reference values for normalization in Fig. 24.

H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

A Pressure side

t

t

C-C Extrados

C Tangent point

R

A

Tangent line -Fix forming zone O

1977

C

Ro

Ri B Clamp side

r0

Geometry-NA Strain-NA B

t

R

Initial Bending Section

t

Intrados O

Fig. 4. Stress–strain distribution of tube in RDB and geometrical specifications.

bending angle, ϕ, and a increased change of bending radius, , as shown in Fig. 5. The analytical derivation is conducted for the bending and unloading processes, respectively. The assumptions are as follows: the cross-section of the tube remains in a plane during bending; the wall thinning and cross-section deformation are not considered in unloading analysis; the plane strain is regarded; the stress–strain response follows the exponent law as  = K(ε0 + ε)n ; the inner side surface of the tube contacts with the groove surface of the bending die during bending process as shown in Fig. 1. During bending stage, the axial (longitudinal) strain at the arbitrary locations can be determined by

 εϕ = ln

R + r0 cos  

 (5)

where  is the curvature radius of the strain neutral layer (shown in Fig. 4), which can be estimated by (E et al., 2009).

=

D Ro × Ri = 2

 R 2

2

D

−1

(6)

where Ro is the outer radius, Ri the inner radius. By using εϕ = − εt , the equivalent strain thus can be obtained as 1+r ε¯ = √ 1 + 2r

 ε2 +



2r 1 + r   εϕ ε εϕ + ε2ϕ = √ 1+r  1 + 2r

(7)

2r  ϕ + ϕ2 = 1+r 

2 −

¯ =



5 r − ϕ 4 1+r

(8)

By substituting Eqs. (7) and (8) into the exponent strain hardening law, the longitudinal stress can be deduced as √ n K(ε0 + ((1 + r)/ 1 + 2r) ln(R + r0 cos /)) (9) ϕ =  (5/4) − (r/(1 + r)) Thus the bending moment M can be numerically calculated by the following equation





D/2

M=2

ϕ ydA = 2



0 



ϕ (ro cos )(ro t d) 0



R + r0 cos  1+r ln ε0 + √  1 + 2r

=C 0





Then the equivalent stress can be obtained by the plane strain assumption

n cos  d

(10)



where C = 2Ktro 2 / (5/4) − (r/(1 + r)). After the unloading, both the stress change and the stain change can be expressed as Mr0 I r0 r0 −  εϕ =   ϕ =

(11) (12)

where I is the inertial moment of the round tubular materials.  (13) (D4 − Di4 ) I= 64 o where Do and Di are the outer and inner diameter of the tube. It is thought that the elastic strain energy is totally released without any residual elastic strain. According to the Hooke’s law  ϕ = Eεϕ and by combining Eqs. (11)–(13), the curvature change before and after unloading is 1 M 1 −  =   EI

(14)

Thus, the growth radius  after unloading can be obtained as  = 1−

  

n √ ε0 + (1 + r)/ 1 + 2r ln(R + r0 cos /) cos  d /EI 

   C

0



(15) The radius growth after springback can thus be obtained Fig. 5. Tube springback after bending deformation (bending region).

 =  − 

(16)

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H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

Fig. 6. Explicit/implicit elastic-plastic 3D-FE modeling for the whole RDB process.

Then, since the length of the fiber of tube before and after unloading is so minor that the following expression can be get ϕ =  ϕ =  (ϕ − ϕ)

(17)

So the change of the bending angle can be obtained

 ϕ =

=

C

1−

 0

 

 ϕ



n √ ε0 + (1 + r)/ 1 + 2r ln((R + r0 cos )/) cos  d EI

ϕ

(18)

Thus, by using Eqs. (6), (15) and (18), both the angular springback and radius growth can be calculated to provide intricate insights to understand the elastic recovery phenomenon in RDB of the HSTT. It is noted that the terms in the curly bracket cannot be explicitly integrated and so its value is numerically approximated by the Trapezoidal numerical integration (Mathworks, 2011). The proposed model considers both the bending specifications and the material properties. 3.3. Explicit/implicit elasto-plastic 3D-FE modeling of the whole RDB process for HSTT A series of 3D-FE half models (shown in Fig. 6, and the video is also provided) of the whole RDB including bending, retracting of balls and unloading are established to quantitatively relate the springback with the bending histories. The major issues in modeling and simulation of the springback of HSTT under RDB loading are summarized as below to obtain the tradeoff between “accuracy” and “efficiency”. The detailed solutions involved in FE modeling can be found in the literature (Li et al., 2007). The accuracy prediction of the springback depends on the reliable calculation of the strains/stress distributions in each forming step. The explicit algorithm is used for solving the bending deformation and balls retracting operation; while the implicit one is employed for unloading process. The results from the bending and ball retracting simulation in Explicit are Imported into standard (Abaqus, 2007). In the static analysis of the springback, an artificial stress state that equilibrates the imported stress state is applied automatically by Abaqus/standard and gradually removed during the unloading process. The displacement obtained at the

end of the process is the springback, and the stresses give the residual stress state. The geometrical nonlinearity is included as well as the damping factor of 0.002 to stabilize the implicit iteration procedures of the springback analysis. Double precision computation is used in the bending stage and the single one for the springback analysis. In bending simulation, the mass scaling feature of 5000 is utilized to improve the computation cost with neglected inertia effect by using the convergence analysis. The Hill (1948)’s anisotropic quadratic yield function is used to describe tube material’s yield behaviors with assuming the rate independent. The 3D linear reduction integration continuum element with eight nodes is used to discretize the tubular material by using the enhanced hourglass control, while the 3D bilinear rigid quadrilateral element is used to model the rigid dies; different mesh density is applied to different regions of tube with the minimum element size of 3 × 3 mm, and four integration points with Simpson integration rule is used through the tube wall thickness with four elements along the thickness direction. The boundary constraints are applied by two approaches to realize the actual process of RDB: “displacement/rotates” and “velocity/angular”. As shown in Fig. 6, both bend die and clamp die are constrained to rotate about the global z-axis simultaneously; pressure die is constrained to translate only along the global x-axis; wiper die is constrained along all degrees of freedom; the mandrel (including mandrel shank and multi-balls) is kept stationary along x-axis during bending, while the mandrel is retracted with the bending deformation is finished; the “connector element” is used to define the “hinge” contact behaviors between mandrel shank and flexible balls. The trapezoidal profile is used to define the smooth loading of all the above tools to reduce inertial effects in explicit simulation of the quasi-static process. For unloading process, all tools are removed and a fixed boundary condition is applied to avoid the rigid motion. The detailed contact conditions and friction information are summarized in Table 5. The Coulomb friction model is used to represent the friction behavior as = p

(19)

where is the frictional shear force, the coefficient of friction, p the pressure force on the contact surface.

H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

Mass scaling factor=40000 Mass scaling factor=10000 Mass scaling factor=5000 Mass scaling factor=1000 Mass scaling factor=500

80

2000

7142 hours estimated 1800

Increment: 1.946e-08

1600

Computation time (hour)

Kinetic energy (mj)

60

1979

40

20

1400 1200

Increment: 1.902e-07

800 600 400

0

737 hours estimated

1000

200

Increment: 4.242e-07 Increment: Increment: Increment: 6.000e-07 Increment: 1.895e-06 1.341e-06 3.788e-06

0

0.0

0.5

1.0

1.5

2.0

40000

2.5

10000

(a) Kinetic energy history with different mass scaling factors

1000

500

100

1

(b) Computation cost with different mass scaling factors 12.5

18

10.0

16

7.5

Wall chanding degree (%)

20

14 o

Springback angle ( )

5000

Mass scaling factor

Time (s)

12 10 8 6 4

Wall thickening degree Mass scaling factor=40000 Mass scaling factor=10000 Mass scaling factor=5000 Mass scaling factor=1000 Mass scaling factor=500 Wall thinning degree Mass scaling factor=40000 Mass scaling factor=10000 Mass scaling factor=5000 Mass scaling factor=1000 Mass scaling factor=500

5.0 2.5 0.0 -2.5 -5.0 -7.5

2 0

-10.0 40000

5000

0

500

1000

10000

20

40

60

80

100

Angle between measure point and initial bending plane (deg)

Mass scaling factor

(c) Springback angle predictions with different mass scaling factors

(d) Wall changing with different mass scaling factors

Cross-section deformation degree (%)

4.0

3.5

3.0

Mass scaling factor=40000 Mass scaling factor=10000 Mass scaling factor=5000 Mass scaling factor=1000 Mass scaling factor=500

2.5

2.0

1.5 0

20

40

60

80

100

Angle between measure point and initial bending plane (deg)

(e) Cross-section deformation changing with different mass scaling factors Fig. 7. Simulation results with different mass scaling factors.

H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

(a) 24 22

Angular springbcak Δϕ[º]

20

10

Exp-Δρ Sim-Δρ Analytical-Δρ

Exp-Δϕ Sim-Δϕ Analytical-Δϕ

9 8

18

7

16 6

14 12

5

10

4

8

3

6

Radius springbcak Δρ[mm]

1980

2

4 1

2 0

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Fig. 8. 3D bent HSTT and the mandrel die with one flexible balls.

Bending angle [º]

4.1. Evaluation of the analytical and numerical models By comparing with the experimental results, both the above analytical and numerical models have been verified. A series of physical bending processes have been conducted with bending angles from 5 to 166.5◦ . The forming parameters for the experiments are shown in Table 4 (in bold fonts). Prior to the comparison, the effects of the mass scaling factor on springback prediction and computation cost are specially discussed by the convergence analysis to achieve the tradeoff between “computation accuracy” and “computation efficiency”. The mass scaling factor is 1, 100, 500, 1000, 5000, 10,000 and 40,000. The total number of the element is 52,606, the bending speed is 0.8 rad/s (which equals the real bending speed), the bending angle is 101◦ , and the processor is Intel Xeon E5410, 2.33 GHz, RAM: 4 GB. Fig. 7 shows the results under different mass scaling factors. Fig. 7(a) shows that there occurs obvious increasing in larger kinetic energy with the mass scaling factor of 40,000, while it is observed that the computation time increases sharply with the decreases in the mass scaling factor as shown in Fig. 7(b). For the mass scaling factor of 1, the estimated computation time is even nearly 300 days. Via Fig. 7(c), it can be seen that, except for the mass scaling factor of 40,000, the springback predictions with the other mass scaling factors are almost the same. Since the unloading simulation depends on the bending history, both the wall changing and cross-section deformation under different conditions are observed. Fig. 7(d) and (e) shows that the values of the mass scaling factors have little effects on both the wall thinning changing degree and the cross-section deformation degree. By comprehensive analysis, the mass scaling factor of 5000 should be suitable in terms of the tradeoff between “computation accuracy” and “computation efficiency”. Fig. 8 shows the HSTT bent parts with bending angles of 20◦ and 120◦ . In the experiments, the wiper die was not used. The wrinkling did not occur. As shown in Fig. 9(a), it is found that the numerical predictions for angular and radius springback agree with the experimental results with the relative error less than nearly 5% and 35%, respectively. The analytical prediction provides the consistent tendency of the elastic recovery with the increase of the bending angles. For the analytical prediction, the discrepancy is mainly originated from the mentioned assumptions in Section 3.2 and uniform stress/strain distributions calculated in the analytical model; for the

19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3

(b)

2.5

Sim-Δt Exp-Δt

Sim-ΔD Exp-ΔD 2.0

1.5

1.0

0.5 o

Cross-seciton deformation degree ΔD[%]

First, both the analytical and numerical models are evaluated. Then, the springback behaviors of the HSTT in the cold tube bending are studied under various forming conditions.

Wall thinning degree Δt [%]

4. Results and discussion

3D-101.3 0

20

40

60

80

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numerical ones, the discrepancy is mainly caused by the idealized contact conditions used in FE models such as unchanged friction conditions and stable tooling movements. Besides the direct comparisons, the verification of the FE models is also conducted in terms of the wall thinning t and cross-section deformation D as shown in Fig. 9(b). The comparisons show that the FE prediction can capture the bending deformation accurately, which is the basic for reliable prediction of the springback phenomenon. 4.2. Springback characterization of HSTT in RDB The above results show that there occurs a significant springback effects for HSTT in RDB (shown in Fig. 9). Fig. 10 shows three springback induced phenomena in RDB of HSTT, viz., the reduction of the bending angle ϕ = ϕ − ϕ , the growth of the bending radius  =  −  and the alleviation of the cross-section deformation D. It is noted that, due to the cross-section deformation along the bending regions, the centerline bending radius  after springback cannot be measured conveniently and accurately. So the inner  is used to identify the radius growth. Without bending radius in  − . special declaration, the radius springback means  = in in Since the sectional springback can improve the bending quality, it is not analyzed in detail in the following context. As shown in Fig. 11, both the analytical and numerical predictions confirm that the angular springback increases linearly

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Fig. 10. Identification of significant springback phenomena in RDB of HSTT.

with the larger bending angles (Lou and Stelson, 2001), and it increases with the larger bending radii. It is noted that, the analytical prediction of ϕ is smaller than the numerical one at the early bending stages; however, it becomes larger than the numerical one when the bending angle reaches certain larger value. The reason is attributed to the unequal bending deformation of the HSTT, which is not fully considered in the analytical modeling. Fig. 12 shows that the local incremental deformation occurs in tube bending, viz., the bending deformation happens near the tangent point, and the finished bending region is unloaded and becomes the transitional region to transfer the clamping force. The transient locally bending region includes both the bending curved region and the straight portions. When the desired bending

20

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process is achieved, the plastically deformed regions are composed of the whole curved bending region and the two straight regions as shown in Fig. 12. Thus, with the multi-tool removed, the elastic recovery happens in both the bending region and two straight regions (shown in Figs. 12 and 13). So, the springback angle ϕ of the tube includes not only the springback induced by the curved bending region, but also two straight transitional regions. Due to the characteristics of the progressive and incremental deformation in bending, the areas of the two straight regions keep little changed with the increases of the bending angles, while the area of the bending region increases with ongoing bending. That is why the linear fitted formula as Eq. (20) can well represent the angular springback tendency in practice. The fixed constant is thought to represent the springback amount of the straight regions; while the proportional constant represents the linear relationship between angular springback and the bending angles. However, the analytical model in Section 3.2 considers only the curved bending region, so the fitting curve of the corresponding prediction passes through the origin point with the linear function ϕ = Fϕ as shown in Fig. 11. At the early bending stages, the fixed springback b of the straight regions dominates the springback of the HSTT, and thus the analytical prediction underestimates the elastic recovery. While at the later bending stages, the value of the Fϕ gradually increases and becomes much larger than the fixed one b, then the analytical prediction overestimates the springback ones. Fig. 11 shows that the springback angle for straight transitional regions is up to 3.5◦ .

180

o

Bending angles [ ] Fig. 11. Springback angle with different bending angles under various bending radii.

(20)

where F is the proportional constant, b the fixed constant. As for the radius growth, Fig. 14 shows that the radius springback is little changed with the larger bending angles, viz., nearly 60◦ in this study. The above observation can be explained by Eq. (15), viz., the radius growth only depends on the material properties and the geometrical dimensions of the tube. The radius springback

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Fig. 12. Local incremental bending deformation in RDB of tube (2D).

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is induced only by the stress release of the curved bending region as shown in Fig. 12. Since the unequal deformation at early bending stages is not considered in the analytical models, the analytical prediction of the radius springback remains constant for all bending angles. Fig. 14 also shows that the radius springback increases with the larger bending radii, which is similar with the tendency of the springback angle. As shown in Fig. 15, large plastic deformation occurs with the smaller bending radius, which causes smaller elastic store energy and thus smaller springback. Under smaller radii, the analytical prediction agrees with the numerical one well, however, the discrepancy becomes larger with the larger bending radii due to unequal bending deformation. For the sectional springback, Fig. 16 shows that there is an obvious alleviation of the cross-section deformation D after unloading. The D after springback decreases 57% more than that before springback for all cases with different bending radii. It is known that the cross-section deformation is induced by the resultant force of the longitudinal tension force and the hoop tension force in the outer tube. During the unloading, the axial tensile force is released sharply and thus the cross-section flattening degree D can be relieved. While, Fig. 17 shows that the sectional springback does not increase with increasing of the bending angle. The reason is that the cross-section remains little changed when the bending

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Fig. 15. Longitudinal elastic and plastic strain distributions along hoop direction of tube during bending, ball retracting and springback.

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Fig. 18. Comparison of the springback of HSTT with other materials.

Fig. 16. Cross-section deformation before and after springback.

4.3. Springback behaviors under variations of the material properties As shown in Fig. 18, under the same bending conditions, both the angular and radius springback of the HSTT is far larger than the ones of 1Cr18Ni9Ti tube and 5052O tube. The springback of the stainless steel tube is slightly larger than the one of the Alalloy tube. The reason is directly attributed to the amount of the residual elastic strain after bending deformation and balls retracting. Fig. 19 shows the longitudinal elastic strain distributions at the outmost and innermost lines of the different tubular materials. It is observed that, for both extrados and intrados, the absolute value of the elastic strain of the Ti-alloy tube is much larger than those of the Al-alloy and 1Cr18Ni9Ti tube. The inhomogeneous distributions of the elastic strain are obvious along the bending regions. Also, the strain distributions along the hoop (circumferential) direction at the middle section for different tubular materials are also considered as shown in Fig. 20. It is found that the strain of the HSTT is the largest among three tubular materials. Thus, Fig. 21 shows that

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both the wall thickening degree and cross-section deformation of the HSTT are the largest. The springback changes under the variations of the material properties are further discussed due to their remarkable effects

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on springback and obvious scattering of the material properties as shown in Table 3. Fig. 22 shows that the Young’s modulus E, strength coefficient K and the anisotropy exponent r are the major material factors to affect the springback fluctuations, while the hardening exponent n and the initial yield stress have relatively little influence on the elastic recovery of the HSTT. The general effects of individual parameters on springback tendency are similar with the ones of Al-alloy tube and 1Cr18Ni9Ti tube. The smaller Young’s modulus E causes the larger springback with larger elastic energy store capacity; the strength coefficient K induces larger springback; the normal anisotropic coefficient r have a remarkable effects on springback with larger bending angles, viz., the springback angle increases with the larger normal anisotropic coefficient. That is why the most significant springback occurs for the HSTT in tube bending, viz., both the anisotropic exponent r and the ratio of the yield strength to Young’s modulus are the largest among the above three tubular materials as shown in Table 2. It is noted that, as shown in Fig. 22, at the latter bending stages with larger bending angles such as 150◦ , the range of the springback variations becomes more significant under the same scattering of the material properties. This is attributed to the coupling effects between bending angles and the material properties. As for the radius growth,

Fig. 22. Variation of angular springback induced by material properties for 2D bending.

90° Max.variation=0.32mm by E E σ K n R

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Fig. 23 shows the similar effects with the ones of the angular springback under variations of the material properties. Thus, it can be summarized that the Young’s modulus E, strength coefficient K and the normal anisotropic exponent r have relatively significant effects on the springback of the HSTT. 4.4. Springback behaviors under variations of the processing parameters Due to the multi-tooling constrained features of the RDB, the springback changes of the HSTT under variations of the major processing parameters are additionally discussed. Four important processing parameters (including the mandrel extension length e, CoF of tube-mandrel, relative push assistant speed and CoF of tube-pressure Vp/V are considered since they have a relatively significant effect on springback compared with the other processing parameters. It is known that the above parameters play great role in achieving the stable bending deformation. The wrinkling or crossdistortion may occur with the small mandrel extension length e, while the overthinning, bump or even crack may occur with the larger e. The relative push assistant speed Vp/V is another controlling parameter to ensure bending quality, viz., the smaller Vp/V should induce the overthinning and larger cross-section deformation, while the larger Vp/V should cause the wrinkling. Also the friction condition on the tube and each tool should be deliberately

Fig. 24. Springback variation induced by tool/processing parameters.

H. Li et al. / Journal of Materials Processing Technology 212 (2012) 1973–1987

1985

Fig. 25. Two level springback compensation methodology for HSTT in RDB.

treated for stable bending and high forming quality (Yang et al., 2011). The variations of the processing parameters are shown in Tables 4 and 5. Fig. 24 shows the springback variations under scatted processing parameters. The nonlinear effects of the processing parameters on the elastic recovery of the HSTT are observed. The variation tendency of the springback radius with the changing of the processing parameters is not similar with the ones of springback angle. The reason is attributed to the unique unequal deformation of tube bending. It is found that, with the given processing parameters, the values of the angular springback fluctuate from 8.02 to 8.71◦ , and the values of the radius springback change from 0.87 to 0.72 mm. The maximum variation range of the springback angle is 0.60◦ induced by the relative pushing assistant speed Vp/V; the maximum range of the radius springback is only 0.12 mm by the Vp/V. It is obvious that the variation amount of the elastic recovery induced by the changing of the processing parameters is far less than the ones caused by bending specifications and the material properties. As shown in Figs. 22 and 23, at the bending angle of 150◦ , the angular springback fluctuates from 10.36 to 14.20◦ , and the radius springback changes from 1.29 to 0.77 mm. The maximum variation range of the springback angle is 3.84◦ induced by the Young’s modulus E; the maximum range of the radius springback is 0.41 mm by the E. The maximum variation of the springback with changing of the

processing parameters is 16% less than the maximum ones under different material properties and geometrical ones. 4.5. Two level springback compensation methodology for RDB of HSTT Since both the angular springback and radius growth of the HSTT are so obvious in tube bending, to achieve the precision bending deformation, both the springback phenomena should be compensated simultaneously. According to the above obtained knowledge about the unloading behaviors of the high strength Ti-alloy tube, a two level iterative compensation methodology is thus be proposed. Fig. 25 shows the detailed strategy, which is articulated as below: • Firstly, for given bending specifications of HSTT, viz., D, t, R, ϕ, the stable bending conditions including suitable tooling combinations and processing parameters should be obtained with wrinkling free and allowed tolerance of wall thinning and cross section degrees. • Via the 3D-FE modeling or the linear fitting curve (shown in Eq. (20)), the bending conditions should be modified by compensation for the springback radius  as 1 =  − 

(21)

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where  is the designed bending radius, 1 the actual bending radius for bend die. • Via 3D-FE simulation, the bending radius 2 under the compensated forming conditions of 1 is obtained and compared with the desired one as





E = 2 − 

(22)

If the bending tolerance is satisfied, then the radius springback compensation procedure is implemented; otherwise, the next iteration process is needed as n+1 = n ± E

(23)

where n is the actual bending radius with nth modified forming conditions, while n+1 is the needed bending conditions for (n + 1)th iterative bending. • Repeating the above procedure until the bending accuracy tolerance E is satisfied. • When the bending radius is compensated, the bending conditions should be modified by compensation for the angular springback via the 3D-FE modeling or linear fitting curve ϕ1 = ϕ + 

(24)

where ϕ is the designed bending angle, ϕ1 the actual bending angle. • Via 3D-FE simulation, the bending angle ϕ2 under the compensated forming conditions of ϕ1 are obtained and compared with the desired one as





Eϕ = ϕ2 − ϕ

Acknowledgements

(25)

If the bending tolerance is satisfied, then the springback compensation procedure is implemented; otherwise, the next iteration process is needed as ϕn+1 = ϕn ± Eϕ

is only related to the bending portion and independent to the bending angles; (2) The difficulty in springback control is due to the variations of both the processing parameters and material properties. Among the parameters, the material properties and the bending specifications determine the remarkable springback effects of the HSTT. Both the angular and radius springback decrease with the smaller bending radii; the angular springback increases linearly with the larger bending angles, while the radius changes remains constant with the increases of the bending angles; compared with the springback variations under different bending specifications and scattered material properties, the fluctuation ranges of the both the angular and radius springback under variations of the processing parameters are far less; the fluctuations of the springback induced by the variations of the material properties become more obvious with the increases of the bending angles; (3) Based on the knowledge of the remarkable elastic recovery, a two level springback compensating methodology is proposed to consider both the angular springback and radius springback for achieving the precision bending deformation of the HSTT. The experimental results verified the above analytical and numerical predictions as well as the developed compensating approach. This can be used to guide the pre-design of the multiple bending dies and the selection of the bending procedures.

(26)

where ϕn is the actual bending angle with nth modified forming conditions, while ϕn+1 is the needed bending conditions for (n + 1)th iterative bending. • Repeating the above procedure until the bending accuracy tolerance E is satisfied. The above methodology has been applied for the springback compensation of the bending specification 9.53 mm × 0.51 mm (D × t) of the HSTT. The desired bending angle and bending radius are 150◦ and 3D, respectively. The bending tolerance for bending angle and radius is 0.5◦ and 0.5 mm. After two iterative searching, the actual bending radius and bending angle should be 25.61 mm and 166.2◦ , respectively. Thus the qualified bent tubular part is achieved with bending angle of 149.7◦ and the bending radius of 28.65 mm. 5. Conclusions Combining with the experimental and analytical methods, the 3D-FE numerical analysis is conducted to characterize the springback phenomenon and identify its behaviors of the HSTT under multi-die constrained RDB. The main results are as follows: (1) The springback of HSTT in RDB is so significant that it should be characterized by three indices including the angular springback, the radius growth and the sectional springback. Both the springback angle and radius should be compensated for precision bending deformation. The angular springback is attributed to the elastic release of both the curved bending region and the two straight transitional ends of tube; While the radius growth

The authors would like to thank the National Natural Science Foundation of China (No. 50905144, 51175429), Program for New Century Excellent Talents in University, NPU Foundation for Fundamental Research (No. JC201028), the fund of the State Key Laboratory of Solidification Processing in NWPU, Natural Science Basic Research Plan in Shaanxi Province (No. 2011JQ6004) and the 111 Project (B08040) for the support given to this research. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmatprotec. 2012.04.022. References ABAQUS Analysis User’s Manual (version 6.7), 2007. Al-Qureshi, H.A., Russo, A., 2002. Spring-back and residual stresses in bending of thin-walled aluminium tubes. Materials and Design 23 (2), 217–222. Boyer, R.R., 1996. An overview on the use of titanium in the aerospace industry. Materials Science and Engineering A 213, 103–114. E, D.X., Guo, X.D., Ning, R.X., 2009. Analysis of strain neutral layer displacement in tube-bending process. Journal of Mechanical Engineering 45 (3), 307–310 (in Chinese). E, D.X., Chen, M., 2010. Numerical solution of thin-walled tube bending springback with exponential hardening law. Steel Research International 81 (4), 286–291. E, D.X., Liu, Y., 2010. Springback and time-dependent springback of 1Cr18Ni9Ti stainless steel tubes under bending. Materials and Design 31 (3), 1256–1261. Gu, R.J., Yang, H., Zhan, M., Li, H., Li, H.W., 2008. Research on the springback of thinwalled tube NC bending based on the numerical simulation of the whole process. Computation Materials Science 42 (4), 537–549. Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London 193, 281–297. Hu, Z., 2000. Elasto-plastic solutions for spring-back angle of pipe bending using local induction heating. Journal of Materials Processing Technology 102, 103–108. Jiang, Z.Q., Yang, H., Zhan, M., Xu, X.D., Li, G.J., 2010. Coupling effects of material properties and the bending angle on the springback angle of a titanium alloy tube during numerically controlled bending. Materials and Design 31 (4), 2001–2010. Li, H., Yang, H., Zhan, M., Sun, Z.C., Gu, R.J., 2007. Role of mandrel in NC precision bending process of thin-walled tube. International Journal of Machine Tools and Manufacture 47 (7–8), 1164–1175.

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