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Citation: Hwang, Y.-M.; Hsu, I.-P.
Die Design and Finite Element
Analysis of Welding Seams during
Aluminum Alloy Tube Extrusion.
Metals 2023,13, 911. https://
doi.org/10.3390/met13050911
Academic Editor: Diego Celentano
Received: 10 April 2023
Revised: 30 April 2023
Accepted: 5 May 2023
Published: 8 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
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4.0/).
metals
Article
Die Design and Finite Element Analysis of Welding Seams
during Aluminum Alloy Tube Extrusion
Yeong-Maw Hwang * and I-Peng Hsu
Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University,
Kaohsiung 804, Taiwan; ipeng5180@gmail.com
*Correspondence: ymhwang@mail.nsysu.edu.tw; Tel.: +886-7-5252000 (ext. 4233)
Abstract:
Hollow tubes are generally manufactured using porthole die extrusion. A finite element
software QForm is used to analyze the material flow of aluminum alloy A6061 tubes inside a specially
designed porthole die during tube extrusion. High welding pressure and shorter transverse seam
length are required for a sound product. Various extrusion conditions and die geometries and
dimensions affect the bonding strength of the products. In this paper, the effects of die geometries on
the welding pressure are discussed using the Taguchi method. The simulation results show that a
higher welding pressure is obtained with a larger porthole radius, a larger welding chamber height,
and a larger bearing length, while a larger bridge width increases the welding pressure slightly. For
transverse seam lengths, a shorter transverse seam length can be obtained with a smaller porthole
radius and a smaller welding chamber height, and a shorter bridge width and bearing length decrease
the transverse seam length slightly. The transverse seam region and flow patterns are observed. Tube
expanding tests were also conducted. From the expanding test results, it is known that the fracture
position did not occur at the welding line and the bonding strength could reach up to 160 MPa.
Keywords:
aluminum alloy tube extrusion; porthole die; finite element analysis; welding pressure;
transverse seam length; expanding test; Taguchi method
1. Introduction
Due to increasing demands of light-weight structures, various tubes, such as round
tubes, thin tubes, square tubes, and asymmetrical-shaped tubes, are widely applied in
various industries. Most of them are manufactured by extrusion processes. According to
different extrusion die design methods, extruded tubes are divided into seam tubes and
seamless tubes. Various tubes with complicated geometry and dimensional accuracy are
used in the automotive and bicycle industries. Different extrusion methods have been
proposed, such as isothermal extrusion, half-solid-state extrusion, high speed extrusion,
and equal-channel angular pressing, etc. Extrusion die design is crucial for a successful
extrusion process [
1
]. In aluminum extrusion processes, friction behaviors at the work-
piece/tooling interface are highly complex, which are affected by local temperature, relative
velocity, contact pressure, geometry, and tooling surface roughness, etc. Wang et al. [
2
] and
Wang and Yang [
3
] summarized the recent developments of the friction testing techniques
for aluminum extrusion processes and detailed comparisons of these techniques. Among
the existing friction testing techniques, the combination of extrusion friction tests and short
sliding distance ball-on-disc tests were recommended.
In aluminum hot extrusion processes, many forming parameters such as extrusion
ratio, ram velocity, and billet temperature affect the extrusion load and the mechanical
properties or the microstructures of the extruded products. Marín et al. [
4
] investigated the
influence of temperature in the extrusion process by finite element analysis. The required
load and the maximum exit velocity were discussed considering different temperatures.
The optimized values of the temperatures in the billet and die were obtained to achieve a
Metals 2023,13, 911. https://doi.org/10.3390/met13050911 https://www.mdpi.com/journal/metals
Metals 2023,13, 911 2 of 16
good quality of the extruded products. Bandini et al. [
5
] used FE code QForm to predict the
microstructure evolution in 6XXX aluminum alloys. Preliminary simulations were carried
out to select optimal friction models and coefficients among the several formulations
available in the code. The numerical results were compared to grid-based visioplasticity
experiments. The optimized friction model and coefficient were then applied in a second
series of simulations to develop a prediction model of microstructure evolution. The
simulated grain size and shape of 6XXX aluminum alloys were compared with experimental
observations to validate the numerical model. Chen et al. [
6
] investigated the effects
of various forming conditions on the extrusion load and product shapes in multi-hole
extrusion of aluminum alloy tubes numerically and experimentally. The finite element
simulation results revealed that the most crucial process parameter is the number of holes
and their locations on the extrusion die. Liu et al. [
7
,
8
] used finite element simulation
to investigate the effects of ram speeds and billet temperatures on the extrusion load
in magnesium alloy AZ31 extrusion with an X-shaped cross-section. The correlations
between the process variables and the response of the extrusion temperature and the peak
extrusion pressure were established from the finite element simulations and verified by
experiments. Sikand et al. [
9
] conducted tube extrusion experiments of AM30 magnesium
alloy using a porthole die and a conical die with a mandrel attached at the ram. They
made comparisons of the microstructure and mechanical properties of the extruded tubes
using the porthole die and conical die. The tubes fabricated using the porthole die showed
significant refinement in microstructure with improved mechanical properties compared to
the tubes fabricated using the conical die. However, the extrusion loads using the porthole
die were higher compared to that using the conical die.
Transverse welds occur at the joint of the billet–billet parts in extrusion processes for
continuous production. Transverse welds introduce a discontinuity at the weld interface
in the extruded long tubes or rods. The strength at the transverse welds is much weaker
compared to the mother metal, thus, the transverse welding regions have to be cut off
after extrusion, which decreases the overall yield of the products. Therefore, the trans-
verse welding length should be controlled as short as possible. Li et al. [
10
] investigated
the formation and metal flow of transverse welds in aluminum extrusion processes us-
ing the finite element simulation. The simulation results revealed that inhomogeneous
metal flow and a transverse welding pattern occurred. The design parameters influencing
the transverse weld length were also discussed. Mahmoodkhani et al. [
11
] developed
a mathematical model of hot extrusion processes of aluminum alloy circular bars and
validated it by experiments. The transverse seam diagram and area percentage of two
materials in the cross-sections of the tubes were inspected. The results showed that the trans-
verse weld was significantly affected by the feeder geometry shape, but the effects of ram
speed, billet material, and temperature on the transverse weld dimensions were negligible.
Zhang et al. [
12
] experimentally and numerically investigated the extrusion transverse
welds of 7N01 aluminum alloy hollow asymmetric square tubes. The transient extrusion
process was simulated based on a finite element software HyperXtrude. The effects of
the process parameters on the cross-sectional area percentage of the transverse seam were
discussed. Bakker et al. [
13
] conducted a series of extrusion experiments of aluminum
alloy hollow rectangular tubes using a porthole die and investigated the effects of the
presence of a charge weld transition zone on the failure mode under tensile tests and
local effective mechanical properties of the extrudate. The evolutionary geometry of the
bonding plane was visualized by serial sectioning of the extrudate. They found that the
mechanical performance was largely controlled by the oxide particle density at the charge
weld boundary. Zhang et al. [
14
] investigated the transverse weld in 7N01 aluminum
alloy hollow tubes used in high-speed trains by experimental analysis coupled with finite
element simulations. Numerical models of transverse welds were also built to analyze
the evolution of transverse welds. The influences of extrusion process parameters and die
structure on the length of transverse welds were discussed. The transverse weld length
Metals 2023,13, 911 3 of 16
was reduced effectively by adjusting the extrusion ratio, ram speed, height of baffle plate,
and sinking depth of the port bridge.
Longitudinal welding seams are an intrinsic characteristic in the extrusion of hol-
low products using a porthole die. The bonding strength at the welding seams affected
by the porthole die design dominates the whole material properties of the extrudate.
Bakker et al. [
15
] investigated the occurrence of defects inside the extrudate in a direct hot
extrusion process of AW-6060 and AW-6082 aluminum alloy billets with an obstacle at the
center of the die. The effects of different geometries of the weld-chamber and the processing
conditions on the quality of the welding seams were discussed. Through computer simula-
tions, conditions related to welding seam formation were modelled and correlated with
the experimental results. Kim et al. [
16
] investigated the effects of an improved porthole
die on the welding pressure using finite element analysis of aluminum tube extrusion. The
expanding test results showed that the welding strength of tubes extruded by the modi-
fied porthole die was improved compared to that made by a conventional porthole die.
Zhao et al. [
17
] conducted experiments and numerical simulations to analyze the metal flow
and welding process during the continuous extrusion of AA6063 aluminum alloys with dou-
ble billets. The results revealed that the oxides on the billet surface affected the microstruc-
ture and mechanical properties of the extrusion welds. The welding lines were mixed with
fine grains of several microns and the surrounding area contained grains with a size of
several hundred microns. They also found that the extrusion welds slightly affected the
tensile strength, but markedly influenced extrudate elongation.
Donati and Tomesani [18]
conducted a series of extrusion experiments of I-shape AA6082 aluminum alloy products
using a two-hole die and investigated the correlation between the die design and the
mechanical properties of the extrudate. The workability area without tearing defects in
the extrusion process was also discussed. The tensile strength and equivalent fracture
strain were evaluated to assess the effectiveness of welding on the extruded products.
Jo et al. [
19
] investigated the effects of process parameters, such as billet temperature and
bearing length, on the welding strength during Al7003 seam extrusion with a porthole
die. The welding pressures were examined through non-steady-state finite element simula-
tions and compared with experimental results. The experimental results showed that the
largest bonding stress could be obtained with a bearing length of 6 mm and an extrusion
temperature of 460 ◦C.
Choi et al. [
20
] proposed a porthole die design with six inlet ports and two die caps
around the die mandrel and used finite element analysis to simulate the material flow of
aluminum alloys inside the die chamber. The position of the welding lines between the
inner and outer tubes was discussed. Extrusion experiments were carried out and the
mechanical properties of the extrudate were improved compared to the general porthole
extrusion tubes. Liu et al. [
21
] used DEFORM 3D software to conduct finite element simu-
lations of tube extrusion processes of AZ31 magnesium alloys. The metal flow behavior
and formation process of welding seams in the porthole die were investigated. They found
as the extrusion speed increases, the temperature, welding pressure, and effective stress
on the welding plane increase simultaneously and the optimal extrusion speed is about
0.5 mm/s for tube extrusion of AZ31 magnesium alloy at forming temperature of
400
◦
C. Lin et al. [
22
] fabricated Zn–10Al–2Cu–0.05Ti (ZA10) alloy tubes by one-pass
and double-pass conform continuous extrusion processes. Heat treatment was also applied
to the double-pass extruded tubes to improve their yield strength, ultimate tensile strength,
elongation, and welding seam quality. A superior yield strength of 283.9 MPa, an ultimate
tensile strength of 328.5 MPa, a lower elongation of 10.2%, and an expansion ratio of 10.3%
were obtained.
Up to now, studies on the welding behavior in tube extrusion were mostly focused on
experimental investigations. In this paper, finite element analysis was used to investigate
the welding behaviors during tube extrusion of aluminum alloys using a specially designed
porthole die. The effects of the die geometries such as welding chamber height, porthole
radius, bridge width, bearing length, etc., on the transverse welding length distributions
Metals 2023,13, 911 4 of 16
and welding pressures at the die exit are systematically discussed. An objective function
with double weighting coefficients combined with the Taguchi method is proposed to
determine an appropriate die geometry and dimension for obtaining a sound product with
better mechanical properties at the longitudinal welds. Finally, tube extrusion experiments
were conducted to validate the finite element modelling and obtain a sound product with a
larger bonding strength at the longitudinal welds.
2. Design of Extrusion Porthole Dies
2.1. Definitions of Longitudinal and Transverse Welding Seams
Longitudinal welding seams occur as the billet materials flow separately through the
bridge and join together in the welding chamber. The joined interfaces inside the tube
product are called longitudinal welding seams. During continuous extrusion, as the front
billet is extruded out and the rear billet is input into the container and extruded forward, the
interfaces between the front and rear billets are called transverse welding seams. When the
extrusion process is suspended to refill a new billet, a circle mark is generated in front of the
bearing part, which is called a stop-mark. The transverse seam length, L
tw
, is the distance
between the stop-mark and joined interface at the front and rear billets. A schematic figure
for longitudinal and transverse welding seams and stop-mark is shown in Figure 1.
Metals 2023, 13, x FOR PEER REVIEW 4 of 16
designed porthole die. The effects of the die geometries such as welding chamber height,
porthole radius, bridge width, bearing length, etc., on the transverse welding length dis-
tributions and welding pressures at the die exit are systematically discussed. An objective
function with double weighting coefficients combined with the Taguchi method is pro-
posed to determine an appropriate die geometry and dimension for obtaining a sound
product with beer mechanical properties at the longitudinal welds. Finally, tube extru-
sion experiments were conducted to validate the finite element modelling and obtain a
sound product with a larger bonding strength at the longitudinal welds.
2. Design of Extrusion Porthole Dies
2.1. Definitions of Longitudinal and Transverse Welding Seams
Longitudinal welding seams occur as the billet materials flow separately through the
bridge and join together in the welding chamber. The joined interfaces inside the tube
product are called longitudinal welding seams. During continuous extrusion, as the front
billet is extruded out and the rear billet is input into the container and extruded forward,
the interfaces between the front and rear billets are called transverse welding seams. When
the extrusion process is suspended to refill a new billet, a circle mark is generated in front
of the bearing part, which is called a stop-mark. The transverse seam length, L
tw
, is the
distance between the stop-mark and joined interface at the front and rear billets. A sche-
matic figure for longitudinal and transverse welding seams and stop-mark is shown in
Figure 1.
Figure 1. Schematic for transverse and longitudinal welding seams.
2.2. Configurations of Porthole Dies
The porthole channels and welding chambers of a porthole die used in this study
were slightly different from those of a traditional die. The porthole channels of traditional
dies are vertically downward to the welding chambers. In this paper, the porthole channel
was designed to extend outward from the die entrance to its exit, as shown in Figure 2. In
addition, a blocker protruding from the mandrel inside the porthole channel was designed
to prevent the billet material flowing directly to the die exit as shown in Figure 2b.
An extrusion die is composed of two parts: (a) a bridge with a mandrel (upper die);
and (b) an outer die with a welding camber (lower die), as shown in Figure 3a,b, respec-
tively. Generally, the outer contour of the welding chamber on the bridge part was de-
signed as a circle. In this paper, circular arcs and straight lines were designed for the outer
contour on the bridge part. A cylindrical surface was designed on the outer die.
Figure 1. Schematic for transverse and longitudinal welding seams.
2.2. Configurations of Porthole Dies
The porthole channels and welding chambers of a porthole die used in this study
were slightly different from those of a traditional die. The porthole channels of traditional
dies are vertically downward to the welding chambers. In this paper, the porthole channel
was designed to extend outward from the die entrance to its exit, as shown in Figure 2. In
addition, a blocker protruding from the mandrel inside the porthole channel was designed
to prevent the billet material flowing directly to the die exit as shown in Figure 2b.
Metals 2023, 13, x FOR PEER REVIEW 5 of 16
(a) (b)
Figure 2. Geometric configurations of porthole channels of porthole dies. (a) Traditional die and (b)
modified die.
(a) (b)
Figure 3. Components of porthole dies. (a) Bridge and mandrel part, and (b) the outer die part.
The cross-sectional dimensions of the extruded products were set as 56.2 mm and 80
mm in the inner and outer diameters, respectively. The geometric parameters or variables
at the bridge part are shown in Figure 4a, where D
D
is the die diameter, R
P
is the porthole
radius, W
B
is the bridge width, and Rc is the corner radius. The corresponding parameter
dimensions are shown in Table 1.
(a) (b)
Figure 4. Geometric parameters in the whole die; (a) top view and (b) longitudinal section view.
Figure 2.
Geometric configurations of porthole channels of porthole dies. (
a
) Traditional die and
(b) modified die.
Metals 2023,13, 911 5 of 16
An extrusion die is composed of two parts: (a) a bridge with a mandrel (upper die);
and (b) an outer die with a welding camber (lower die), as shown in Figure 3a,b, respectively.
Generally, the outer contour of the welding chamber on the bridge part was designed as a
circle. In this paper, circular arcs and straight lines were designed for the outer contour on
the bridge part. A cylindrical surface was designed on the outer die.
Metals 2023, 13, x FOR PEER REVIEW 5 of 16
(a) (b)
Figure 2. Geometric configurations of porthole channels of porthole dies. (a) Traditional die and (b)
modified die.
(a) (b)
Figure 3. Components of porthole dies. (a) Bridge and mandrel part, and (b) the outer die part.
The cross-sectional dimensions of the extruded products were set as 56.2 mm and 80
mm in the inner and outer diameters, respectively. The geometric parameters or variables
at the bridge part are shown in Figure 4a, where D
D
is the die diameter, R
P
is the porthole
radius, W
B
is the bridge width, and Rc is the corner radius. The corresponding parameter
dimensions are shown in Table 1.
(a) (b)
Figure 4. Geometric parameters in the whole die; (a) top view and (b) longitudinal section view.
Figure 3. Components of porthole dies. (a) Bridge and mandrel part, and (b) the outer die part.
The cross-sectional dimensions of the extruded products were set as 56.2 mm and
80 mm in the inner and outer diameters, respectively. The geometric parameters or variables
at the bridge part are shown in Figure 4a, where D
D
is the die diameter, R
P
is the porthole
radius, W
B
is the bridge width, and Rc is the corner radius. The corresponding parameter
dimensions are shown in Table 1.
Metals 2023, 13, x FOR PEER REVIEW 5 of 16
(a) (b)
Figure 2. Geometric configurations of porthole channels of porthole dies. (a) Traditional die and (b)
modified die.
(a) (b)
Figure 3. Components of porthole dies. (a) Bridge and mandrel part, and (b) the outer die part.
The cross-sectional dimensions of the extruded products were set as 56.2 mm and 80
mm in the inner and outer diameters, respectively. The geometric parameters or variables
at the bridge part are shown in Figure 4a, where D
D
is the die diameter, R
P
is the porthole
radius, W
B
is the bridge width, and Rc is the corner radius. The corresponding parameter
dimensions are shown in Table 1.
(a) (b)
Figure 4. Geometric parameters in the whole die; (a) top view and (b) longitudinal section view.
Figure 4. Geometric parameters in the whole die; (a) top view and (b) longitudinal section view.
Table 1. Dimensions of geometric parameters at the bridge part.
Die diameter, DD[mm] 238
Porthole radius, RP[mm] 67.5
Bridge width, WB[mm] 31
Corner radius, Rc [mm] 12
Metals 2023,13, 911 6 of 16
The geometric parameters or variables at the welding chamber of a porthole die are
shown in Figure 5, where H
I
and H
O
are the inner and outer bearing heights, respectively;
H
P
is the porthole height; H
M
is the die height; and H
C
is the welding chamber height. The
corresponding parameter dimensions are shown in Table 2.
Metals 2023, 13, x FOR PEER REVIEW 6 of 16
Table 1. Dimensions of geometric parameters at the bridge part.
Die diameter, D
D
[mm]
238
Porthole radius, R
P
[mm] 67.5
Bridge width, W
B
[mm] 31
Corner radius, Rc [mm] 12
The geometric parameters or variables at the welding chamber of a porthole die are
shown in Figure 5, where H
I
and H
O
are the inner and outer bearing heights, respectively;
H
P
is the porthole height; H
M
is the die height; and H
C
is the welding chamber height. The
corresponding parameter dimensions are shown in Table 2.
Figure 5. Geometric parameters at the welding chamber of the porthole dies.
Table 2. Dimensions of the geometric parameters at the welding chamber.
Inner bearing height H
I
[mm]
7.5
Outer bearing height H
O
[mm] 7
Porthole height H
P
[mm] 65
Die height H
D
[mm] 140
Welding chamber height H
C
[mm] 25
The objective of this study was to design the die parameters to obtain a higher weld-
ing pressure and a shorter transverse seam length. To ensure a successful extrusion pro-
cess, the stress distributions inside the die and extrusion loads have to be smaller than the
yielding stress and machine capacity, respectively.
3. Finite Element Simulations of Hot Extrusion of Aluminum Alloy Tubes
3.1. Finite Element Modelling and Simulation Parameters
An explicit and dynamic finite element code “QForm” was adopted to analyze the
plastic flow paern of the aluminum alloy billet within the porthole die cavity during tube
extrusion. During the simulations, it is assumed that the billet is rigid plastic, and the die,
the container, as well as the flow guide are all rigid. Auto-mesh division was chosen and
finer meshes were set around the exit of the die to avoid element crush or fracture after
the tube material flowed out from the die. The Levanov friction mode was adopted at the
interfaces between the billet and the die, container, and the ram [5]. The flow stresses of
aluminum alloy A6061 from the QForm database at a temperature of 500 °C and under
different strain rates are shown in Figure 6.
Figure 5. Geometric parameters at the welding chamber of the porthole dies.
Table 2. Dimensions of the geometric parameters at the welding chamber.
Inner bearing height HI[mm] 7.5
Outer bearing height HO[mm] 7
Porthole height HP[mm] 65
Die height HD[mm] 140
Welding chamber height HC[mm] 25
The objective of this study was to design the die parameters to obtain a higher welding
pressure and a shorter transverse seam length. To ensure a successful extrusion process, the
stress distributions inside the die and extrusion loads have to be smaller than the yielding
stress and machine capacity, respectively.
3. Finite Element Simulations of Hot Extrusion of Aluminum Alloy Tubes
3.1. Finite Element Modelling and Simulation Parameters
An explicit and dynamic finite element code “QForm” was adopted to analyze the
plastic flow pattern of the aluminum alloy billet within the porthole die cavity during tube
extrusion. During the simulations, it is assumed that the billet is rigid plastic, and the die,
the container, as well as the flow guide are all rigid. Auto-mesh division was chosen and
finer meshes were set around the exit of the die to avoid element crush or fracture after
the tube material flowed out from the die. The Levanov friction mode was adopted at the
interfaces between the billet and the die, container, and the ram [
5
]. The flow stresses of
aluminum alloy A6061 from the QForm database at a temperature of 500
◦
C and under
different strain rates are shown in Figure 6.
Metals 2023,13, 911 7 of 16
Metals 2023, 13, x FOR PEER REVIEW 7 of 16
Figure 6. Flow stresses of aluminum alloys used in finite element simulations.
The dimensions of the extruded tube products were 11.9 mm thick and 80 mm in
diameter. The structure of a die set was composed of a ram, a container, a die, a die holder,
a bolster, a sub-bolster, and a pressure ring, as shown in Figure 7. The front three parts
were used to deform the billet material and obtain a desired product geometry. The rear
four parts were used to support the die holder and make the die holder fix easily in the
extrusion machine. The inner diameter of the container was 183.5 mm. The dimensions of
the billets were 177.8 mm in diameter and 740 mm long. They were cut off by a hot cuing
machine. The diameter of the ram was slightly smaller than the inner diameter of the con-
tainer. The dimensions of the die were 238 mm in diameter and 140 mm high. Although
the die holder, bolster, sub-bolster, and pressure ring do not influence the material flow
of the billet, they were still set up in the finite element simulations. The dimensions of the
bolster are 300 and 96 mm in the outer and inner diameters, respectively, and 120 mm in
height. The sub-bolster had an outer diameter of 350 mm, an internal geometry of 210 mm,
and a width of 120 mm. There was a rectangular hole inside the sub-bolster which was
210 mm in length and 120 mm in width. The pressure ring was placed in the extruder, and
the dimensions were determined by the capacity of the extruder. An extruder of 2100 tons
was used in the FE simulations and experiments of aluminum alloy tube extrusion. The
material parameters and forming parameters used in the FE simulations are shown in Ta-
bles 3 and 4, respectively.
Figure 7. Components of complete die set.
Figure 6. Flow stresses of aluminum alloys used in finite element simulations.
The dimensions of the extruded tube products were 11.9 mm thick and 80 mm in
diameter. The structure of a die set was composed of a ram, a container, a die, a die holder,
a bolster, a sub-bolster, and a pressure ring, as shown in Figure 7. The front three parts
were used to deform the billet material and obtain a desired product geometry. The rear
four parts were used to support the die holder and make the die holder fix easily in the
extrusion machine. The inner diameter of the container was 183.5 mm. The dimensions
of the billets were 177.8 mm in diameter and 740 mm long. They were cut off by a hot
cutting machine. The diameter of the ram was slightly smaller than the inner diameter
of the container. The dimensions of the die were 238 mm in diameter and 140 mm high.
Although the die holder, bolster, sub-bolster, and pressure ring do not influence the material
flow of the billet, they were still set up in the finite element simulations. The dimensions
of the bolster are 300 and 96 mm in the outer and inner diameters, respectively, and
120 mm in height. The sub-bolster had an outer diameter of 350 mm, an internal geometry of
210 mm, and a width of 120 mm. There was a rectangular hole inside the sub-bolster which
was 210 mm in length and 120 mm in width. The pressure ring was placed in the extruder,
and the dimensions were determined by the capacity of the extruder. An extruder of
2100 tons was used in the FE simulations and experiments of aluminum alloy tube extrusion.
The material parameters and forming parameters used in the FE simulations are shown in
Tables 3and 4, respectively.
Metals 2023, 13, x FOR PEER REVIEW 7 of 16
Figure 6. Flow stresses of aluminum alloys used in finite element simulations.
The dimensions of the extruded tube products were 11.9 mm thick and 80 mm in
diameter. The structure of a die set was composed of a ram, a container, a die, a die holder,
a bolster, a sub-bolster, and a pressure ring, as shown in Figure 7. The front three parts
were used to deform the billet material and obtain a desired product geometry. The rear
four parts were used to support the die holder and make the die holder fix easily in the
extrusion machine. The inner diameter of the container was 183.5 mm. The dimensions of
the billets were 177.8 mm in diameter and 740 mm long. They were cut off by a hot cuing
machine. The diameter of the ram was slightly smaller than the inner diameter of the con-
tainer. The dimensions of the die were 238 mm in diameter and 140 mm high. Although
the die holder, bolster, sub-bolster, and pressure ring do not influence the material flow
of the billet, they were still set up in the finite element simulations. The dimensions of the
bolster are 300 and 96 mm in the outer and inner diameters, respectively, and 120 mm in
height. The sub-bolster had an outer diameter of 350 mm, an internal geometry of 210 mm,
and a width of 120 mm. There was a rectangular hole inside the sub-bolster which was
210 mm in length and 120 mm in width. The pressure ring was placed in the extruder, and
the dimensions were determined by the capacity of the extruder. An extruder of 2100 tons
was used in the FE simulations and experiments of aluminum alloy tube extrusion. The
material parameters and forming parameters used in the FE simulations are shown in Ta-
bles 3 and 4, respectively.
Figure 7. Components of complete die set.
Figure 7. Components of complete die set.
Metals 2023,13, 911 8 of 16
Table 3. Material parameters used in FE simulations.
Material Al 6061
Extrusion type Direct extrusion (die is filled)
Ram speed 4.1 mm/s
Billet temperature 510 ◦C
Billet length 740 mm
Billet diameter 177.8 mm
Table 4. Forming conditions used in FE Simulations.
Die material AISI H-13
Die temperature 480 ◦C
Bolster, Sub-bolster temperature 25 ◦C
Ram temperature 420 ◦C
Container temperature 420 ◦C
Friction model Default
(Revanov friction)
Extrusion ratio 9.7
Figure 8a,b show the flow patterns of the new and old materials on the cross-sections
of the extrude at positions of 320 mm and 650 mm, respectively, from the stop-mark. As a
three-porthole die was used, a three-hold flow pattern of new material appeared inside the
old material. Clearly, the area ratio of the new material on the cross-section at a position of
650 mm away from the stop-mark is larger than that at a position of 320 mm away from the
stop-mark. The dimensions of the extruded tube products were 11.9 mm thick and 80 mm
in diameter.
Metals 2023, 13, x FOR PEER REVIEW 8 of 16
Table 3. Material parameters used in FE simulations.
Material Al 6061
Extrusion type Direct extrusion (die is filled)
Ram speed 4.1 mm/s
Billet temperature 510 °C
Billet length 740 mm
Billet diameter 177.8 mm
Table 4. Forming conditions used in FE Simulations.
Die material AISI H-13
Die temperature 480 °C
Bolster, Sub-bolster temperature 25 °C
Ram temperature 420 °C
Container temperature 420 °C
Friction model Default
(Revanov friction)
Extrusion ratio 9.7
Figure 8a,b show the flow paerns of the new and old materials on the cross-sections
of the extrude at positions of 320 mm and 650 mm, respectively, from the stop-mark. As a
three-porthole die was used, a three-hold flow paern of new material appeared inside
the old material. Clearly, the area ratio of the new material on the cross-section at a posi-
tion of 650 mm away from the stop-mark is larger than that at a position of 320 mm away
from the stop-mark. The dimensions of the extruded tube products were 11.9 mm thick
and 80 mm in diameter.
(a) (b)
Figure 8. Flow paerns of new material at different cross-sections from the stop-mark. (a) X = 320
mm, (b) X = 650 mm.
3.2. Control Factors and Levels in Die Parameters
The dimensions of the die were kept as 238 mm in outer diameter and 140 mm in
height. The parameters on the porthole and bridge parts were porthole radius (RP), bridge
width (WB), and porthole corner radius (Rc), as shown in Figure 4a. The longitudinal sec-
tion view of the whole die is shown in Figure 4b. The parameters in the whole die were
the porthole height (HP), welding chamber height (HC), outer bearing height (HO), welding
chamber diameter (DC), and porthole channel inclination angle (ϕ). Only the parameters
that influence material flow and welding behavior significantly were selected as the con-
trol factors and are discussed below. The selected control factors and levels are shown in
Table 5.
Figure 8.
Flow patterns of new material at different cross-sections from the stop-mark.
(a) X = 320 mm, (b) X = 650 mm.
3.2. Control Factors and Levels in Die Parameters
The dimensions of the die were kept as 238 mm in outer diameter and 140 mm in
height. The parameters on the porthole and bridge parts were porthole radius (R
P
), bridge
width (W
B
), and porthole corner radius (Rc), as shown in Figure 4a. The longitudinal
section view of the whole die is shown in Figure 4b. The parameters in the whole die
were the porthole height (H
P
), welding chamber height (H
C
), outer bearing height (H
O
),
welding chamber diameter (D
C
), and porthole channel inclination angle (
ϕ
). Only the
parameters that influence material flow and welding behavior significantly were selected
Metals 2023,13, 911 9 of 16
as the control factors and are discussed below. The selected control factors and levels are
shown in Table 5.
Table 5. Control factors and levels used in the Taguchi method.
Factors Levels
1 2 3
A Bridge width WB(mm) 31 34 37
B Porthole radius Rp(mm) 67.5 72.5 77.5
C Welding chamber height Hc (mm) 25 35 45
D Outer bearing height Ho (mm) 3 7 11
3.3. Simulation Results and Objective Function
The simulation results of the average welding pressure (P
LW
) and transverse welding
seam length (L
TW
) for Taguchi cases are shown in Table 6. The responses of each fac-
tor on the average welding pressure and transverse welding seam length are shown in
Figures 9and 10, respectively. For the welding pressure, the larger the better case. A
higher welding pressure can be obtained with a higher value of every factor. For transverse
welding seam length, the smaller the better case. A shorter length can be obtained with a
smaller welding chamber height and porthole radius and with a larger bridge width and
outer bearing length. The bridge width and outer bearing length influence the transverse
welding seam length slightly. The responses of welding chamber height and porthole ra-
dius to the welding pressure and transverse welding seam length are contradictory, which
means as these factors increase, both the welding pressure and transverse welding seam
length increase simultaneously. The objective of this study was to make the welding pres-
sure of the product over a required value and reduce the transverse welding seam length
as much as possible. Therefore, a compromising objective function has to be proposed
to consider the responses to the welding pressure and transverse welding seam length
simultaneously. If only the maximum welding pressure is considered, the optimized levels
for each factor are 77.5 mm for the porthole radius, 37 mm for the bridge width, 45 mm for
the welding chamber height, and 11 mm for the outer bearing length. All the simulation
results including the original die design are shown in Table 6.
Table 6. Simulation results by the Taguchi method.
L9 A B C D
Average Welding
Pressure
PLW (MPa)
Transverse
Welding Seam
Length
LTW (mm)
1 1 1 1 1 63.6 739
2 1 2 2 2 76.8 882
3 1 3 3 3 88.0 1133
4 2 1 2 3 74.1 750
5 2 2 3 1 74.7 1043
6 2 3 1 2 78.7 857
7 3 1 3 2 74.9 808
8 3 2 1 3 80.4 730
9 3 3 2 1 78.8 1064
PMax 3 3 3 3 88.6 1082
Original
1 1 1 2 72.0 664
Metals 2023,13, 911 10 of 16
Metals 2023, 13, x FOR PEER REVIEW 10 of 16
Figure 9. Responses of each factor on the welding pressure.
Figure 10. Responses of each factor on the transverse welding seam length.
A compromising objective function J was proposed to consider the responses to the
welding pressure and transverse welding seam length simultaneously as below:
J𝑃′
𝑃
𝛼
𝐿′
𝐿
𝛼
(1)
where P’
LW
and P
LW
are the welding pressures with the modified die design and the origi-
nal die design, respectively. L’
TW
and L
TW
are the transverse weld lengths with the modi-
fied die and the original die, respectively. α
1
and α
2
(=0~1) are weighting coefficients for
welding pressure and transverse seam length, respectively. As the response on the trans-
verse seam length is the smaller the beer, a minus sign is aached on the term of the
transverse seam length.
There are two simulation results in the formulation of J. One is the welding pressure
at the longitudinal weld seam and the other is the length of the transverse weld seam. The
welding pressure at the longitudinal weld seam is the larger the beer, whereas the lon-
gitudinal weld seam length is the smaller the beer, therefore, there is a minus sign in
Figure 9. Responses of each factor on the welding pressure.
Metals 2023, 13, x FOR PEER REVIEW 10 of 16
Figure 9. Responses of each factor on the welding pressure.
Figure 10. Responses of each factor on the transverse welding seam length.
A compromising objective function J was proposed to consider the responses to the
welding pressure and transverse welding seam length simultaneously as below:
J𝑃′
𝑃
𝛼
𝐿′
𝐿
𝛼
(1)
where P’
LW
and P
LW
are the welding pressures with the modified die design and the origi-
nal die design, respectively. L’
TW
and L
TW
are the transverse weld lengths with the modi-
fied die and the original die, respectively. α
1
and α
2
(=0~1) are weighting coefficients for
welding pressure and transverse seam length, respectively. As the response on the trans-
verse seam length is the smaller the beer, a minus sign is aached on the term of the
transverse seam length.
There are two simulation results in the formulation of J. One is the welding pressure
at the longitudinal weld seam and the other is the length of the transverse weld seam. The
welding pressure at the longitudinal weld seam is the larger the beer, whereas the lon-
gitudinal weld seam length is the smaller the beer, therefore, there is a minus sign in
Figure 10. Responses of each factor on the transverse welding seam length.
A compromising objective function J was proposed to consider the responses to the
welding pressure and transverse welding seam length simultaneously as below:
J=
P0
LW
PLW
×α1−L0
TW
LTW
×α2(1)
where P
0LW
and P
LW
are the welding pressures with the modified die design and the
original die design, respectively. L
0TW
and L
TW
are the transverse weld lengths with the
modified die and the original die, respectively.
α1
and
α2
(=0~1) are weighting coefficients
for welding pressure and transverse seam length, respectively. As the response on the
transverse seam length is the smaller the better, a minus sign is attached on the term of the
transverse seam length.
There are two simulation results in the formulation of J. One is the welding pressure
at the longitudinal weld seam and the other is the length of the transverse weld seam.
The welding pressure at the longitudinal weld seam is the larger the better, whereas the
longitudinal weld seam length is the smaller the better, therefore, there is a minus sign in
Metals 2023,13, 911 11 of 16
front of the term of L
0TW
/L
TW
. The extent of importance for these two factors is dependent
on the ratio of weighting coefficients, α1/α2.
Several different weighting coefficients are set, and the corresponding objective func-
tion values J are shown in Table 7. For the largest welding pressure case P
Max
, the corre-
sponding transverse seam length, L
0TW
, is larger than the original case by about 400 mm.
The J value for case P
Max
is not a maximal value among all the cases. The maximum J value
occurred at case 8. The J value becomes larger for a larger weighting coefficient
α1
. If the
welding pressure is more important than the transverse seam length,
α1
should be larger
and
α2
should be smaller. Clearly, case 8 with A3B2C1D3 is the best combination from the
Taguchi analysis.
Table 7. Objective function values with variable weighting coefficients.
Case
JP0
LW
(MPa)
L0
TW
(mm)
α1/α2
0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2
1 63.6 739 −0.11 0.08 0.28 0.48
2 76.8 882 −0.13 0.11 0.35 0.59
3 88.0 1133 −0.24 0.05 0.34 0.64
4 74.1 750 −0.05 0.17 0.38 0.60
5 74.7 1043 −0.27 −0.01 0.26 0.52
6 78.7 857 −0.10 0.14 0.38 0.62
7 74.9 808 −0.09 0.14 0.36 0.59
8 80.4 730 0.01 0.23 0.45 0.67
9 78.8 1064 −0.25 0.02 0.29 0.55
PMax 88.6 1082 −0.20 0.09 0.37 0.66
Original 72.0 664 0.00 0.20 0.40 0.60
3.4. Discussion
With the modified die design, the effects of various die design factors on the welding
pressure and transverse welding seam length obtained by finite element simulations are
summarized in Table 6. For a good design factor combination, a sound product with a
large welding pressure at the longitudinal welding seam and a small transverse weld-
ing seam length is desired in a continuous extrusion process with a porthole die design.
Sometimes these two objectives are conflicting, which means it is difficult to obtain a
maximal welding pressure and a minimal transverse welding seam length simultaneously
using a die factor combination. Therefore, sometimes trade-offs have to be made. For
example, if welding pressure is more important, as long as the welding pressure value
reaches a certain required level, the transverse welding seam length could act as a sacrifice.
In this paper, an objective function with double weighting coefficients combined with
the Taguchi method was proposed to determine the extent of importance between the
welding pressure and transverse welding seam length. From Table 6, it is known that the
maximal welding pressure occurred in the case with a combination of A3B3C3D3, whereas
the minimal transverse welding seam length occurred in the case with a combination
of A1B1C1D2. The extent of importance for welding pressure and transverse welding
seam length is dependent on the weighting coefficient ratio,
α1
/
α2
, as shown in Table 7.
α1
/
α2
= 0.5 denotes equal importance between the welding pressure and transverse weld-
ing seam length. From Table 7, it is known that the maximal objective function J value
occurred in case 8 for all the
α1
/
α2
ratios of 0.5/0.5, 0.6/0.4, 0.7/0.3, and 0.8/0.2, which
means if welding pressure is more important, then the combination of case 8 is an appro-
priate die geometry and dimension for obtaining a sound product with better mechanical
properties at the longitudinal welds.
Metals 2023,13, 911 12 of 16
4. Experiments of Hot Extrusion of Aluminum Alloy Tubes
The extrusion experiments of aluminum alloy A6061 tubes were conducted using a
2100-ton extrusion machine. The experimental extrusion conditions are the same as those
in the finite element simulations and are shown in Tables 3and 4. The compositions of the
aluminum alloy A6061 used in the tube extrusion experiments are given in Table 8.
Table 8. Compositions of the aluminum alloy A6061.
Ingredients Si Mg Cu Zn Fe Cr Mn Ti Other Al
Composition
(wt%) 0.5–0.8 0.7–1.2 0.15–0.4 0.25 0.7 0.02–0.35 0.15 0.15 0.15 Bal
4.1. Measurements of Transverse Seam Length
Corrosion tests are usually used for observations of longitudinal or transverse welding
seams. A solution of sodium hydroxide (NaOH) with a concentration of 1:10 to water was
used to corrode aluminum alloy at longitudinal and transverse sections of extruded tubes
at room temperature for a period of 50 min. Corrosion tests were conducted to observe the
interface of the transverse welding seam. The boundaries at the transverse welding seam
on a longitudinal section of the extruded tube is shown in Figure 11, from which the starting
and ending points of the transverse seam length can be observed. The boundaries at the
transverse welding seam on a cross-section of the extruded tube is shown in Figure 12,
from which the cross-sectional area ratio of the new material to the old material can
be calculated.
Metals 2023, 13, x FOR PEER REVIEW 12 of 16
4. Experiments of Hot Extrusion of Aluminum Alloy Tubes
The extrusion experiments of aluminum alloy A6061 tubes were conducted using a
2100-ton extrusion machine. The experimental extrusion conditions are the same as those
in the finite element simulations and are shown in Tables 3 and 4. The compositions of the
aluminum alloy A6061 used in the tube extrusion experiments are given in Table 8.
Table 8. Compositions of the aluminum alloy A6061.
Ingredients Si Mg Cu Zn Fe Cr Mn Ti Other Al
Composition
(wt%) 0.5–0.8 0.7–
1.2 0.15–0.4 0.25 0.7 0.02–0.35 0.15 0.15 0.15 Bal
4.1. Measurements of Transverse Seam Length
Corrosion tests are usually used for observations of longitudinal or transverse weld-
ing seams. A solution of sodium hydroxide (NaOH) with a concentration of 1:10 to water
was used to corrode aluminum alloy at longitudinal and transverse sections of extruded
tubes at room temperature for a period of 50 min. Corrosion tests were conducted to ob-
serve the interface of the transverse welding seam. The boundaries at the transverse weld-
ing seam on a longitudinal section of the extruded tube is shown in Figure 11, from which
the starting and ending points of the transverse seam length can be observed. The bound-
aries at the transverse welding seam on a cross-section of the extruded tube is shown in
Figure 12, from which the cross-sectional area ratio of the new material to the old material
can be calculated.
The comparisons of cross-sectional area ratios using original and modified die de-
signs are shown in Figure 13. The numerical and experimental new material area percent-
ages at different positions from the stop-mark between the original and modified die de-
signs are shown in the figure. From the figure, it is known that the new material area
percentage at the position of about 250 mm from the stop-mark increases dramatically
and gradually reaches 100% at about 700 mm from the stop-mark. Clearly, a slightly
shorter transverse welding seam length is obtained using the modified die design. The
tendency of the simulation results is the same as that of the experimental values.
Figure 11. Boundaries at transverse welding seams on a longitudinal section of an extruded tube.
Figure 12. Boundaries at a transverse welding seam on the cross-section of an extruded tube.
Head part
Head part
Head
Figure 11. Boundaries at transverse welding seams on a longitudinal section of an extruded tube.
Metals 2023, 13, x FOR PEER REVIEW 12 of 16
4. Experiments of Hot Extrusion of Aluminum Alloy Tubes
The extrusion experiments of aluminum alloy A6061 tubes were conducted using a
2100-ton extrusion machine. The experimental extrusion conditions are the same as those
in the finite element simulations and are shown in Tables 3 and 4. The compositions of the
aluminum alloy A6061 used in the tube extrusion experiments are given in Table 8.
Table 8. Compositions of the aluminum alloy A6061.
Ingredients Si Mg Cu Zn Fe Cr Mn Ti Other Al
Composition
(wt%) 0.5–0.8 0.7–
1.2 0.15–0.4 0.25 0.7 0.02–0.35 0.15 0.15 0.15 Bal
4.1. Measurements of Transverse Seam Length
Corrosion tests are usually used for observations of longitudinal or transverse weld-
ing seams. A solution of sodium hydroxide (NaOH) with a concentration of 1:10 to water
was used to corrode aluminum alloy at longitudinal and transverse sections of extruded
tubes at room temperature for a period of 50 min. Corrosion tests were conducted to ob-
serve the interface of the transverse welding seam. The boundaries at the transverse weld-
ing seam on a longitudinal section of the extruded tube is shown in Figure 11, from which
the starting and ending points of the transverse seam length can be observed. The bound-
aries at the transverse welding seam on a cross-section of the extruded tube is shown in
Figure 12, from which the cross-sectional area ratio of the new material to the old material
can be calculated.
The comparisons of cross-sectional area ratios using original and modified die de-
signs are shown in Figure 13. The numerical and experimental new material area percent-
ages at different positions from the stop-mark between the original and modified die de-
signs are shown in the figure. From the figure, it is known that the new material area
percentage at the position of about 250 mm from the stop-mark increases dramatically
and gradually reaches 100% at about 700 mm from the stop-mark. Clearly, a slightly
shorter transverse welding seam length is obtained using the modified die design. The
tendency of the simulation results is the same as that of the experimental values.
Figure 11. Boundaries at transverse welding seams on a longitudinal section of an extruded tube.
Figure 12. Boundaries at a transverse welding seam on the cross-section of an extruded tube.
Head part
Head part
Head
Figure 12. Boundaries at a transverse welding seam on the cross-section of an extruded tube.
The comparisons of cross-sectional area ratios using original and modified die designs
are shown in Figure 13. The numerical and experimental new material area percentages at
Metals 2023,13, 911 13 of 16
different positions from the stop-mark between the original and modified die designs are
shown in the figure. From the figure, it is known that the new material area percentage
at the position of about 250 mm from the stop-mark increases dramatically and gradually
reaches 100% at about 700 mm from the stop-mark. Clearly, a slightly shorter transverse
welding seam length is obtained using the modified die design. The tendency of the
simulation results is the same as that of the experimental values.
Metals 2023, 13, x FOR PEER REVIEW 13 of 16
Figure 13. Comparisons of cross-sectional area ratios using original and modified die designs.
4.2. Tube Expansion Tests
The extrusion experiments were conducted with the modified die and optimized
forming conditions. The welding strength of the extruded tube at the longitudinal welding
seams were determined by expansion tests. The expansion test results of the tube section
at the position within the transverse welding zone are shown in Figures 14 and 15,
whereas those out of the transverse welding zone are shown in Figures 16 and 17. A cone-
shaped die was designed and a universal testing machine was used to conduct tube ex-
pansion tests. Tube sections that 100 mm long were taken from the extruded tubes and
were used as the specimens. The loading curve during the expansion tests was recorded.
After the expansion tests, the appearance of a tube section taken with a distance of 300
mm from the stop-mark is shown in Figure 14. Clearly, the new and old materials on the
cross-section have not bonded completely. The loading curve during the expansion test is
shown in Figure 15.
(a) (b)
Figure 14. Appearances of a tube section after expansion tests. (a) Top view, and (b) perspective
view.
Figure 13. Comparisons of cross-sectional area ratios using original and modified die designs.
4.2. Tube Expansion Tests
The extrusion experiments were conducted with the modified die and optimized
forming conditions. The welding strength of the extruded tube at the longitudinal welding
seams were determined by expansion tests. The expansion test results of the tube section at
the position within the transverse welding zone are shown in Figures 14 and 15, whereas
those out of the transverse welding zone are shown in Figures 16 and 17. A cone-shaped
die was designed and a universal testing machine was used to conduct tube expansion
tests. Tube sections that 100 mm long were taken from the extruded tubes and were used
as the specimens. The loading curve during the expansion tests was recorded. After the
expansion tests, the appearance of a tube section taken with a distance of 300 mm from
the stop-mark is shown in Figure 14. Clearly, the new and old materials on the cross-
section have not bonded completely. The loading curve during the expansion test is shown
in Figure 15.
Metals 2023, 13, x FOR PEER REVIEW 13 of 16
Figure 13. Comparisons of cross-sectional area ratios using original and modified die designs.
4.2. Tube Expansion Tests
The extrusion experiments were conducted with the modified die and optimized
forming conditions. The welding strength of the extruded tube at the longitudinal welding
seams were determined by expansion tests. The expansion test results of the tube section
at the position within the transverse welding zone are shown in Figures 14 and 15,
whereas those out of the transverse welding zone are shown in Figures 16 and 17. A cone-
shaped die was designed and a universal testing machine was used to conduct tube ex-
pansion tests. Tube sections that 100 mm long were taken from the extruded tubes and
were used as the specimens. The loading curve during the expansion tests was recorded.
After the expansion tests, the appearance of a tube section taken with a distance of 300
mm from the stop-mark is shown in Figure 14. Clearly, the new and old materials on the
cross-section have not bonded completely. The loading curve during the expansion test is
shown in Figure 15.
(a) (b)
Figure 14. Appearances of a tube section after expansion tests. (a) Top view, and (b) perspective
view.
Figure 14.
Appearances of a tube section after expansion tests. (
a
) Top view, and (
b
) perspective view.
Metals 2023,13, 911 14 of 16
Metals 2023, 13, x FOR PEER REVIEW 14 of 16
Figure 15. Loading curve during the expansion test for a tube section with a 300 mm distance from
the stop-mark.
Figures 16 and 17 show the appearance of the tested tube and the loading curve dur-
ing the expansion test, respectively, for tube section at a position of 500 mm in front of the
stop-mark. The expansion tests were used to understand the welding strength at the lon-
gitudinal welding seams. Clearly, fracture occurs at the tube itself not at the longitudinal
welding seams, which means the welded materials have bonded completely and the
bonding strength at the longitudinal welding seams is stronger than the tube itself. The
loading curve during the expansion test is shown in Figure 16. Clearly, two anaclastic
points were observed. The expansion tests were not completed, and the maximum load
for the fracture point was much higher than 500 kN.
(a) (b)
Figure 16. Appearances for a tube section taken at a position of 500 mm in front of the stop-mark.
(a) Top view, and (b) side view.
Tail part
Tail
Figure 15.
Loading curve during the expansion test for a tube section with a 300 mm distance from
the stop-mark.
Metals 2023, 13, x FOR PEER REVIEW 14 of 16
Figure 15. Loading curve during the expansion test for a tube section with a 300 mm distance from
the stop-mark.
Figures 16 and 17 show the appearance of the tested tube and the loading curve dur-
ing the expansion test, respectively, for tube section at a position of 500 mm in front of the
stop-mark. The expansion tests were used to understand the welding strength at the lon-
gitudinal welding seams. Clearly, fracture occurs at the tube itself not at the longitudinal
welding seams, which means the welded materials have bonded completely and the
bonding strength at the longitudinal welding seams is stronger than the tube itself. The
loading curve during the expansion test is shown in Figure 16. Clearly, two anaclastic
points were observed. The expansion tests were not completed, and the maximum load
for the fracture point was much higher than 500 kN.
(a) (b)
Figure 16. Appearances for a tube section taken at a position of 500 mm in front of the stop-mark.
(a) Top view, and (b) side view.
Tail part
Tail
Figure 16.
Appearances for a tube section taken at a position of 500 mm in front of the stop-mark.
(a) Top view, and (b) side view.
Metals 2023, 13, x FOR PEER REVIEW 15 of 16
Figure 17. Loading curve during an expansion test for a tube section with a 500 mm distance from
the stop-mark.
From the expansion tests, it is known that there are two kinds of loading curves dur-
ing the expansion tests. The strength of the tube product with a curve of two anaclastic
points is higher than that with a monotonic curve. The tube sections behind the stop-mark
are weaker than those far in front of the stop-mark, because the tube sections in front of
the stop-mark are the joining sections of new and old materials. The tube sections 500 mm
ahead from the stop-mark show a curve of two anaclastic points and have a stronger
strength.
The simulated mean welding pressure using the case of P
max
is 88.6 MPa, as shown in
Table 6. The present authors have derived a formula for calculating the mean welding
pressure. From the expansion test results of pushing force, the experimental mean weld-
ing pressure could be obtained as 89.1 MPa. The comparison between these two values
could validate the simulation results of welding pressures.
5. Conclusions
The finite element software QForm was used to analyze the flow paern of billets
during hot extrusion of aluminum alloy A6061 tubes. The effects of the die geometries
such as welding chamber height, porthole radius, bridge width, bearing length, etc., on
the welding pressure and transverse seam length were discussed. The simulation results
showed higher welding pressures were obtained as all the geometric factors increased.
For the effects on the transverse seam length, larger bridge widths and outer bearing
lengths, and smaller porthole radii and welding chamber heights decreased the transverse
weld seam length. Porthole radii and welding chamber heights had different effects on
the welding pressure and transverse seam length. An objective equation J was proposed
to evaluate the effects of the welding pressure and transverse seam length simultaneously.
The maximal value J was obtained with the forming conditions of 37 mm in bridge width,
72.5 mm in porthole radius, 25 mm in welding chamber height, and 11 mm in outer bear-
ing length. The transverse welding seam length with the revised die design was 1300 mm,
which is 300 mm shorter than that with the original die design.
Author Contributions: Conceptualization, Y.-M.H.; formal analysis, I.-P.H.; writing—review and
editing, Y.-M.H.; Figure drawing, I.-P.H. All authors have read and agreed to the published version
of the manuscript.
Tube section at 500 mm in front of stop-mark
Figure 17.
Loading curve during an expansion test for a tube section with a 500 mm distance from
the stop-mark.
Metals 2023,13, 911 15 of 16
Figures 16 and 17 show the appearance of the tested tube and the loading curve
during the expansion test, respectively, for tube section at a position of 500 mm in front
of the stop-mark. The expansion tests were used to understand the welding strength
at the longitudinal welding seams. Clearly, fracture occurs at the tube itself not at the
longitudinal welding seams, which means the welded materials have bonded completely
and the bonding strength at the longitudinal welding seams is stronger than the tube itself.
The loading curve during the expansion test is shown in Figure 16. Clearly, two anaclastic
points were observed. The expansion tests were not completed, and the maximum load for
the fracture point was much higher than 500 kN.
From the expansion tests, it is known that there are two kinds of loading curves
during the expansion tests. The strength of the tube product with a curve of two anaclastic
points is higher than that with a monotonic curve. The tube sections behind the stop-mark
are weaker than those far in front of the stop-mark, because the tube sections in front
of the stop-mark are the joining sections of new and old materials. The tube sections
500 mm ahead from the stop-mark show a curve of two anaclastic points and have a
stronger strength.
The simulated mean welding pressure using the case of P
max
is 88.6 MPa, as shown
in Table 6. The present authors have derived a formula for calculating the mean welding
pressure. From the expansion test results of pushing force, the experimental mean welding
pressure could be obtained as 89.1 MPa. The comparison between these two values could
validate the simulation results of welding pressures.
5. Conclusions
The finite element software QForm was used to analyze the flow pattern of billets
during hot extrusion of aluminum alloy A6061 tubes. The effects of the die geometries
such as welding chamber height, porthole radius, bridge width, bearing length, etc., on
the welding pressure and transverse seam length were discussed. The simulation results
showed higher welding pressures were obtained as all the geometric factors increased. For
the effects on the transverse seam length, larger bridge widths and outer bearing lengths,
and smaller porthole radii and welding chamber heights decreased the transverse weld
seam length. Porthole radii and welding chamber heights had different effects on the
welding pressure and transverse seam length. An objective equation J was proposed to
evaluate the effects of the welding pressure and transverse seam length simultaneously.
The maximal value J was obtained with the forming conditions of 37 mm in bridge width,
72.5 mm in porthole radius, 25 mm in welding chamber height, and 11 mm in outer bearing
length. The transverse welding seam length with the revised die design was 1300 mm,
which is 300 mm shorter than that with the original die design.
Author Contributions:
Conceptualization, Y.-M.H.; formal analysis, I.-P.H.; writing—review and
editing, Y.-M.H.; Figure drawing, I.-P.H. All authors have read and agreed to the published version
of the manuscript.
Funding: This research was funded by National Science and Technology Council of the Republic of
China under Grant no. MOST 106-2622-E-110-006-CC3.
Data Availability Statement: Not applicable.
Acknowledgments:
The authors would like to extend their thanks to the National Science and
Technology Council of the Republic of China under Grant no. MOST 106-2622-E-110-006 -CC3. The
advice and financial support of NSTC are greatly acknowledged.
Conflicts of Interest: The authors declare no conflict of interest.
Metals 2023,13, 911 16 of 16
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