Analyzing the Tribological Phenomena in Hot Extrusion Processes by

using New Torsion-Tribo Test

Pavel Hora

1, Maysam Gorji

1, Joachim Maier

2

1ETH Zurich, Institute of Virtual Manufacturing, Zurich, Switzerland

2WEFA Singen GmbH, Singen, Germany

ABSTRACT:

During the extrusion processes very complex adhesion and friction effects between the die

surface and the extruded material occur. They have a strong influence on the velocity distribution

in the profile as well as on the life term behavior of the tools.

In the framework of this study, a recently developed experiment which is called, “Torsion-Tribo

testing” will be presented. The test allows the investigation of low and high pressure load cases.

The experimental layout of the test tools and specimen, the evaluation method will also be

presented.

The experimental data enable the investigation of the friction due to contact pressure, rotational

velocity and temperature. Those data are used to determine the parameters of an advanced friction

model.

1. A NEW EXPERIMENTAL MODEL

One of the oldest problems in physics and certainly one of the most important influences from practical

point of view is friction. Extrusion processes are very sensitive to frictional effects. If they cannot be

controlled, the process cannot be controlled either. Frictional forces have to be reasonably evaluated in the

simulation of forming processes.

Highly sensitive frictional effects in extrusion processes were analyzed by the multi-hole die extrusion

experiments of the IVP benchmark [1, 2, 3]. It is possible to develop tools which allow a significant

influence of parameters such as position of holes, cross-section area and length of bearings. The type of

tools designed for this purpose and extruded material is shown in Figure 1.

cross-section area Cross-section position Friction Length

Figure1: Multi-Hole Extrusion with considering the influence of geometry. Benchmark Extrusion Zurich

2005. Cooperators: SPZ-TU_Berlin & WEFA test Die 1.15 [1, 2, 3]

In the past decades, different experimental methods were presented to investigate the friction

phenomena by considering various testing conditions. Pin-on-disc, block-on-cylinder and rotating-disc

measurements are some of the important experimental setups discussed in literatures [4, 5, 6, 7].

The disadvantage of these tests is their completely different contact compared to the real case. In

extrusion processes the contact surface between the billet and the tooling is not small. Therefore none of

the mentioned experimental setups are representative of the frictional phenomena in aluminum extrusion.

Also, in the extrusion process, the most important parameters which influence the frictional properties of

the bodies in contact are temperature, pressure and the relative velocity. For these reasons, the methods

allow only a qualitative prediction of the real behavior.

To investigate the friction behavior in extrusion processes, a new friction test setup has been

developed, which enables the investigation of the influence of the mentioned quantities on the frictional

behavior of the material. As shown in Figure 2(left), the setup uses a torsion machine as the testing facility,

and this enables performing of experiments at different temperatures, angular velocities and axial forces.

Figure 2: [Left] Torsion testing machine, [Right] Schematic view of experimental setup. Also, tools and the

specimen for cylindrical test

The specimen placed between two tools was heated up by inductive heating to the test temperature, for

example T = 400 °C within 60s, and afterward the temperature was kept constant for 120s. The temperature

of the specimen is controlled using a thermocouple which is spot welded on the surface of the Tool1

(Figure2 (right)).

This assembly is axially and rotationally loaded on the torsion testing machine at specific temperatures,

so the specimen undergoes a plastic deformation under thermal-mechanical conditions. The required torque

is then measured during the whole test by the torsion machine.

Depending on the chosen specimen geometry, low pressure as well as the high pressure can be

investigated with this method. In the first case the specimen has a shape of a conical tube, whereas in the

second case the specimen shows a hollow cylindrical shape (Figure 3).

Figure 3: [Left] Conical tube specimen for low pressure configuration, [Right] Hollow cylindrical specimen

for high pressure configuration

Due to the volume constraints in the high-pressure configuration, the cylindrical geometry allows a

significant increase of the hydrostatic pressure. This is the major advantage of the cylindrical specimen

with respect to pressure sensitivity.

The Low Pressure configuration test has already been presented in [8,9]. The reader is referred to them

for detailed discussions concerning the conical specimens. Tools with different coatings and the schematic

experimental layout for this setup are depicted in Figure 4.

Figure 4: [Left] Tools and the specimens for Low Pressure Configuration for different coatings, [Right]

Schematic view of conical test experimental setups

2. EXPERIMENTAL RESULTS

This section summarizes the results of the experimental investigations of the high-pressure case using

the cylindrical specimens. Figure 5 shows the deformed ring after the test. The difficulty in the evaluation

of this configuration is the correct detection of the zones where the slip occurs. Based on finite element

modeling and experimental observation, most of friction occurs at inner surface as well as on the surface

between the rotating tool and cylindrical specimen.

Figure 5: Deformed hollow aluminum alloy (Al6110A) cylindrical specimen after the experiment

Figure 6 (left) shows the measured moment for different angular velocities at a constant temperature T

= 450°C and a constant axial force F = 1200N. Torsion values increased with higher velocities, whereas by

increasing the temperature, torsion decreased; see Figure 6 (right). The average value of measured torsion

is used for the computation of evaluation of equation (6).

Figure 6: [Left] Torsion values at different angular velocities, constant temperature T = 450°C and an axial

force F = 1200N, [Right] Relation between stable torsion and relative velocity at different temperatures by

considering a constant normal load 1200N.

0.125 0.25 1.25 2.5

The relationship between torsion and velocity at a specific axial force and temperature is shown in

Figure 7 (left). Figure 7 (right) depicts the influence of axial loading on torsion at a constant temperature

for different rotational velocities. Torsion increases when the axial force or velocity increases.

Figure 7: [Left] Torsion values at constant temperature T = 400°C and an axial force F = 1800N, [Right]

Relation between torsion and angular velocity at different axial forces by considering a constant

temperature T = 400°C.

3. FRICTION MODELS

As mentioned before, from the physical point of view friction is a very complex phenomenon. Various

models have been developed to describe friction and evaluate frictional forces. In bulk metal forming the

critical shear stress, when the material plastically flows, is a limiting value for the maximal friction stress.

This is the typical case in the extrusion contact.

The pressure applied on the surface of the workpiece can be much higher than the yield stress.

Frictional stress cannot exceed the shear flow stress or the shear failure stress of the material. Coulomb’s

law may overestimate the friction forces although the frictional coefficient may seem to be reasonable. As

it is shown in Figure 8, Coulomb’s law is then no longer suitable under these circumstances where the

normal stress becomes large.

Figure 8: Deviation of the Coulomb model from the real observed case [10]

It is clear that the friction stress on the surface of the workpiece is one component of the stress tensor

which determines the local yield state. If the von-Mises flow rule is used, the yield condition is:

( )

( )

( )

(Equation 1)

where denotes the yield stress.

Assuming that the shear stress is the friction force per unit area in the x-direction, then in the

extreme case when all other stress components are zero, i.e. we obtain:

0.125 0.25 1.25

√ (Equation 2)

If other components are not zero, the friction stress must be smaller. A friction coefficient m is often

employed to describe the friction stress as:

√ (Equation 3)

The factor m may vary between “0” and “1” according to different stress states [11]. This model assumes a

constant interfacial shear stress unlike Coulomb friction. When m = 1, the model assumes sticking friction.

For those reasons it is physically more reasonable to replace the Coulomb friction model by the so

called shear friction model. The weakness of this model is the fact, that if the profile will not be deformed

any more, then the strain rate dependent yield stress drops to zero (see Figure 9). To avoid this case Hora

and Karadogan [3, 8] have proposed a modified version with a minimal friction for zero strain rates:

√ (Equation 4)

Figure 9: frictional behavior during hot aluminum extrusion between billet and tooling

In addition, the material behavior was described with a modified Zehner-Hollomon equation as

proposed by Tong [12]:

(Equation 5)

where A, Q, m, β, N and n are material constants. is the true stress [MPa], R is the ideal gas constant and

equal to 8.314 [J/mol K], T is the absolute temperature [°K], φ and are strain and strain rate, respectively.

Aluminum alloy EN AW-6110A is the tested material which is used as an extruded material. The Chemical

composition of EN AW-6110A is given in table 1. Material constants based on equation 5 have been shown

in table 2. Also, the flow curve of this kind of material at different temperatures is shown in Figure 10.

Table1: Chemical composition of EN AW-6110A according to [13]

Cu Mn Mg Cr Zn

0.7-1.1 0.50 0.30-0.8 0.30-0.9 0.7-1.1 0.05-0.25 0.2

Table2: Zehner-Hollomon parameters for Al6110A

A Q m β N

0.9653 2.6e+04 1 0.1733 14.236

Figure 10: Flow curve of EN AW-6110A at different temperatures and constant strain rate

3.1 Evaluation Methods

The difficulty in the evaluation of the High Pressure-Torsion Compression Test (HP-TCT) is the

detection of the zones where the slip occurs.

Depending on the inner or outer radius (see Figure 11), the moment in inner and outer surface can be

calculated by equation where is shear stress at a specific temperature. A and R show contact

cross area and radius, respectively. By evaluating this equation and considering , yields

. This shows that the inner contact interface tends to slip earlier. Based on the finite element

simulation, we can say that most of the friction occurs in the front and inner surfaces between the rotating

tool and the specimen. So, the total moment is calculated by using equation (6):

(Equation 6)

where:

(Equation 7)

is the moment of the inner surface and is the moment of the front surface between specimen and

the rotating tool. is a contribution of outer and back contact surfaces which can be found by comparing

the torsion results of finite element modeling and experimental values.

Figure 11: Dimension and defined surfaces of the cylindrical specimen

Investigation of friction phenomena (i.e., slip and stick, wear, etc.) is a difficult task. Therefore, finding

a proper friction model for the numerical simulation of processes is also difficult.

It is noteworthy that we do not intend to involve all the factors to describe friction, neither it is possible

for users from industry to determine many parameters by complicated experiments. We seek a simple but

effective description to calculate the frictional forces.

Based on the experimental data, a simplified equation for the computation of the friction coefficient is

proposed in equation (8). This model relates the friction coefficient m to pressure and relative velocity:

{ [ (

)

]} (

)

(Equation 8)

where is a preliminary friction. A, B, q, n and k are constants value. These values at a constant

temperature of 400°C are shown in Table 3. P and are pressure and relative velocity, respectively.

and are references values. This leads to a more general description of the experimental and numerical

results.

Table3: parameters of Equation 8 at temperature 400°C

[MPa] [mm/s] A B q n k

0. 1583 250 8 0. 9258 0.0383 18.5631 1.9518 0.3259

Figure 12 shows the friction coefficient at different relative velocities and pressures. The friction

coefficient increases by increasing the relative velocity or pressure. This investigation shows that by

increasing the velocity the friction coefficient tends to approximate a saturation value.

Figure 12: Friction coefficient as a function of relative velocity and pressure at the constant temperature

400°C

Figure 13 shows the fitting surface, based on the aforementioned equation, which is used to compute

the torsion and friction coefficient at constant temperature T = 400°C. The applicability of the model will

be checked by comparison of the real behavior of four holes extrusion test with numerical results. This is

ongoing and will present in future work.

Figure 13: computed values using equations 8 for the constant temperature T = 400°C

4. SIMULATION OF HP-TCT

Simulating of High Pressure, Torsion Compression Test has been done by LS_DYNA. LS-DYNA is

designed for transient dynamic analysis of highly nonlinear problems. The essential ingredient determining

the solution properties is the use of an explicit time integration scheme.

Figure 14 depicts temperature distribution through the experiment at three different time steps.

Fortunately finite element simulation shows that there is a homogeneous temperature distribution after 180

seconds heating up and before applying mechanical loading.

Figure 14: temperature distribution of hollow cylindrical specimen during heating up of specimen

Also the effective plastic strain of specimen after the test (compression and torsion) in inner and outer

surface of the specimen has been shown in Figure 15.

Figure 15: Plastic Strain in inner and outer surface of hollow cylindrical specimen

5. CONCLUSIONS

In comparison with conventional friction test setups, the presented experiments represent more

conditions similar to hot extrusion operations. The presented experimental setup enables the investigation

of the friction due to contact pressure, rotational velocity and temperature. The experimental data are used

to determine the parameters of the introduced numerical model, which relates the friction coefficient with

the angular velocity and axial force for a constant temperature. The presented experimental and numerical

results show the applicability of this new test and they encourage further developments of the models.

Introducing models based on physical phenomena still remains a challenge. Incorporating the temperature

dependence of the friction coefficient and determination of the model parameters based on an inverse

optimization procedure is the subject of the current research.

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