Effect of punch profile radius and localised compression

INTERNATIONAL Mechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – AND TECHNOLOGY (IJMET) © IAEME
6359(Online) Volume 3, Issue 3, Sep- Dec (2012)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
IJMET
Volume 3, Issue 3, September - December (2012), pp. 517-530
© IAEME: www.iaeme.com/ijmet.asp ©IAEME
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)
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EFFECT OF PUNCH PROFILE RADIUS AND LOCALISED
COMPRESSION ON SPRINGBACK IN V-BENDING OF HIGH
STRENGTH STEEL AND ITS FEA SIMULATION
Vijay Gautam1, Parveen Kumar2, Aadityeshwar Singh Deo3
1
(Department of Mechanical Engineering, Delhi Technological University, Road, Delhi-
110042, India, vijay.dce@gmail.com)
2
110042, India, dahiya.sonu1@gmail.com)
3
110042, India, dce.aaditya@gmail.com)

ABSTRACT

Spring-back is a very common and critical phenomenon in sheet metal forming operations,
which is caused by the elastic redistribution of the internal stresses after the removal of
deforming forces. Spring-back compensation is absolutely essential for the accurate geometry
of sheet metal components. In this study an experimental investigation was carried out to
determine the effect of punch corner radii on springback in free V- bending operation. The
springback compensation was done by localised compressive stresses on bend curvature by
the application of compressive load between punch and the die. This experimental springback
phenomenon was analysed and validated by an Explicit finite element program using
ABAQUS 6.10. In order to determine spring-back in V-bending operation, six numbers of
‘‘V’’ shaped dies and punches with required clearances were designed and fabricated with
included angle of 90° for bending of high strength sheet metal with thicknesses: 0.85, 1.15
and 1.55mm. Keeping other parameters same increase in punch corner radius increases the
springback and increase in sheet thickness reduces the springback. Springback compensation
by localised compressive stress showed negligible springback and the same results were
supported by FEA simulations. This model is very useful to control springback on a press
brake equipped with controlled computer integrated data acquisition system.

Keywords: Bending dies, Explicit solution, Mn-High Strength steel, Springback, V-bending.

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME

1. INTRODUCTION

Bending is one of the most important sheet metal forming operations by which a straight
length of metal strip is transformed into a curved one with the help of suitably designed die
and punch. It is very common process of forming steel sheets and plates into channels, drums,
automotive and aircraft components.

Especially V-Bending process has been thoroughly studied and there is plenty of literature
available, among which the most important contribution is Hill's basic theory on pure
bending of sheet metals[l]. Hill has derived the complete solution for pure bending of a non-
hardening sheet and showed the shift of the neutral surface during bending. Lubahn and
Sachs [2] studied the bending of rigid perfectly plastic materials in cases of both plane stress
and plane strain, and they predicted no change in material thickness by assuming that the
surfaces, including the neutral surface, Crafoord [3]considered the Bauschinger effect by
assuming the constant yield surface on reverse straining by fibres overtaken by the neutral
surface. And he predicted obvious thickness thinning of rigid-strain-hardening metal sheets.

Pure bending is rarely achieved in actual bending process, except that, it is the desired
profile of a bend than the temporal stress and strain distribution that is important. The
assumptions made in the study of pure bending are generally different from real conditions in
v-die bending. Unlike pure bending, V-die bending is not a steady process. A sheet metal is
laid over a die and bent as the punch inserts into the die, the bending moment and curvature
vary continuously along the sheet and during the deformation, the sheet is stressed in tension
on one surface and compression on the other, it is shift of the neutral surface during bending
that complicates the analysis[4].

The stress state is complex in bending. Around the neutral plane, the stress must be elastic
because complete tensile and compressive stress-strain curves of the material are traversed on
both bend side. When the forming tool is removed from the metal, the elastic components of
stress cause spring back which changes both the angle and radius of the bent part as shown in
Fig.1. The part tends to recover elastically after bending, and its bend radius becomes larger.
This elastically-driven change in shape of a part upon unloading after forming is referred to
as spring back.

Figure 1: terminology for springback in bending [5]
Spring-back causes following problems in sheet-metal forming:

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1) The assembly of the sheet metal components becomes problematic thereby increasing the
assembly time and reducing the productivity.
2) In automobile industry different punch corner radius are used for different bending
operations which in turn affects the spring-back in components.
3) A wide range of thickness is used in sheet-metal components which again affects the
spring-back.
4) High strength sheets are preferred for automotive body as to reduce the thickness which
results in reduction of the overall weight of the vehicle. Lighter vehicles are in demand for
higher fuel efficiency.

However, spring-back characteristic of IFHS has not been investigated widely and very
little information is available about its behaviour during V-bending operations.

Both material parameters and process parameters affect springback, parameters such as
elastic modulus, yield strength, strain hardening ability and thickness of the sheet metal as
well as die opening, punch radius and so on interfere the springback in a very complicated
way.

Figure 2: Methods of reducing springback in V-bending operations [5].

We can calculate springback approximately, in terms of the radii Ri and Rf i.e. initial and
final radius of bend curvature (Fig.1) as[5] :

ோ௜ ோ௜ ோ௜
= 4(ா௧)ଷ − 3 ቀா௧ቁ + 1 (1)
ோ௙

Note that springback increases as the R/t ratio and yield stress Y of the material increases
and the elastic modulus E decreases [5].

2. COMPENSATION FOR SPRINGBACK
In general practice there are different ways for springback compensation as shown in the
Fig.2 :over-bending (In Fig.2 (a) & (b)), coining or bottoming the punch (shown in Fig.2 (c)
and (d)), stretch bending and warm bending[5].

Over-bending is an effective way to compensate for the springback, this can be done in air
bending by adjusting the punch/ die angle or punch stroke. Several trials may be necessary to
obtain the desired results. Stelson and co-workers have introduced an adaptive control model
[6-8] and this model estimates the material characteristics of a sheet being bent from the
punch force-displacement data taken early in the bending process, and the in-process

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measured parameters are then used in the calculation of the current final punch position so
that the elastic springback can be compensated by over-bending and desired unloaded angle
of a bend can be obtained. By this model, disturbances in operation due to variations in
material characteristics of a sheet will not affect the modelling results. To predict the loaded
shape and the springback of a sheet being bent, however, strenuous measurement and
calculation must be performed. In analysis of springback in v-die bending, the curvature of a
sheet metal subjected to bending needs to be known. In most analyses, the inner radius of a
bend is commonly assumed to be the same as that of the punch. In fact, the radius of
curvature is a function of both material and process parameters. If the radius of a punch is of
the same order of the sheet thickness, the radius of curvature underneath the punch will be
larger than that of the punch, while a sufficiently large punch will cause a smaller bending
curvature [9].

Another method is stretch bending, in which the part is subjected to tension while being
bent, the springback is reduced as the neutral surface is shifted out of the sheet metal [10].
Since the springback decreases as yield stress decreases, all other parameters being the same,
bending may also be carried out at elevated temperatures to reduce springback known as
warm bending [11].

Little data is available for springback compensation by bottoming the punch or coining
and hence localised compression was the main objective of the study.

3. MATERIAL SELECTION & METHODOLOGY
Materials and techniques for cutting weight from vehicles and thereby improving fuel
efficiency, are a part of routine automotive engineering practice. Large reductions in weight
while maintaining size and enhancing vehicle utility, safety, performance, ride and handling
are often thought of as the driving force for future vehicles [12].The body of a car, including
the interior, accounts for nearly 40% of the car’s total weight and offers a high potential for
lightweight construction [13]. Materials for car body panels require certain specific
characteristics to meet the industry’s challenges: rationalisation of specifications for leaner
inventory, improved formability for reduced rejection rate and better quality. Higher Strength
Low Alloy (HSLA) steels of thinner gauges are getting preference for weight reduction and
the resulting better fuel economy. Other quality characteristics under demand are higher yield
stress (strength), toughness, fatigue strength, improved dent resistance as well as corrosion
resistance in materials used for body panels for improved durability and reliability.
Keeping in view of the above factors low carbon high strength steel, was chosen for the
springback study and the sheet metal was procured from leading automobile manufacturer
with thickness 0.85, 1.15 and 1.55mm. Chemical analysis of the material as per the ASTM-
E415-08 reveals that the material is high Manganese and low Carbon and the composition of
the steel is given in TABLE 1.

Table 1: Chemical composition of HS-steel (wt %)
C Si Mn P S Ti Nb Al
0.077 0.013 1.4 0.05 0.011 0.04 0.001 0.032

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The microstructure of high strength steel was revealed and carefully studied under
magnification of 200X. The microstructure shown in the Fig. 3 depicts the fine grains of
ferrite and complex Manganese Carbides uniformly distributed in ferrite matrix responsible
for high strength of the steel.

Figure 3: microstructure of high strength steel at 200x showing complex carbides in the
matrix of ferrite
3.1. Tensile Properties of High Strength Steel
The tension tests were carried out as per ASTM standard E 8M-04 (2004) on INSTRON
4482, 100KN machine, in strength of materials laboratory at DTU Delhi. The HS sheets of
0.85, 1.15 and 1.55mm thickness were tested for the mechanical properties. The tension test
specimens were cut from the sheet metal at 0° i.e. parallel to, inclined at 45° and
perpendicular at 90° with respect to the rolling direction of the sheet metal. The tensile testing
of material was carried out with standard size specimen as shown in Fig.4.

Figure 4: tensile specimens cut as per ASTM-E8M in direction parallel to, perpendicular to
and inclined at 45° to the rolling direction
The typical stress strain curve obtained from the tests is shown in Fig.5 to Fig. 7. Since the
departure from the linear elastic region cannot be easily identified, the yield stress was
obtained using the 0.2 % offset method. UTS was determined for the maximum load and
original cross section area of specimen. The tensile properties of the specimens show that the
sheet metal is slightly anisotropic. Hence it can be regarded as isotropic material.

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Table 2: Mechanical properties of High Strength steel sheet

Young’s Direction Strength Strain
Sheet thickness σy yield
Modulus wrt. Coefficient hardening
metal (mm) (MPa)
(MPa) rolling (k) coefficient(n)

0˚ 355 791.39 0.188
High
0.85 210000 45˚ 367 762.0 0.179
strength
90˚ 376 785.4 0.179

0˚ 312 744.7 0.199
High
1.15 210000 45˚ 320 730.18 0.190
strength
90˚ 314 741.7 0.188

0˚ 315 735.9 0.196
High
1.55 210000 45˚ 319 732.0 0.192
strength
90˚ 324 716.51 0.184

Stress- Strain curve for 0.85mm sheet
600
engg stress
stress in MPa

400 strain curve
X-0-1
200

0 stress
strain
0 0.2 0.4 curve:x-90-
-200
strain in mm/mm 1

Figure 5: engineering stress strain curve of 0.85mm thick sheet as obtained from tensile test
on UTM, depicting that the metal is almost isotropic.

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stress -strain curve for 1.15mm sheet
500
400 stress

stress in MPa
strain
300
curve Y-0-1
200
100 stress
0 strain
-100 0 0.2 0.4 curve: y-
45-1
strain in mm/mm


stress strain curve for 1.55mm sheet

600
engg stress
strain
Stress in MPa

400
curve z-0-1
200
engg stress
0
strain
0 0.2 0.4 curve z-45-
-200
strain in mm/mm 1


The strain hardening exponent (n) and the strength coefficient (K) values are calculated
from the stress strain data in uniform elongation region of the stress strain curve. The plot of
log (True stress) versus log (True strain) which is a straight line is plotted. The power law of
strain hardening is given as:

σ = K. εn (2)

Where, σ and ε are the true stress and true strain.

Taking log on both sides:

log (σ) = log (K) + n. log (ε) (3)

This is an equation of straight line the slope of which gives the value of ‘n’ and ‘K’ can be
calculated taking inverse natural log of the y-intercept of the line (i.e. ln (K)) as shown in
Fig.8.

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log stress strain curve
n=0.188, K=791.39MPa
6.8

Ln(true stress)
y = 0.188x + 6.673
6.6
R² = 0.999 6.4 log stress strain
curve
6.2
6
5.8 Linear (log
stress strain
-4 -2 0 2 curve)
Ln (true strain)

Figure 8: calculation of n and k value of high strength steel

3.2. Fabrication of Bending Tools
As discussed earlier two sets of dies and punches with the punch corner radius 7.5 mm and 10
mm were required for the experimental setup of V-bending in addition to other accessories.
The included angle for dies and punches were kept as 90°.

The D-2 tool steel for cold working was selected for the bending dies. The drawings of
tooling were made in CATIA-V5 as shown in the Fig.9 and Fig.10. The DXF file was used in
EDM-wire cut to fabricate the dies and punches. A total of six dies and two punches were
designed with two different punch corner radii. The clearance between dies and punch was
made equal to sheet thickness to avoid the localized compressive stresses during bending
operation. The dies and punches were designed with a holding shank of 25mm length and
12.5mm thickness for easy holding and proper alignment in UTM. The setup was designed
for UTM for capturing the data for load and deflection.

After fabrication the dies and punches were hardened and tempered in Metallurgy
laboratory. D-2 steel dies and punches were heated to 910°C in a muffle furnace for 4hrs.
And hardened in air and then tempered at 250°C. After air hardening the hardness was 65Rc
and after tempering the hardness was 62HRc.

Figure 9: a CAD drawing of the v-die showing various dimensions

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Figure 10: a CAD drawing of the v-punch showing various dimensions

4. FEA SIMULATIONS: RESULTS AND DISCUSSIONS
The FEA simulations for the above experimental procedure were carried out using ABAQUS
6.10 in CAD lab. The material model for 2D deformable blank was prepared as isotropic
hardening following power law of hardening, with young’s Modulus of Elasticity as
210000MPa and Poisson ratio of 0.3 with structure insensitive elastic constants for steel.

The plastic data of the steel was directly taken from data acquisition of UTM were true
stress and strain. The plastic strain at stress level 350MPa was 0.0, and at 445MPa strain was
0.058mm/mm. The dies and punches were modelled as 2D analytical rigid requiring no
meshing properties. The friction condition between the punch and blank was frictionless and
a friction value of 0.1 was used between blank and the die.

Table 3: Different part attributes used in the FEA Model

PARTS 2D

DIE ANALYTICAL RIGID

PUNCH ANALYTICAL RIGID

BLANK DEFORMABLE

The simulation results are listed as below:

Case-1.Bending of HS steel 0.85mm thick with punch corner radii 7.5mm.



Case-4.Bending of HS steel 0.85mm thick with punch corner radii 10mm.



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CASE 1: High Strength steel 0.85mm thick with punch corner radii 7.5mm.

Figure 11: overlay plot showing springback of HS 0.85mm thick sheet with punch corner
radius of 7.5mm.


radius of 7.5mm


radius of 7.5mm

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CASE 4: High Strength steel 0.85mm thick with punch corner radii 10mm.

radius of 10mm

CASE 5: High Strength steel 0.9mm thick with punch corner radii 10mm.

radius of 10mm

CASE 6 High Strength steel 1.55mm thick with punch corner radii 10mm.

radius of 10mm

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Table 4: Comparison of springback values in experimental and simulation results by bending
with punch corner radius of 7.5mm when no compensation was done.

SHEET CONFORMING
ROLLING EXPERIMENTAL BY SIMULATION
THICKNESS BENDING
DIRECTION (IN DEGREE) (IN DEGREE)
(mm) LOAD (N)

0.85 0˚ 200 4.61˚ 4.12˚

0.85 45˚ 200 5.66˚ 4.46˚

0.85 90˚ 200 4.81˚ 4.33˚

1.15 0˚ 400 3.21˚ 2.41˚

1.15 45˚ 400 3.90˚ 2.21˚

1.15 90˚ 400 3.64˚ 2.10˚

1.55 0˚ 800 1.92˚ 1.62˚

1.55 45˚ 800 2.78˚ 2.13˚

1.55 90˚ 800 2.12˚ 1.92˚

Table 5: Comparison of springback values in experimental and simulation results by bending
with punch corner radius of 10mm when no compensation was done.

SHEET CONFORMING BY
ROLLING EXPERIMENTAL
THICKNESS BENDIG SIMULATION
DIRECTION (IN DEGREE)
(mm) LOAD(N) (IN DEGREE)

0.85 0˚ 200 5.76˚ 5.45˚

0.85 45˚ 200 5.99˚ 5.15°

0.85 90˚ 200 5.76˚ 5.54˚

1.15 0˚ 400 4.14˚ 3.48˚

1.15 45˚ 400 4.49˚ 3.18˚

1.15 90˚ 400 4.91˚ 3.79˚

1.55 0˚ 800 2.18˚ 2.56˚

1.55 45˚ 800 2.94˚ 2.44˚

1.55 90˚ 800 2.98˚ 2.17˚

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Table 6: Table depicts final spring-back values after spring-back compensation due to
localisation of compressive stresses.

INITIAL FINAL
SHEET ANGLE ANGLE SPRING-BACK BY
ROLLING Load
THICKNESS EXPERIMENTAL SIMULATION
DIRECTION (N) ( ɵi ) (in (ɵf) (in
(mm) (IN DEGREE) (IN DEGREE)
degree) degree)

0.85 0˚ 1200 44.95˚ 44.57˚ 0.3805˚ Nil

0.85 45˚ 1200 44.95˚ 44.25˚ 0.7009˚ Nil

0.85 90˚ 1200 44.95˚ 43.43˚ 0.5212˚ Nil

1.15 0˚ 3000 44.92 44.71 0.2101˚ Nil

1.15 45˚ 3000 44.92˚ 44.48˚ 0.4416˚ Nil

1.15 90˚ 3000 44.92˚ 44.33˚ 0.5868˚ Nil

1.55 0˚ 4000 44.96˚ 45.6˚ -0.6351˚ Nil

1.55 45˚ 4000 44.96˚ 45.46˚ -0.4966˚ Nil

1.55 90˚ 4000 44.96˚ 44.72˚ -0.2416˚ Nil

Discussions: when a sheet metal is bent as discussed above, it will be in compression on
punch side and tension on die side, and at the mid surface it has elastic stress component
which primarily depends on bend angle. When localised compression is applied then the
neutral surface vanishes forcing the sheet section in compression only and springback is
compensated by localised compression.

5. CONCLUSIONS
With reference to the above studies and results following conclusions are drawn:

1. When the bending load was low and enough to conform to the shape of the die then
considerable value of springback was seen experimentally and by numerical simulations.

2. It was confirmed by numerical simulation that as the sheet thickness increases the spring-
back decreases.

3. It was determined that as the punch corner radii increases the spring-back effect increases
significantly keeping other factors same. The result is in agreement with some of the
literatures [14].

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4. Experiments show that the spring-back can be effectively compensated by localization of
compressive stresses by the increase in the load in the final phase of bending when the
sheet is conforming to the shape of the die fully. Experiments show negligible springback
value but these values should be carefully used while designing the toolings for v-bending
operation. Thicker sheets showed negative springback but the same was not reflected in
the numerical simulation results.

6. ACKNOWLEDGEMENTS

The Authors thank the Management of Delhi Technological University for their continuous
support and constant encouragement to carry out this research work.

REFERENCES
[1]. R Hill, the mathematical theory of plasticity Oxford, London, 1950.
[2]. J. Lubahn et al, Bending of an ideal plastic metal, Transactions of the ASME, Volume
72, 1950, 201-208.
[3]. R. Crafoord, Steel sheet surface topography and its influence on friction in a bending
under tension friction test, International Journal of Machine Tools and Manufacture, Vol. 41,
issues 13-14, 2001, 1953-1959.
[4]. Z. Tan et al, An empiric model for controlling springback in V-die bending of sheet
metals, Journal of Materials Processing Technology, 34, 1992, 449-455.
[5]. S. Kalpakjian and R. Schmid, manufacturing processes for engineering materials 4th
edition( Pearson Education Inc., 2003).
[6]. K. A. Stelson and D.C. Gossard, An Adaptive Pressbrake control using an Elastic-Plastic
Material Model, ASME, Journal of Engineering for Industry, 104, 1982, 389-393.
[7]. S. Kim and K. A. Stelson, Real time identification of workpiece material characteristics
from measurements during brakeforming, ASME Journal of Engineering for Industry, 105,
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[8]. A. K. Stelson, An Adaptive Pressbrake Control for Strain Hardening Materials, ASME
Journal of Engineering for industry, 108, 1986, 127-132.
[9]. K. J. Weinmann and R.J. Shippell, Bending of HSLA steel Plate, 6th North America
Metal Working Research, Conf. Proc., April-1978, Florida, USA.
[10]. ZaferTekiner, An experimental study on the examination of springback of sheet metals
with several thicknesses and properties in bending dies, Journal of Material Processing
Technology, 145, 2004, 109-117.
[11]. J. Yanagimoto and K. Oyamada, Springback of High-Strength Steel after Hot and
Warm Sheet Formings, Annals of CIRP, Vol. 54/1, 2005, 213-216.
[12]. De Cicco J.M., Projected fuel savings and emmissons reductions from light vehicle fuel
economy standards, Transportation Research, Part-A: Policy and Practice, Vol. 29, no.3,
1995, 205-228.
[13]. Auto Steel Partnership, Tailor welded blank design and manufacturing manual,
Southfield, MI, Report, 2001.
[14]. W.D. Carden, R. H. Wagoner et al, Measurement of springback, International journal of
Mechanical sciences, 44, 2002, 79-101.

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