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 afj910@uowmail.edu.au, bjwzhaocn@gmail.com, cjiang@uow.edu.au

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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