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Numerical modelling of micro deep drawing with aluminium-copper composite considering surface roughness
Fanghui Jia1, a, Jingwei Zhao1,b, Liang Luo1,, Haibo Xie1 and Zhengyi Jiang1,c * 1School of Mechanical, Material, Mechatronic and Biomedical Engineering, University of
Wollongong, NSW 2522, Australia [email protected], [email protected], [email protected]
Keywords: Micro deep drawing; Al-Cu composite; Voronoi; Finite element method; Surface roughness
Abstract. In this paper, two-layer aluminium (Al)-copper (Cu) laminate composite blank was used
to investigate the deformation behaviour of Al-Cu composite in microscale. Finite element (FE)
modelling of micro deep drawing (MDD) combined with springback was conducted. With the
consideration of size effects, Voronoi tessellations based on the real grain sizes were developed in
FE models and each grain was assigned with their own properties. In addition, the information of
surface roughness was also assigned to the Voronoi model to further improve the accuracy of
simulation results. Finally, experiments were conducted to verify the simulation results. It shows
that the new FE model considering surfaces roughness can provide accurate simulation results than
other models.
Introduction
With the increasing demand of microparts in fields of electronics, bio-mechanical and aerospace,
microforming is becoming more and more important for modern industries. Compared with other
microforming methods, such as micromachining, micro wire electrical discharging machining
(EDM) and lithographic technologies, micro deep drawing (MDD) possesses the advantages of high
productivity, low production cost, high product quality, and less pollution [1, 2].
Metal composites are becoming popular because they provide customisable materials for specific
applications. Aluminium (Al)-copper (Cu) composite possesses the advantages of both low cost and
high conductivity, which is a preferred material for electrical [3, 4]. As a result, micro drawn parts
made of Al-Cu composite will have a potential application in micro electronic industry.
In metal forming, the interface behaviour between tools and workpieces is a significant factor,
determining the forming limit of the forming process and the quality of the produced products.
Although a number of researches on tribology in metal forming have been conducted on large scale
process, there are only a few studies on the effects of tribology in microforming process. Gong et al.
[5] and Azushima [6] studied the effects of friction and lubricants in microforming, and developed
models for describing the change of friction coefficient. Deng et al. [7] and Luo et al. [8]
established numerical simulation models and investigated the effects of surface roughness on
microforming process of pure metal. However, there are few numerical studies on microforming
with consideration of composite material, and investigation on the formability and the interaction
behaviour of composite material in microforming is therefore essential.
In this paper, two-layer Al-Cu composite was used to investigate its formability in MDD
process. FE model based on the real grain tessellations of both Al and Cu was established through
Voronoi diagram. The information of mechanical properties and surface roughness was assigned to
each Voronoi tessellation to represent the real grains of the composite materials. Furthermore, the
surface roughness of the blank was considered and represented by thickness distribution in the
Voronoi model. Finally, MDD experiments with Al-Cu composite material were conducted to
verify the FE simulation results.
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Proceedings of the 20th International Symposium on Advances in Abrasive Technology 3-6 December, Okinawa, Japan
FE simulation models
Material. The as-received Al-Cu composite blanks were cold rolled from the thickness of 235 µm
to a final thickness of 50 µm in order to meet the specification of die set in MDD experiments. The
rolled blanks (40 µm for Al and 10 µm for Cu) were heat-treated at 400 ºC for 2 minutes under
argon gas protection. In order to assign the real grain size of both materials to the FE model to
consider size effects in micro forming, the microstructure of the blanks was observed using a digital
microscope. The average grain sizes of Al and Cu were determined 25 and 120 µm respectively.
Voronoi model. FE model of MDD with Al-Cu composite blank was created by using ABAQUS,
as shown in Fig. 1. In order to reduce the computing time and improve the calculation efficiency, a
quarter of the blank was considered. All the parameters used in this model were the same as those in
MDD experiments. The mechanical properties of the annealed aluminium and copper are shown in
Table 1.
For the FE model, the blank was built as a deformable part, while the punch, die and blank
holder were regarded as rigid. The continuum shell elements are three-dimensional
stress/displacement elements for modelling structures that are generally slender, with a shell like
response but the continuum element topology. Continuum shell element has geometrical structure in
thickness, and a high accuracy in contact modelling which includes two-sided contact and the same
analysis efficiency compared with conventional shell element can be achieved. Since the sample
was roll-bonded by two materials, the model of blank was divided into two layers for both
materials, as shown in Fig. 2. The two layers were defined being tied together, and there was no
sliding in the interface during the forming process. In this paper, the friction coefficients used were
0.3 for punch-blank contact and 0.05 for both die-blank and holder-blank contacts.
Fig. 1. (a) FE model of MDD and (b) geometry parameters of the model.
Fig. 2. Blank model of Al-Cu composite material.
Table 1. Mechanical properties of Al and Cu in the Al-Cu composite after annealing.
Material Elastic modulus
[GPa]
Poisson’s
ratio
Yield strength
[MPa]
Tensile
strength [MPa]
Cu 79.3 0.33 70.6 211.5
Al 110 0.3 34.9 136.2
(a) (b)
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Because the basic FE model cannot describe the information of size effects, the model with
Voronoi diagram was therefore introduced. Voronoi structures can be employed to characterise
material properties in microscale owing to the similarity between their geometrical features and
material’s micro structures. The Voronoi model was built based on the real grain size of Cu and Al.
Because the grains of both materials become more uniform in annealing process, centroid Voronoi
method in which voronoi cells are in the same shape and size was used. All the Voronoi cells were
classified into five groups, and each group was assigned different material parameters. Fig. 3 shows
the Voronoi model of both layers, and each colour in the model indicates one cell group.
As the cell boundaries of Al and Cu will get crossed on the interface of the two layers, bad mesh
quality and lower computing efficiency will be caused. To solve this problem and ensure the size of
cells keep unchanged, the boundaries of Cu cells were refined to match the boundaries of Al cells.
The refined Voronoi model is shown in Fig. 4.
Fig. 3. The Voronoi model of layer (a) Al and (b) Cu.
Fig. 4. (a) Refined boundaries of Cu grains and (b) refined Voronoi model of Cu.
Surface roughness. Surface roughness has more influence on microforming than macroforming,
due to size effects. Since surface roughness is produced by the uneven thickness of the blank
surface, the values of roughness asperity are related with the thickness of the blank at different
areas. Therefore, the information of surface roughness can be represented by distribution of
thickness. Based on the Voronoi tessellation created, each cell group in the model can be assigned a
distinct thickness, which can represent the surface roughness on grain scale.
Parameters of Ra, Rq, Rsk and Rku are commonly used in the description of surface roughness.
Ra is the arithmetic average asperity height, Rq is the root mean square roughness, Rsk is the
skewness and Rku is the kurtosis. The expression of Ra based on area are shown in Eq. 1 [9]. In
order to simplify the numerical calculation, Eq. 1 can be discretised to Eq. 2. Meanwhile, the
equations of Rq, Rsk and Rku are shown in Eqs. 3-5 respectively [9].
(a) (b)
(a) (b)
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Proceedings of the 20th International Symposium on Advances in Abrasive Technology 3-6 December, Okinawa, Japan
Ra =1
S∮|Z(S)| dS (1)
Ra =∑Si|Zi−
∑SiZi∑Si
|
∑ Si (2)
𝑅𝑞 =√∑𝑆𝑖(𝑍𝑖−
∑𝑆𝑖𝑍𝑖∑𝑆𝑖
)2
∑𝑆𝑖 (3)
𝑅𝑠𝑘 =1
𝑅𝑞3 [
∑𝑆𝑖(𝑍𝑖−∑𝑆𝑖𝑍𝑖∑𝑆𝑖
)3
∑𝑆𝑖] (4)
𝑅𝑘𝑢 =1
𝑅𝑞4 [
∑𝑆𝑖(𝑍𝑖−∑𝑆𝑖𝑍𝑖∑𝑆𝑖
)4
∑𝑆𝑖] (5)
where Z is the asperity height of peaks or valleys, Zi is the asperity average height of an individual
Voronoi cell, S is the area of the forming sample, and Si is the area of one individual cell. The
surface roughness was measured by the KEYENCE VK-X100-3D Laser Scanning Microscope and
the mean values are listed in Table 2.
Table 2 Surface roughness parameters of Al and Cu layers.
Material 𝑹𝒂[µm] 𝑹𝒒[µm] 𝑹𝒔𝒌 𝑹𝒌𝒖 𝑹𝐩[µm] 𝑹𝐯[µm]
Al 0.21 0.27 -0.1235 0.45221 2.04 2.06
Cu 0.20 0.26 0.3537 4.8288 2.81 2.11
Based on Eqs. 2-5, the thickness of each Voronoi cell group can be obtained if the values of Zi are solved. MATLAB was used to solve the values of Zi in this study. The thickness of each cell
group can be calculated with the thickness of Al and Cu, along with each asperity height based on
Eqs. 6 and 7. Then, the thickness distributions of each layer can be obtained as shown in Fig. 5.
𝑇𝑖𝐴𝑙 = 40 + 𝑍𝑖 (6)
𝑇𝑖𝐶𝑢 = 10 + 𝑍𝑖 (7)
Fig. 5. Grain thicknesses of (a) Al and (b) Cu layers.
(a)
(b)
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Springback model. Springback will occur when the forming part is released from the forces of
forming tool in plastic forming. Springback should be considered in the FE model in order to
improve the accuracy of simulation results. After the simulation of MDD, all the rigid bodies and
interaction were removed from the model. Only the drawn cup and constraints on it were employed
for the following simulation. Finally, implicit solver was used for the springback analysis.
MDD experiments
MDD experiments were conducted to verify the simulation results. The experiments were tested
on the Desk-top servo press machine DT-3AW with the annealed Al-Cu samples. The die sets have
the same size as that shown in Fig. 1. The drawing speed of the punch was set as 0.1 mm/s.
Drawing forces and depth were recorded during the drawing process, which were used to further
analyse the relationship between drawing force and stroke. Then 3D laser-scanning microscope was
used to observe the drawn cup and the formability of the drawn cup with Al-Cu composite blank
was analysed.
Results and discussion
In order to investigate the formability of Al-Cu composite blanks in MDD and the influence of
surface roughness on microforming, the non-Voronoi model, the Voronoi model with constant
thickness and the Voronoi model considering surface roughness (defined as SR-Voronoi model)
were established, and the simulation results were compared with the experimental results.
Fig. 6 shows the drawing forces obtained from FE models and experiments. Five experiments
were repeated under the same processing condition, and the average drawing forces were obtained.
It can be seen that all curves from simulations and experiments have the similar trend, although
there is a little difference of the strokes when the force reaches the maximum value. For the three
FE models, the curves have the same trend initially and then achieve the maximum force at the
stroke of 0.62 mm. It can be explained that although different cell groups have different material
properties, the overall effects of different cell properties on drawing force are balanced resulting in
a close trend to that in non-Voronoi model. Also, as the flow stress in some cells is higher than the
mean values, the maximum forces will become greater than that in non-Voronoi model. Because
different thicknesses in different areas of the blank may result in an increase of friction, the peak
force of SR-Voronoi model is higher as compared with the Voronoi model and closer to the
experimental results.
Fig. 6. Drawing forces from experiments
and simulation results.
Fig. 7. Outlines of the drawn cup from
simulation results.
The shape and geometry of the drawn cup are important factors to evaluate the formability
of the drawn cups. The outlines of the drawn cups were chosen to compare. The coordinates
of the nodes on the outlines were extracted from the simulation results, as shown in Fig. 7. It
can be seen that the outlines of the basic model and the Voronoi model are almost coincided
while the radius of the SR-Voronoi model is greater as compared with the other two models.
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Proceedings of the 20th International Symposium on Advances in Abrasive Technology 3-6 December, Okinawa, Japan
Lager mouth radius indicates springback occurs more significantly. Some thin sections in the
deformation area undertaken the same stress has more stain. Therefore, the strain energy was
higher for the SR-Voronoi among all the simulation models. Also, the different material layer
and properties on the blank intensify the unevenness of strain distribution on the blank. After
springback, the residual stress and strain in the blank are released and then, the SR-Voronoi
model exhibits more springback than that with the other two models.
In order to verify the simulation results, the side-wall angle of the drawn cup in
experiments was measured and compared with those from FE simulation results. The angle of
drawn cup in experiments is about 59.52º which is much closer to 61.09º from the SR-
Voronoi model, while the angels are 64.56º from the other two models.
To analyse the change of surface roughness, the value of Ra was extracted from both
experimental and simulation results. The side wall area was chosen for analysis, and then the
surface roughness was measured from actual drawn cup and calculated from simulation
results, as shown in Table 3.
Table 3 Comparison of surface roughness Ra from experimental and simulation results.
Results 𝑹𝒂
Blank Side wall of drawn cup
Experiment 0.21 µm 0.97 µm
Non-Voronoi model 0 µm 0.02 µm
Voronoi model 0 µm 0.06 µm
SR-Voronoi model 0.21 µm 0.43 µm
Because the original blank in Non-Voronoi model and Voronoi model without considering
surface roughness is flat, both values of Raare 0 µm. It can be seen that the surface roughness
of experimental and simulation results has been increased after deep drawing. Due to each
cell in the measured area undertaken different stresses, which caused different deformation,
and also Al and Cu have different relationships of strain and stress, as a result, the surface
roughness therefore increased. By comparison, the results of Voronoi model considering the
surface roughness is closer to the experimental one.
Conclusions
1. A new FE model which considers grain heterogeneity and surface roughness was
developed, and was applied to simulate the MDD process with Al-Cu composite blank.
Then the drawability and the influences of surfaces roughness on microforming were
investigated.
2. Compared with the basic model, the accuracy of Voronoi models which include grain
properties has been improved. The results of Voronoi models are close to the
experimental ones in terms of drawing force.
3. When the information of surface roughness and springback is embedded to the Voronoi
model, the calculated drawn cup shows the best shape accuracy compared with the
experiment results among all the FE models.
4. Surface roughness of the drawn cup increased from both experiment and simulation
results, and still the result from SR-Voronoi model is closer to the actual drown cup.
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Acknowledgements
The research is supported by the CSC scholarship (201508110196) from China
Scholarships Council and the International Postgraduate Tuition Award (IPTA) from
University of Wollongong.
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Proceedings of the 20th International Symposium on Advances in Abrasive Technology 3-6 December, Okinawa, Japan