AbstractThe aim of the present paper is to evaluate the possibility of producing low-cost, small-batch, polymer sheet components by means of single point incremental forming (SPIF) at room temperature. During the research work, five different thermoplastic materials were incrementally formed into cones with an increasing wall angle on a conventional CNC milling machine. In designed experiments, significant process parameters were found, and influential material properties were identified. The experimental results confirm that SPIF of commercial polymer sheets at room temperature has potential for the manufacture of complex parts with very high depths

Franzen, V.

Kleiner, M.

Kwiatkowski, L.

Martins, P.A.F.

Tekkaya, A.E.

Elsevier - Publisher Connector 

CIRP Annals - Manufacturing Technology 58 (2009) 229–232
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology
journal homepage: http://ees.elsevier.com/cirp/default.aspSingle point incremental forming of polymers
P.A.F. Martins a, L. Kwiatkowski b, V. Franzen b, A.E. Tekkaya (2)b,*, M. Kleiner (1)b
a IDMEC, Instituto Superior Tecnico, TU Lisbon, Portugal
b IUL, Institute of Forming Technology and Lightweight Construction, TU Dortmund, Baroper Str. 301, 44227 Dortmund, GermanyA R T I C L E I N F O
Keywords:
Incremental forming
Polymer
Cold forming
A B S T R A C T
The aim of the present paper is to evaluate the possibility of producing low-cost, small-batch, polymer
sheet components by means of single point incremental forming (SPIF) at room temperature. During the
research work, ﬁve different thermoplastic materials were incrementally formed into cones with an
increasing wall angle on a conventional CNC milling machine. In designed experiments, signiﬁcant
process parameters were found, and inﬂuential material properties were identiﬁed. The experimental
results conﬁrm that SPIF of commercial polymer sheets at room temperature has potential for the
manufacture of complex parts with very high depths.
 2009 CIRP.1. Introduction
Conventional technologies for producing polymer parts are
based on heating-shaping-cooling manufacturing routes and are
closely linked to mass production due to economic limitations. To
meet the demands of decreased life-cycles, short development and
production lead times and to allow a cost-efﬁcient small-batch
production of polymer parts, ﬂexible production techniques are
necessary.
With a similarmotivation formetals, a new sheetmetal forming
process was developed within the past years, called single point
incremental forming (SPIF) [1].
Extending the scope of application to other materials than
metals, the ﬁrst breakthrough was recently performed by Franzen
et al. [2], who showed that SPIF can be successfully utilized for
producing sheet parts made of polyvinylchloride (PVC). Conical
parts with a continuously increasing wall angle c, were
manufactured with a conventional SPIF set-up (Fig. 1).
Le et al. [3] published a preliminary set of experimental results
for the SPIF of PP (polypropylene). The research work plan was
built upon design of experiments (DoE) and comprised the study of
the inﬂuence of step size, tool size, feed rate, and spindle speed on
the overall formability of PP sheets with 3 mm initial thickness.
Two failure modes, similar to those previously observed by
Franzen et al. [2] in PVC, were reported.
Franzen et al. [4] extended the scope of their investigation
including four additional polymers. They investigated the effect of
the initial drawing angle on the formability. It is shown that the
variation in color, which is observed especially in PVC, can be
related to the variation in density, derived from the development
of crazes.
Taking into account the above described state-of-the-art, the
focus of the current paper is twofold: (i) determination of process
limits and (ii) evaluation of product properties. Fracture forming* Corresponding author.
0007-8506/$ – see front matter  2009 CIRP.
doi:10.1016/j.cirp.2009.03.095limit diagrams are introduced to determine formability. Accuracy
and color variations of SPIF parts are comprehensively evaluated.
Five different polymers, polyoxymethylene—POM, polyethy-
lene—PE, polyamide—PA, polyvinylchloride—PVC and polycarbo-
nate—PC, with material structures varying from high-crystalline
(POM) to amorphous (PC), were investigated in this paper. The ﬁrst
part focuses on thematerial characterization introducing a fracture
forming limit diagram for PVC. After that, the formability of
truncated conical shapeswith a continuously increasingwall angle
is analyzed by means of experiments, and, ﬁnally, material
evaluation criteria are introduced.
2. Material characterization
The yield stress sY and the modulus of elasticity E of the
polymers were determined by means of tensile tests. The
specimens were machined in accordance with the ASTM D 638
norm. The testing speed was set to 50 mm/min. The density of the
polymers was measured utilizing a pyknometer. Fracture tough-
ness Rwas evaluated from tensile tests performed on double-edge
notched (DEN) specimens (Fig. 2). The approach considers the total
work of fracture Wt to be broken down into two distinctive
components
W t ¼ Wp þW f (1)
the energy Wp absorbed by the plastically deforming region and
the energy Wf related to the creation of new surfaces. Wf is also
known as the ‘essential work of fracture’ [5]. Fracture toughness R
is computed from the speciﬁc essential work of fracture wf ¼
W f =at under limiting conditions of the length of the ligament a
being equal to zero with t as the sheet thickness.
The formability of the polymer sheets was evaluated by means
of tensile tests and bi-axial circular (Ø 100 mm) and elliptical
(Ømajor 100; Øminor 63 mm) hydraulic bulge tests (Fig. 3).
In case of PVC, experimental observations revealed that neck
formation is suppressed in hydraulic bulge tests so that traditional
forming limit diagrams (FLDs) are inapplicable to describe failure.
Fig. 1. Experimental setup and conical polymer parts.
Fig. 2. Speciﬁc work of fracture wf for DEN specimens.
Fig. 3. Fracture forming limit diagram of PVC.
P.A.F. Martins et al. / CIRP Annals - Manufacturing Technology 58 (2009) 229–232230Instead, fracture forming limit diagrams (FFLDs) were employed.
Local necking and ductile fracture are competitivemodes of failure
in metallic materials [6] but in the case of PVC necking seems to be
suppressed. The technique utilized for obtaining the experimental
fracture forming limit (FFL) of PVC requiredmeasuring thickness at
fracture in order to obtain the ‘gauge length’ strains (e1, e2). The FFL
plotted in Fig. 3 can be approximated by a straight line with the
expression e1 + 0.28e2 = 0.74. All measured material parameters
are summarized in Table 1.
3. Experiments
In the experiments, commercial polymer sheets with a uniform
thickness of t0 = 2 and 3 mm were analyzed.
The experimental study was performed on a Deckel Maho CNC
machining center equipped with a simple tool set-up comprising
the following components: (i) the blank holder with a backing
plate and (ii) the single-point forming tool (Fig. 1). The polymer
sheet, which was ﬁxed by the blank holder, was progressively
formed by the forming tool. The tool path was generated with the
CAM module of the commercial software CATIA V5. No correction
methods were included in the tool path in order to observe the full
deviation of the part geometry, mainly inﬂuenced by springback.
To investigate the formability in the incremental cold forming
process, a conical geometry was chosen. It was characterized by anTable 1
Measured properties of polymers.
Polymer Structure Density (kg/m3) Elastic modu
POM H-C 1404 2894
PE (HD) M-C 966 961
PA M-C 1129 2028
PVC L-C 1469 2835
PC A 1187 2330initial drawing angle C0, followed by a continuously increasing
drawing angle C (Fig. 1). During the forming process the material
failed due to thinning.
Ham and Jeswiet [7] presented the identiﬁcation of the main
inﬂuencing parameters on the formability in SPIF for metals by
means of DoE. They identiﬁed the material type, material
thickness, the tool size, the shape of the part, and the incremental
step size as main parameters. Following their approach, (i) the
polymer material, (ii) the thickness of the sheet t0, and (iii) the tool
radius rtool, and the initial drawing angle C0 were identiﬁed as
signiﬁcant process parameters for SPIF of polymers. These
parameters were varied in a full factorial design at two different
stages (Table 2). The tool path strategy, the vertical step size Dz,
and the feed rate f remained ﬁxed.
The target value of the DoE is the maximum drawing angle
Cmax, which is directly related to the depth h of the part. After
measuring the depth of the tool position at material failure, the
angle c can be calculated by the sine law.
To keep the process temperatures on a low constant level, a
soap-based emulsion was applied between the forming tool and
the polymer sheet.
The geometrical shape of the manufactured parts was
measured with a 3D digitalizer of GOM. The digitalized shape
was re-imported into a CAD system and compared with the
original CAD model to analyze the deviation.
4. Results and discussion
4.1. Modes of failure
The experiments showed the following failure modes:(i) Mlus (Mode 1: crack opening along the circumferential direction at
the transition zone between the inclined wall and the corner
radius of the parts (Fig. 4a).(ii) Mode 2: development of wrinkles along the inclinedwall of the
parts (Fig. 4b).(iii) Mode 3: crack opening along the bisector direction in the
inclined wall of the parts (Fig. 4c).The morphology of the cracks in failure mode 1 and its
propagation paths along the circumferential direction are similar
to those usually found in the SPIF of metals. Themorphology of the
wrinkles in failure mode 2 is an indication of twisting as a result of
the circular tool path. Themorphology of the cracks in failuremode
3 indicates shearing. It could be observed that this failure mode is
related with the initial surface integrity of the polymer sheets.Pa) Yield stress (MPa) Fracture toughness (kJ/m2)
67.6 Brittle
25.3 22.2
52.9 29.6
52.4 24.1
63.6 22.7
Fig. 4. Failure modes that are experimentally observed in the SPIF of polymers.
Table 2
Process parameters.
Initial drawing angle, C0 Tool radius, rtool Initial thickness, t0 Tool path Step size, Dz Feed rate, f
Variable Fixed
408 5 mm 2mm Unidirectional 0.5 mm 1500 mm/min
608 7.5 mm 3mm
P.A.F. Martins et al. / CIRP Annals - Manufacturing Technology 58 (2009) 229–232 2314.2. Strains at failure
The experimental technique for measuring the principal strains
(e1, e2) in the SPIF parts involved the utilization of an adhesive grid
with 2 mm initial diameter circles (Fig. 5). The solid markers refer
to experimental strains at failure and were obtained from grid
elements placed just outside the crack since they represent the
condition of the thinned sheet at the onset of fracture.
The results conﬁrm that SPIF of a truncated PVC conical shape is
performed under plane strain conditions and also show that the
formability in the SPIF of PVC is limited by fracture without
signiﬁcant previous necking.
4.3. Inﬂuences on the formability
Fig. 6 shows the results of the designed SPIF experiments. For
the investigated materials, an increase of rtool reduces the
maximum drawing angle Cmax and increases the initial drawing
angle C0.
The increase of the initial sheet thickness t0 has a positive
inﬂuence on the formability. In contrast to metals, the formability
of polymers is strongly inﬂuenced by the value of the initial
drawing angle C0.
The average maximum drawing angle Cmax exhibits a value of
about 75.48. A comparison of these results with those reported in
[1] for different types of metallic materials leads to the conclusion
that the formability of polymers is generally higher than that of
metals. While PA and PVC show a formability near the average, the
maximum drawing angle for PE reaches a high value ofCmax = 818.
PC shows a slightly lower maximum drawing angle than the
average and POM failed very early in the forming process and is not
considered in the ﬁgures.
4.4. Accuracy of the shaped parts
The evolution of the normalized springback with the initial
drawing angle C0 for polymer sheet blanks with 2 and 3 mmFig. 5. Experimental strains of a PVC part.thickness is shown in Fig. 7. The normalized springback is
calculated as the ratio of the drawing angle deviation between
the speciﬁed (CAD) and the actual drawing angles to the CAD
drawing angle. The original CAD geometry was utilized for
generating the tool path.
The results indicate that springback rises with an increasing
initial drawing angle C0 and falls with an increasing thickness of
the sheet blanks. This means that the achievable accuracy of a SPIF
part made of a polymer sheet blank with 3 mm initial thickness is
higher than that of a sheet blank of the same material with 2 mm
initial thickness. The experimental data also conﬁrm that PVC SPIF
parts show the least geometrical deviations compared to the
original CAD geometry, PC the second least, and PA and PE parts
present the largest deviations.
4.5. Variation of the color through cold forming
Tensile tests as well as SPIF experiments show that particularly
the color of PVC and PE changes during forming (Fig. 8). The
variation of the color is expressed by the ratio of the RGB values
before and after forming.
The dark grey color of PVC turns into a light grey after forming.
The initially black PE becomes grey in the formed zone. PA also
changes its appearance by becoming more transparent. POM and
PC look the same after forming. Franzen et al. [4] related the stress
whitening effect of PVC to the density of the material, which is
signiﬁcantly decreased in the formed zone. To determine the
change in the color of the material, snapshots of unformed and
formed zones of the specimens are taken under identical lighting
conditions. A comparison of the RGB values of the photographs
provides information on the color change.
4.6. Material evaluation
In order to simplify the choice of polymers for SPIF applications,
a material selection criterion based on ductility, springback andFig. 6. Main effects on the formability.
Fig. 9. Material evaluation chart.
Fig. 7. Normalized springback.
Fig. 8. Change in color after forming.
P.A.F. Martins et al. / CIRP Annals - Manufacturing Technology 58 (2009) 229–232232color variation features as well as the cost of raw materials is
introduced as a spidergraph (Fig. 9).
The material with the best properties is deﬁned as the
benchmark and set to 100%.
The ductility factor DF of a material is characterized by the
square of the ratio of fracture toughness R to yield stress sY
DF ¼ R
sY
 2
(2)
DF is derived from fracture mechanics. The greater the ductility
factor, the higher is the material resistance to crack growth. As a
consequence, formability should increasewith increasingDF. PE and
PA reach the highest values (Fig. 9). The results presented in Fig. 5
show, that PE and PA show the best formability in the incremental
cold forming process, which justiﬁes the application of DF.
The springback factor SF of a material part is characterized by
the ratio between the yield stress sY and the product of thickness t
and elasticity modulus E
SF ¼ sY
tE
(3)
The SF is inherent to the theory of sheet forming. The larger the SF,
the larger the elastic recovery upon unloading and the poorer the
accuracy of the SPIF parts is likely to be. In Fig. 9, PVC shows the
highest values, followed by POM. Hence, PVC is set as 100% and
provides the lowest springback and, therefore, the best part
accuracy. This is conﬁrmed in Fig. 7. PA provides a high normalized
springback, which results in a low part accuracy and a low
springback factor SF.
The aesthetic factor AF is deﬁned as the normalized variation of
the three additive primary colors of the original RGB triplet of the
polymer sheet
AF ¼ jðDr;Dg;DbÞjjðr; g; bÞ0j
(4)
The results in Fig. 9 are related to the amount of variation in
color of the formed parts that is induced during the SPIF ofpolymers. POM and PC show only a slight change in color and,
hence, reach the highest values AF.
The cost factor CF is deﬁned as the ratio between the cost of the
cheapest potential material Cc available for a speciﬁc SPIF
application and that of the material being evaluated C
CF ¼ Cc
C
(5)
The cheapest materials with the highest CF are PE and PVC.
5. Conclusion
It has been shown that a high formability can be obtained in
incremental cold forming of thermoplastic materials. The achieved
forming limits in SPIF are in accordance with the fracture forming
limit curves introduced and measured during the material
characterization. The suitability of materials to be processed by
SPIF was evaluated, taking into account ductility, springback, and
aesthetic as well as cost aspects. PE and PA showed a very high
ductility and are suitable for parts with largewall angles. PVC has a
low springback and should be used if a high part accuracy is
demanded. PC showed only a slight change in color during the
incremental cold forming process and is recommended in case of
high surface quality demands. POM presented the poorest
performance of all investigated polymers because it has a very
limited ductility. Its utilization should not be considered for
producing SPIF parts. PA showed the highest springback, which
decreases part accuracy unless a modiﬁed tool path is used.
Acknowledgement
The work of MSc Joa˜o Paulo Neves during the investigation is
greatly acknowledged.References
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