Int. Journal of Applied Sciences and Engineering Research, Vol. 2, Issue 4, 2013
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Research article
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ISSN 2277 – 9442
Barreling of solid composite (Lm6/Sicp) cylinders under uni
axial compressive load
1
Joardar H, 1Das N.S, 2Sutradhar G, 3Singh.S
Department of Mechanical Engineering, C.V Raman College of Engineering, Bhubaneswar, Orissa, India
2
Department of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal, India
3
Department of Mechanical Engineering, KIIT University, Bhubaneswar, Orissa, India
DOI: 10.6088/ijaser.020400006
1
Abstract: Axisymmetric compression tests on solid composite (LM6/SiCp) cylinders under various
lubrication conditions and aspect ratio (height/diameter), suggest that the resulting curvatures of the barrels
formed fit closely to circular arcs, the radii of which follow a power law with respect to the true axial
compressive stress. The true compressive stress-strain curve obtained from the experimental data shows
that of all the lubricants tested the specific forming energy is minimum for a teflon sheet type lubricant.
Key words: LM6/SiCp Composite, barreling, cold upsetting.
1. Introduction
In recent years there has been an increasing recognition of the advantages of using metal matrix composites
for manufacture of engineering components using forming methods (Lindroos and Talvite 1995). This is
because these materials blend superior mechanical properties (high stiffness and strength, good ductility,
toughness and wear resistance) with improved thermal characteristics and can be fabricated at competitive
cost with relative ease (Trojanová et al 2004). The properties of metal matrix composites are influenced by
a number of factors such as the type of reinforcing agent, its particle size, weight or volume fraction,
processing conditions and secondary forming, heat treatment operations to which these are subjected prior
to their use (Christophe et al 1996). Especially, shaping of composites by cold forging has now become
very attractive because of its high production rate and also because it refines the grain structure of the
deforming billet thereby enhancing its mechanical properties. Hence, there is a critical need for
understanding the basic concepts and deformation mechanics of composite forging so that the use may be
made of the potential of the process (Nair et al 1985; Hashim et al 1999). Many investigators due to its
relevance in metal forming applications have carried out a series of investigations on cold upset forging of
solid cylinders. Another significant aspect of axisymmetric compression from the standpoint of testing the
mechanical manufacturing properties of metals is the estimation of their forming limits up to plastic
instability and fracture (Shaw and Avery 1980). In upsetting the existence of frictional constraints between
the dies and the work piece directly affect the plastic deformation of the later. When a solid cylinder is
compressed axially between the punch and a bottom platen, the work piece material in contact with the
surfaces undergoes heterogeneous deformation that results in ‘‘barrelling’’ of the cylinder. Friction at the
faces of contact retards the plastic flow of metal on the surface and in its vicinity. A conical wedge of a
relatively undeformed metal is formed immediately below it while the rest of the cylinder surface
experiences high strains and bulges out in the form of a barrel. This demonstrates that the metal most easily
moves towards the nearest free surface which is the point of least resistance, which is a well known
principle in plastic deformation. However, the use of lubricants reduces the degree of bulging and under the
condition of ideal lubrication, bulging can be reduced to zero. Also, friction could not be eliminated during
upset forging and it is necessary to use a correction factor for bulging during the die design. Kulkarni and
Kalpakjian (1969) examined the arc of barrelling, assuming it to be circular or parabolic, whereas Schey et
al. (1982) presented a comprehensive report on the geometrical factors that affect the shape of the barrel.
Yang et al. (1991) developed an upper bound solution for determination of the forging load and the
deformed bulge profile during upset forging of cylindrical billets considering the dissimilar frictional
conditions at flat die surfaces. Chen and Chen (2000) developed a theoretical solution for the prediction of
flow stresses during the upsetting operation considering the barrelling effect.
Earlier investigations have made no experimental attempt to relate the dimensional output of the cylinder-
—————————————
*Corresponding author (e-mail: hillol_joardar@yahoo.com)
Received on June 2013; Accepted on July 2013; Published on August 2013
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
platen system, such as barrel radius, barrel diameter etc., considering the different frictional conditions at
the work piece as the composite materials and platens interface. The purpose of the present study is to find,
experimentally, shape of the barrel of a metal matrix composite prepared from an aluminium alloy (LM6)
reinforced by silicon carbide particulates is studied using the upset test, cylinders of a different aspect ratio
(H/D) are subjected to axisymmetric compression on a Universal Testing Machine under both dry and
lubricated conditions and the deformation geometry is studied under various friction conditions. The
parameters of friction are measured by the ring compression test. Once the shape of the barrel is known, an
expression for the barrel radius can be formulated, expressed as a power function of the compressive stress.
The barrel radius is considered useful for the practical evaluation of the power requirement during the
forming process. Using an extrapolation technique (Banerjee 1985; Cook and Larke 1945), true stress-true
strain curves has been plotted for different lubrication conditions under different aspect ratios.
2 Experimental studies
2.1 Fabrication of MMCs
The discontinuous MMCs used in this study were prepared following the stir casting route. The matrix
closely confirmed to the LM6 aluminium alloy and the reinforcement was silicon carbide (SiC) particulates.
The composition of LM6 is tabulated in Table 1.
Table 1: Chemical Composition (LM6)
Elements
Si
Cu
Mg
Fe
Mn
Ni
Zn
Pb
Sb
Ti
Percentage
(%)
1013
0.1
0.1
0.6
0.5
0.1
0.1
0.1
0.05
0.2
Al
Remaining
To prepare the specimens the aluminum alloy was melted in an electric resistance furnace having a clay
graphite crucible. The melt was mechanically stirred by an impeller after addition of 5 wt% of pre-heated
silicon carbide particles (pre heat temperature=9000C average particle size =37μm). The processing of the
composite was carried out at a temperature of 7500C with a stirring speed of 500 rpm. Cylindrical
specimens of 20 mm diameter and different heights corresponding to set of aspect ratios (height/diameter =
0.5, 1.0, 1.5) were prepared from the composite bar. Specimens were annealed for 2h at 3000C and allowed
to cool in furnace.
2.2 Ring compression test
To carry out the ring compression test, the standard ring specimen ratio of 6:3:2 was used. Ring
compression tests were made with rings using the dry condition and same lubricants as those used in the
solid cylinder compression tests. In metal forming interface friction plays an important role. It controls the
magnitude of the redundant work, the magnitude of the metal forming load and the stress and strain
distribution in the deforming medium. The interface friction may be quantified either by a friction factor m
(   mk , k = shear stress of work material) or a coefficient of friction

(Coulomb’s law, 
  p ). In
the present study the friction shear factor ( m ) values were determined by the ring compression test
(experimentally) as shown in Figure1. Figure 2 (a) shows the calibration curves for determination of
friction shear factor (m) and the geometry of rings after compression is presented in Figure 2 (b).
2.2 Compression test of cylinders
In these tests, two cases were conducted: dry and lubricated compression. Four types of lubricants were
used: graphite, white grease, teflon and MoS2. In all cases lubrication was applied on the top and bottom
faces of the cylinders and dies by hand. In the case of teflon, thin single sheets of 50.8 × 10-6 m thickness
were used. Lubrication was reapplied whenever the specimen was removed to be measured and the
specimens were carefully cleaned with acetone so as to provide a similar friction condition before
deformation. One type of material was used: LM6 aluminium alloy with 5 weight percentage of silicon
carbide particles. The experiments were carried out on a 150 metric ton capacity hydraulic press with 2.1
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Int. Journal of Applied Sciences and Engineering Research, Vol. 2, Issue 4, 2013
Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
mm/s ram speed. The upper and lower dies of the press were made of hot worked steel and hardened in
53HRc and their surfaces were ground. Extreme care was taken to place the axis of the cylindrical specimen
concentric with the axis of the ram. For each test, five specimens (of the same dimensions) were taken and
deformed to different lubrication and dry condition.
Figure 1: Friction factor obtained for different lubricants
Other gross dimensions, such as the maximum diameter and the instantaneous height after each test, were
measured with a ball point micrometer. Because of the intersection of the solid surfaces, the diameter of the
contact face was difficult to measure accurately with the micrometer; it was therefore, calculated from an
expression derived on the basis of constant volume deformation (see Appendix). The deformation load was
recorded directly during the deformation of each sample. The true stress-strain curves in uniaxial
compression were obtained by an extrapolation technique of the incremental loads and the corresponding
height reductions for the cylinders of different aspect ratios. Firstly, the loads and the percentage reduction
of heights were noted for a set of 5 specimens of different aspect ratios: height/diameter = 0.5, 0.75 and
1.00. Now, assuming volume constancy during deformation and barreling, stresses were calculated in each
2
2
case, using a simple expression:   8F  (3H o Do / H  D2 ) (see Appendix), where σ the
compressive stress, F the load, Ho and Do the initial height and the initial diameter, respectively of the
cylinder; D2 and H were the maximum diameter and instantaneous height of the specimen respectively.
Figure 2: (a) The calibration curves in term of m; (b) Ring compression specimen after compression.
3. Results and discussion
The radius of curvature for each arc was calculated theoretically. Thus, knowing the radius of curvature R
of the barrel, the initial height Ho and the initial diameter Do of the cylinder, as well as the instantaneous
height of the barrel at each load increment, the other important geometrical parameters of the barrel, such
as, the maximum barrel diameter D2 (measured value) and the diameter at the contact surface D1 in each
load increment, was formulated (see Appendix) as follows
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437
Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
3H 0 D02
 2D22
H
2
( H  ( D2  D1 ) 2 )
R
(4( D2  D1 ))
D1 
(a) Original cylinder
…. (1)
…. (2)
(b) Instantaneous barrel
Figure 3: Work piece configurations before and after the deformation
(a)
(b)
(c)
Figure 4: The barrel radii after each stage of loading at different lubricating conditions (Aspect
ratio 0.5, 0.75 and 1.00)
It is seen in figure 4 that the difference between the curvatures, for different lubricant and different aspect
ratios, is less significant when the axial stress is high; this is because, under the high pressure more metalJoardar H et al.,
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Int. Journal of Applied Sciences and Engineering Research, Vol. 2, Issue 4, 2013
Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
to-metal contact between the cylinder and the platens occurs, thereby increasing the surface friction and
thus reducing the influence of the different lubricants employed and same result for different aspect ratios.
Figure 5: The barrel radii after each stage of loading at different aspect ratio (Dry and MoS2
Lubricating condition)
Figure 5 shows that increasing the aspect ratio significantly increased the barrel radius when subjected to
the same axial stress for same value of friction factor (m). The logarithmic value of the barrel radius is
plotted against the logarithmic value of the true axial stress in figure 6. Firstly, the straight line trends
indicate that in all cases an empirical power law may be established (see Appendix):
R  A  m
…. (3)
where R is the barrel radius, σ is the true axial compressive stress and A, m are empirical constants.
Secondly, the straight lines are not parallel to each other, implying thereby that the rate of change of barrel
radius with respect to the compressive stress exhibits a major difference with different lubrication
conditions for all the different aspect ratios. Figure 7 shows that the straight lines were very closely parallel
to one another, implying thereby that the rate of change of the barrel radius with respect to the compressive
stress did not exhibit a major difference over a range of aspect ratios l/d between 0.5 and 1.00, both under
dry as well as MoS2 lubricating conditions. Instantaneous heights and the maximum barrel diameters were
measured and for each deformation level, true axial stresses were calculated by extrapolation method; the
corresponding axial compressive strains were calculated from their relative heights,   ln H H o  .
Thus, for each aspect ratio of 0.75 and 1.00 a separate stress-strain curve was obtained.
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
Figure 6: Logarithmic presentations of the results of figure 4
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
Figure 7 logarithmic presentations of the results of figure 5
Figure 8: Relationship between the instantaneous maximum diameter and the instantaneous height
Figure 9 (a and b) show such two sets of curves where dry friction and four other lubricants were employed.
Each of the two figures of figure 9 (a and b) suggests that teflon was the best lubricant, followed by white
grease, MoS2, graphite and dry friction, because in any of these sets of curves the stress required to reach a
determined value of strain was minimum of teflon lubrication and increased in magnitude in the following
order: white grease, MoS2, graphite and dry friction. Another way of interpretation is the Specific Forming
Energy, as defined by the energy required to deform plastically a unit volume of work-piece (cylinder)
material and as measured by the area bounded by the stress-strain curve, was minimum for the teflon
lubricant and maximum for dry friction, with white grease, MoS2, graphite in the intermediate order.
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
Figure 9: Effect of lubricants on the true stress-strain curves in compression
4. Conclusions
1. The profile of the barrel fits closely to a circular arc during each stage in the axial compression of
solid cylinders.
2. The radius of the barrel decreases exponentially with increasing true stress.
3. The logarithmic plot of the barrel radius against the axial stress indicates a straight-line
relationship. The straight line trends indicate that in all cases an empirical power law may be
established.
4. The rate of change of barrel radius with respect to the compressive stress differs over the range of
lubrication conditions but the rate of change of the barrel radius with respect to the compressive
stress did not exhibit a major difference over a range of aspect ratios l/d between 0.5 and 1.00.
5. The specific forming energy required for plastically deforming the material is minimum for the
teflon lubricant and maximum for dry friction, with white grease, MoS2, graphite in the
intermediate order.
Appendix
Geometrically, in figure 3(b)
R 2  (R  x) 2  (H 2) 2
…. (A.1)
where x 
( D2  D1 )
2
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
or
x 2  2Rx 
H2
0
4
…. (A.2)
Solving for x,
x  R  R2  H 2 4
Since x  R , the positive sign makes no sense.
 x  R  R2  H 2 4
…. (A.3)
Applying volume constancy between the initial cylinder any instantaneous barrel,

12

H (2 D22  D12 ) 
4
H o Do2
…. (A.4)
Solving for D12,
D12 
3H 0 D02
 2D22
H
…. (A.5)
From equation (A1),
( H 2  ( D2  D1 ) 2 )
R
(4( D2  D1 ))
…. (A..6)
Substituting D1 for (D2-2x) in equation (A.4) and simplifying,
3D22  4D2 x  4 x 2 
3H o Do2
0
H
Where solving for x,
x
D2 1 3H o Do2

 2 D22
2 2
H
…. (A.7)
From equation (A3),
R
x H2

2 8x
…. (A.8)
Since the value of x is very small relative to H (x/H ≤0.1), the first term in equation (A.8) can be neglected,
so that
R
H2
8x
…. (A.9)
From equations (A.7) and (A.9)
RH
2
 D 1 3H D 2

o o
8 2 
 2D22 
H
 2 2

…. (A.10)
From the results of experiment (see Figure 8)
D2 Do  BH H o 
m
…. (A.11)
where B and m are empirical constants. Substituting equation (A.11) into equations (A.10),
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Barreling of solid composite (Lm6/Sicp) cylinders under uni axial compressive load
R
H2
m
2 m 

Do B  H 
1 3H o Do2
2 2 H 


 
 
8
 2Do B 
 2  H o 
2
H
H
 o  

…. (A.12)
The relationship between true stress (σ) and true strain (ε) can be expressed by the following empirical
equation
  K n
…. (A.13)
where K and n are empirical constants and ε = ln (H/Ho).
From equations (A.12) and (A.13)
R  C  m1
…. (A.14)
which establishes the straight line logarithmic relationship between R and σ.
Average Compressive Stress (σ).
We assume an average instantaneous area 
  D22  D12 

4 
2


For any given load F, the normal average compressive stress,
 F
  D22  D12 

4 
2
8F
 
2
2
  D2  D1
…. (A.15)


Substituting D12 from equation (A.5) in equation (A.15) and simplifying,
 3H o Do2

 D22 
 H

  8F  
…. (A.16)
The corresponding normal compressive strain (ε) was calculated simply from,
  ln H H o 
…. (A.17)
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