A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S

Volume 54 2009 Issue 4

M. KADKHODAYAN∗, I. ZAFARPARANDEH∗

AN INVESTIGATION INTO THE INFLUENCE OF BLANKHOLDER FORCE ON SPRINGBACK IN U-BENDING

BADANIE WPŁYWU SIŁY DOCISKACZA NA SPRĘŻYNOWANIE PRZY ZAGIĘCIACH TYPU „U”

Springback is the main defect in U-channel forming process. Applying the blankholder force is one of the ways of solvingthe problem. On the other hand the value of the blankholder force should be chosen carefully. In this paper the relation of theblank-holder force and final springback, taking a benchmark of NUMISHEET’93 2-D draw bending and using a commercialFEM code has been studied. The simulations are pre-formed for AA5754-O and DP-Steel. In order to probe the relation, fivedifferent values are utilized in simulations. It is found that springback increases for the middle values of the blankholder forcewhere the stretching and bending have equal effects on the blank. The maximum required punch loads are compared for thedifferent values of blankholder force.

Keywords: blankholder force, springback, U-bending

Sprężynowanie jest głównym mankamentem w procesie formowania zagięć typu „U”. Zastosowaie siły dociskacza jest jed-nym ze sposobów rozwiązania tego problemu. Z drugiej strony, wartość siły dociskacza powinna być precyzyjnie wyznaczana.W niniejszej pracy omawiany jest związek siły dociskacza i końcowego sprężynowania, przy zastosowaniu wzorca NUMISHE-ET’93 2-D oraz wykorzystaniu dostępnego na rynku kodu FEM. Symulacje zostały wykonane dla stali DP i AA5754-O. Wcelu przetestowania wspomnianego związku, w symulacjach wyznaczono pięć różnych wartości. Zaobserwowano, iż zginaczemają taki sam wpływ na materiał. Porównywane są maksymalne wymagane obciążenia tłocznika dla różnych wartości siłydociskacza.

1. Introduction

Springback is generally defined as the additional de-formation of sheet metal parts after removing the load.In recent years, the high strength steels and aluminumalloys are increasingly used for sheet metal parts in theautomotive industry to reduce mass. However, duringusing materials with higher ratios of yield strength toelastic modulus, precise prediction and control of spring-back become essential [1]. The precision in dimension isa major concern in sheet metal bending process becauseof the considerable elastic recovery during unloadingleading to springback. The elastic recovery is influencedby a combination of various process parameters suchas tool shape and dimension, contact friction condition,material properties, thickness and so on. U-bending pro-cess is often used to manufacture sheet parts like chan-nels, beams and frames. In this process, the sheet metalusually undergoes complex deformation history such asstretch-bending, stretch-unbending and reverse bending.

When the tools are removed, in addition to springback,sidewall curl often happens, which makes the predictionof springback become more difficult. Different methods,such as analytical method, semi-analytical method andfinite element method (FEM), have been applied to pre-dict the sheet springback of U-bending.

Samuel [2] used a finite element (FE) program,MARC package to analyze the axi-symmetric U-bendingprocess. He investigated the effect of tool geometry andblankholder force on the final shape after springback.Experimental prediction of springback and determina-tion of final geo-metry within a reasonable tolerance istime consuming and expensive. Lee and Kim [3] fo-cused on the evaluation of springback occurring in thesheet metal flange drawing by controlling some processfactors like punch corner radius (PR), die corner radius(DR), and blank holding force. Esat et al. [4] carried outspringback analysis of different aluminum sheets withdifferent thicknesses and explored the relation betweenthe amount of springback and total equivalent plastic

∗ DEPARTMENT OF MECHANICAL ENGINEERING, FERDOWSI UNIVERSITY OF MASHHAD, 91775-1111, MASHHAD, IRAN

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strain and also equivalent plastic stress. They concludedthat the material with higher yield strength and smallerequivalent plastic strain has higher amount of springbackthan the material with lower yield strength and higherequivalent plastic strain.

In recent years, the rapid development of computertechnologies enables numerical simulation of sheet metalforming operations and finite element codes to be used inan industrial environment. The springback prediction insheet metal forming processes using FEA has been stud-ied by many researchers in the past. Cho et al. [5] car-ried out a numerical investigation on springback equiv-alent plastics in plane strain ’U’ bend-ing process bythermo-elastoplastic FEA. Li et al. [6] mainly dealt withmaterial hardening to analyze ’V’ bending and showedthat the material-hardening model directly affects onspringback simulation accuracy. Choudhry and Lee [7]accounted inertial effects in the FEA of sheet metalforming process. Papeleux and Ponthot [8] dis-cussednumerically the effect of blank holder force, friction,spatial integration, etc. on the forming response. Chouand Hung [9] carried out FEA of several springbackreduction techniques such as over bending, stretching,arc bottoming, pinching die, spanking and movement(double bend) techniques used in ’U’ channel bending.Math and Grizelj [10] reported springback and residualstresses of bent plates, designed for assembling sphericaltanks made of steel, using elasticplastic incremental FEcalculations and experimental validation. Lei et al. [11]analyzed the free bending and square cup deep draw-ing to predict the springback, stress distribution, etc. forstainless steel using finite element method (FEM). Ragaiet al. [12] investigated the effect of sheet anisotropy onthe springback of stainless steel 410 draw-bend speci-mens experimentally as well as through finite elementsimulations. Furthermore, they studied the influence ofblankholder force and coefficient friction on the amountof the final springback.

In manufacturing industry, it is still a practical prob-lem to predict the final geometry of the part after spring-back and to design appropriate tooling in order to com-pensate the springback. Liu et al. [13] proposed a methodto control the forming process of a U-shaped part bythat a reasonable blank-holder force curve can be easi-ly gained. Comparing with constant blankholder force,higher forming quality can be obtained in both avoidingcracking and improving dimension accuracy. Hama et al.[14] proposed new techniques of the sheet metal formingsimulation utilizing the Nagata patch for describing thetool surfaces. They performed a two-dimensional drawbending process using Nagata and polyhedral patchesfor tool model and studied the tool modeling accuracyon springback simulation. Yoshida et al. [15] investi-

gated springback behavior and shape control techniquesfor high strength steels. They studied effects of differentparameters such as applying reverse bending in die gap,applying compression in thickness direction, etc.

The aim of this paper is to investigate the rela-tion between the springback and blank-holder force inU-bending process by means of the finite element pro-gram, ABAQUS. For this purpose, different values ofblankholder force are preformed for two different mate-rials.

2. Fe modeling

In this part a computer simulation for the stamp-ing process is conducted in two major steps. Firstly, aforming analysis is conducted, including the blank andtooling, in order to determine the sheet metal deforma-tion during the stamping process. Secondly, the sheetmetal springback deformations following the removal ofstamping tooling are computed using the forming stressdistribution and the deformed geometry along with thick-ness distribution. There are some fundamental differ-ences in the characteristics of both computation phases.The forming process is controlled by the time-dependentinteractions of the blank and stamping tooling through africtional contact-interface which results in some grossshape changes of the sheet metal. Consequently, thecomputational modeling of the forming process necessi-tates an incremental formulation due to the geometricallynon-linear kinematics of sheet metal deformation involv-ing large displacements, large rotations and finite plasticstrains. On the other hand, the springback deformationsof a typical stamping part are relatively small comparedwith the sheet thickness and are mainly caused by theunbalanced through-thickness stresses of the sheet onceit is taken out of stamping tooling. With the progress ofFE methods along with the computational hardware andsoftware technologies, the explicit and implicit incre-mental formulations have been developed for the processmodeling and analysis. The explicit dynamic and staticincremental methods have found widespread use in themodeling and analysis of 3-D sheet metal forming dueto its ability of better contact handling and relatively lowcomputational cost when compared to the implicit staticincremental method. In the forming analysis phase, aninitially flat sheet is placed between the stamping die el-ements usually involving the die, punch and blankholder.It is common in sheet metal forming analysis to includethe surface of the tooling in the FE model, rather thanthe complete geometry as rigid geometric entities.

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TABLE 1Basic material properties for the three test materials

AA5754-O DP-Steel

Thickness (mm) 1.5 1.2

Young’s

Modulus (GPa) 73.25 205.35

Poisson’s ratio 0.33 0.3

Yield strength

(MPa) 102.4 358.7

Ultimate tensile

strength (MPa) 234.2 570.9 3

The 2D draw-bending problem in NUMISHEET’93as shown in Figure 1 is a case studied in this pa-per for two materials: AA5754-O and DP-Steel. Thematerials basic properties are summarized in Table 1.To obtain numerical efficiency, the simulation of theU-bending process is modeled in the finite element pro-gram ABAQUS Explicit, while the springback analysisis simulated in ABAQUS Standard as it would take along time to obtain a quasi-static solution of springbackanalysis in ABAQUS Explicit. It was found in the liter-ature that several authors (Hibbit [16]; Jiang [17]; Lee[18]) used shell elements in their modeling of sheet met-al forming processes. This type of element accounts forthe change of thickness in its output variables, unlikesolid and plane strain elements. This facilitates gettingthe final thickness after deformation in sheet metal form-ing processes. For instance, half of the blank is modeledwith a total of 300 shell elements (S4R) for a blankstrip, about five millimeter width and 9 integration pointsthrough the thickness [19], with the symmetry boundarycondition along the Y axis. Mass densities used for thedynamic explicit code are 2.7 gr/cm3 for aluminum al-

loy and 7.8 gr/cm3 for high strength steel. The punchvelocity was speed up to 10 m/s in the dynamic explicitcode without mass scaling and resulted in very smalloscillation in the kinetic energy which is acceptable fora quasi static process. The springback parameters θ1 andθ2 studied by this benchmark are shown in Figure 2.

3. Results and discussions

Applying force on blankholder is a traditional wayto compensate springback by making the blank becomesmore plastic (increasing the plastic strains) and causinghigher stretching in the blank. On the other hand, in-creasing the amount of this factor carelessly may leadto undesirable enlargement of maximum required punchload in the forming process. Therefore, an appropri-ate simulation of the process using different values ofblankholder force and a thorough investigation of theirinfluences on the amount of springback may help thedesigner to choose the optimum value. In order to studythe relation between the blankholder force and spring-back, six different values are selected that consists of:2.5, 5, 10, 15, 20 and 25 kN.

In Table 2 the results of springback for different val-ues of blankholder force and two materials are presented.It should be pointed out that the higher amount of θ1 andsmaller amount of θ2 expresses the higher springback. Itis found that for the DP-Steel, increasing the force up to10 kN, lead to the higher amount of springback. Afterpassing this value, the springback starts to decrease andfor 25 kN reaches to its minimum amount. This fact isclearly shown in Figure 3. As it can be observed, 10 kNand 5 kN are the critical values of blankholder forcesfor DP-Steel and AA5754-O, respectively.

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Fig. 1. The 2D draw bending

Fig. 2. The springback parameters (at the punch and die corners)

Paying more attention to the results shown in Fig-ure 3, displays that for the variation of θ2 with the blankholder force, 5 kN is the critical point for the both mate-rials. Increasing the force from 5 kN to 25 kN results in2.6% and 0.6% variation for θ1, and 5% and 8% varia-tion for θ2 for AA5754-O and DP-Steel, respectively. As

the initial blank thickness is larger for the aluminum al-loy, AA5754-O considerably exhibits smaller amount ofspringback after unloading. It should be noted howeverthat with the same initial blank thickness, DP-Steel willhave smaller springback [20].

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TABLE 2Springback results for different values of blankholder force

BF θ1(◦) θ2(◦)(kN)

AA575 DP- AA575 DP-4-O Steel 4-O Steel

2.5 100.27 103.22 82.48 815 101.02 104 82.45 80.9210 100.88 104.2 83.57 81.5615 99.54 103.75 84.66 81.9220 99.05 103.48 85.03 82.425 97.66 102.53 86.68 87.66

97

98

99

100

101

102

103

104

105

0 5 10 15 20 25

Blankholder force(kN)

Th

eta

1

DP-Steel

AA5754-O

80

81

82

83

84

85

86

87

88

0 5 10 15 20 25

Blankholder force(kN)

The

ta2

DP-Steel

AA5754-O

Fig. 3. Springback parameters versus blankholder value

Four elements on the top layer of the sheet areselected in order to investigate the evolution of plas-tic strain during the process, Figure 4. The characteris-tic number of each element specifies the distance fromthe centerline. Figure 5 displays the history of equiv-alent plastic strain for the selected elements when theblankholder force is assumed to be 2.5 kN and the ma-terial is DP-Steel. It may be observed from the figurethat the elements number 62 and 30 attain the highestand the lowest amount of equivalent plastic strain at theend of process, respectively.

Fig. 4. Sample elements which are considered in order to investigatethe deformation regime

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Process history(s)

Eq

uiv

ale

ntp

lastic

strain

element62

element40

element35

element30

Fig. 5. History of equivalent plastic strain for the specified elementsduring the forming process

The process consists of simultaneous bending andstretching where for lower values of blankholder forcebending is dominant. By enlarging the force, the influ-ences of bending and stretching become almost equal,hence, springback increases. For larger forces, stretch-ing will be more dominant. As the blank becomes moreplastic (plastic strains increases), the portion of elasticstrains decreases, consequently springback reduces. Inorder to understand the process more precisely, the val-ues of elastic strain for a sample element located 62mmaway from the center line, on top layer of the blank isshown in Figure 6. It is found that for the lower blankholder forces the elastic strain increases initially whilefor the higher amounts, 25 kN, it reaches to a minimumvalue. For instance, for the DP-Steel, the elastic strain is0.00172, 0.0019 and 0.0007 for 2.5 kN, 10 kN and 25kN, respectively. One of the important parameters thatshould be taken into consideration while increasing theblankholder force is the maximum punch load. Naturally,applying larger force on holder causes larger punch loadthrough the process. Therefore, regarding the variationof springback, increasing the blankholder force shouldbe preformed in a manner that the required load forthe punch be reasonable. In Figure 7 the required maxi-

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mum punch loads for the different values of blankholderforces applied in the process are shown. As it can beobserved, the punch load for 25 kN is approximately

more than three times of the load for 2.5 kN. For eachcase, DP-Steel needs a considerable higher punch loadthrough the process than the AA5754-O.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

2.5 10 25

Blankholder force(kN)

Ax

iale

las

tic

str

ain

DP-Steel

AA5754-O

Fig. 6. Amount of axial elastic strain for different values of blankholder force

The springback phenomenon depends basically onthe through-thickness stress gradients [21]. Figure 8demonstrates the distribution of axial (longitudinal)stress through the DP-Steel blank thickness. The differ-ence in amount of stress for two points located in front ofeach other on top and bottom of the blank is the smallestwhen the blankholder force is 25 kN and is the largestwhen it is 5 kN.

4. Conclusions

The influence of blankholder force on springbackthrough the finite element method by means of ABAQUSis studied in this paper. Simulations were preformed fortwo materials, i.e. AA5754-O and DP-Steel. It was found

that enlarging the blankholder force did not always guar-antee the reduction of springback and the middle valuescan increase the springback. Both stretching and bendingexisted during the process where act in opposite direc-tions. For some mid-values of blankholder forces, theireffects become close to each other and reduce the plasticzone; hence, springback will be increased. Investigatingthe history of strain during the process for a sampleelement revealed that for the mid-values of force, por-tion of the elastic strain increases undesirably, whereascontinuing enlargement of the force led to reduction ofthis portion. Finally, the obtained results showed thatincreasing the blankholder force inaccurately may resultin augmentation of the maximum required punch loadsignificantly.

0

1

2

3

4

5

6

7

8

9

2.5 5 10 15 20 25

Blankholder force(kN)

Ma

xim

um

pu

nch

load

(kN

)

DP-Steel AA5754-O

Fig. 7. Maximum required punch load for the two materials

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Axial straess(Pa)

Dis

tanc

efro

mthe

mid

-su

rface

(mm

)

2.5kN

5kN

10kN

25kN

Axial Stress(Pa)

Fig. 8. Distribution of the axial (longitudinal) stress through the blank thickness for the elements located 62mm away form the centerline

REFERENCES

[1] M. F i r a t, U-channel forming analysis with an empha-sis on springback deformation, Journal of Materials andDesign 28, 147-154 (2007).

[2] M. S a m u e l, Experimental and numerical predic-tion of springback and side wall curl in U-bending ofanisotropic sheet metals, Journal of Materials ProcessingTechnology 105, 382-393 (2000).

[3] S.-W. L e e, Y.-T. K i m, A study on the springbackin the sheet metal flange drawing, Journal of MaterialsProcessing Technology 187, 89-93 (2007).

[4] V. E s a t, H. D a r e n d e l i l e r, M. I. G o k l e r, Fi-nite element analysis of springback in bending of alu-minium sheets, Journal of Materials and Design 23,223-229 (2002).

[5] J. R. C h o, S. J. M o o n, Y. H. M o o n, S. S. K a n g,Finite element investigation on springback characteris-tics in sheet metal U-bending process, Journal of Mate-rials Processing Technology, 141, 109-116 (2003).

[6] X. L i, Y. Y a n g, Y. W a n g, J. soBao, S. L i, Effectof material-hardening mode on the springback simula-tion accuracy of V-free bending, Journal of MaterialsProcessing Technology, 123, 209-211 (2002).

[7] S. C h o u d h r y, J. K. L e e, Dynamic plainstrain fi-nite element simulation of industrial sheetmetal formingprocesses, International Journal of Mechanical Sciences36, 189-207 (1994).

[8] L. P a p e l e u x, J. P. P a n t h o t, Finite element sim-ulation of springback in sheet metal forming, Journalof Materials Processing Technology 125-126, 785-791(2002).

[9] I. N. C h o u, C. H u n g, Finite element analysis and op-timization on springback reduction, International Jour-nal of Machine Tools and Manufacturing 39, 517-536(1999).

[10] M. M a t h, B. G r i z e l j, Finite element approach inthe plate bending process, Journal of Materials Process-ing Technology 125-126, 778-784 (2002).

[11] L. P. L e i, S. M. H w a n g, B. S. K a n g, Finite ele-ment analysis and design in stainless steel sheet formingand its experimental comparison, Journal of MaterialsProcessing Technology 110, 70-77 (2001).

[12] I. R a g a i, D. L a z i m, J. A. N e m e s, Anisotropyand springback in draw-bending of stainless 410: ex-perimental and numerical study, Journal of MaterialsProcessing Technology 166, 116-127 (2005).

[13] G. L i u, Z. L i n, W. X u, Y. B a o, Variable blankhold-er force in U-shaped part forming for eliminating spring-back error, Journal of Materials Processing Technology120, 259-264 (2002).

[14] T. H a m a, T. N a g a t a, C. T e o d o s i u, A. M a k i -n o u c h i, H. T a k u d a, Finiteelement simulation ofspringback in sheet metal forming using local interpola-tion for tool surfaces, International Journal of Mechan-ical Sciences 50, 175-192 (2008).

[15] T. Yo s h i d a, T. K a t a y a m a, K. H a s h i m o -t o, Y. K u r i y a m a, Shape control techniques for highstrength steel in sheet metal forming, Nippon Steel Tech-nical Report, No. 88, 2003.

[16] Hibbit, Karlsson & Sorensen, Inc. (2003) ABAQUSStandard User’s Manual Version6.5.

[17] W. J i a n g, Study of two-surface plasticity theory, Jour-nal of Engineering Mechanic 120, 2179-2200 (1994).

[18] C. L e e, J. C a o, Shell element formulation of mul-tistep inverse analysis for axisymmetric deep drawingprocess, International Journal of Numerical Methods inEngineering 50, 681-706 (2001).

[19] M. G. L e e, D. K i m, c. K i m, M. L. W e n -n e r, K. C h u n g, Springback evaluation of automotivesheets based on isotropic-kinematic hardening laws andnon-quadratic anisotropic yield functions, part III: appli-cations, International Journal of Plasticity 21, 915-953(2005).

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[20] M. K a d k h o d a y a n, I. Z a f a r p a r a n d e h, Onthe relation of equivalent plastic strain and springbackin sheet draw bending, International Journal of MaterialForming 1, 141-144 (2008).

[21] M. C. O l i v e i r a, J. L. A l v e s, B. M. C h a -p a r r o, L. F. M e n e z e s, Study on the influence ofwork-hardening modeling in springback prediction, In-ternational Journal of Plasticity 23, 516-543 (2007).

Received: 10 February 2009.