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A Finite Element study of the Deformability of Steel
Jiadi Fana, Qi Ruib, Jingyi Wangc
aMechanical Engineering, Master of Engineering, [email protected] bMechanical Engineering, Master of Engineering, [email protected]
cMechanical Engineering, Master of Engineering, [email protected]
Deep drawing is a widely used manufacturing method in industrial area. However, improper
method to simulate a certain deep drawing process of 42CrMo high-strength steel. We studied the
mechanism of common defects, simulate different forming conditions (forming temperature,
forming rate, and holding force), and refine the blank size. Finally, we found the most proper
forming conditions and blank size for this process. Our study will optimize forming condition,
enhance productivity, and reduce waste.
1. Introduction
1.1 There are three major parts in a stamping
mold- punch, die and blank holder. In a
normal stamping process, the blank would
deform under the constraints of the blank
holder and ide as the punch goes down.
Several parameters (forming temperature,
forming rate, and holding force) which
determine the forming condition should be
considered to avoid the potential defects like
the wrinkling and fracture. Also, improper
forming conditions may raise the cost of
manufacture and waste time. This report uses
finite element method to analyze the process
and get the proper range of important
parameters by using ABAQUS-a finite element
analysis software.
1.2 Mechanism of common defects
1.2.1 Wrinkling
During deep drawing process, metal flows
from large perimeter area to small perimeter
area. Under minimum principal stress 3 [1],
the blank will be thickened. Uneven
thickening will lead to wrinkling. Wrinkling
increases the surface friction coefficient, and
stop metal from flowing inside. In application,
we need a reasonable holding force to
provide a restriction to avoid wrinkling.
Figure 1 Wrinkling during deep drawing
1.2.2 Fracture
The friction between holder and blank, die
and holder will block metal from flowing. If
the friction is too big, the metal at the bottom
corner will over-thinning, lead to fracture.[2]
Figure 2 Fracture during deep drawing
1.3 The influence of different forming
condition.
1.3.1 Temperature influence
The deformability of metal will improve as
temperature rises, shows in figure 3. [3]
Figure 3 Relation between temperature and
Maximum strentch depth.
Under higher temperature, the deformability
of metal is better. However, good
deformability may lead to over-thinning at
the corner, and reduce the quality of product.
What is more, higher temperature is also
more temperature expensive. From former
research, the suggested forming temperature
of 42CrMo steel is 550-850℃[3]
1.3.2 Holding force influence
Oversize holding force can lead to fracture
defect. And undersize holding force can lead
to wrinkling defect, which will both reduce
the fluidity of metal, shows in Figure 4.
Figure 4 Relation between holding force and
Maximum strength depth.
1.3.3 Strain rate influence
Under large strain rate, the deformability of
metal is poor, which is more like to lead to
fracture. Under small strain rate, the
deformability of metal is good. However,
small strain rate will reduce the productivity.
1.4 Material
In this study, we use 42CrMo high-strength
steel as material. 42CrMo (American Grade:
AISI 4140) is one of the representative
medium carbon and low alloy steels. Its good
comprehensive mechanical properties lead to
the application of many universal parts. Some
of its mechanical parameters are shown in
Table 1 below.
Max
imu
m s
tret
ch d
epth
(m
m)
Simulation Experiment
Temperature ℃
Max
imu
m s
tret
ch d
epth
(m
m)
Simulation Experiment
Holding Force (MPa)
Density (Kg/m^3)
Young’s Modulus (Gpa)
Poison’s ratio
7,830 210 0.31
Table 1 mechanical parameters of 42CrMo
The true stress-strain cure in different
temperatures and strain rate are shown in
Figure 5. [4] We can see that the
deformability of 42CrMo increase as
temperature increases and strain rate
decreases.
Figure 5 true stress-strain curve in different
temperatures and strain rate[4]
2. Case description
We specifically use ABAQUS to simulate the
manufacturing process of bakeware. The
geometry of bakeware shows in Figure 6.
Figure 6 2D geometry of model
In the implement of ABAQUS, a quarter of
entire model is used, because geometrical
symmetry. The ABAQUS model, including
punch, die, holder, and blank, shows in Figure
7.
Figure 7 ABAQUS model
The punch, holder, and die are defined as
rigid shell. Blank is deformed shell with
thickness of 1mm. The symmetry boundary
condition (BC) is implemented for all parts. A
load is implemented on the holder as holding
force. For the die, all degree of freedom are
fixed. Blank and punch can only move in y
direction. The BC of punch is a displacement -
50mm in y direction, which is the depth of the
bakeware. The plastic data is from
experiment data from figure 5.
(b)
3.Result
3.1 Different temperatures
Strain rate was set as 1, holding force was
10kN. The forming process under 600℃ and
650℃ were compared. Shows in Figure 8.
(a)
(b)
Figure 8 forming results in 600℃(a),
650℃(b)
The scale in figure 8 is thickness after forming.
The blue area is the bottom corner, which is
the thinnest area after forming. At 600℃, the
corner thickness is 0.6848, at 650℃, the
corner thickness is 0.6604.
3.2 Different strain rates
The temperature was chosen as 600℃,
holding force was 10kN. The forming
processes under strain rate 0.1 and 1
were compared. Figure 9. After forming , at
=0.1, the corner thickness is 0.7057, at
=1, the corner thickness is 0.6848.
(a)
(b)
Figure 9 Results in =0.1(a) and =1(b)
3.3 Different holding forces
The temperature was chosen as 600℃, strain
rate was 0.1. Choose different holding
force and compared the result. Figure 10.
(a)
(c)
Figure 10. (a)F=5kN, (b)F=10kN, (c)F=30kN
In (a), we can see the uneven thickness after
forming, it is wrinkling. In (c) the corner
thickness became 40% of original thickness,
which can be treated as fracture. In (b), the
corner thickness is 0.7067.
3.4 refine the size of blank
After deep drawing process, the extra blank
needs to be cut off. If the original blank size is
too big, it will be a huge waste. The
temperature was chosen as 600℃, strain
rate was 0.1. Holding force is 10kN.
Choose different original blank size.
(a)
(b)
(c)
Figure 11 (a)400*400mm, (b)300*300mm, (c)
240*240mm.
4.Discussion
From the simulation results, we notice that all
the thinnest area occur at the bottom corner.
So, the corner is the area that most likely to
generate fracture. In this paper, if the
thickness after forming becomes 70% or low
of the original thickness, it can be treated as
fracture.
In Figure 8, the thickness at corner influence
that 42CrMo’s deformability at higher
temperature is better. However, as the
thickness ratio are both under 0.7, it is
unnecessary to simulate at temperature
higher than 650℃.
In Figure 9, the results reflect that
42CrMo’s deformability at lower strain
rate is better. However, at =1, the
thickness ratio is <0.7, so we choose =0.1
as optimized strain rate.
Figure 10 shows the influence of holding
forces. After several simulations, we found
reasonable holding force range is 7-13kN.
Figure 11 shows the blank size refining. For
the given bakeware size, 240*240mm original
blank size is good enough.
5.Conclusions
The critical criterion when we choose
forming condition is 1) Guarantee the
production quality. 2) Reduce the waste of
energy and material. 3)Enhance the
productivity. So, we choose the optimized
forming condition as followings:
Forming temperature T=600 ℃
Strain rate =0.1
Holding force F=7-13kN
Original blank size 240*240mm
In these forming conditions, the simulation
result shows in Figure 12.
Figure 12 Result in optimized forming
conditions
References [1]James A Szumera. (2003). The Metal
Stamping Process
[2] Lim, Y. Process Control for sheet-metal
stamping
[3]Gu, T. (2012). Research on ductile fracture
criterion of hot stamping. China
Academic Journal Electronic Publishing
House, 50-64.
[4]Guo-Zheng, Q. (2013). Characterization for
Dynamic Recrystallization Kinetics
Based on Stress-Strain Curves. In Recent
Developments in the Study of
Recrystallization (p. 9). Intech.