The main reason for using lubricants in metal forming processes is to reduce
the interfacial friction between the tool and workpiece. The reduction of interface
friction provides many benefits to the fabrication process and end product.
For example, the process-forming load can be lowered, tool life can be extended,
and final product defects can be minimised. In current manufacturing processes
involving metal forming, it is necessary to use lubricants that avoid or reduce
environmental pollution. Dry and low viscosity lubricants have been used in
metal working processes, which contain reactive or non-reactive chemical additives
that contribute to environmental pollution. Accordingly, some studies have been
conducted to investigate the use of ultrasonic vibration as a non-chemical lubrication
medium (Murakawa and Jin, 2001).
Since Blaha and Langenecker (1955) reported that the
yield strength reduction was due to superimposed ultrasonic vibration in tensile
testing of zinc crystals, many other similar studies have been carried out.
Several theories have been developed to explain the observed phenomena, including
energy absorption due to moving dislocations, superposition effects of oscillating
stress, reduction in internal friction, material properties, dynamic effects
of vibrated tools (Astashev, 1983) and reduction of
interface friction (Perotti, 1978; Huang
et al., 2002).
A large number of investigations have observed that vibratory energy can reduce
frictional forces. One publication (Winsper et al.,
1970) postulated five possible mechanisms that could improve the frictional
condition under the influence of a vibratory load: (1) separation of surfaces
and cyclic re-establishment of the lubricant film on the contacting surface.
(2) Friction force vector reversal due to movement of the tool. (3) Heating
of asperities possibly reducing the shear strength. (4) Pumping of lubricants
to provide better lubrication conditions, and (5) Cleaning effect which permits
efficient bonding of the lubricant to the metals being deformed.
The effects of ultrasonic vibration on friction during upsetting tests have
been studied (Perotti, 1978) and it has been suggested
that under an applied longitudinal ultrasonic load there is a reduction in interface
friction. This effect has also been observed for applied radial mode ultrasonic
vibrations. A recent study (Huang et al., 2003)
of longitudinal and radial ultrasonic upsetting of plasticine reported that
ultrasonic vibration significantly reduced the interface friction and the upsetting
force due to a thermal reduction in the coefficient of friction.
This study aims to investigate the numerical stress-strain relationship when
radial oscillatory stress is superimposed on a static stress during ultrasonic
compression tests of aluminium specimens under different coefficient of friction,
μ. A series of Finite Element (FE) models were developed to investigate
the effects of changes in friction and material properties in the simulations
of ultrasonic compression tests, by comparing the stress-strain relationships
derived from the previous experimental study (Daud and Lucas,
FINITE ELEMENT SIMULATION
Aluminium was used as the metal model. The material properties of aluminium,
derived from the previous static tension test (Daud, 2006),
were, Young modulus 69 GPa, yield stress 60 MPa and Poissons ratio 0.33.
Classical metal plasticity was used to define the plastic strain by using the
following equation (ABAQUS, 2002),
where, εp1 is true plastic strain, εt is true
total strain, εe1 is true elastic strain, σ is true stress,
and E is Youngs Modulus. The material is initially isotropic, homogeneous
and incompressible such that the volume of each element of the model remains
constant. The behaviour of aluminium is treated as elastic-plastic with low
strain hardening. The material was deformed under steady-state conditions at
room temperature and no temperature effects were induced.
The compression simulation was carried out using a commercial finite element code, ABAQUS, with implicit solution. Half of the specimen was meshed using 2D axis-symmetric 4-node elements. The upper and lower platens were assumed to be rigid bodies, modelled as an analytically rigid surface. Figure 1 shows the problem description of static and ultrasonic compression. To allow for manageable computational time, whilst ensuring that the effects of ultrasonic oscillation could be evaluated, the ultrasonic excitation was applied for very short time intervals in the FE models.
Static and radial ultrasonic (RU) compression simulations: The static-ultrasonic
compression simulations were performed using the following procedure.
||Problem description of the static and ultrasonic compression
Initially, the specimen was deformed under static loading by applying a constant
velocity of 5 mm min-1 to the upper platen. By controlling the total
time step, at post-yield or 22 % reduction of the specimen height, ultrasonic
excitation was superimposed on the lower platen during plastic deformation at
a frequency of 20 kHz and radial vibration amplitude, A0 of 4μm.
To allow for manageable computational time, the ultrasonic excitation was applied
for 0.8 secs in the FE models. Subsequently the model returned to its static
loading condition before the simulation was stopped when the specimen was compressed
to approximately 50 % of its original height. Figure 2 shows
the original and deformed meshes of the compression model.
For the second series of FE models, the effect of a change in the numerical
value of the coefficient of friction during the interval of ultrasonic excitation
was investigated. In this case, during static compression the coefficient of
friction was set at 0.25 and, during ultrasonic excitation, the coefficient
of friction was changed. Two different values were used; μ = 0 for frictionless
and μ= 0.15. A friction value of 0.15 was chosen because it is consistent
with reductions reported in previous studies. Maximum reductions in the coefficient
of friction of 35 % and 40 % have typically been reported previously and the
reduction to a value of 0.15 represents a 40 % reduction in coefficient of friction
which was reported in a study of ultrasonic strip drawing (Rozner,
||(a) Original and (b) deformed mesh profiles of a cylindrical
DISCUSSION OF FE MODEL RESULTS
In some previous investigations, radial ultrasonic excitation has been applied
in the study of a wire drawing process. In most cases, the application of ultrasonic
excitation onto the drawing die, giving a tangential oscillation relative to
the specimen motion, reduced the drawing force and it was suggested that this
reduction was caused by a reduction in interface friction (Susan
and Bujoreanu, 1999). Since the oscillatory stress was not measured, there
were conflicting interpretations of the measured data and of the possible factors
that could reduce the mean stress. It was not known whether a change in friction
or stress superposition effects or both caused the reduction in mean stress.
The numerical effects on stress-strain behaviour were examined when a constant
dry interface friction coefficient, μ = 0.25, was applied during static
and ultrasonic excitation intervals.
||FE model showing an interval of RU excitation for a constant
coefficient of friction μ = 0.25, inset shows zoomed view of oscillatory
||Measured static and RU compression test for dry surface showing:____
static and stress, ---- path of max. And min. oscillatory stress (Daud
and Lucas, 2007)
Figure 3 shows the calculated stress-strain curve for static
and radial ultrasonic (RU) intervals for μ = 0.25. At the onset of RU excitation,
the mean oscillatory stress reduced by approximately 4 MPa from the static stress.
However the measured stress reduction of the ultrasonic interval in the previous
work (Daud and Lucas, 2007) as shown in Fig.
4 seems to be higher at 9 MPa. Also, at a strain of 0.2188, the peak-peak
oscillatory stress amplitude is 3 MPa which agrees quite well with the 4 MPa
peak-peak stress amplitude measured as reported in the previous experiments
(Daud and Lucas, 2007). It can be observed in the FE
data in Fig. 3, RU simulations contribute to a drop in the
maximum oscillatory stress from the static stress for a constant coefficient
of friction for static and RU compressions and this does not fit with the classic
oscillatory stress superposition definition as described by (Kirchner
et al., 1985).
||FE model showing an interval of RU excitation for zero friction,
μ = 0, inset shows zoomed in view of oscillatory stress amplitude
||Combining Fig. 3 and 5
for RU excitation, showing ____ for μ = 0.25, ----- for μ = 0,
left shows zoomed in view of oscillatory stress amplitude (which is too
small to be visible for μ = 0)
For radial mode ultrasonic excitation, the friction force and excitation force are co-axial and the ultrasonic excitation force modifies the friction force vector cyclically. It is therefore expected that the friction force is modified even though the coefficient of friction is constant and that this accounts for the drop in maximum oscillatory stress from the static stress in RU compression simulations under a constant interface friction coefficient.
The investigation using the FE model was continued by changing the interface
friction coefficient from dry to a friction free condition, μ = 0. Figure
5 shows a compression test simulation with μ = 0 throughout, and with
an interval of ultrasonic excitation (which cannot be seen in the main figure
but it is visible in the zoomed inset). During the interval of RU excitation
there is no measurable change in the mean stress and no significant peak-peak
stress amplitude was calculated. Figure 6, compares the two
previous figures, illustrating how the oscillatory stress amplitude for μ=
0 is extremely small and therefore not visible in the figure.
||FE model showing static RU compression; coefficient
of friction, μ = 0.25 during static compression and change to friction
free, μ = 0 during RU compression, left expanded scale of ultrasonic
||FE model showing static RU compression for coefficient
of friction, μ = 0.25 during static compression and μ = 0.15 during
RU compression, left expanded scale of ultrasonic stress interval
Figure 6 also shows that the difference between the static
stress and mean oscillatory stress at a strain of 0.219 for μ = 0.0 is
6 MPa, which is less than the measured mean reduction of 9 MPa (Daud
and Lucas, 2007) when RU was superimposed on the static load during compression.
The above models do not satisfactorily represent the experimental results of
the mean flow stress reduction under applied RU excitation during compression
tests. The FE model was therefore developed by adjusting the coefficient of
friction from a value, which represents a dry surface to a friction free surface
during RU excitation. Figure 7 illustrates the numerical effects
on the stress-strain relationship. By changing the numerical friction coefficient
from μ = 0.25 for a dry surface to a frictionless surface, μ= 0, during
applied RU excitation, the mean oscillatory stress is now significantly reduced
from the static stress.
||Measured static and RU compression test for lubricated surface
showing: ____ static and mean stress, ----- path of max. and min. oscillatory
For applying ultrasonic excitation at a strain of 0.219, 15 MPa reduces the
mean stress from the static stress but there is no measurable peak-peak oscillatory
stress amplitude. For a friction free contact there is no resistance to sliding
and no friction force, and the force in the radial direction at the contact
surface is only due to the ultrasonic excitation force. The calculated oscillatory
force response is therefore of very low amplitude, leading to a low oscillatory
stress amplitude in the calculated stress-strain relationship.
There are dissimilarities between the FE model data and the experimental results.
Firstly, the measured reduction in the mean stress from static to RU excitation
is 9 MPa (Daud and Lucas, 2007), for all surface conditions,
however the FE model predicted 15 MPa. The peak-peak stress amplitude from the
RU compression experiments was consistently 4 MPa (Daud
and Lucas, 2007), for all surface conditions, whereas the FE model predicts
a peak-peak oscillatory stress amplitude of only 0.01 MPa.
Another FE model was developed, where the coefficient of friction was maintained
at μ= 0.25 during static compression, and was changed to μ = 0.15
during the ultrasonic compression interval. From the calculated stress-strain
relationship, as illustrated in Fig. 8, a close agreement
is now achieved with the previous measured stress-strain data under dry and
lubricated surface conditions (Daud, and Lucas, 2007)
as shown in Fig. 4 and Fig. 9 respectively.
The reduction in mean stress, which was measured from the experiments, is identical
to the reduction, which is predicted by the FE model. At a strain of approximately
0.229 MPa reduces the mean stress from the static stress. The measured peak-peak
stress amplitude at the same strain value is 4 Mpa from experimental results
and predicted at 3 Mpa from simulation data. This result agrees with previous
studies (Blaha and Langenecke, 1955; Daud,
2006) which claim that the interface friction can be reduced if the specimen
is subjected to a radial ultrasonic excitation during a static deformation process.
From the present investigation, however, it can be concluded that during RU
compression, the interface friction coefficient is reduced to the same value
under dry and lubricated surfaces and the use of lubricants does not further
improve the interface friction under RU compression.
A numerical investigation into RU compression was carried out under different interface friction. The numerical data has been compared with the data of the previous similar experimental works. The experimental data solely unable to differentiate the stress reduction during RU compression was due to reduction of interface friction or due to change in material properties. The FE data in this study suggested that the application of RU during compression test has significantly reduced the interface friction. However there has no reduction in material properties predicted. The FE data also suggested that the application of lubricant during RU compression test has not significantly further reduced the interface friction if compared to the same test carried out without using lubricant.