The present work aims to investigate the distribution of strains in incremental sheet metal forming process using different geometries. Four shapes were used to develop the strain paths: truncated cone, pyramid, dome, and circular generatrix are formed in incremental sheet forming process. The difference in strain paths depends on the difference in the geometric shapes of the formed parts. Circle grid analysis was used to obtain strain paths along the parts. Strains distribution was evaluated by circular grid system (CGS) where a pattern of a small circle was electrochemically etched on the sheet. The sheet is deformed during forming and the deformation of the circle is measured and analyzed to explore the behavior of strains distribution in incremental sheet metal forming. The curvature of the part is a large or plane wall the strain mode is plane strain stretching and became biaxial stretching or uniaxial tension with the rotational symmetric surfaces.

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 1106-1111, Article ID: IJMET_10_01_113
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=01
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
EFFECT OF GEOMETRIC SHAPE VARIETY ON
STRAINS DISTRIBUTION OF FORMED PARTS
IN INCREMENTAL SHEET METAL FORMING
PROCESS
Harith Yarub Maan
Department of Industrial Management, College of Administration and Economics
University of Baghdad, Baghdad, Iraq
ABSTRACT
The present work aims to investigate the distribution of strains in incremental sheet
metal forming process using different geometries. Four shapes were used to develop the
strain paths: truncated cone, pyramid, dome, and circular generatrix are formed in
incremental sheet forming process. The difference in strain paths depends on the
difference in the geometric shapes of the formed parts. Circle grid analysis was used to
obtain strain paths along the parts. Strains distribution was evaluated by circular grid
system (CGS) where a pattern of a small circle was electrochemically etched on the sheet.
The sheet is deformed during forming and the deformation of the circle is measured and
analyzed to explore the behavior of strains distribution in incremental sheet metal
forming. The curvature of the part is a large or plane wall the strain mode is plane strain
stretching and became biaxial stretching or uniaxial tension with the rotational symmetric
surfaces.
Keyword: Strains Distribution, Incremental Forming, Circle Grid Analysis
Cite this Article: Harith Yarub Maan, Effect of Geometric Shape Variety on Strains
Distribution of Formed Parts in Incremental Sheet Metal Forming Process, International
Journal of Mechanical Engineering and Technology, 10(01), 2019, pp.1106–1111
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&Type=01
1. INTRODUCTION
Incremental sheet metal forming (ISMF) is one of the most advanced techniques used in sheet
metal forming process which characterized by the high formability, cost low and high flexibility
in the appropriate production of small batches and prototypes for complex shapes with simple
tooling controlling by CNC machine[1-3]. Due to the difference in the ISF process from other
forming processes, due to the nature of the concentric deformation and the small moving
deformation zone, the behavior of the deformation varies according to the process variables and
the geometry of the part. One of the most important factors determining the success of the process
of incremental forming is the angle of draw, which is defined as the largest angle allows the
forming of material during the process without failure and with one pass [1], which depends

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mainly on the type of material, the thickness of the sheet, the parameters of the process, the
condition of friction between the tool and sheet, and type of the process single or two-point
incremental sheet metal forming. Although the maximum wall angle gives important information
to the designer, the distribution of strains of the material awards the most important information
about how the metal deforms and what levels of strains during the process. In addition, the
geometry of the part to be executed affects the type of strains. Thinning in the sheet during SPIF
fundamentally depends on the maximum wall angle and deformation imposed on the sheet
predicted by the sine law (t=tosine ) as shown in Fig 1. [4].
Figure. 1. Experimental setup of ISF process
The formability in incremental forming expressed by maximum wall angle or by the thinning
limit of the sheet where the maximum thinning followed sine law [5, 6].Two parts tested with
constant and varies slope along depth to examine the forming limit presented by G. Hussain et al
[7]. The result shows the higher formability can achieve with parts have a varied slope than the
constant slope. A decrease in the curvature of the part (geometrical) causes a decrease in the
formability [8] where the length of contact increases leading to change the strain path to biaxial
strain and finally occurring failure. G. Hussain et al [9] studied the influence of curvature of
product profile on the formability of AL sheet and developed an empirical model to examination
the formability. The curvature effect on the formability depends slightly. When the curvature is
small there is an improvement in formability and decreases with the increase of radius of the
specimen. Two geometries of test part were analyzed by the study carried out by G. Hussain et
al [10] to evaluate formability. The result concluded that size in the horizontal plane of
geometrical shape affected on the formability.
The present work aims determined the distribution of strains for formed parts in incremental
sheet forming process with different geometries. The influence of part geometry on the strain
path during forming was investigated experimentally. Four shapes were used to develop the strain
paths: truncated cone, pyramid, dome, and circular generatrix are formed in two-point
incremental forming (TPIF).
2. EXPERIMENTAL SETUP
The incremental process was performed on a 3-axis CNC milling machine (C-tek KM-80D), as
shown in Fig 2. The experimental work was achieved to aluminum alloy (AL 1050) with an initial
sheet size of 290 x 290 x 0.9 mm. The sheet lubricated with oil engine lubricant to prevent wear
and damage of surface during forming. A hemispherical head tool with 12 mm was mounted on
the spindle on CNC machine with a feed rate of 600 mm/min and step over (Δz) 0.5 mm. A
variety of geometries have been selected to illustrate the distribution of strains in ISF (see
Fig. 3). Four shapes were used to develop the strain paths: A truncated cone with wall angle 70°,
with inner diameter of 66mm and outer diameter of 77mm and pyramid with 50x50 mm with

3. Effect of Geometric Shape Variety on Strains Distribution of Formed Parts in Incremental Sheet Metal
Forming Process
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height of 60 mm and dome with radius of 60 mm and circular generatrix are formed with 60mm
inner diameter and 145mm outer diameter by TPIF. The Mechanical Properties for Al-1050 Sheet
listed in Table.1.
Figure. 2. Experimental setup of ISF process
Table.1.Mechanical Properties for Al-1050 Sheet.
material
Tensile
strength
(Mpa)
Yield
strength
(Mpa)
Elastic
modulus
(Gpa)
Poisson’s
Ratio
Density
(kg/m3)
Total
elongation
(%)
Max
elongation
(mm)
Percent
elong. at
max
load (%)
(mm)
Al-1050 105 70 70 0.33 2700 4 1.89 1.5
Figure. 3. Geometries of formed parts.
After forming the circles will be changed into ellipses which can be measured to calculate
major and minor strains produced in the final part. After sheet metal is formed the marked circles
will deform into ellipses of different sizes as shown in Fig. 4. The Strain is calculated from the

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following formula. In order to measure true strains from the formed part, 1.7 mm diameter circle
grid pattern was printed by electrochemically etching on the surface of the sheet. The grid of
circles was printed on the lower surface area of the sheet because it cannot resist the effects of
the contact condition (rotational speed of spindle and friction) during forming.
Figure. 4. Deformation of the circle during the ISF process
The values of strains were calculated as follows:
Where R is original radius of circle, d1 and d2 is the major and minor axis respectively

5. Effect of Geometric Shape Variety on Strains Distribution of Formed Parts in Incremental Sheet Metal
Forming Process
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Figure. 5. Strain distribution in TPIF of formed product; (a) Dome shape
(b) Pyramid shape (c) Truncated cone (d) Circular generatrix
3. RESULTS AND DISCUSSION
The result of distribution of strain for the truncated cone is shown in Fig .5(a). The deformation
pattern of true strain show plain strain stretching with higher formability. The points of the high
value of the strain located in the large base of the cone and this are evidence that curvature has
an impact on the behavior of strains during the formation. The points with small strain values are
located at the top of cone especially at the beginning of the formation. Some points located in
negative side of forming limit diagram.
From Fig. 5(b). The results show that the deformation pattern is plain strain stretching with
lower strain value which located on top the dome, which is the point with the low values in the
drawing. As the angle of wall increases, the value of curvature increases and this is evident during
the process. Therefore, the behavior of the strain is change to the biaxial strain, in addition to the
increase of the levels of strain compared to the other products. This is evidence that curvature has
an effect on the pattern of the strain during formation. As shown in Fig.5(c), in pyramid shape
the deformation pattern that shown is plain strain stretching where most points are concentrated
on the major axis of true strain with some movement towards the positive quarter of the diagram.
This indicates that the absence of curvature in a geometric shape, the distributions of strain will
be in one style, In addition to the type of strains will be homogeneous. In circular generatrix form
as shown in Fig. 5(d), the strain mode appears with uniaxial tension where the points in the bottom
base of the part have a plain strain stretching and with more curvature toward the top the strain
behavior changes and moves in the negative direction of the minor strain.
4. CONCLUSION

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This study presented an experimental work to obtain a distribution of strains during TPIF for
varied formed parts. The variation of curvature affects the shape of the strain patterns as
summarized:
• It has been shown that a very high level of strains can be obtained in ISF.
• Strain distributions along the profile of part give an indicator to the behavior of
deformation during ISF.
• When the minor strain is too small or equal to zero, the distortion is plane-strain
stretching and this is clearly observed in major-minor strain space related to the
pyramid shape, this is due to the absence of curvature.
• Strain distributions in dome shape as shown in the results appears the behavior of
biaxial stretching because of the curvature, which gives higher values in the minor
strain compared to other models in addition to a high level of formability.
• The type of deformation mode specified according to the geometrical shape.
• When the curvature of the part is a large or plane wall the strain mode is plane strain
stretching and became biaxial stretching or uniaxial tension with the rotational
symmetric surfaces.
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