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Numerical Simulation of Residual Stress during Stamping-forging
Forming of 2024 Aluminum Alloy Sheet Metal
Da Li, Lei Deng, Xinyun Wang*, Junsong Jin and Juchen Xia
State Key Lab of Material Processing and Die&Mould Technology, Huazhong University of Science
and Technolog, Wuhan, Hubei, 430074, China
*wangxy_hust@163.com
Keywords: Residual Stress, Stamping-forging Forming, 2024 Aluminum Alloy, Sheet Metal,
Numerical Simulation.
Abstract. The unreasonable residual stress field in sheet part has an adverse effect on the
dimensional accuracy and performance. A forming method combined stamping and forging was
proposed to reduce the residual stress of the sheet part. The residual stress field in 2024 aluminum
alloy V-shaped piece after bending and forging was analyzed by the finite element software Abaqus.
The results showed that the stamping-forging forming process can significantly reduce the residual
stress in round corner of V-shaped piece, and simultaneously decrease springback and improve the
dimensional precision of sheet part.
Introduction
2024 aluminum alloy is widely used in the manufacture of aerospace vehicle structures because of
its excellent mechanical properties and workability [1]. In order to obtain high strength and
toughness, the material must be underwent solution and aging treatment, or be plastic formed, after
which the residual stress is more or less remained in the alloy. Because the residual stress is in a
larger proportion of the yield strength, substantial creep, fatigue failure, stress corrosion cracking
and other failure phenomena of part easily occur during use, and seriously affects dimensional
accuracy and life of aerospace structures [2]. Therefore, in order to obtain good performance and
lightweight aerospace parts, the new forming method of sheet parts with low residual stress is
urgently needed to be developed.
Several researchers have studied the plastic forming and process parameters of sheet parts and
presented some methods to improve the residual stress distribution. R. Greze [3] discussed the
effect of temperature during deep drawing on springback from room temperature to 200℃, and
found that the increasing temperature tends to decrease the residual stress gradient in the cup wall.
M.S. Ragab [4] studied the effect of ironing on the magnitude and distribution of bending residual
stress in deep drawn cups, and found that the residual stress can be reduced greatly with small
ironing strain. A. Gisario [5] prevented springback by using high power laser to scan the pre-bent
aluminium alloy sheet metal, and optimized the residual stress field in the sheet. M. Koc [6] studied
two different methods of cold working (compression and stretching) to reduce the residual stress of
quenched 7050 aluminium alloy forged block, and found that both methods can reduce the residual
stress more than 90%.
In recent years, cold stamping-forging forming technology, a new type of sheet metal forming
process, is rapidly developed. This technology was first proposed by Japanese researcher Nakano
Takashi in the early 1990s [7]. Stamping-forging forming process consists of the characteristics of
stamping and forging. It can be used to form the local thickening of complex parts because
upsetting, extrusion and other three-dimensional bulk forming processes are integrated into
blanking, bending, deep drawing, flanging and other common sheet metal forming processes [8,9].
Based on the deformation characteristics of stamping-forging forming process, a forming method
including stamping and forging is proposed to adjust the residual stress field in this paper. The
distribution of residual stress in 2024 aluminum alloy V-shaped piece after bending and
stamping-forging is analyzed by numerical simulation. And the influence of bending angle and the
relative bending radius on residual stress is also discussed.
Advanced Materials Research Vols. 602-604 (2013) pp 1903-1909
Online available since 2012/Dec/13 at www.scientific.net
? (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.602-604.1903
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 129.219.96.235, National Cheng Kung University, Tainan, Taiwan-10/01/14,11:48:02)
Stress analysis during elastic-plastic bending
In the bending process, the bend radius of sheet decreases gradually with the punch be pushed
down,while the degree of deformation grows increasingly. The inner and outer edges of sheet
firstly reach the yield condition and start to occur plastic deformation. If the punch continues to be
pushed down, the fibers yielded in the plate gradually increase from outside to inside. In the round
corner of bending deformation zone, the inner and outer layers are a plastic region and the middle
layer belongs to the elastic region. That is to say the elastic-plastic deformation occurred in the
plate. For the ideal elastic-plastic bended sheet, the bending moment epM is shown in Eq. (1) [10]:
22
ep
1
Mb(2h-)
12
ζσ=. (1)
where b is the plate width, h the plate thickness, ζ the thickness of the elastic region, and σ the
bending stress.
The unloading process is equivalent to imposing a reverse elastic bending moment -epMon the
plate, and the residual stress is the superposition of bending stress and elastic unloading stress,
which is shown in Fig. 1.
(a) (b) (c)
Fig.1 Residual stress after elastic-plastic bending in the bending round corner: (a) bending
stressσ; (b) elastic unloading stressσ′; (c) residual stressrσ
The residual stress can be determined from Eq. (2) [10]:
22
3
(3)
1()
2rs
hZ
Z
h
ζζ
σσ
???
=?≥??
??
i
22
3
(3)2
()
2
s
rs
hZ
ZZ
h
ζσζ
σσ
ζ
???
=??
??
ii
ii. (2)
where sσ is the yield strength and Z is the distance between the neutral layer and the calculated
position.
As shown in Fig. 1, the distribution of residual stress in the plate after unloading is more
complex. In the bending process, the bending stress is simple tension and compressive stress, while
the residual stress is showing alternative distribution of tension and compressive stress after
unloading to maintain balance in the plate. The inner layer of round corner remains residual tension
stress and the outer layer remains residual compressive stress. This state is caused by different
deformation mode in the inner and outer layers during bending process.
The stamping-forging forming process proposed in this paper can adjust the residual stress field
by changing the deformation mode of bending round corner. Its schematic is shown in Fig. 2.
1904Progress in Materials and Processes
Fig.2 Schematic of the stamping-forging forming process
In Fig. 2, r is the inner radius of the bending round corner; t is the thickness of sheet; α is the
bending angle; and s is the distance between punch and sheet. The relative bending radius is
calculated by r/t. The thickening degree of upsetting can be determined by the ratio of s and t. First,
the punch is pushed down until the distance between the die and the punch reaches t. In this process,
the bending deformation of sheet is occurred. Then the punch is fixed after it is shifted up to a
distance of s. Both pressing blocks on each side are pushed along the inclined wall of the die. The
thickening of sheet is occurred with upsetting force, and the sheet finally fit with the punch. In the
upsetting process, the round corner and straight side of the sheet both occurs the plastic
deformation.
Finite element simulation of stamping-forging process
Simulation scheme. Two bending angles (α=90°, 120°) and two relative bending radii (r/t=2.5,
3) were selected in the numerical analysis of bending and stamping-forging process of 2024
aluminum alloy V-shaped piece. And the thickening degree was 10%.
Material properties test. The material used in this study was cold-rolled 2024 aluminum alloy
plate of length 60 mm and thickness 2 mm. Its heat treatment condition was T4. In order to obtain
material properties needed in the finite element simulation, the uniaxial tensile test of aluminum
plate at room temperature was conducted. Tensile specimens were prepared by wire electrical
discharge machining along the rolling direction. The tensile tests were conducted in a universal
testing machine (Zwick/Roell Z020) and the tensile speed was 1 mm/min. The plastic section of
true stress-strain curve is shown in Fig. 3. It can be seen from the change in the trend of the curve
that the fracture mode of alloy is brittle fracture at room temperature. The maximum true plastic
strain is 0.171 and the fracture stress is 679 MPa. The yield strength and elastic modulus measured
in the test are 395 MPa and 70 GPa, respectively.
Fig.3 The plastic section of true stress-strain curve
Establishment of finite element model. The 2-D finite element models of the bending and
stamping-forging process were established by Abaqus/Explicit, as shown in Fig.4. Due to the ratio
of width to thickness is larger than 8, the deformation process can be regarded as a plane strain
process. A two-dimensional and four-node plane strain element with reduced integration and
Advanced Materials Research Vols. 602-6041905
hourglass control [11], CPE4R element, was used to mesh the aluminum plate. Contact condition
adopted the penalty contact condition with a tangential friction coefficient of 0.1. The Young’s
Modulus of 70 Gpa, Poisson’s ratio of 0.31, and constitutive relationship were derived from tensile
test data. After the simulation of the forming process, the residual stress field after springback was
calculated by Abaqus/Standard.
(a) (b)
Fig.4 Finite element models: (a) bending model (α=90°); (b) stamping-forging model (α=90°)
Results and discussion
Stress and strain distribution after bending and stamping-forging. In order to clearly observe
and coMPare internal residual stress in different forming processes, the stress and strain distribution
in V-shaped piece when bending angle is 90°and relative bending radius is 2.5 are shown in Fig. 5.
(a) (b)
(c) (d)
(e) (f)
Fig.5 Stress and strain distribution before and after stamping-forging (α=90°, r/t=2.5): (a)Equivalent
plastic strain after bending; (b) Equivalent plastic strain after stamping-forging; (c) X-axis plastic
strain after bending; (d) X-axis plastic strain after stamping-forging; (e) X-axis residual stress after
bending; (f) X-axis residual stress after stamping-forging
1906Progress in Materials and Processes
We can see from Fig. 5(a) that the equivalent plastic strain of non-deformation zone in the
straight side is zero, and the deformation is mainly occurred at the round corner. The equivalent
strain gradually decreases from the inner and outer edges to the neutral layer in where strain is zero.
In Fig. 5(b), the equivalent strain is greater than that of piece without upsetting shown in Fig. 5(a),
and tends to be uniform at the round corner. This indicates that the plastic deformation has occurred
in the whole plate under the upsetting force.
Fig. 5(c) shows that x-axis plastic strain value of inner layer is negative, while the outer value is
positive, which indicates the fibers of inner layer are compressed and the outer ones are stretched.
The maximum compressive strain in the inner side of round corner is 0.142, and the maximum
tension strain in the outer side of round corner is 0.154. After upsetting, the maximum compressive
strain is 0.152, and the maximum tension strain is 0.147, as shown in Fig. 5(d). It illustrates the
increased compressive strain in the plate after upsetting can compensate part of the tension strain,
which can make stretched fibers to be recovered.
The x-axis residual stress distribution after bending is shown in Fig. 5(e). In non-deformation
zone the residual stress is nearly zero, while in deformation zone the inner layer remains residual
tension stress and the outer layer remains residual compressive stress. The maximum residual
tension and compressive stress are 241 MPa and 284 MPa, respectively. In Fig. 5(f), the inner and
outer layers of round corner all remain residual compressive stress after upsetting, while the middle
region remains residual tension stress. In the straight wall, the residual stress is within the range of
±2 MPa, while at the round corner, the maximum tension and compressive stress are reduced to 95
MPa and 90 MPa, respectively. This indicates the residual stress has been significantly reduced
after upsetting.
Residual stress field after stamping-forging. After stamping-forging, the distribution of x-axis
residual stress xσ was determined along the sheet thickness. 70 integration points were selected
along the path shown in Fig. 6. The residual stresses of profiles are shown in Fig. 7.
Fig. 6 Measurement path of x-axis residual stress at the bending section
(a) (b)
Fig. 7 Residual stress profiles before and after stamping-forging: (a) α=90° ; (b) α=120°
Advanced Materials Research Vols. 602-6041907
In Fig. 7(a) and (b), the residual stress distribution in bended parts are basically the same under
different conditions. There is residual tension stress in the inner surface, and alternative distribution
of tension stress and compressive stress from inner to outer. On both sides of plate’s neutral layer,
there exist two peak values of residual tension and compressive stress. However, the trend of
residual stress distribution after upsetting has been changed. The residual tension stress in inner
layer is transformed into compressive stress. And it remains residual tension stress within the range
from 0.5 mm to 1.5 mm in the plate.
The maximum residual tension and compressive stress after bending increases with increasing of
relative bending radius and bending angle. The maximum tension stress reaches 261 MPa, and the
maximum compressive stress reaches 307 MPa. After stamping-forging the residual stress reduction
is all more than 60%. It can be seen that the upsetting process makes distinct improvement on the
residual stress field. The plate is divided into two regions in bending process. Inner layer is
compressed and occur compressive strain. Outer layer is stretched and occur tension strain. During
the upsetting process, part of the tension strain of outer layer is compensated and tends to be
compressive strain. Therefore, bending-upsetting can significantly improve the distribution of the
residual stress field, which is beneficial to improve the dimensional accuracy and performance in
sheet metal forming.
Forming accuracy after stamping-forging. In elastic-plastic bending deformation, the plastic
strain will be retained in the plate after unloading, while the elastic deformation recovers. So it is
inevitable to lead to springback. Too large springback angle will seriously affect the dimensional
accuracy and the using performance of parts. In this paper, the influence of stamping-forging
process on forming accuracy is also obtained.
Fig. 8 Springback angle before and after stamping-forging
The relationship between springback angle and relative bending radius under different condtions
is shown in Fig. 8. The springback angles after bending are all positive, and increase with
increasing of bending angle and relative bending radius. After upsetting, the springback angles are
all negative, and the maximum reachs -1.9°. The outer zone of round corner is elongated and inner
zone is shortened during bending. After unloading, the recovery trend of both zones make the plate
straight, so it appears a springback angle. However, after upsetting, because both inside and outside
areas are compressed, the recovery trend can be offset by each other.
Due to the negative springback angle appeared after upsetting, we can assume that there must be
a moment of zero in the transition process from positive to negative. It is suggested that we can
achieve zero springback by changing the upsetting reduction, which has a positive significance on
the control of dimensional accuracy in forming process of plate parts.
Conclusions
A new method to adjust the residual stress field based on stamping-forging process was proposed in
this paper. The following conclusions can be drawn from this study.
(1) The residual stress field in 2024 aluminum plate after bending appeared to be an alternative
distribution of tension and compression stress with large gradient. The maximum residual stress
appeared at both sides of the neutral layer, and its amplitude was within the range of ±300 MPa.
1908Progress in Materials and Processes
After upsetting, the stress gradient became relatively small. There remained residual compression
stress in the inner and outer layers of round corner, while residual tension stress in the middle zone.
The amplitude was reduced to the range of ±100MPa. Therefore, the stamping-forging forming
process is an effective method to reduce the residual stress in 2024 aluminum alloy plate.
(2) Due to inner and outer areas were all subjected to large compressive deformation during
stamping-forging process, the springback was commendably improved by upsetting. In addition, the
negative springback was appeared after upsetting, which provides a suggestion for the study of
changing the upsetting reduction to adjust the springback compensation, even to achieve the zero
springback.
Acknowledgements
The authors wish to express sincere gratitude for the grant of China National Science and
Technology Major Project (No. 2011ZX04016-051).
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Advanced Materials Research Vols. 602-6041909
Progress in Materials and Processes
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Numerical Simul