CHARACTERIZATION OF POLYMERS FOR APPLICATION IN SHEET-

BULK FORMING
Cristiano G. H. Castro
Instituto Superior Técnico, University of Lisbon, Portugal
E-mail: cristiano.castro@tecnico.ulisboa.pt

Abstract
Nowadays, a new manufacturing technology is being developed, known as sheet-bulk forming (SBF),
allowing to obtain compact parts with high-complexity details, in an economic and environmentally
advantageous manner comparing to other manufacturing processes, for low production series, like
injection molding.

However, since only metallic materials are being study for SBF, this work intend to study the viability to
extend this new manufacturing technology to polymeric sheets, in particular to PC and PVC with 3 and
5 mm of thickness. In that way, an extensive characterization of these materials is necessary, comprising
tensile tests, stack compression tests, double notch tensile tests and shear tests. The shear tests, due
to the presence of a new approach, have in this work their first application in polymers.

The mechanical properties of the polymeric sheets in study were determined by the tensile tests, without
noticeable presence of anisotropy regarding the direction of extrusion. Both tensile and compression
tests exhibit similarities in the results. As to the double notch tensile tests, both PVC sheets presented
viable results, whereas PC exhibited some difficulties, making necessary a more thorough investigation.
No valid results were obtained by means of the new shear test.

Further investigation must be conducted regarding the formability of these materials.

Keywords: Polymeric sheet, PC, PVC, Formability, Sheet-bulk forming, Numerical analysis.

1. Introduction
Nowadays, the majority of manufacturing processes are only capable of producing high complexity
component at high prices, due to a presence of a significant amount of waste during production. This
fact led to a search of new economic and environmentally friendly cost effective methods capable of
producing compact parts with high complexity details. Sheet-bulk forming (SBF) can be found among
these new methods. SBF is a new manufacturing technology which allows to obtain geometric details
located outside of the original non-deformed sheet surfaces (see Figure 1 (a)) by combining both
advantages of sheet forming and bulk forming.

This new technology, now in development, already presents results within metals. However, it is of major
importance to analyze the possibility of extend this methodology to parts made from polymeric sheets.

Thus, mechanical, fracture and formability characterizations should be conducted firstly in the polymeric
sheets being study, namely PC and PVC with 3 and 5 mm of thickness (𝑡), in order to determine their
properties, assessing material flow and formability. Therefore, four different types of tests were
performed: tensile tests, stack compression tests, double notch tensile tests and shear tests.

1
 (a) (b)

Figure 1 – (a) Loading directions in sheet-bulk forming (SBF) processes (Bragança et al., 2016); (b) Details of the initial plastic
shear zone (in the specimen left side) and deformed plastic zone (in the specimen right side) (Silva et al., 2016).

Tensile tests were used to determine the mechanical resistance of the materials being study. On the
other hand, compression tests allow to reach higher levels of deformation, since there is no necking.
Also, several operational conditions regarding manufacturing processes are best represented by this
last type of tests. One way or another, since this work is about polymeric sheets, known by having
different behaviors in tension and compression, the presence of compression tests is essential to
validate the results in tension (Alves et al., 2011). However, conventional compression tests are not
suitable to sheet materials, due to their low aspect ratio, ℎ⁄𝐷 (specimen height over specimen
diameter). Therefore, and in order to contemplate the aspect ratio range necessary to be in the presence
of valid results (1 < ℎ⁄𝐷 < 3, according to Alves et al., 2011), stack compression tests must be
conducted, in which several discs of sheet material are stacked to form a cylindrical specimen.

Mode I fracture toughness, being the capability of the material to absorb energy while in plastic
deformation, can be determined by three different criteria: J-integral, COD (crack opening displacement)
and EWF method. This last one is the most used from all three, since it presents more advantages. With
this method, and taking into consideration the total work of fracture (𝑊𝑓 ), the essential work of fracture
(𝑊𝑒 ), which one is directly related with the fracture toughness of the material, can be determine.
However, there is a major lack of consensus in the scientific community about this subject, driven by a
deficiency in standardization (Bárány et al., 2010).

At last, Silva et al. (2016) developed a new approach to conduct shear tests that will be applied in this
investigation (see Figure 1 (b)). It is worth knowing that this new shear test was only applied to metals.
Therefore, this work will analyze the possibility to expand the SBF applicability to polymers, as well as
the validity of this new shear test in this material class.

2. Experimentation
Since there are four different types of tests going on to determine the mechanical properties and to
characterize the formability of the PC and PVC sheets of 3 and 5 mm of thickness, a closer look should
be given to the way they were employed in this investigation.

2
2.1. Tensile tests
The tensile tests followed the ASTM D638 (2010) standard (see Figure 2 (a)). The specimens were cut
out from the supplied sheets at 0º, 45º and 90º with respect to the direction of extrusion (DE). It is worth
mentioning that the test speed was 𝑣 = 5 mm/min and the tests were conducted in a universal testing
machine INSTRON model 4507 with two pairs of HDRE (high resolution digital extensometers), one
measuring in the force direction and the other in the width direction.

la
D
lc
l0
W

h
r
b0

lt

(a) (b)

Figure 2 – Schematic representation of: (a) type I specimens used in the tensile tests. Identification of the controlled dimensions
(adapted from Cristino e Martins, 2013); (b) stack compression specimens, in which ℎ = 𝑍 ∙ 𝑡,with ℎ being the height of the
specimen, 𝑍 the number of stacked discs and 𝑡 the theoretical thickness of the discs (adapted from Cristino e Martins, 2013).

2.2. Stack compression tests

The procedure presented by Alves et al. (2011) and Silva et al. (2016) was followed in this investigation,
due to the lack of proper standardization for stack compression tests (see Figure 2 (b)). The specimens
were composed by several circular discs of material sheet with 15 mm of diameter and were tested
using a hydraulic testing machine INSTRON model SATEC 1200 and compression plates, under a test
speed 𝑣 = 5 mm/min.

2.3. Double notch tensile tests

The double notch tensile tests were the most demanding from all four test types, in part due to the lack
of standardization, as happened to the stack compression tests. Therefore, with regard to this
investigation, the work model followed by Silva et al. (2016) was behind all the experimental process
(see Figure 3 (a)).

l0
l0 Detalhe A l1 l2

l0 Detalhe A
W
W

A
W

A
a

d d d a

(a) (b)

Figure 3 – Schematic representation of the specimens: (a) DNTT, used in double notch tensile tests (adapted from Cristino e
Martins, 2013); (b) DNST for shear tests according to the new testing approach.

3
These specimens are called as DNTT specimens (double notch tensile test specimens) due to the
presence of a ligament and due to the loading type, being cut out from the supplied sheets at 0º and
90º DE. The ligaments length presented values 𝑎 = 8, 10, 15, 20 e 25 mm before introducing small pre-
cracks in the corresponding notches (see Table 1). These pre-cracks aim to ensure the linearity of the
fracture propagation. The notch width presented a value 𝑑 = 3 mm.

Table 1 – Values associated to the dimensions of specimens DNTT and DNST.

Test type 𝑾 (mm) 𝒍𝟎 (mm) 𝒍𝟏 (mm) 𝒍𝟐 (mm) 𝑑 (mm) 𝒂 (mm)

8
10
Double notch
50 150 - - 3 15
tensile
20
25
2.5
3 5
Shear 45 100 30 35 10
2
1
4

As happened for the tensile tests, the universal testing machine is the same. However, in these ones,
there is no use of the HDRE.

2.4. Shear tests

The shear tests were performed accordingly to the new test developed by Silva et al. (2016), which
takes into consideration a DNST specimen (double notch shear test) (see Figure 3 (b)) with two
ligaments with values varying between 𝑎 = 2.5, 5 and 10 mm, for a notch width 𝑑 = 3 mm, and 𝑎 = 2
and 4 mm, for a notch width 𝑑 = 1 mm (see Table 1). There is no presence of pre-cracks, since the fact
that the specimens are being loaded in shear ensures a proper fracture development.

For this type of tests was used the same machine as for the stack compression tests (hydraulic testing
machine INSTRON model SATEC 1200), with the presence of a small difference in the apparatus.
Instead of resort to compression plates, the tool was developed specifically to this type of test and to
the geometric profile of the specimens (Silva et al., 2016). Again, it was used a test speed 𝑣 = 5 mm/min.

3. Finite element modelling

In order to validate the experimental results, several numerical simulations were performed for the tests
in study. These simulations were conducted through the finite element modelling program I-form,
considering a bi dimensional model (Nielsen et al., 2013). However, firstly, a set of sensitivity analysis
was carried on for the stack compression tests, in order to find some of the ideal simulation parameter.
Between these analyses was possible to identify a test speed analysis, a mesh dimension analysis, a
time increment analysis, coefficient of friction analysis and aspect ratio, ℎ/𝑑, analysis.

Some of the simulation models for each one of the several tests can be found in Figure 4.

4
 Upper grip Punch
Upper grip
Specimen Upper plate Specimen

Specimen

Tool
Lower plate
Tool

(a) (b) (c) (d)

Figure 4 – Schematic representation of the simulation model for the: (a) tensile test; (b) stack compression test of a specimen
with three discs with 3 mm of thickness; (c) double notch tensile test of a specimen with ligament length 𝑎 = 15 mm; (d) shear
test of a specimen with ligament length 𝑎 = 10 mm.

It is worth mentioning that the construction of the several numeric models considered Raghva-Caddell-
Atkins plasticity criteria and a rigid-plastic model.

In the case of the double notch tensile simulation models, despite the experimental analysis with all the
ligament lengths, it was only considered specimens with ligament lengths 𝑎 = 8, 15 and 25 mm. The
same happened to the shear simulation models, where only the specimens with 𝑎 = 2.5 and 10 mm
were considered.

4. Results and discussion

After testing, it was possible to reach the following results on the mechanical (tensile and stack
compression tests), fracture (double notch tensile tests) and formability characterization of the PC and
PVC sheets.

4.1. Tensile tests

In Figure 5 (a) is possible to visualize the configuration of a PVC specimen before and after the tensile
test.

(a) (b)

Figure 5 – Representative image of the PVC specimens used in the: (a) tensile tests, before and after deformation (from up to
down); (b) stack compression tests with three discs of 𝑡 = 3 mm, before and after deformation (from left to right).

It is possible to visualize a high degree of deformation in the specimens after the tensile tests. This
happens not only for PVC but also for PC. Also, a near inexistent level of anisotropy, due to the direction
of extrusion, is present in both this material, which can be confirmed by the superposition between the
several evolution curves of nominal stress with extension.

5
When comparing both experimental and numerical result from tensile tests, some similarity is observed
(Figure 6 (a)). However, the numerical evolution doesn’t quite reach the experimental one, being the
plastic part of the numerical evolution unable of represent the propagation of the necking throughout the
specimen, then experiencing a continuous drop.

EXP h/D = 0.21

2.5 200
FEM h/D = 0.20
Experimental EXP h/D = 0.42
FEM h/D = 0.40

Effective stress (MPa)

2 FEM 1 disc EXP h/D = 0.61
150
FEM h/D = 0.60
EXP h/D = 0.82
Force (kN)

1.5 FEM h/D = 0.80

2 discs
EXP h/D = 1.05
100 3 discs FEM h/D = 1.00
1 4 discs
5 discs
50
0.5

0 0
0 20 40 60 80 100 0 0.5 1 1.5 2 2.5
Displacement (mm) Effective extension
(a) (b)
Figure 6 – (a) Evolution of force with displacement for experimental and numerical tensile tests conducted in PVC specimens
with 𝑡 = 3 mm; (b) evolution of the effective stress with the effective extension for experimental and numerical stack
compression tests conducted in specimens composed by PVC discs with 𝑡 = 3 mm (number of stacking discs varying from 1 to
5).

4.2. Stack compression tests

From the stack compression point of view, the representation of a specimen before and after
deformation can be visualized in Figure 5 (b).

Figure 6 (b) depicts the experimental and numerical evolutions of the effective stress with the effective
extension, for a stack compression specimen with a variation of the number of discs. A close similarity
between both evolution types is concluded from Figure 6 (b), for a long value of extension, what allows
to consider that the numerical simulation quite well represents the experimental behavior of the
materials. This happens not only for PVC specimens, but also for PC.

Experimentally, an upper limit was established for the number of discs that may be part of the stack
without compromise the specimen stability. This number is five for PVC and PC discs with 3 mm of
thickness and three for the ones with 5 mm of thickness. A lower limit to assure a quasi-static behavior
of the results can be also definable for both the material, being three the minimum number of discs.

4.3. Material properties

Table 2 presents some of the main material properties obtainable from tensile testing.

Table 2 – Main material properties for the material in study obtained from tensile tests.

Thickness
Load type Material 𝝈𝒚 (MPa) 𝑬 (GPa) 𝝈𝒇 (MPa) 𝑨 (%)
(mm)
3 64.4 2.6 64.2 106.5
PC
5 65.7 2.6 63.6 106.9
Tension
3 52.2 3.2 37.1 110.4
PVC
5 52.9 3.3 36.5 128.8

6
Where 𝐸 represents the Young modulus, 𝜎𝑦 the yield stress, 𝜎𝑓 the fracture stress and 𝐴 the elongation.

The Young modulus for both PC and PVC sheets and the fracture stress for PC present considerable
similarities in the values when compared to the work of Silva et al. (2012). However, the values of yield
stress, 𝜎𝑦 , for both PC and PVC and the fracture stress, 𝜎𝑓 , of PVC sheets show some discrepancies. It
must be held in mind that the thickness in both investigations are different, which may be the cause for
some of this disparities.

4.4. Double notch tensile tests

Double notch tensile tests, at first, were developed considering a test speed 𝑣 = 5 mm/min, as it had
been done in the case of tensile and stack compression tests. However, the presence of fragile fractures
(see Figure 7) forced this test parameter to change in order to obtain a ductile fracture, since this is the
only way possible to successfully apply the EWF method.

2.0 Fragile fracture; v = 0.1 mm/min

Ductile fracture; v = 0.5 mm/min
Ductile fracture (WPC); v = 0.75 mm/min
1.5
(a)
Force (kN)

(c)
1.0

(b)
0.5 (a) (b)

0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Displacement (mm)
(c)

Figure 7 – Comparative evolution of force with displacement resulting from the different types of fracture obtained through
double notch tensile tests for PC specimens oriented at a 0° DE, with 𝑡 = 3 mm and 𝑎 = 8 mm. Visualization of the fracture zone
for each one of the considered cases and of a specimen used in tests.

As seen in Figure 7, not only pre-cracked specimens were tested but also specimens without pre-cracks
(WPC). From the deformation depicted in Figure 7 (c) is possible to understand why specimens without
pre-cracked ligaments should not be used in double notch tensile tests, since, instead of fracturing, this
kind of specimens undergoes a first stage of necking before actual fracture. It is almost like having a
tensile test before the actual double notch tensile test, what is not acceptable.

Performing several of this tests to the ligaments in study, by changing the value of 𝑣 it was possible to
identify what can be named as a ductile test speed range. In other words, a test speed range where is
possible to obtain a ductile fracture of the specimens.

However, PVC specimens had no problems when tested with a test speed 𝑣 = 5 mm/min, what allowed
to obtain results like the ones represented in Figure 8.

This way, and contrarily to what happened with PC specimens, since all fractures had ductile behavior,
it was possible to determine the fracture toughness values, 𝑅, for both PVC thicknesses (see Table 3).

7
 4

3.5 EXP a = 8 mm
FEM a = 8 mm
3 (c) (a) 𝑎 = 8 mm
EXP a = 15 mm
FEM a = 15 mm
Force (kN)

2.5
EXP a = 25 mm
2 FEM a = 25 mm
(b)
1.5

1 (b) 𝑎 = 15 mm
(a)
0.5

0
0 1 2 3 4 5 6
Displacement (mm)
(c) 𝑎 = 25 mm

Figure 8 – Evolution of force with displacement for double notch tensile experimental and numerical tests conducted in PVC
specimens with 𝑎 = 8, 15 and 25 mm and 𝑡 = 3 mm. Visualization of the fracture zone and of a used test specimen.

Table 3 – Mode I fracture toughness for PVC sheets with 𝑡 = 3 and 5 mm.

Thickness R
Material
(mm) (kJ/m2)
3 19.2
PVC
5 16.1

The fracture toughness values presented in Table 3 lie under the values from the work of Silva et al.
(2012) on PVC sheets with 2 mm of thickness. This goes against the expected, whereas an increase in
the sheet thickness should be associated to an increase in the fracture toughness. However, an
explanation to this may be related to different material suppliers or batches of PVC sheets responsible
for slightly different material properties.

Considering the numerical results for some of these specimens, a substantial similarity is observed
between experimental and numerical results (see Figure 8). However, it is possible to identify a certain
increasing discrepancy the bigger the ligament length, what can be understood as a pre-crack effect.

4.5. Shear tests

EXP a = 2.5 mm
5
FEM a = 2.5 mm
4 EXP a = 10 mm
Force (kN)

FEM a = 10 mm
3

0
0 5 10 15 20
Displacement (mm)

(a) (b) (c)

Figure 9 – (a) Evolution of force with displacement for shear experimental and numerical tests conducted in PVC specimens
with 𝑡 = 5 mm, 𝑑 = 3 mm and 𝑎 = 2.5 and 10 mm; (b) representative image of a PVC shear specimen with 𝑑 = 3 mm and 𝑎 = 10
mm after deformation; (c) representative image of the ligaments deformation profile, obtained numerically for a PVC shear
specimen with 𝑑 = 3 mm and 𝑎 = 10 mm.

8
About the shear tests, it is important to refer again the use of the new test developed by Silva et al.
(2016). Since this investigation was the first one to address the expansion of this test to polymeric
materials, no reference had been set to compare results with. However, tests were executed, being the
results obtained clearly revealing of an incorrect behavior of the specimens’ deformation (see Figure 9
(a)). To be more specific, and taking Figure 9 (b) as a visual aid, it was to expect the development of a
mode II fracture, due to the shear loading. However, the deformed plastic shear zone indicates the start
of what can be named as a mode I type of fracture, clearly not expectable for this tests. Figure 9 (c)
reinforces, by a numerical point view, the loading pattern involved in this new shear test. The curves of
force with displacement showed also an odd evolution, helping to understand this new test inability for
shear test the polymeric material in this study.

4.6. Formability characterization

It is possible to evaluate the material formability for the polymeric sheet materials, here investigated,
through all the information obtained from this four test types. The formability is given by a fracture point
of view, since all the testing were done towards that objective. Therefore, the fracture forming limit lines,
FFL, are represented in Figure 10.

1.0 Tensile, t = 3 mm 1.0 Tensile, t = 3 mm

0.9 Tensile, t = 5 mm 0.9 Tensile, t = 5 mm
DNTT, t = 3 mm y = -0.7446x + 0.5465 DNTT, t = 3 mm
0.8 0.8
FFL (t = 3 mm) DNTT, t = 5 mm
0.7 0.7 FFL (t = 3 mm)
0.6 0.6 FFL (t = 5 mm)
y = -0.1464x + 0.5661
0.5 ε1 y = -1.2717x + 0.3716 0.5 ε1
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
0.0 0.0
-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
ε2 ε2
(a) (b)
Figure 10 – Principal strain space obtained from several tests conducted in specimens with = 3 mm and 𝑡 = 5 mm of: (a) PC; (b)
PVC. Representation of the FFL for the several specimen thicknesses.

It is worth noticing the absence of the PC 5 mm thickness sheet’s FFL. This happens because there are
no valid results for double notch tensile tests in this case. The same is applied for all shear results.

5. Conclusion
This document intended to study the viability to extend the new manufacturing technology of sheet-bulk
forming (SBF) to polymeric material, more specifically to PC and PVC sheets of 3 and 5 mm of thickness.
In order to accomplish this, mechanical, fracture toughness and formability characterizations are of most
importance to fully understand the materials properties. Therefore, four types of tests were used in this
investigation: tensile tests, compression tests, double notch tensile tests and shear tests.

From the tensile tests was observed high levels of necking before fracture. However, there were no
significant signs of anisotropy due to the direction of extrusion. The differences between the mechanical

9
properties of the polymers loaded in tension and compression were studied with stack compression
tests.

A wide range of conclusions is obtained from the double notch tensile tests. First of all, as result of the
tests to PC specimens, a fragile fracture was observed, jeopardizing the use of EWF method for this
material. It was concluded that the fracture behavior changes with the test speed, 𝑣. Therefore, it was
possible to establish a range of test speeds, especially when talking about PC sheets with 3 mm of
thickness, where the fracture mechanism was ductile, making possible the application of the EWF
method. On the other hand, this situation was not observed for PVC sheets, allowing the determination
of the mode I fracture toughness.

The application of the new shear test, developed by Silva et al. (2016) and already applied to an
aluminium alloy, to PVC and PC revealed the impossibility to obtain valid results, due to a non-
recognizable evolution of force with displacement. Therefore, a mode II fracture toughness value was
also not defined.

It is highly recommended, before any kind of extension of SBF to polymeric materials, to further
investigate the double notch tensile tests of PC sheets and to retry the shear tests, this time with different
parameters and different geometry specimens more suitable to polymeric materials.

References
Alves L.M., Nielsen C.V., Martins P.A.F. (2011). Revisiting the Fundamentals and Capabilities of the
Stack Compression Test. Experimental Mechanics, 51, 1565-1572.

ASTM D638-10, Standard Test Method for Tensile Properties of Plastics, ASTM International, West
Conshohocken, PA, 2010.

Bárány T., Czigány T., Karger-Kocsis J. (2010). Application of the essential work of fracture (EWF)
concept for polymers, related blends and composites: A review. Progress in Polymer Science, 35, 1257-
1287.

Bragança, I.M.F., Silva, C.M.A., Alves, L.M., Martins, P.A.F. (2016). Joining sheets perpendicular to one
other by sheet-bulk metal forming. The International Journal of Advanced Manufacturing Technology,
85, 1-10.

Nielsen, C.V., Zhang, W., Alves, L.M., Bay, N., Martins, P.A.F. (2013). Modeling of Thermo-Electro-
Mechanical Manufacturing Processes with Applications in Metal Forming and Resistance Welding.
London, UK: Springer-Verlag.

Silva, M.B., Marques T., Martins, P.A.F. (2012). Single-point incremental forming of polymers. In J.
Paulo Davim (Ed.), Mechatronics and manufacturing engineering: Research and development (pp.
293-331). Cambridge, UK: Woodhead Publishing.

Silva, C.M.A., Silva, M.B., Alves, L.M., Martins, P.A.F. (2016). A new test for determining the mechanical
and fracture behavior of materials in sheet-bulk metal forming. Journal of Materials: Design and
Applications, 1-11 (available online).

10