TEMPLATE FOR ACADEMICA SCIENCE JOURNAL

JOURNAL OF AL-QADISIYAH FOR
ENGINEERING SCIENCE

Vol. 11, No. 2

ISSN: 1998-4456

EFFECT OF DIE ANGLE AND FRICTION COEFFICIENT ON
TEMPERATURE AND STRESS DISTRIBUTION IN THE EXTRUSION

PROCESS

Dr. Hazim Ismael Radhi

Thi – Qar University – Engineering College - Mechanical Department

E-mail- Hazemismaeel2003@gmail.com

Dr. Lattif Shekher Jabur

Southern Technical University - Technical Institute of Nasiriyah - Mechanical Technics Department

E-mail- lsh58@stu.edu.iq

Abstract: : Extrusion, among other types, is one of the most important forming processes
due to its high productivity, lower cost and its good ability to improve the physical and
mechanical properties of extruded materials. FE simulation was carried out on ABAQUS
software ver.6.9. to study the distribution of stress and temperature which created through
the extrusion process. The results of present study are accentuated that, there is a
complicated relationship between stress and temperature distribution relative to die angle
and friction coefficient. It was found, in the range of tested cases, at friction coefficient of
more than ( 0.08 ), for ( 45o ) die angle, the maximum value of temperature is twice higher
than that of ( 75o ), hence the die angle has more significant effect on state of stress and
temperature than that of friction coefficient. Nevertheless, a high die angle ( α = 75o )
emerged low value of maximum temperature due to easily flow of material toward the die
orifice. Furthermore, there are a gradual increasing of vonMises criterion and temperature
with increasing the friction coefficient while they are decreasing with increasing the die
angle.

Keywords: stress and temperature distribution, die angle, friction coefficient, deformation.

INTRODUCTION

Aluminum and its alloys are extensively used in different forming process to produce long, strong pieces of
formed metal from one solid piece. As well as extrusion of aluminum alloys offers a relatively cheap method of
producing complex shapes with high geometric tolerance [1]. Tiernam P. et al. [2] used finite element analysis
to evaluate the influence of reduction ratio, die land height and die angle on the extraction force during cold
extrusion of high grade ( AA 1100 ) aluminum. They presented, the largest extrusion force obtained when the
die angle, die exit diameter and die land are ( 15o, 5mm, 4mm ) respectively. Evan W. Albert et al. [3] studied
direct extrusion of aluminum wire by FE analysis to mitigate manufacturing defects. They concluded,the
increasing the ram velocity leads to decrease both of turbulence and stress irregularities because of time
decreasing in which the die surface and billet are in contact.

By using port hole die method, the effect of convex die angle that would optimize the strength and a load of
hot extrusion process of ( A 16061) alloy of aluminum tube, have been investigated by Sangamesh Sirsgi et al.
[4]. The authors were reported, with the numerical analysis of the process, the maximum stress is created on
the corners of square tube. Also, finite element simulation employed to study the distribution of strain,

mailto:Hazemismaeel2003@gmail.com
mailto:lsh58@stu.edu.iq

JOURNAL OF AL-QADISIYAH FOR
ENGINEERING SCIENCE

Vol. 11, No. 2

ISSN: 1998-4456

temperature and effective stress of direct extrusion of titanium alloy [5]. They investigated the influence of
different design and process parameters on maximum ram speed, applied pressure and strain and stress
distribution. Adeosun S. O. [6] studied mechanical properties response of extruded aluminum ( 6063 ) alloy by
using plain carbon and tool steel dies at different die entry angles. They employed finite element analysis to
investigate the effect of die angle on maximum extrusion pressure and hardness of extrudate. They reported
that, by taken into account the cost of manufacturing process, plain carbon steel can successfully replace tool
steel as a die material without losing the desirable products. And the maximum extrusion pressure and the
hardness of extruded parts are increased as the die entry angle increased. Tool steel and mild steel dies used
to study the extrusion characteristic of cold, hot and annealed billets of wrought aluminum alloy [1]. Die angles
ranging from (15o to 90o) adopted to measure the extrusion pressure, linear strain, extrusion ratio and surface
hardness of extrusion products. The authors concluded, cold extrusion was easier at high die angles than that
at lower die angles and the highest linear strain was obtained for cold extrusion billets by using tool steel die
with (90o) die angle. Also, the results revealed that the tool steel dies achieved superior extrusion response
relative to die which made of mild steel.Rafid Jabbar Mohammed [7] utilized commercial finite element code
Deform – 3D to investigat the type of metal flow and stress distribution of ( Al – 1100 ) rod extrusion.The
author reported, the finite element model was successfully simulating the stress distribution in direct rod
extrusion. He found, the optimum die angle reduces the magnitude of normal, shear and effective stresses.

In this present study, FEM was employed to investigate the distribution of stress and temperature which
created during direct extrusion of commercial aluminum for different values of die angle and friction coefficient.
Finite element simulation was carried out on ABAQUS software V. 6.9 [8].

1. MATERIALS AND FINITE ELEMENT MODEL

The billet materials is aluminum alloy which its mechanical and thermal properties are listed in Table (1) [9].
Figure (1) indicates the FE model of the extrusion process. The analysis is adopted on consideration of
coupled temperature displacement condition. The diameter and the length of the billet are ( Do = 60 mm,
Lo = 180 mm ) respectively. The billet goes through a die with an opening diameter of ( Di = 40 mm ), it means,
the extrusion ratio is ( 2.25, where extrusion ratio = Do2 /Di2 ).Three values of die angle ( α = 45o , 60o and 75o )
and ten values of friction coefficient ( μ ) from ( 0.01 to 0.1; with 0.01 for each step ) are used to study their
effect on stress and temperature distribution which generated during the extrusion process.

The use of computing software in the simulations of metal forming process, such as extrusion, rolling and
drawing, is the most logical approach to achieve the reducing of unnecessary consumption of resources as
time, energy and scrap material [3]. FE simulation of this study was carried out on ABAQUS V.6.9. CAX4T
elements are used to mesh the billet which is considered as deformable part while the container defined as
rigid surfaces. CAX4T is a 4 - nodes axisymmetric thermally coupled quadrilateral, and 2D meshes of both
billet and container are created [5,8,10].The extrusion process is displacement controlled so that
corresponding displacement is applied on the top of the billet.

Table 1: Mechanical and thermal properties of Aluminum billet [9]

properties The values

Density 2700 Kg / m3

Young's Modulus 69 x 103 MPa

Poisson's ratio 0.33

Conductivity 204 at 0oC w /m.k
225 at 300 oC w /m.k

Inelastic heat fraction
0.9

Specific heat 880 J/ kg k

Expansion coefficient 8.42 x 10-5 1/k

JOURNAL OF AL-QADISIYAH FOR
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Vol. 11, No. 2

ISSN: 1998-4456

Figure 1 : Dimension of Finite Element Simulation model

2. RESULTS AND DISCUSSION

2.1. STRESS DISTRIBUTION

Figure ( 2 ) illustrates the location of maximum vonMises stress ( SVM ) at a different stage of extrusion process
at friction coefficient equal ( μ = 0.05 ) and die angle ( α = 60o ). It is clear that when the billet reaches the first
bend in the container, the value of maximum vonMises stress is small ( 131.9 MPa ) because ( at this region )
the billet material starts deforming plastically. Then it increases gradually throughout the flow of the billet's
material to the die outlet. The maximum value of vonMises stress (251.1 MPa ) occurs at the end of extrusion
stage when the extrusion products go out of the die orifice. A similar trend was found with different values of
friction coefficient and die angle, and also with the distribution of shear stress ( S12 ) as shown in figures ( 3 ).

Figure 2: Location of maximum vonMises stresses ( SVM ) at different stage of extrusion
process for friction coefficient, μ = 0.05 and die angle = 60o.

JOURNAL OF AL-QADISIYAH FOR
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Vol. 11, No. 2

ISSN: 1998-4456

Figure 3 : Location of maximum shear stress ( S12
) at different stage of extrusion process for

friction coefficient, μ = 0.05 and die angle = 60o.

The change in the state of principle stress ( S22 ) and plastic strain ( PE22 ) for die angle ( α = 60o ) and friction
coefficient ( μ = 0.05 ) during the extrusion process can be obviously seen in figures ( 4 & 5 ). From figure (4),
it is clear that when the billet material flows throughout the die, the material in the corners of container and die
was under compressive stress. Also, it can be noticed, the maximum principle stress ( S22 ) which is tensile
stress localizes in the surface areas of the extrudate, whilst the compressive stress exists in the core of
extruded parts. Figure (5) reveals the changes that have taken place in plastic strain ( PE22 ) through the
extrusion process.

Figure 4: Distribution of principle stress(S22) of
extrusion process for die angle = 60o
and friction coefficient, μ = 0.05.

Figure 5 : Distribution of plastic strain ( PE22 ) of
extrusion process for die angle = 60o
and friction coefficient, μ = 0.05.

JOURNAL OF AL-QADISIYAH FOR
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Vol. 11, No. 2

ISSN: 1998-4456

2.1.1. EFFECT OF FRICTION COEFFICIENT ON STRESS DISTRIBUTION

The variation of maximum vonMises stress with friction coefficient for different die angles are shown in figure
(6). It is obvious that the increasing of friction coefficient leads to increase the value of maximum vonMises
stress. Also, it can be seen, there is a significant effect of die angle in such manner; the bigger the die angle,
the less value of maximum vonMises stress is. This can be attributed to the bigger die angle achieve more
easily flow of billet material through the die, leading to a decrease in the extrusion force that needed to press
the billet to go through the die outlet.

Figure 6: The variation of vonMises stress ( SVM )
verse friction coefficient for different die angles.

In addition to another parameter that affects on stress and strain state during extrusion process,the frictional
condition at the billet – container and billet – die contributes strongly in determining the characteristics of
stresses and plastic strain that exist in extruded products. Figures ( 7, 8 and 9 ) demonstrates the variation of
vonMises ( SVM ), principle ( S22 ) and shear ( S12 ) stresses with friction coefficient for ( 60o ) die angles. It is
evident that the increasing of friction coefficient leads to increase the maximum values of all stresses. The
results accentuated that the maximum values of SVM, S22 and S12 are ( 265 MPa, 158.8 MPa and 75.98 MPa )
respectively, and for tested cases, these results attained at maximum value of friction coefficient which is
equal to ( 0.1 ). These results mean, as the coefficient of friction increases, larger frictional forces is, so larger
extrusion force is needed to overcome this force which resists the material's flow through the container and
die. Then consequently, higher stresses exist during the extrusion process with a high value of friction
coefficient.

JOURNAL OF AL-QADISIYAH FOR
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Vol. 11, No. 2

ISSN: 1998-4456

b
c

Figure 7 : Effect of friction coefficient on vonMises stress ( SVM ) for 60

o die angle ; a- μ= 0.00,
b- μ=0.02, c- μ = 0.04, d – μ =0.06, e- μ=0.08 and f- μ = 0.1.

Figure 8 : Effect of friction coefficient on principle stress ( S 22 ) for 60

o die angle ; a- μ= 0.00,
b- μ =0.02, c- μ = 0.04, d – μ =0.06, e- μ=0.08 and f- μ = 0.1.

JOURNAL OF AL-QADISIYAH FOR
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ISSN: 1998-4456

2.1.2. EFFECT OF DIE ANGLE ON STRESS DISTRIBUTION

Die angle has a direct effect on the level of maximum stresses and strains of extrusion process. The variation
of maximum values of ( SVM , S22 , S12 ) for different die angles and friction coefficient are shown in figures
( 10, 11 and 12 ). The results were exhibited that the maximum values of stress, strain and contact pressures
for ( α = 75o ) die angle are lower than those for ( α = 45o ). It means, the bigger the die angle, the lower values
of maximum stress are. This can be attributed to the fact, the bigger die angle achieves more easily flow of the
billet's material throughout the die, hence decreasing the extrusion forces that needed to press the billet to go
toward the die outlet and consequently fewer values of maximum stresses and strains. These results are
consistent with result have been found by Adeosun S. O. et al.[1].

Figure 10 : Effect of die angles on VonMises stress ( SVM ) for coefficient of friction μ = 0.06 ;
a- α = 45o , b- α = 60o, c- α = 75o.

Figure 9: Effect of coefficient of friction on shear stress ( S12 ) for 60
o die angle ; a- μ= 0.00,

b- μ=0.02, c- μ = 0.04, d – μ =0.06, e- μ=0.08 and f- μ = 0.1

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ISSN: 1998-4456

Figure 11 : Effect of die angles on principle stress ( S 22 ) for friction coefficient μ = 0.06 ; a- α = 45

o ,
b- α = 60o, c- α = 75o.

Figure 12 : Effect of die angles on shear stress ( S 12 ) for friction coefficient μ = 0.06 ; a- α = 45

o ,
b- α = 60o, c- α = 75o.

2.2. Temperature distribution

The relationship between the maximum temperature and friction coefficient for different die angle is shown in
figure (13). It is evident that the increasing of friction coefficient leads to increase the value of maximum
temperature.The temperature distribution and location of maximum values of ( 60o ) die angle for different
friction coefficient are illustrated in figure ( 14 ). It is clear that the maximum temperature exists on the surface
of extrudate part in the region when the material enters toward the die, it is in the interfacial contact surface
between the material and wall of the die.

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a b

Figure 14 : Temperature distribution and location of maximum values for 60o die angle and
friction coefficient of ; a - μ = 0.02 , b - μ = 0.06.

2. 2.1. Effect of friction coefficient on temperature distribution

The variation of maximum temperature, which generates during the extrusion process for ( α = 60o ) with
different values of friction coefficient, is shown in figures 13 and 15. There is a gradual increasing in maximum
value of temperature with increasing the friction coefficient. The maximum temperature for (α = 60o ) at
frictionless condition is ( 62.77 oC ) and it increases to ( 80.53 oC ) at ( μ = 0.1 ), it means, the the difference
percentage is ( 22% ) while for (α = 45o ) and (α = 75o ) are ( 34% and 7.6% ) respectively. These results prove
that, the friction coefficient at the interfacial surface between the billet's material and the walls of both
container and die, has a significant effect on the level of maximum temperature which created through the
extrusion process. This can be explained as; when the friction coefficient increases, more friction force exist
between the contact surfaces and it will produce more heat. Hence the maximum value of material's
temperature which exists inside the die will also increase. These results are consistent with results that have
been found by Salode A. M. [11].

Figure 13 :The releationship between maximum
temperature and coefficient of friction for
different die angles.

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b
c

Figure 15 : Effect of friction coefficient o on Temperature ( NTII ) for 60o die angle a- μ= 0.0,
b- μ=0.02, c- μ = 0.04, d – μ =0.06, e- μ=0.08 and f- μ = 0.1

On another hand, and despite the fact of, materials deform easily at high temperature due to the softening
effect, nevertheless the high level temperature which created through the extrusion process, is undesirable
because of the intensity of dead metal zone formation will increases. Also, a high temperature affects the
elastic and plastic properties of the billet and die material, resulting in increasing the level of plastic
deformation of extruded material and/or increasing the deflection of the die [11].

2.2.2. EFFECT OF DIE ANGLE ON TEMPERATURE DISTRIBUTION

The effect of die angle on the maximum value of extruded parts' temperature is shown in figures ( 16 and 17 ).
There is a reverse relationship between the die angle and maximum temperature. In the range of tested cases
of friction coefficient, the maximum temperature for ( α = 45o ) is higher than that for ( α = 75o ), and for

( μ > 0.08 ) it is more than twice higher. They are ( 106.2 oC, 76.86 oC, 51.74 oC ) at ( μ = 0.08 ) for die angles
of ( 45o, 60o and 75o ) respectively. The results are revealed that the maximum temperature is substantially
influenced by the die angle in such a manner; a low die angle leads to difficult flow of material throughout the
containeranddietowardthedieoutlet,resultingwithincreasing in the friction at billet – container and billet – die
interfaces, which caused large amount of heat generation, consequently increasing the process temperature.

Figure 16 : Effect of die angles on temperature ( NTII ) for coefficient of friction μ = 0.02 ; a- α = 45o,
b- α = 60o, c- α = 75o.

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ISSN: 1998-4456

Figure 17 : Effect of die angles on temperature ( NTII ) for friction coefficient μ = 0.06 ;
a- α = 45o , b- α = 60o, c- α = 75o.

VI. Conclusion

The influence of stress and temperature distribution by die angle and friction coefficient have been
investigated using finite element analysis. The die angle has a significient effect on temperature distribution of
billet ( i.e. high die angle will decrease the temperature distribution and vice versa ). Furtheremore, the finite
element simulation of process was illustrated that, the maximum values of vonMises stress and temperature
are attain at die angle of ( 45o ) and friction coefficient of ( 0.1 ).

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JOURNAL OF AL-QADISIYAH FOR
ENGINEERING SCIENCE

Vol. 11, No. 2

ISSN: 1998-4456

8. ABAQUS CAE ver. 6.9, 2009, Example problems Manual; standard User's Manual.

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