Materials and Design 53 (2014) 797–808

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Materials and Design

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Technical Report

Thinning and spring back prediction of sheet metal in the deep drawing
process
H. Zein, M. El Sherbiny ⇑, M. Abd-Rabou, M. El shazly
Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza, Egypt

a r t i c l e i n f o a b s t r a c t

Article history: The spring back simulation helps to get the required tolerance of the punch travel distance. This tolerance
Received 27 May 2013 is needed in getting the required height of the final drawn part. Prediction of the forming results as spring
Accepted 23 July 2013 back, determination of the thickness distribution and of the thinning of the sheet metal blank reduces the
Available online 2 August 2013
production cost of the material and time. In this paper, A Finite Element (FE) model is developed for the 3-
D numerical simulation of sheet metal deep drawing process (Parametric Analysis) by using ABAQUS/
EXPLICIT FEA program with the proper material properties (anisotropic material) and simplified bound-
ary conditions. The FE results are compared with experimental results for validation. The developed
model predicts the spring back, the thickness distribution and thinning of the blank as affected by the
die design parameters (geometrical parameters and physical parameters). Furthermore, with numerical
simulation, working parameters such as punch force, the blank holder force, and the lubrication require-
ments can be determined without expensive shop trials.
Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The objective of the work is to successfully simulate the deep

drawing process. The literature contains both experimental and
Traditionally, most metal forming techniques have been tested numerical results which are in reasonable agreement with each
experimentally using trial-and-error or empirical methods, which other and therefore is being set as the benchmark for comparison
are expensive and time consuming approaches, as dies, blank hold- purposes.
ers and punches need to be manufactured. By making use of finite The incentive for doing this research is that deep drawing has
element analysis the prediction of punch force, the blank holder come to a stage in the current industrial state of the art that
force, the thickness distribution through sections of the metal requires the most efficient, low-cost, manufacturing route to be
and the lubrication requirements can be determined. This can sig- taken at all times.
nificantly reduce the production costs, for higher quality contain- Colgan and Monaghan [2] have taken a statistical approach,
ers by reducing the lead time to production and provides based on experimental design using orthogonal arrays to ascertain
engineers the ability to respond to market changes with greater which factors most influence the deep drawing process. Four hun-
speeds. In doing this, the level of knowledge in how various mate- dred tests were carried out on blanks cut from drawing quality
rials interact at the contact surfaces are enhanced, and the data for mild steel EN10130 FeP01 of 1 mm thickness. Their work estab-
dealing with specific materials are also increased, which is another lished that the punch/die radii have the greatest effect on the
positive outcome. thickness of the deformed mild steel cups. It was made apparent
It is also known, that for the majority of food and drink contain- that the smaller the die radii, the greater the force on the blank,
ers, the cost of the processed metal accounts for 50–70% of the resulting in thinner wall thicknesses. It was also shown that the
total cost [1]. From the manufacturer’s point of view, a reduction type of lubrication is very much affecting the force on the punch.
in material usage is of massive importance to cost reductions. Although they concluded that the die radii were noted as a prom-
Reduction of material can be done by decreasing the wall thickness inent factor, they did not provide enough substance to account for
of the containers, whilst also retaining adequate strength to allow other factors affecting the deep drawing process.
the container to serve its purpose, without fear of failure. The de- The problem is also addressed by Demirci et al. [3] for the deep
signer must meet these expectations, but also, must determine drawing process of AL1050 by performing experiments and finite
the material requirements and properties which are suitable for element analysis using ANSYS/LS-DYNA, investigating the effects
the food or drink being packaged. of the blank holder forces on differences in the cup wall thickness.
The results show that under constant pressure the base of drawn
⇑ Corresponding author. Tel.: +20 1006044616; fax: +20 237746016. cups remains at a constant value until thickness drops dramatically
E-mail address: mgsherbiny@eng.cu.edu.eg (M. El Sherbiny). near the cup corners and follows exponential variation towards the

0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.matdes.2013.07.078
798 H. Zein et al. / Materials and Design 53 (2014) 797–808

outer edge on the cup flange. Taking into account the anisotropic focus in forming simulation has now moved towards the Finite Ele-
properties of the material they concluded that forces exceeding ments (FE) method [17,18]. High strength steels and aluminum,
10 MPa may result in tearing in the cup walls. used for lightweight products, show particularly large spring back
Jawad [4] confirms the previously stated point that increasing [19]. The calculation of spring back has been implemented in most
the punch radii can slightly decrease the punch load and vice versa. commercial forming simulation software packages. However, for
He investigated the effects of punch radii on maintaining the inter- industrial deep drawn products, the accuracy of the results has
facial contact between the punch and the blank, and punch load on not yet reached an acceptable level [20].
thickness through a section of the drawn cup, and finally predicted When the FE spring back simulation has proven to be reliable,
the resulting localized strain and stress distribution. He concluded the results of this simulation were used for tool shape optimization
that frictional forces act mainly through the edge of the punch in a loop. This speeds up the development of the tool set significantly,
shearing manner, with little effect on the flat section. [21]. However, the successful simulation of the deep drawing pro-
Vladimirov et al. [5] presented the derivation of a finite strain cess is very much dependent on successful modeling of the deep
material model for plastic anisotropy and nonlinear kinematic drawing process for numerical analysis. This paper intends to ap-
and isotropic hardening. The work is applied numerically to the proach the deep drawing process of thin walled, mild steel, cylin-
drawing of cylindrical and square shaped cups. They show that drical containers, by means of a finite element analysis.
the numerical simulations, can be suitably extracted from the com-
plex mathematical material models and that the phenomena of 2. Simulation of deep drawing process
anisotropic properties can still be accounted for even with large
deformations. Fereshteh-Saniee and Montazeran [6] predicted 2.1. Finite element model
forming load by using various finite element types, and the strain
thickness distributions are produced, [4]. The authors also show Fig. 1 shows a sketch for drawing a circular cup. The important
that the use of shell 51 elements of the finite element package give dimensions shown in Fig. 2, of the blank, die, punch, and blank
a much higher agreement with the experimental results, as com- holder are given in Table 1. Due to the symmetry, the numerical
pared with the results using visco solid 106 elements. In making analysis of the deep-drawing process was performed by using only
these comparisons, Fereshteh-Saniee and Montazeran use a for- one quarter of 3D numerical model to reduce the computational
mula derived by Siebel in [7] to produce an analytical solution to time. The model is shown in Fig. 3.
which the level of agreement between the various methods can Discrete rigid form was used to model the punch, die and
generally be accepted. holder, whose motion was governed by the motion of a single
Meguid and Refaat [8] used a method of variation inequalities node, known as the rigid body reference node. Die, punch, and
to develop an analytical method to model the frictional contact holder were meshed with R3D4 elements. Therefore, only the
in elastoplastic models which undergo large deformations. The ef- blank sheet metal (224 mm diameter  1 mm thickness) was con-
fect of nonlinearities arising due to either the geometry or the sidered deformable with a planar shell base and meshed with re-
materials used in the model is handled by using the updated duced integration S4R shell type element [22].
Lagrangian formulation.
Having arrived at a point where the material can be modeled to 2.2. Material properties
a very high degree of accuracy and the forming loads can be pre-
dicted to complete the drawing process, one may consider various The blank is made of mild steel [23]. The material is modeled as
frictional combinations at the contacting surfaces aiming at mini- an elastic–plastic material with isotropic elasticity, using the Hill
mizing such forming loads, and hence cost analysis can be carried anisotropic yield criterion for the plasticity to describe the aniso-
out for the manufacture of the container. tropic characteristics of the sheet metal within the simulation
Spring back is the amount of elastic distortion a material has to
go through before it becomes permanently deformed, or formed. It
is the amount of elastic tolerance, which is to some extent present
in every material, be it ductile, and annealed metal or hard steel. In
ductile materials, the spring back is much lower than in hard met-
als, with dependence on the Young’s modulus of elasticity of a par-
ticular material. The amount of spring back increases with greater
yield strength or with the material’s strain-hardening tendency.
Cold working and heat treatment both increase the amount of
spring back in the material. Comparably, the spring back of low-
strength steel material will be smaller than that of high-strength
steel and spring back of aluminum will be two or three times high-
er [9].
Elastic spring back can be briefly defined as a dimensional
change generated in the part, which occurs due to elastic recovery
after the tool is released. This phenomenon causes the dimensional
deviations [10]. Importance of spring back prediction is significant
also from economical aspects [11]. Nowadays, spring back phe-
nomenon is the current issue in automotive industry, considering
use Ultra High Strength Steel (UHSS), Advanced High-Strength
Steel (AHSS), Complex Phase (CP) Steel, High Strength Steel (HSS)
etc. which have high strength [12]. Handy tables [13,14] and
graphs [15] have been used for some time as traditional ways to
predict spring back.
After the relatively limited analytical models of forming pro-
cesses, for example for stretch-bending of metal sheets [16], the Fig. 1. Sketch of the drawing dies assembly.
 H. Zein et al. / Materials and Design 53 (2014) 797–808 799

Fig. 2. Geometry of drawing dies assembly.

Table 1
Basic geometrical parameters. Fig. 4. Plastic true stress vs. plastic true strain curve of mild steel.

Parameter Dimension in mm
Blank size radius (BR) 112
Blank thickness (t) 1 Table 2
Punch radius (PR) 56 Blank material [23].
Punch nose radius (rp) 4
Young’s modulus (E) 206 GPa
Die radius (DR) 57.67
Poissorrs ratio (v) 0.3
Die shoulder radius (rd) 6
Density (q) 7800 kg/m3
Radial clearance between punch radius and 1.67
Yield stress r0 167 MPa
die radius (wc)
Anisotxopic yield criterion R11 1
Cup height of the first draw (h) 63.69
R22 1.0402
R33 1.24897
R12 1.07895
R13 1
R23 1

2nd category is the drawing operation parameters

(5) Blank holder force (BHF)

(6) Lubrication:
 Coefficient of friction between punch/blank (lp),
 Coefficient of friction between holder/blank (lh), and
 Coefficient of friction between die/blank (ld)

The study of the influence of the tool geometry parameters and

the physical parameters on thinning of sheet metal in the deep
drawing process have been made, according to recommended geo-
metrical values of these parameters from the code, Table 3 [9].

3. Validation of the model

Fig. 3. The model assembly scheme in FEM.
Colgan and Monaghan [2] performed an experimental and
numerical analysis of the process and therefore a comparison be-
program (ABAQUS/EXPLICIT). Fig. 4 shows the true stress, true tween the present works with the values which have been re-
strain curve of the material behavior, whilst Table 2 shows the corded for the blank thickness of the deep drawn cup may be
material properties. used to validate the model. Fig. 5 shows the typical shape charac-
teristics and thickness variations of a partially drawn blank. Thick-
ening occurs in the flange area and some stretching and necking
2.3. The die design parameters

The die design parameters are classified into two categories. Table 3
1st. category is the drawing tool geometry parameters Quoted parameters [9].

Die shoulder radius (rd) rd = (6–10) t For first draw

(1) Die shoulder radius (rd) Punch nose radius (rp) rp = (3–4) t For 6.3 mm 6 dp < 100 mm
(2) Punch nose radius (rp) rp = (4–5) t For 100 mm 6 dp < 200 mm
rp = (5–7) t For 200 mm 6 dp
(3) Sheet metal thickness (t)
Radial clearance (wc) wc = (1.75–2.25) t For steel, deep drawing
(4) Radial clearance (wc)
800 H. Zein et al. / Materials and Design 53 (2014) 797–808

Table 4
Geometrical parameters.

Blank size radius (BR) 38 mm

Blank thickness (t) 1 mm
Punch radium (PR) 19.7 mm
Punch nose radius (rp) 2 mm
Die radius (DR) 20.85 mm
Die shoulder radius (rd) 2 mm
Radial clearance (wc) 1.15 mm
Cup height of the first draw (h) 20 mm

Table 5
Physical parameters.

Young’s modulus (E) 200 GPa

Fig. 5. Deformation and necking of workpiece.
Poisson’s ratio (v) 0.3
Tangent modulus (Et) 0.5 GPa
occurs in the sidewall, just above the punch nose radius [2]. They Density (q) 7800 kg/m3
Yield stress (r0) 200 MPa
measured the sheet metal blank thickness at 8 locations. Therefore,
Friction coefficient (l) 0.1
8 values of thickness were taken from the generated data, at dis- Blank holder force (BHF) 18 KN
tances corresponding to these lengths as shown in Figs. 6 and 7.
Tables 4 and 5 show the model dimensions and materials prop-
erties for the model respectively. The present model is made and
analyzed on ABAQUS/EXPLICIT FEA program. Table 6
Comparison between published results and present predictions for wall thickness in
The results are shown in Table 6. The values obtained from the
mms.
present results correspond to the thickness at the closest node to
the corresponding locations of Ref. [2] along the cup cross section. Experimental [2] FEA Predicted [21] Present FEA
Obviously these locations cannot be exactly the same due to 1 1.132 1.11 1.13926
automatic mesh generation, and therefore small differences in 2 1.032 1.08 1.08072
3 0.888 1.01 0.97214
4 0.83 0.955 0.83777
5 0.823 0.799 0.75774
6 0.871 0.844 0.78593
7 0.966 0.942 0.94598
8 0.979 0.958 0.95945
Average 0.94013 0.96225 0.93487

thickness variations are expected. The locations of Ref. [2] are de-
fined in Fig. 8, whilst both thickness and locations of the present
model are demonstrated in Fig. 9. It is shown in Table 6 that the
average thickness distribution in the blank of the present FEA mod-
el is more close to the average obtained from the experimental re-
sults [2]. Since thinning is our primary concern, comparisons of
Fig. 6. Thickness measurement locations on the drawn cup for the model
validation.
results at thinnest point are of particular interest. At point 4 the
present FE results are much closer to the experimental value. How-
ever point 5 shows slightly lower values as compared with their FE
results [2]. Furthermore the present results are very close to the
published numerical results with differences which do not exceed
2.9% on average. It is even closer to the experimental results with
differences which do not exceed 0.6% on average.

Fig. 7. Corresponding thickness values locations for the model validation. Fig. 8. Measured thickness locations on the drawn cup.
 H. Zein et al. / Materials and Design 53 (2014) 797–808 801

Fig. 11. Variation of the sheet metal thinning with the die shoulder radius (rd).
Fig. 9. Thickness locations on the drawn cup for the present FEA model.

Table 8
Effect of die shoulder radius (rd) on the springback percentage in sheet metal.
Table 7
Effect of die shoulder radius (rd) on sheet metal thickness distribution. rd (mm) 2 4 6 8 10 12 14
Measured thickness rd (mm) Springback % 0.596 2.321 0.788 1.282 0.300 0.515 0.638
(mm) at locations
4 6 8 10 12
1 1.2069 1.2157 1.2150 1.2065 1.1966
2 1.1658 1.1697 1.1544 1.1541 1.1612
3 1.0105 1.0560 1.0675 1.0830 1.0834
4 0.9338 0.9723 0.9892 0.9972 1.0022
5 0.8959 0.9268 0.9359 0.9458 0.9551
6 0.9258 0.9296 0.9293 0.9310 0.9312
7 0.9720 0.9732 0.9747 0.9747 0.9746
8 0.9904 0.9927 0.9918 0.9923 0.9921
Average 1.0126 1.0295 1.0322 1.0356 1.0370

Fig. 12. Variation of the springback percentage in sheet metal with the die shoulder
radius (rd).

times sheet thickness which is in good agreement with published

values [24]. Also, the geometry of die influences the spring back
of sheet metal blank in the deep drawing processes. Table 8 and
Fig. 10. Distribution of sheet metal thickness with the die shoulder radius (rd, mm). Fig. 12 show the spring back percentage for different values of
the die shoulder radius (rd).
These results show that for the die shoulder radius (rd) that is
4. Results and discussion
less than six times the thickness of the blank (t), the cup has a large
value of the spring back percentage, whilst for (rd) greater than or
4.1. The tool geometry parameters
equal (10t), the spring back percentage have smaller values. So, the
die shoulder radius (rd) should be 10 times sheet thickness, which
4.1.1. The die shoulder radius (rd)
again is in good agreement with published values [24].
The geometry of die influences the thickness distribution and
thinning of sheet metal blank in the deep drawing processes. Table
7 and Fig. 10 show thickness distribution for different values of the 4.1.2. The punch nose radius (rap)
die shoulder radius (rd). Fig. 11 shows thinning of sheet metal with The geometry of punch influences the thickness distribution
the die shoulder radius (rd). and thinning of sheet metal blank in the deep drawing processes.
These results show that for the die shoulder radius (rd) that is Table 9 and Fig. 13 show thickness distribution with the punch
less than six times the thickness of the blank (t), the cup fails nose radius (rp). Fig. 14 shows thinning of the sheet metal with
due to increasing in thinning, whilst for (rd) greater than (10t), the punch nose radius (rp). It has been shown that for a punch nose
thinning is stable. So, the die shoulder radius (rd) should be 10 radius (rp) that is less than three times the thickness of the blank
802 H. Zein et al. / Materials and Design 53 (2014) 797–808

Table 9 Table 10
Effect of punch nose radius (rp) on sheet metal thickness distribution. Effect of punch nose radius (rp) on the springback percentage in sheet metal.

Measured thickness rp (mm) rp (mm) 2 3 4 5 6 7

(mm) at locations
2 3 4 5 6 Springback % 2.820 2.644 0.788 1.711 1.150 0.679
1 1.2208 12147 l.2157 1.1942 1.2002
2 1.1580 1.1470 1.1697 1.1510 1.1710
3 1.0443 1.0414 1.0560 1.0441 1.0551
4 0.9717 0.9724 0.9723 0.9736 0.9734
5 0.9286 0.9272 0.9268 0.9265 0.9250
6 0.9203 0.9223 0.9296 0.9383 0.9440
7 0.9812 0.9786 0.9732 0.9695 0.9680
8 0.9890 0.9914 0.9927 0.9904 0.9907
Average 1.0267 1.0244 1.0295 1.0234 1.0284

Fig. 15. Variation of the springback percentage in sheet metal with the punch nose
radius (rp, mm).

Table 11
Effect of blank thickness (t) on sheet metal thickness distribution.
Fig. 13. Distribution of sheet metal thickness with the punch nose radius (rp, mm).
Measured thickness t (mm)
(mm) at locations
0.6 0.8 1 1.4 l.8
1 0.6973 0.9416 1.2157 1.6606 2.1740
2 0.6676 0.9006 1.1697 1.6034 1.0951
3 0.6292 0.8423 1.0560 1.4283 1.8505
4 0.5854 0.7811 0.9723 1.3320 1.7042
5 0.5663 0.7497 0.9268 1.2668 1.5952
6 0.5592 0.7499 0.9296 l.2550 1.6059
7 0.5839 0.7795 0.9732 1.3493 1.7474
8 0.5896 0.7917 0.9927 1.3732 1.7873
Average 0.6098 0.8171 1.0295 1.4086 1.8200

cesses. Table 11 and Fig. 16 show thickness distribution with sev-

eral values of the blank thickness (t), whilst Fig. 17 shows the
percentage of thinning of sheet metal with different blank thick-
ness (t).
The average distribution of the blank thickness is increasing
with increasing the blank thickness. Also, the% of thinning is
Fig. 14. Variation of the sheet metal thinning with the punch nose radius (rp).
increasing with increasing the blank thickness. Slightly thicker
materials can be gripped better during the deep drawing process.
Also, thicker sheets have more volume and hence can be stretched
(t), the cup fails due to increased thinning, whilst for (rp) greater
to a greater extent with increasing in thinning.
than 3t, thinning is somewhat stable.
The original blank thickness has some effect on the springback
In addition, the geometry of punch influences the spring back of
of sheet metal in the deep drawing processes. Table 12 and Fig. 18
sheet metal blank in the deep drawing processes. Table 10 and
show the spring back percentage for several values of the blank
Fig. 15 show the springback percentage with different values of
thickness (t). It has been shown that the springback percentage
the punch nose radius (rp). It has been shown that for a punch nose
decreases with increasing the blank thickness. This agrees in trend
radius (rp) that is greater than six times the thickness of the blank
with published results [25].
(t), the cup have small values for the springback percentage, whilst
for (rp) smaller than (4t), the spring back percentage is increasing.
4.1.4. Radial clearance (wc)
4.1.3. Sheet metal blank thickness (t) Radial clearance is an important parameter, formulated as the
The original blank thickness has some effect on the thickness difference between die radius and punch radius (wc = DR–PR).
distribution and thinning of sheet metal in the deep drawing pro- Table 13 and Fig. 19 show the thickness distribution for different
 H. Zein et al. / Materials and Design 53 (2014) 797–808 803

Fig. 16. Distribution of sheet metal thickness with the blank thickness (t).
Fig. 18. Variation of the springback percentage in sheet metal with the blank
thickness (t).

Fig. 19. Distribution of sheet metal thickness with the radial clearance (wc, mm).

Fig. 17. Variation of % the sheet metal thinning with the blank thickness (t).
for the radial clearance (wc) that is less than the blank thickness
(t), the cup fails due to increased thinning. Whilst for the radial
clearance (wc) greater than the blank thickness (t), thinning is sta-
Table 12
Effect of blank thickness (t) on the springback percentage in sheet metal.
ble. The radial clearance which is less than (0.5t) is not acceptable
because the percentage of reduction in thickness is more than 45%,
t (mm) 0.8 0.9 1 1.1 while the maximum allowable percentage of reduction in thick-
Springback % 5.909 4.940 0.788 0.674 ness is 45% [9].
Table 14 and Fig. 21 show the variation of the springback per-
centage with the radial clearance (wc).
It is shown that the springback percentage is reduced with
Table 13
Effect of radial clearance (wc) on sheet metal thickness distribution. increasing the radial clearance (wc). In addition, for the radial
clearance (wc) that is less than the blank thickness (t), the cup fails
Measured wc (mm)
due to increased thinning.
thickness (mm)
0.4 0.8 1.2 1.67 2 2.4 2.8
at locations
1 1.1159 1.2252 1.2094 1.2157 1.1927 1.1964 1 1929 4.2. The physical parameters
2 1 1084 1.1442 1 1503 1.1697 1.1430 1.1750 1 1533
3 1.1009 1.0038 1.0464 1.0560 1.0393 1.0475 1.0410 4.2.1. Blank holder force (BHF)
4 07842 0.9697 0.9740 0.9723 0.9727 0.9706 0.9734
5 0.8780 0.9248 0.9270 0.9268 0.9254 0.9246 0.9273
The blank holder force (BHF) required to hold a blank flat for a
6 0.9258 0.9300 0.9295 0.9296 0.9298 0.9298 0.9295 cylindrical draw varies from very little to a maximum of one third
7 0.9714 0.9757 0.9737 0.9732 0.9732 0.9730 0.9728 of the drawing pressure [26]. Table 15 and Fig. 22 show thickness
8 0.9824 0.9938 0.9930 0.9927 0.9923 0.9923 0 9917 distribution with the blank holder force (BHF), whilst Fig. 23 shows
Average 0.9825 1.0247 1.0254 1.0295 1.0211 1.0261 1.0227
thinning of the blank with the blank holder force (BHF).
The higher the blank-holder force, the greater will be the strain
over the punch face, however the process is limited by the strain in
radial clearance (wc), whilst Fig. 20 shows thinning of the blank the side-wall. If the tension is reached to its maximum value, the
with the radial clearance (wc). side-wall will fail by splitting [27]. It has been shown that the
It is shown that the distribution in sheet metal thickness is cup collapse due to thinning with the increase of the blank holder
increasing with reducing the radial clearance (wc). In addition, force (BHF) over 0.5 ton. Table 16 and Fig. 24 show the springback
804 H. Zein et al. / Materials and Design 53 (2014) 797–808

Fig. 22. Distribution of sheet metal thickness with the blank holder force (BHF,
ton).
Fig. 20. Variation of the sheet metal thinning with the radial clearance (wc).

Table 14
Effect of radial clearance (wc) on the springback percentage in sheet metal.

we (mm) 0.4 0.8 1 1.1 1.2 1.4 1.67

Springback % failure 5.262 2.301 1.886 0.788

Fig. 23. Variation of the sheet metal thinning with the blank holder force (BHF).

Table 16
Effect of blank holder force (BHF) on the springback percentage in sheet metal.

BHF (ton) 0.1 0.5 1 3 5 7 8

Springback % 0.823 0.788 0.822 0.902 0.566 2.406 3.144

Fig. 21. Variation of the springback percentage in sheet metal with the radial
clearance (wc, mm).

Table 15
Effect of blank holder force (BHF) on sheet metal thickness distribution.

Measured BHF (ton)

thickness (mm)
0.1 0.5 1 3 5 8 10
at locations
1 1.1683 1 2157 1 1815 1 1831 1.2107 1.1908 1.1872
2 1.1908 1 1697 1 1031 1.1402 1 1211 1.1309 1 1309
3 1 0555 1 0560 1.0288 1.0587 0.9850 1 0231 1 0318
4 0.9735 0.9723 0.9464 0.9698 0 9591 0.9148 0.9059
5 0.9264 0.9268 0.9048 0.9019 0.9068 0.8968 0.8961
6 0.9276 0.9296 0.8797 0.8844 0.8861 0.8681 0.8529
7 0.9726 0.9732 0 9511 0.9480 0.9544 0.9472 0 9415
8 0.9921 0.9927 0.9663 0.9696 0.9702 0 9619 0.9588
Average 1.0259 1.0295 0.9952 1.0070 0.9992 0.9917 0.9881 Fig. 24. Variation of the springback percentage in sheet metal with the blank holder
force (BHF).
 H. Zein et al. / Materials and Design 53 (2014) 797–808 805

Fig. 26. Distribution of sheet metal thickness with the Coefficient of friction
Fig. 25. Friction areas when a deep drawing a cup. (A) Friction area between sheet between punch/blank (lp).
metal blank and holder and sheet metal blank die; (B) friction area between sheet
metal blank and the die radius and (C) friction area between sheet metal blank and
the punch edges; FP, total drawing force; FH, blank holder force.

Table 17
Effect of punch coefficient of friction (lp) on sheet metal thickness distribution.

Measured lp
thickness (mm)
0.05 0.1 0.25 0.5 0.7 0.9 1
at location
1 1.2033 1.2142 1.2157 1.2064 1.2037 1.2044 1.2046
2 1.1600 1.1522 1.1697 1.1646 1.1694 1.1545 1.1446
3 1.0528 1.0464 1.0560 1.0508 1.0490 1.0435 1.0434
4 0.9722 0.9721 0.9723 0.9734 0.9730 0.9727 0.9729
5 0.9280 0.9273 0.9268 0.9267 0.9272 0.9270 0.9269
6 0.9176 0.9202 0.9296 0.9350 0.9371 0.9389 0.9397
7 0.9427 0.9538 0.9732 0.9786 0.9795 0.9806 0.9809
8 0.9658 0.9762 0.9927 0.9960 0.9967 0.9969 0.9971
Average 1.0178 1.0203 1.0295 1.0295 1.0273 1.0273 1.0263

percentage with different values of the blank holder force (BHF). Fig. 27. Variation of the sheet metal thinning with the coefficient of friction
between punch/blank (lp).
The higher the blank-holder force, the greater will be the strain
over the punch face, however the process is limited by the strain
in the side-wall. If the tension is reached to its maximum value,
the side-wall will fail by splitting [27]. It has been shown that Table 18
the springback percentage is stable with increasing of blank holder Effect of punch coefficient of friction (lp) on the springback percentage in sheet
metal.
force (BHF), when BHF is smaller than or equal 5 ton. But the
springback percentage is increasing with increasing of BHF above lp 0.05 0.1 0.25 0.5 0.7 0.9 1
5 ton. Springback % 2.489 2.421 0.788 1.826 2.199 2.568 2.332

4.2.2. Coefficient of friction parameters for the highest possible coefficient of friction on the punch edge.
In Sheet Metal Forming processes, such as deep drawing, fric- This demonstrates the first significant rule for lubrication in this
tion plays an important role. Together with the deformation of case: neither the punch nor the sheet metal blank should be lubri-
the sheet, the friction determines the required punch force and cated in this area. Even if this consideration was optimal for an iso-
the blank holder force. Consequently, the friction influences the lated forming operation and force transfer, one still must consider
energy which is needed to deform a sheet material. Friction also punch wear. This friction area requires lubrication in the boundary
influences the stresses and strains in the work piece material mode with a high coefficient of friction and anti-wear behavior
and, hence, the quality of the product. Therefore, it is important [28]. Table 17 and Fig. 26 show thickness distribution with the
to control the friction between the tools and the work piece. In coefficient of friction between punch/blank (lp). Fig. 27 shows
no other forming operation are the friction and, as a result, the thinning of the blank with the variation of the coefficient of friction
lubricating conditions so complex. Fig. 25 shows the different fric- between punch and blank (lp).
tion areas of the deep drawing operation [28]. For fluid lubricant, it has been shown that the distribution in
sheet metal thickness is decreasing with increasing the coefficient
4.2.2.1. Coefficient of friction between punch/blank (lp). The drawing of friction between punch and blank (lp). For solid lubricant and
force in the flange necessary to form the sheet metal is applied by dry lubricant, the distribution in sheet metal thickness is stable
the punch on the base of the cup and transferred from there with increasing the coefficient of friction between punch and blank
through the wall into the flange. This transmission of force calls (lp).
806 H. Zein et al. / Materials and Design 53 (2014) 797–808

Fig. 29. Distribution of sheet metal thickness with the coefficient of friction
Fig. 28. Variation of the springback percentage in sheet metal with the coefficient between holder/blank (lh).
of friction between punch/blank (lp).

Table 19
Effect of holder coefficient of friction (lh) on sheet metal thickness distribution.

Measured lh
thickness (mm)
0.05 0.08 0.11 0.125 0.14 0.16 0.18
at locations
1 1.2166 1.2162 1.2158 1.2157 1.2155 1.2157 1.2160
2 1.1763 1.1731 1.1705 1.1697 1.1684 1.1665 1.1654
3 1.0609 1.0580 1.0565 1.0560 1.0538 1.0531 1.0515
4 0.9752 0.9740 0.9729 0.9723 0.9717 0.9710 0.9704
5 0.9272 0.9271 0.9269 0.9268 0.9267 0.9266 0.9265
6 0.9304 0.9301 0.9298 0.9296 0.9294 0.9292 0.9289
7 0.9735 0.9734 0.9733 0.9732 0.9732 0.9731 0.9730
8 0.9930 0.9929 0.9928 0.9927 0.9927 0.9927 0.9926
Average 1.0316 1.0306 1.0298 1.0295 1.0289 1.0285 1.0280

For fluid lubricant, it has been shown that the thinning of sheet
metal is increasing by small values with increasing the coefficient Fig. 30. Variation of the sheet metal thinning with the coefficient of friction
of friction between punch and blank (lp). On the other hand, for between holder/blank (lh).

solid lubricant and dry lubricant, the thinning increases with

increasing the coefficient of friction between punch/blank (lp). Ta-
Table 20
ble 18 and Fig. 28 show the springback percentage with different Effect of holder coefficient of friction (lh) on the springback percentage in sheet
values of the coefficient of friction between punch and blank (lp). metal.
For fluid lubricant, the springback percentage reduces with
lh 0.05 0.08 0.11 0.125 0.14 0.16 0.18
increasing the coefficient of friction between punch and blank
Springback % 1.086 0.977 0.833 0.788 0.733 0.590 0.495
(lp). On the other hand, for solid lubricant, it has been shown that
the springback percentage is increasing with increasing of the coef-
ficient of friction between punch and blank (lp). Also, for dry lubri-
cant, the springback percentage is increasing with increasing the coefficient of friction between holder and blank (lh). It is noted
coefficient of friction between punch and blank (lp). that the suitable lubricant for the holder/blank interface is the fluid
lubricant. When the coefficient of friction between holder and
blank (lh) increases, the average value of the thickness distribution
4.2.2.2. Coefficient of friction between holder/blank (lh). The main gets slightly stable. But the thinning of the cup is increasing with
aim of deep drawing lubrication is to achieve minimum friction increasing the coefficient of friction between holder and blank
in the blank holder area. This includes the lubrication on the blank (lh). Table 20 and Fig. 31 show the springback percentage with
holder side, which, as much as possible, should be a lubricant ring different values of the coefficient of friction between holder and
in order to reduce the friction in the region of the punch edge to blank (lh).
make it as little as possible. However, in the case of high viscosity It is noted that the suitable lubricant for the holder/blank inter-
oils and drawing pastes, if the applied lubricant film is excessive, face is the fluid lubricant because of the small values of the spring-
there is the risk that hydrostatic effects on the blank holder side back percentage. When the coefficient of friction between holder
of the flange can cause reduction of sheet metal contact with the and blank (lh) increases, the springback percentage is decreasing.
blank holder resulting in wrinkling [28].
Table 19 and Fig. 29 show thickness distribution with different 4.2.2.3. Coefficient of friction between die/blank (ld). In this case the
values of the coefficient of friction between holder and blank (lh), aim of lubrication is to achieve a minimum coefficient of friction
whilst Fig. 30 shows thinning of the blank with the variation of the with minimum wear. Even excessive lubrication of the sheet metal
 H. Zein et al. / Materials and Design 53 (2014) 797–808 807

Fig. 32. Distribution of sheet metal thickness with the coefficient of friction
between die/blank (ld).

Fig. 31. Variation of the springback percentage in sheet metal with the coefficient
of friction between holder/blank (lh).

Table 21
Effect of die coefficient of friction (ld) on sheet metal thickness distribution.

Measured ld
thickness (mm)
0.05 0.08 0.11 0.125 0.14 0.16 0.18
at locations
1 1.2188 1.2163 1.2087 1.2157 1.2087 1.2085 1.2013
2 1.1710 1.1723 1.1522 1.1697 1.1682 1.1559 1.1511
3 1.0582 1.0580 1.0540 1.0560 1.0475 1.0482 1.0477
4 0.9780 0.9759 0.9737 0.9723 0.9717 0.9697 0.9684
5 0.9320 0.9300 0.9281 0.9268 0.9260 0.9242 0.9223
6 0.9343 0.9325 0.9304 0.9296 0.9282 0.9269 0.9249
7 0.9753 0.9747 0.9738 0.9732 0.9728 0.9718 0.9710
8 0.9941 0.9937 0.9931 0.9927 0.9923 0.9914 0.9906
Average 1.0327 1.0317 1.0267 1.0295 1.0269 1.0246 1.0222

Fig. 33. Variation of the sheet metal thinning with the coefficient of friction
surface on the die side normally does not create a problem. Only on between die/blank (ld).
parts with large surface areas and a high percentage of stretch
drawing, such as car body parts can excessive lubricant quantities
lead to unacceptable deviations in form [28]. Table 22
Table 21 and Fig. 32 show thickness distribution with different Effect of die coefficient of friction (ld) on the springback percentage in sheet metal.
values of the coefficient of friction between die and blank (ld),
ld 0.05 0.08 0.11 0.125 0.14 0.16 0.18
whilst Fig. 33 shows thinning of the blank with the variation of
Springback % 2.195 1.421 1.648 0.788 0.968 0.770 0.659
the coefficient of friction between die and blank (ld).
These results show that the proper lubricant for the die/blank
interface is the fluid lubricant. In addition, the average value of
the thickness distribution is reduced with increasing the coeffi-
cient of friction between die and blank (ld). Finally, the thinning
in the drawn cup is increasing with increasing the coefficient of
friction between die and blank (ld).
Table 22 and Fig. 34 show the springback percentage with dif-
ferent values of the coefficient of friction between die and blank
(ld).
These results show that the proper lubricant for the die/blank
interface is the fluid lubricant with higher values of the coefficient
of friction between die and blank (ld). In addition, the springback
percentage is decreasing with increasing the coefficient of friction
between die and blank (ld) above (ld = 0.11). But, for lower values,
the springback percentage is increasing with reducing of the coef-
ficient of friction between die and blank (ld).
On the product design side of the cup deep drawing, one is usu-
ally concerned with two main objectives. First is minimizing geo-
metrical errors by reducing spring back effects on the cup
geometry, and second is minimizing excessive thinning to main- Fig. 34. Variation of the springback percentage in sheet metal with the coefficient
tain uniform thickness, integrity, and functioning of the product. of friction between die/blank (ld).
808 H. Zein et al. / Materials and Design 53 (2014) 797–808

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