5. Upsetting and Forging
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Transcript of 5. Upsetting and Forging
Effect of Temperature: At elevated temperatures, the rate of strain hardening (represented by the
strain hardening exponent) falls rapidly in most metals. The flow stress
and tensile strength, measured at constant strain and strain-rate, also drop
with increasing temperature.
FIGURE: Typical effects of
temperature on stress-strain curves.
Temperature affects the modulus of
elasticity, yield stress, ultimate
tensile strength, and toughness of
materials.
Decreasing the strain rate has the same effect on the flow stress as raising
the temperature but at much lower rates.
FIGURE: The effect of strain rate on the ultimate tensile strength of
aluminum. Note that as temperature increases, the slope increases thus,
tensile strength becomes more sensitive to strain rate as temperature
increases.
Hot Working:
Hot working takes advantage of the decrease in flow stress at high
temperature to lower tool forces, equipment size, and power
requirements.
Hot working is defined as working above the recrystallization
temperature so that the work metal recrystalizes as it deforms. The
resultant product is in an annealed state.
However, hot working has some undesirable effects:
1. Lubrication is more difficult. Many hot working processes are done
without lubrication.
2. The work metal tends to oxidize forming a scale layer that causes loss
of metal and roughened surfaces. Processing under inert atmosphere is
prohibitively expensive and is applied only in case of reactive metals
such as titanium.
3. Tool life is shortened because of heating. Sometimes scale breakers
are employed and rolls are cooled by water spray to minimize tool
damage.
4. Poor surface finish and loss of precise gauge control.
5. Lack of work hardening is undesirable where the strength level of a
cold worked product is needed.
Because of these limitations, it is common to hot roll steel to about 6 mm
thickness. The product is then pickled to remove scale, and further rolling
is done cold to ensure good surface finish, and optimum mechanical
properties.
Temperature rise during deformation:
The heat generated by mechanical work raises the temperature of the
metal during plastic deformation. As shown earlier,
w d
Only a small fraction of this energy is stored. This fraction drops from
5% initially to 1 or 2% at high strains. The rest is released as heat. If
deformation is adiabatic, i.e., no heat transfer to the surroundings, the
temperature is given by:
CC
dT a
Where a is the average value of over the strain interval 0 to , is
the density, C is the mass heat capacity, and is the fraction energy
stored as heat ( about 0.98).
Any temperature increase causes the flow stress to drop leading to
thermal softening, especially at high strain-rates where heat cannot be
transferred to surroundings.
Deformation work
One concern regarding forming operations is the prediction of externally
applied loads needed to cause the metal to deform (flow) to the required
shape.
Uncertainties: frictional effects, non-homogeneous deformation, and true
manner by which strain hardening occurs during complex deformations.
Due to these uncertainties, the exact values of force requirements are
seldom predictable.
Ideal work of deformation:
The process is assumed to be ideal in the sense that external work is
completely utilized to cause deformation only. Effects of friction and
non-homogeneous deformation are ignored. Assuming power-law for
strain- hardening materials:
dkdW n
i
Where )/ln(ln 00
AAl
l
.
1
1
n
KW
n
i
If other forms of work hardening or idealized relations are more
appropriate, they would be used.
E.g., when a mean flow stress σm is sometimes used over the range of
homogeneous strain:
miW , and by comparing with the previous equation:
11
nn
k n
m
Effect of friction, redundant work, and mechanical efficiency:
Frictional work per unit volume, fW is consumed at the interface between
the deforming metal and the tool faces that constrain the metal.
Redundant work rW is due to internal distortion in excess of that needed
to produce the required shape.
FIGURE: Deformation of grid patterns in a workpiece to compare ideal
deformation and inhomogeneous deformation with additional shearing,
which requires higher work (redundant)
Then the actual work is the sum of the three terms:
rfia WWWW
In general, it is difficult in practice to separate fW from rW since they are
not mutually independent. The deformation efficiency is then defined
as:
a
i
W
W
Often in practice, varies between 0.5 and 0.65.
Analysis of forming processes:
Several techniques have been developed for modeling of forming
processes for the purpose of understanding the pattern of metal flow,
calculation of load and energy requirements, and proper design of the
tooling required to carry out the process.
These techniques are classified as follows:
1. Slab analysis: or free body-equilibrium approach. This is the
simplest and most widely applied method.
2. Slip line field method: based on a presumed deformation field that is
geometrically consistent with the shape change.
3. Upper bound analysis: predicts a load that is at least equal to or greater
than the exact load needed to cause plastic flow.
4. Finite element analysis: based on numerical approach, and accordingly
gives near actual results.
Slab Analysis:
The method is based on carrying out a force balance on a slab of metal of
differential thickness in the deforming body. The resulting differential
equation is solved using pertinent boundary conditions. The technique
assumes homogeneous deformation, i.e. no internal distortion.
Direct compression in plane strain
Ideal deformation of a billet with circular or rectangular cross section
between flat platens, leads to a reduction in height and uniform increase
in area. Considering volume constancy, the area corresponding to any
height is calculated as:
(9.1)
However, lateral friction at the billet-platen interfaces leads to restriction
of material flow on these surfaces causing a barrel shape of the lateral
sides, and a consequent increase in the pressure required to carry out the
upsetting process as shown in Fig... The pressure ascends symmetrically
from the edges of the billet, reaching maximum value at the center,
forming what is known as the friction hill. The average pressure, and
accordingly the force required to carry out the upsetting process will
therefore increase due to friction.
FIGURE: (a) Ideal deformation of a solid cylindrical specimen
compressed between flat frictionless dies (upsetting). (b) Deformation in
upsetting with friction at the die-workpiece interfaces.
FIGURE: Grain flow lines in upsetting a solid steel cylinder at elevated
temperatures. Note the highly inhomogenous deformation and barreling.
The different shape of the bottle, section of the specimen (as compared
with the top) results from the hot specimen resting on the lower, cool die
before deformation proceeded. The bottom surface was chilled; thus it
exhibits greater strength and hence deforms less than the top surface.
The following Fig. represents a billet with rectangular section under
compression through platens. The billet width is a, and height is h. The
figure shows also the stresses on a vertical element in that section. As
discussed earlier, plane strain condition assumes that the thickness of the
section in the third direction (b) is much larger than the side (a), such that
there is no strain in that thickness, i.e. ( h<a<<b). This condition
resembles actual open-die forging of long shafts or blooms between flat
platens.
h
dx
a/2
x
y
σy
σy = P
µσy
µσy
σxσx + dσx
σy
σy
σxσx + dσx
dx
b
σx + σy
2σz=
Fig. .. Stresses on an element in plane-strain upsetting between flat dies
Considering a force balance on the element (slab) in the x direction:
0)()(2 hddxph xxx
xhdpdx 2
x & y (taken as –p) are principal stresses. For plane strain
deformation, the flow stress (σf) is calculated from the Eq. (σ1 – σ3 = σf) ,
and considering the maximum difference between the two yield criteria
as stated earlier, then; ffx p 15.1)( ' ,
Where '
f is the flow yield stress under plane strain = 1.15 σf.
Considering the flow stress to be constant (perfect plastic material),
differentiation of the above equation gives: dσx = - dp
hdppdx 2 or dxhp
dp 2
At 2/ax , 0x , and '
fp , so the solution is:
)29(2
2exp
'
x
a
h
p
f
The maximum value of p occurs at the center line, with a maximum
value: )3.9(exp
max
'
h
ap
f
A plot of '/ fp versus x gives the friction hill as shown in Fig..a.
a
h
a/2
x
h
0
1
a) Sliding friction
a/2
xb) Sticking friction
0
1
p/σ'f
σx/σ'f1+
e
µha
2h
Fig. .. Pressure distribution and horizontal stress distribution in plane
strain upsetting with sliding (a) and sticking (b) friction
To calculate σx : )4.9(1)
2(
2
''
xa
hffx ep
Average pressure
The mean or average pressure is of great interest as it can be used to
calculate the applied force on the contact area.
dxea
pdxa
px
a
h
a
f
a
a
)2
(22
0
'2
0
22
)5.9(2
1'
h
ap fa
Then the upsetting force is given by:
Sticking friction at the interface
To avoid shearing of the workpiece at the billet-platen interface, fp ,
as explained earlier, where f is the shear yield strength of the billet
material (equal to half the flow stress). Since, 12
f
p
, thus 5.0 if
sliding friction is to take place. If the limit at which sliding friction is
exceeded, sticking takes place. To calculate the pressure distribution
under sticking, the frictional forces indicated previously as p is replaced
by the shear yield strength '5.0 ff in the previous analysis, which
leads to:
)6.9(2/
1' h
xap
f
This equation represents a linear variation of p with x, i.e. linear friction
hill. The maximum value which occurs at the centerline is:
)7.9()2
1('
maxh
ap f
A plot of the pressure distribution under sticking friction is shown in Fig.
..b. for comparison with the case of sliding friction. The average pressure
with sticking friction is:
)8.9()4
1('
h
aP fa
Since pressure is maximum at the center, then sticking starts primarily at
the center of the interface area and spreads outwards. However, there
could be a case where the outer parts may still be under sliding friction.
The point of intersection x1 between the exponential relation represented
by Eq. 9.2, and the linear relation represented by Eq. 9.6, is the point
separating the sticking and the sliding area, where:
)9.9()2
1ln(
221
hax
Pressure distributions
at rectangular
sections: FIGURE: Normal stress
(pressure) distribution in
the compression of a rectangular workpiece with sliding friction under
conditions of plane stress, using the distortion-energy criterion. Note that the
stress at the corners is equal to the uniaxial yield stress, Y.
FIGURE: Increase in contact area of a rectangular specimen (viewed
from the top) compressed between flat dies with friction. Note that the
length of the specimen has increased proportionately less than its width.
Forging of a solid cylindrical workpiece:
The upsetting of a cylindrical workpienc is modeled using the same
analysis followed with a rectangular specimen in the previous section.
However, cylindrical coordinates are applied as shown in Fig. 9.16, using
stress components σr in the radial direction, σө in the tangential direction,
and σz in the axial direction.
r = d2
r dr
h
dθ
dθ
2
σr
σθ
µσz
dθ
σr + dσr
σz
σz
σθ
dθ
2
µσz
Fig. Stresses on an element during upsetting of a cylindrical specimen
Following a similar approach for the case of plane strain, a similar
equation is obtained:
0)()(2
2Pr2
ddrrhd
hdrddrdhrd rrr
0Pr2 rr hrddrhdrhdr
For axisymmetric flow, r , then; r
For yielding , frz , back substitution gives the pressure
distribution:
)10.9()
2(
2x
d
h
f
ep
Notice the similarity with Eq. 9.2, and that the flow stress is used in Eq.
9.10 directly without multiplying by 1.15. This is indicative that in the
case of axial symmetry, the two yield criteria coincide.
The average pressure: )11.9()3
21(
h
rp fa
The upsetting force is: )4/( 2dpF a
The value of the coefficient of friction can be estimated to be 0.05 to
0.1 for cold forging, and 0.1 to 0.2 for hot forging.
Under sticking friction the stress distribution again is linear:
FIGURE: Ratio of average die pressure to yield stress as a function of
friction and aspect ratio of the specimen: (a) plane-strain compression;
and (b) compression of a solid cylindrical specimen.
Notice the similarity of equations for both plane strain and cylindrical
billets, and same trends of the results representing change of the upsetting
)12.9())2/(
1(h
xdp f
pressure with the width/height (aspect) ratio at both conditions as shown
in Fig. 9.17. It should be observed that:
higher aspect ratios lead to higher pressures at the same frictional
conditions.
that the pressures are higher for a plane-strain specimen compared
to a cylindrical specimen with the same aspect ratio, and the same
frictional conditions.
Impression-die forging:
FIGURE: Schematic illustration of stages in impression-die forging.
Note the formation of flash, or excess material that is subsequently
trimmed off.
Accurate calculation of forces in impression-die forging is difficult. To
simplify force calculation, a pressure-multiplying factor Kp is
recommended:
Where F is the forging load, A is the projected area of the forging
(including the flash), and σf is the flow stress of the material.
Typical Kp ranges are shown in the following table:
Forging Shape Kp Kh
Simple shapes, without flash Simple shapes, with flash Complex shapes, with flash
3-5 5-8 8-12
2 – 2.5 3 4
The capacity of the press to be used should have a rated maximum force
well above the estimated load.
During forging under hot working conditions, the strain rate affects the
stresses required to carry out the process. The strain rate is calculated as
given:
1
0
11
0. 1)ln(
h
v
dt
dh
hh
h
dt
d
dt
d
Where v is the relative velocity between the platens.
To obtain an approximate estimate of the strain rate in impression-die
forging:
V
Av
h
v
m
m .
Where V is the volume of the metal, and A is the projected area.
Similarly, an average strain may be estimated as:
)ln()ln( 0
)
0
V
Ah
h
h
m
m
As hammers are rated according to their energy, the energy required for
forging is calculated approximately from the equation:
hmf VKE
Where E is the forging energy, and Kh is the multiplying factor for
hammers obtained from the previous table. The rated hammer capacity
should be greater than the estimated energy.
In hot forging forces are much reduced with heated dies, but these
preheated dies require very slow forging speeds.
Ring compression test for determination of µ during forming:
The ring-compression test is an experimental method used for the
determination of frictional conditions in bulk metal forming. The concept
of the test is the increasing or decreasing of the inner diameter of a short
ring specimen when it is compressed between two flat, parallel platens. If
the friction is low (good lubrication) the internal diameter increases;
while if the friction is high (poor lubrication) the internal diameter is
decreases as shown in Figure
Low Friction(Good Lubrication) High Friction(Poor Lubrication)