1
Mechanical Metallurgy and Industrial Metal
Working Processes
Professor Dr. Md. Aminul Islam
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Chapter One
Theory of Elasticity and Plasticity
Experience shows that all solid materials can be deformed when subjected to external load. It is
further found that up to certain limiting loads a solid will recover its original dimensions when
the load is removed. The recovery of the original dimensions of a deformed body when the load
is removed is known as elastic behaviour. The limiting load beyond which the material no longer
behaves elastically is the elastic limit. If the elastic limit is exceeded, the body will experience a
permanent set or deformation when the load is removed. A body which is permanently deformed
is said to have undergone plastic deformation. For most materials, as long as the load does not
exceed the elastic limit, the deformation is proportional to the load. This relationship is known as
Hooke's law; it is more frequently stated as stress is proportional to strain. Hooke's law requires
that the load-deformation relationship should be linear. However, it does not necessarily follow
that all materials which behave elastically will have a linear stress-strain relationship. Rubber is
an example of a material with a nonlinear stress-strain relationship that still satisfies the
definition of an elastic material. Elastic deformations in metals are quite small and require very
sensitive instruments for their measurement. Ultrasensitive instruments have shown that the
elastic limits of metals are much lower than the values usually measured in engineering tests of
materials. As the measuring devices become more sensitive, the elastic limit is decreased, so that
for most metals there is only a rather narrow range of loads over which Hooke's law strictly
applies. This is, however, primarily of academic importance. Hooke's law remains a quite valid
relationship for engineering design.
1. Observation of Elastic-Plastic Behaviours from Standard Tests
In this section, a number of phenomena observed in the material testing of metals will be noted.
Consider the following key experiment, the tensile test, in which a small, usually cylindrical,
specimen is gripped and stretched at some given rate of stretching. The force required to hold the
specimen at a given stretch is recorded, Fig.1. If the material is a metal, the deformation remains
elastic up to a certain force level, the yield point of the material. Beyond this point, permanent
plastic deformations are induced. On unloading only the elastic deformation is recovered and the
specimen will have undergone a permanent elongation (and consequent lateral contraction). In
the elastic range the force-displacement behaviour for most engineering materials (metals, rocks,
plastics, but not soils) is linear. After passing the elastic limit (point A in Fig.1), the material
undergoes plastic flow.
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Figure 1: Stress-strain behaviour of a typical engineering material.
Further increases in load are usually required to maintain the plastic flow and an increase in
displacement; this phenomenon is known as work hardening or strain hardening. In some cases,
after an initial plastic flow and hardening, the force-displacement curve decreases. If the
specimen is unloaded from a plastic state (B) it will return along the path BC shown, parallel to
the original elastic line. This is elastic recovery. The strain which remains upon unloading is the
permanent plastic deformation. If the material is now loaded again, the force-displacement curve
will retrace the unloading path CB until it again reaches the plastic state. Further increases in
stress will cause the curve to follow BD. After the onset of plastic deformation, the material will
be seen to undergo negligible volume change, that means it is incompressible.
There are two different ways of describing the force F which acts in a tension test. First,
normalizing with respect to the original cross sectional area of the tension test specimen Ao, one
has the nominal stress or engineering stress:
𝑭
𝒏 = 𝑨 --------------- (1)
𝒐
Alternatively, one can normalize with respect to the current cross-sectional area A, leading to the
true stress:
𝑭
𝒕 = 𝑨 ---------------- (2)
𝒕
Here F and At are both changing with time. For very small elongations, within the elastic range
say, the cross-sectional area of the material undergoes negligible change and both definitions of
stress are more or less equivalent. Similarly, one can describe the deformation in two alternative
ways. Denoting the original specimen length by lo and the current length by l, one has the
nominal strain as follows:
𝒏 =
𝒍−𝒍𝒐
𝒍𝒐
--------------- (3)
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Alternatively, the true strain is based on the fact that the “original length” is continually
changing; a small change in length dl leads to a strain increment d=dl/ l and the total strain is
defined as the accumulation of these increments:
𝒕 =
𝒍 𝒅𝒍
𝒍𝒐 𝒍
𝒍
= 𝒍𝒏 𝒍 -------------- (4)
𝒐
The true strain is also called the logarithmic strain. At small deformations, the difference
between these two strain measures is negligible, Fig.2.
Figure 2: Relationship between true and engineering stress-strain
behaviour of a typical engineering material.
The true and engineering stress-strains are related through the following relationship:
𝒕 = 𝒍𝒏 𝟏 + 𝒏 -------------- (5)
𝒍
𝒕 = 𝒏 𝒍 --------------- (6)
𝒐
2. The Bauschinger Effect
If one takes a virgin sample and loads it in tension into the plastic range and then unloads it and
continues on into compression, one finds that the yield stress in compression is not the same as
the yield strength in tension, as it would have been if the specimen had not first been loaded in
tension. In fact the yield point in this case will be significantly less than the corresponding yield
stress in tension. This reduction in yield stress is known as the Bauschinger effect. The effect is
illustrated in Fig.3.
Stress (MPa)
5
0
0
Strain%
0
Figure 3: Schematic diagram showing Bauschinger effects.
This reduction in the yield stress of polycrystalline metal specimens following pre-strain in the
opposite direction was reported by German scientist Bauschinger in 1881.
2.1. Evaluation of the Magnitude of the Bauschinger Effect
There are three established parameters used to assess the absolute values of the Bauschinger
effect: the stress, strain and energy parameters (Fig.4).
Figure 4: Stress-strain curves for (a) the Bauschinger effect stress-parameter and (b) the Bauschinger
effect strain and energy parameters: σr0.2 and σr0.5 the yield stress at 0.2% and 0.5% reverse strain, Δσs
-permanent work-softening, εp - pre-strain, εr – “Bauschinger strain”, the strain in the reverse direction
corresponding to the point of reverse stress equal to the maximum pre-stress σp, Ep – energy spent
during pre-strain, Es – energy saved during reverse straining due to the Bauschinger effect, shown by
the shaded area.
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In the literature there are four different mathematical expressions of the stress parameters. These
are related to different points on the forward-reverse stress-strain curve (Fig.4a). The stress
parameter βσ1 describes the relative decrease in the yield stress from forward to reverse
deformation:
---------------- (7)
-------- (7)
Here σp is maximum pre-stress and σr is the yield stress in the direction of reverse strain (point
of the stress-strain curve deviation from the straight line, normally around 0.1% reverse strain).
The stress parameters βσ2, βσ3 and βσ4, calculated using stress values at 0.2 % and 0.5 % reverse
strain, show the rate of property restoration during reverse straining after the yield drop:
-------------- (8)
Here σr0.2 and σr0.5 are stresses at 0.2 % and 0.5 % reverse strain. As the yield stress represents
the start of dislocation slip (with acting back stress from the obstacles, in the case of reverse
deformation) parameter βσ1 describes the “short range” work softening. As the work hardening
rate depends on material chemistry (carbon content and alloying) and microstructure (phases,
precipitates and dislocation density), the parameters βσ2, βσ3 and βσ4 represent “long range”
work-softening and show how permanent the Bauschinger effect is when deformation increases
in the reverse direction. The Bauschinger strain parameter describes the amount of deformation
in the reverse direction needed to reach the pre-stress level of stress (Fig.4b):
-------------- (9)
Here εp is plastic pre-strain and εr is plastic strain in the reverse direction for the point of equal
stress value to the pre-stress. The Bauschinger energy parameter describes the amount of energy
needed during the reverse deformation to reach the pre-stress level of stress:
-------------- (10)
Here Ep is the energy spent during pre-strain and Es is energy saved during reverse straining
due to the Bauschinger effect (Fig.4b).
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2.2. Causes of the Bauschinger Effect
There are several principal Bauschinger effect theories. Among them the back stress theory will
be described here in Fig.5. During forward plastic deformation moving dislocations interact with
different obstacles (other dislocations, grain boundaries and precipitates) preventing their further
propagation. This generates a back stress around the contact point resisting further progress of
similarly signed dislocations. During the reverse deformation this back stress repels the
dislocations from the obstacles in the opposite direction, namely in the direction of reverse strain.
Thus the stress field helps to move the dislocation in the direction of reverse strain and the
reverse yield stress drops by the level of the back stress (Fig.5a). According to the back stress
theory an increase in dislocation density increases the number density of dislocation dislocationinteraction sites and consequently the level of back stress. Thus the Bauschinger effect should be
larger in a material with a higher dislocation density. But with an increase in initial dislocation
density (and/or pre-strain) the number of mobile dislocations can decrease. This occurs due to
immobilization of moving dislocations by pile-ups and possible formation of cell structures,
where mobile dislocations in the cell interior are many times lower in density than the total
number accumulated in the cell walls. Thus with an increase in dislocation density it is possible
to expect a maximum in the Bauschinger effect and then a decrease after some level of prestrain. However, this maximum has not been observed so far in the reported literature, due to
pre-strains used being below 8%.
Figure 5: Schematic diagram of the (a) dislocation-dislocation and (b) dislocation-particle interaction.
In an alloyed material, precipitated particles also act as interaction sites increasing the level of
back stress (Fig.5b). Thus, increasing the particle volume fraction and their number density will
increase the number of interactions between dislocations and particles and hence the back stress.
However, not all the particles equally contribute to dislocation pinning. When particles are
coherent with the matrix the cutting mechanism operates. In this case the dislocation retardation
force will depend on particle chemistry, as particle composition influences its mechanical
strength. When particles are incoherent the bowing mechanism operates. In this case the
dislocation retardation will depend on interparticle spacing, as, with a decrease in interparticle
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spacing, the dislocation curvature energy needed for a dislocation to pass increases.
Predominance of one or another mechanism depends on the average particle size, as, with an
increase in particle size, the particles lose coherency with the matrix lattice. Thus particle
number density is not enough to assess the influence of precipitates on the Bauschinger effect.
Particle chemistry, size and distribution should also be taken into account.
2.3. Consequence of Bauschinger Effect
Metal forming operations result in situations exposing the metal workpiece to stresses of
reversed sign. The Bauschinger effect contributes to work softening of the workpiece, for
example in straightening of drawn bars or rolled sheets, where rollers subject the workpiece to
alternate bending stresses, thereby reducing the yield strength and enabling greater cold
drawability of the workpiece. The increase of Bauschinger strain led to in shorter fatigue life.
3. Stress-Strain Behaviours of Engineering Materials
The relationship between strain and stress is of fundamental importance to both the metallurgists
and the design engineers. This information is usually contained in the stress/strain diagram for
the material, where stress is the ordinate and strain the abscissa. Depending upon the properties
of the material being tested, various kinds of diagrams can be obtained.
(a) Rigid Behaviour
As the term implies the body is completely rigid and undergoes no strain under applied stress.
Even if the stress in increased to very high values the body remains undeformed. The stressstrain diagram is simply a line on the ordinate up to the maximum applied stress. This property is
ideal for many applications, particularly in civil engineering, but it is not normal in crystalline
metals. Tungsten carbide is one material which approximates to this behaviour, (Fig.6).
Figure 6: Stress-strain behaviour of a perfectly rigid material.
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(b) Linear Elastic Behaviour
This is the situation when a body undergoes deformation under the action of the applied stress,
but once the stress is removed the deformation disappears and the body reverts to its original
shape and dimensions. Figure 7 shows typical elastic behaviour.
Figure 7: Stress-strain behaviour of a perfectly liner elastic material.
(c) Plastic Behaviour
This is the situation when a body undergoes deformation or strain under the action of an applied
stress and that the strain is permanent and persists after the removal of the applied stress. This
behaviour is shown by Fig.8.
Figure 8: Stress-strain behaviour of a perfectly plastic material.
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(d) Failure
In all cases failure or fracture will occur if the applied stress is progressively increased. In the
case of tensile stresses, failure is by rupture into two parts. The ability of the material to resist
failure under the action of an applied stress is called it strength. It will be seen later that there are
many definitions of strength. The strength at rupture under a tensile is called the Ultimate Tensile
Strength. The behaviour of actual materials will consist of a combination of these individual
oders of deformation, Fig.9.
Rigid/Plastic
Rigid/Elastic
Elastic/Plastic
Figure 9: Failure of various types of materials.
It is found that metals tend to behave in an elastic-plastic manner. Thus the understanding of
elastic-plastic behaviour is very important in metal shaping.
4. Work Done During Tensile Deformation
The area under the true stress-strain curve is of considerable significance in that it is another
unique characteristic of the metal under test. It is the product of the abscissa and the ordinate, i.e.
 and this can be better understood by staring from the units involved:
𝑵
𝒎𝒎𝟐
×
𝒎𝒎
𝒎𝒎
=
𝑵𝒎𝒎
𝒎𝒎𝟑
=
𝒎𝑱
𝒎𝒎𝟑
----------- (11)
This is the work done per unit volume. The area under the curve is a measure of the work done
or energy required to deform unit volume of the metal. If the total volume is known then the total
work done can be found.
Total work done =  ----------- (12)
This can be derived by a rigid mathematical analysis in the following way:
Work done = Force × distance moved,
 𝒅𝒘 = 𝑭 × 𝒅𝒍,
but
𝒅 =
𝒅𝒍
𝒍
, 𝒊. 𝒆. 𝒅𝒍 = 𝒍𝒅
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Force = stress × area = A,
𝒅𝒘 =  𝑨𝒍 𝒅 = 𝑽 𝒅 ------------ (13)
and
4.1. Elastic Work Done
The elastic portion of the stress-strain curve is given by / = 𝐸 when E is Young‟s Modulus. If
 = 𝐸 is substituted in the above equation (13) then the following is obtained:
𝒅𝑾𝒆𝒍 = 𝑽𝑬 𝒅
𝟐
𝑾𝒆𝒍 = 𝑽𝑬  𝒅 = 𝑽𝑬 𝟐
𝟐
𝑾𝒆𝒍 = 𝑽 𝟐𝑬 ------------------ (14)
Or
4.2. Plastic Work Done
Over the plastic portion of the stress-strain curve  = 𝐾 𝑛 . By substituting in equation (13) then
the following is obtained:
𝒅𝑾𝒑𝒍 = 𝑽𝑲𝒏 𝒅
𝒅𝑾𝒑𝒍 = 𝑽𝑲 𝒏 𝒅 =
𝑾𝒑𝒍 =
𝑾𝒑𝒍 =
or
𝑽𝑲𝒏+𝟏
𝒏+𝟏
𝒐𝒓
𝑽
𝒏+𝟏
𝑽𝑲𝒏+𝟏
𝒏+𝟏
------------ (15)
5. Compression
When a specimen is loaded in compression the behaviour is also elastic/plastic, but cross-section
increases as the height decreases and to maintain deformation rapidly increasing loads are
necessary. This is due to the combination of work hardening and constantly increasing crosssection. In most compression tests the load required rapidly exceeds that available from even the
largest testing equipment. This in one, but not the only reason why compression tests are not
widely used. If the results of such tests are recorded as true tress/true with all side effects
eliminated then both tensile and compression tests give identical curves.
6. Strains in Tension and Compression
The convention that tensile strains are positive and compression strains negative can be
supported by calculations from basic principles.
𝒆𝒕𝒆𝒏𝒔𝒊𝒐𝒏 =
𝒍𝟏 −𝒍𝟎
𝒍𝟎
𝒕𝒆𝒏𝒔𝒊𝒐𝒏 = 𝑰𝒏
𝒆𝒄𝒐𝒎𝒑 =
𝟎
𝒍𝟏
𝒍𝟎
𝒉𝟎 –𝒉𝟏
𝒉𝟎
𝒄𝒐𝒎𝒑 = 𝑰𝒏
𝒍
= 𝒍𝟏 − 𝟏
= 𝑰𝒏 𝟏 + 𝒆𝒕𝒆𝒏𝒔𝒊𝒐𝒏
𝒉
= 𝟏 − 𝒉𝟏
𝟎
𝒉𝟏
𝒉𝟎
= 𝑰𝒏 𝟏 + 𝒆𝒄𝒐𝒎𝒑
+ ve because 𝑙1 > 𝑙0 ,
+ ve as above,
- ve because 𝑕1 𝑕0 ,
- ve as above,
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This can lead to confusion in the study of those mechanical working processes which depend on
compression such as rolling, forging and extrusion and it is normal to reverse the convention, so
that compressive strains are positive.
𝒆𝒄 =
𝒄 =
𝒉𝟎 −𝒉𝟏
𝒉𝟎 𝒅𝒉
𝒉𝟏 𝒉
𝒉𝟎
𝒉
= 𝟏 − 𝒉𝟏 ,
𝟎
= 𝑰𝒏
𝒉𝟎
= 𝑰𝒏
𝒉𝟏
𝟏
𝟏−𝒆𝒄
.
In metal working process the amount of deformation is not normally given as strain but rather as
the fractional or percentage reduction in height, thickness or cross-sectional area,
i.e.
𝒓=
or
𝑹=
𝑨
𝑨𝟏
𝒓 = 𝟏 − 𝑨𝟏 𝒐𝒓
𝑨𝟎
𝟎
𝑨𝟎 −𝑨𝟏
𝑨𝟎
𝑨𝟎 −𝑨𝟏
𝑨𝟎
𝟏𝟎𝟎,
= 𝟏 − 𝒓,
But since 𝑨𝟎 𝒍𝟎 = 𝑨𝟏 𝒍𝟏
𝒕𝒉𝒆𝒏
𝒍
𝟏
𝒍𝟎
𝒍𝟏
= 𝟏 − 𝒓,
 − 𝑰𝒏 𝒍𝟏 = 𝑰𝒏 𝟏−𝒓
𝟎
The following table shows values of strain for different values of deformation:
10% elongation
10% compression
Doubling length
Halving length
Compression to zero
𝒆

𝒓
+0.1
-0.1
+1.0
-0.5
-1.0
+0.095
-0.104
+0.693
-0.693
-
0.1
-0.11
+0.5
-1
Problem 1: In a tensile test on an annealed steel testpiece (E 200kN/mm2), diameter 13mm,
gauge length 50mm, the following results were obtained. Yield load 24.1 kN, maximum load
43.4kN, breaking load 39.8kN. Final length at fracture 69mm. Calculate (a) yield stress, (b)
ultimate tensile stress, (c) elastic elongation, (d) percentage elongation, (e) why does fracture
occur at lower load?
Solution
(a) 181N/mm2, (b) 299N/mm2, (c) 4.53×10-3, (d) 35%.
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Problem 2: In a tensile test an annealed steel piece 13mm diameter, 50mm gauge length the
following results were obtained:
Load kN
Length mm
Load kN
Length mm
10
50.019
67.5
50.889
20
50.0381
70
51.270
30
50.057
72.1
51.515
40
50.070
70.4
52.030
50
50.236
68.0
52.134
60
50.495
62.3
52.181
65
50.699
61.1
52.235
Draw (a) True stress/strain curve.
(b) Determine Young‟s Modulus.
Solution:
Nominal S
Load L
𝐿
(kN)
𝑠=
𝑁/𝑚𝑚4
𝐶. 𝑆. 𝐴.
10
75.2
20
150.4
30
225.6
40
300.8
50
374.9
60
451.1
65
488.7
67.5
507.5
70
526.3
72.1
542.1
70.4
529.3
68
511.3
62.3
468.4
61.1
459.4
True stress
75.2
150.5
225.8
301.2
377.7
455.5
495.4
516.4
539.4
558.2
550.4
532.7
488.5
479.5
𝑙1 − 𝑙0
mm
0.019
0.038
0.057
0.070
0.235
0.495
0.699
0.889
1.270
1.515
2.030
2.134
2.184
2.235

Young Modulus =  over elastic portion
301.2
= 1.372 = 219.5 𝑘𝑁/𝑚𝑚2 .
𝑒 × 10−3
0.373
0.747
1.112
1.373
4.608
9.706
13.706
17.431
24.902
29.702
39.804
41.843
42.824
43.824
 × 10−3
0.373
0.747
1.111
1.372
4.597
9.659
13.613
17.281
24.597
29.273
39.032
40.991
41.932
42.891
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Problem 3: Assuming that the volume of the specimen in question 2 was 13,300mm3 calculate
the percentage of the total work done during the tensile test due to elastic deformation.
Solutions:
2
𝐸𝑙𝑎𝑠𝑡𝑖𝑐 𝑤𝑜𝑟𝑘 = 𝑉 2𝐸0
where 𝑜 is the yield stress,
(301.2)2 ×10 3
= 133,300 × 2×219.5×10 3 𝐽
= 2.75 𝑀𝐽
𝑣
𝑃𝑙𝑎𝑠𝑡𝑖𝑐 𝑤𝑜𝑟𝑘 = 𝑛+1
where  and  are values at the Ultimate Tensile Stress and Strain,
𝑁
 = 562 𝑚 𝑚 2 ,  = 42.9 × 10−3
A value of n can be found by plotting a log/log graph for the plastic region.
Plastic
377.7
455.5
495.4
516.4
539.4
588.2
Log 
2.577
2.658
2.695
2.713
2.732
2.747
Since

4.597× 10−3
9.659× 10−3
13.613× 10−3
17.281× 10−3
24.597× 10−3
29.273× 10−3
Log 
-2.338
-2.015
-1.866
-1.762
-1.609
-1.534
 = 𝑘𝑛
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log  = log 𝐾 + 𝑛 𝑙𝑜𝑔 
𝑛
𝑙𝑜𝑔 1 −𝑙𝑜𝑔 2
𝑙𝑜𝑔 1 −𝑙𝑜𝑔 2
where 1,2 are two points on the log/log plot,
i.e.
𝑛=
2.70−2.60
−1.792 — −2.263
0.10
= 0.471 = 0.212,
 Plastic work done = 13,300 × 562 × 42.9 × 10−3 × 10−3 𝐽/1.212
= 264.6 𝐽
Problem 4: The strength coefficient = 550 MPa and strain-hardening exponent = 0.22 for a
certain metal. During a forming operation, the final true strain that the metal experiences = 0.85.
Determine the flow stress at this strain and the average flow stress that the metal experienced
during the operation.
Solution: Flow stress f = 550(0.85)0.22 = 531 MPa.
Average flow stress f = 550(0.85)0.22/1.22 = 435 MPa.
Problem 5: A metal has a flow curve with strength coefficient = 850 MPa and strain-hardening
exponent = 0.30. A tensile specimen of the metal with gage length = 100 mm is stretched to a
length = 157 mm. Determine the flow stress at the new length and the average flow stress that
the metal has been subjected to during the deformation.
Solution: ε = ln (157/100) = ln 1.57 = 0.451
Flow stress f = 850(0.451)0.30 = 669.4 MPa.
Average flow stress f = 850(0.451)0.30/1.30 = 514.9 MPa.
Problem 6: A particular metal has a flow curve with strength coefficient = 35,000 lb/in2 and
strain-hardening exponent = 0.26. A tensile specimen of the metal with gage length = 2.0 in is
stretched to a length = 3.3 in. Determine the flow stress at this new length and the average flow
stress that the metal has been subjected to during deformation.
Solution: ε = ln (3.3/2.0) = ln 1.65 = 0.501
Flow stress f = 35,000(0.501)0.26 = 29,240 lb/in2.
Average flow stress f = 35,000(0.501)0.26/1.26 = 23,206 lb/in2.
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Problem 7: For a certain metal, the strength coefficient = 700 MPa and strain hardening
exponent = 0.27. Determine the average flow stress that the metal experiences if it is subjected to
a stress that is equal to its strength coefficient K.
Solution: f = K = 700 = Kεn = 700ε.27 ε must be equal to 1.0.
f = 700(1.0).27/1.27 = 700/1.27 = 551.2 MPa
Problem 8: Determine the value of the strain-hardening exponent for a metal that will cause the
average flow stress to be 3/4 of the final flow stress after deformation.
Solution: f = 0.75 f
Kεn/(1+n) = 0.75 Kεn
1/(1+n) = 0.75
1 = 0.75(1+n) = 0.75 + 0.75n
0.25 = 0.75n n = 0.333
Problem 9: In a tensile test, two pairs of values of stress and strain were measured for the
specimen metal after it had yielded: (1) true stress = 217 MPa and true strain = 0.35, and (2) true
stress = 259 MPa and true strain = 0.68. Based on these data points, determine the strength
coefficient and strain-hardening exponent.
Solution: Solve two equations, two unknowns: ln K = ln σ - n ln ε
(1) ln K = ln 217 – n ln 0.35
(2) ln K = ln 259 – n ln 0.685
(3) ln K = 5.3799 – (-1.0498)n = 5.3799 + 1.0498 n
(4) ln K = 5.5568 – (-0.3857)n = 5.5568 + 0.3857 n
5.3799 + 1.0498 n = 5.5568 + 0.3857 n
1.0498 n – 0.3857 n = 5.5568 – 5.3799
0.6641 n = 0.1769 n = 0.2664
ln K = 5.3799 + 1.0498 (0.2664) = 5.6596 K = 287 MPa
17
Problem 10: A tensile bar was machined with a stepped gage section consisting of two regions
of different diameters. The initial diameters of the two regions were 2.0 cm and 1.9 cm. After a
certain amount of stretching in tension, the diameters of the two regions were measured as 1.893
cm and 1.698 cm, respectively. Assuming the tensile strain hardening is described by  = Kn
find n for the material.
Solution:
18
Chapter Two
Cold and Hot Working of Metals
During the process of shape change which accompanies mechanical working the volume of the
mass remains constant and an increase in length such as in rolling is accompanied by a decrease
in thickness. As deformation is applied to a structure consisting of one kind of deformable
grains, they will become elongated. At the same time, mechanical properties become directional
along with anisotropic microstructures and properties. However, this situation might be changed
through selection of working temperatures. The behaviour of a duplex structures is very similar
except that the two phases or types of grains, e.g. α and β, are likely to react differently to the
deformation process. For example α may be soft and ductile, whilst β may be hard and brittle,
will, therefore, tend to fracture and appear as orientated fragments or stringers in the longitudinal
direction. A duplex structure will tend to become more anisotropic than a single phase structure.
At very high degrees of deformation the structure appears fibrous because the grains have been
so elongated as to lose their individual characteristics. All structural metals have approximately
the same ductility as measured by percentage elongation. An annealed metal will have
approximately 35% elongation; whilst a metal which has been cold worked 80% will have only
approximately 2% elongation before failure in a tensile test.
1. Cold Working
Plastic deformation of metals below the recrystallization temperature is known as cold working.
It is generally performed at room temperature. In some cases, slightly elevated temperatures may
be used to provide increased ductility and reduced strength. Cold working offers a number of
distinct advantages and for this reason various cold working processes have become extremely
important. Significant advances in recent years have extended the use of cold forming and the
trend appears likely to continue. The toughness, as measured by the Izod or Charpy test,
increases with working up to a maximum and then gradually decreases. It is found, in practice,
that the hardness and strength of most metals increase by 2.5 to 3 times the annealed value as a
result of cold working. The best combination of properties is usually found in the longitudinal
direction and the worst in the short transverse direction, because the grain elongation in the
direction of working, i.e. in the longitudinal direction, Fig.1.
19
Figure 1: Microstructural changes after sever cold working, (a) as received and
(b) severe cold worked.
Ductile metals become stronger when they are deformed plastically at temperatures well below
the melting point. The reason for strain hardening is the increase of dislocation density with
plastic deformation. The average distance between dislocations decreases and dislocations start
blocking the motion of each other. %CW is just another measure of the degree of plastic
deformation as well as the hardness and strength of the materials, Fig.2.
Figure 2: Effect of degree of cold working on the strength and ductility of cold worked materials.
20
Cold forming processes, in general, are better suited to large scale production of parts because of
the cost of the required equipment, tooling and power consumption. In comparison with hot
working, the advantages of cold working are:
1. No heating is required
2. Better surface finish is obtained
3. Better dimensional control is achieved; therefore no secondary machining is generally needed.
4. Products possess better reproducibility and inter-changeablity.
5. Better strength, fatigue and wear properties of material.
6. Directional properties can be imparted.
7. Contamination problems are almost negligible.
Along with many advantages, cold working processes also have some disadvantages which are:
1. Higher forces are required for deformation.
2. Heavier and more powerful equipment is required.
3. Less ductility is available.
4. Metal surfaces must be clean and scale free.
5. Strain hardening occurs (may require intermediate annealing).
6. Undesirable residual stresses may be produced.
It has been mentioned that cold working process elongates the grains in direction of working,
increases the dislocation levels and makes the structures to be hardened (Fig.2), which is called
work hardening. Work hardening is one of the characteristic properties of most metallic alloys; it
is also probably the most useful since it is the fundamental cause of their tenacity, or their
capacity, in the presence of internal flaws or geometrical defects, to resist loading. The
maximum amount of uniform plastic deformation in tensile straining depends on the work
hardening coefficient of the material. A high work hardening coefficient, therefore, facilitates
more deformation and complex forming operations without premature failure, Fig.3.
Figure 3: Effect of strain hardening exponent on the deformation behaviours of materials.
21
Work hardening of course strongly influences the mechanical energy expended to shape a
material by plastic deformation, for example during rolling, etc. Work hardening also controls
the amount of energy stored in the material as a consequence of plastic deformation. It, therefore,
strongly governs the behaviour of the metal during subsequent softening by annealing. Finally,
many high volume components such as beverage cans are directly used in the work hardened
state, so the hardening capacity and the stability of the work hardened state are important
practical issues. Modern theories of work hardening started by Taylor and the concept of crystal
dislocations and have continued ever since. There is no universally accepted theory of work
hardening but much empirical knowledge and many models which share a certain number of
common features; these are the points that are developed here. This chapter starts with a
description of work hardening at relatively low temperatures where thermally activated processes
do not play a major role, typically for homologous temperatures below 0.4Tm. It then continues
with an analysis of plastic flow at high temperatures where material viscosity effects are
important. In both the cases, the relation to dislocation behaviour will be emphasized.
During progressive loading in a simple tensile test, a metal first deforms elastically, Fig.3 and
then at the yield stress (denoted y) begins to deform plastically, such that on unloading to zero
force, the metal retains a permanent shape change which determines the amount of plastic
deformation. The important quantities are the stress , usually taken as the force per unit area,
and the strain, for example, the relative elongation in a tensile test. For plastic strains greater than
about 10%, the true strain  defined by ln(l/lo), which has the important property of additivity for
successive strains. In Fig.3, the slope of the curve in the plastic regime is used to define the work
hardening coefficient n:
The onset of necking in a tension test specimen corresponds to the ultimate tensile strength of the
material. Note that the slope of the load–elongation curve at this point is zero, and it is there that
the specimen begins to neck. The specimen cannot support the load because the cross-sectional
area of the neck is becoming smaller at a rate that is higher than the rate at which the material
becomes stronger (strain hardens). The true strain at the onset of necking is numerically equal to
the strain hardening exponent, n, of the material. Thus, the higher the value of n, the higher the
strain that a piece of material can experience before it begins to neck. This observation is
important, particularly in regard to sheet-metal-forming operations that involve the stretching of
the workpiece material. It can be seen in the following Table that annealed copper, brass and
stainless steel have high n values; this means that they can be stretched uniformly to a greater
extent than can the other metals listed.
22
Problem 1: Assume that a material has a true stress–true strain curve given by  =
1000000.5psi. Calculate the true ultimate tensile strength and the true and engineering UTS of
this material.
Solution: Because the necking strain corresponds to the maximum load, the necking strain for
this material is  = n = 0.5.
Now, the true ultimate tensile strength is  = 1000000.5 = 70,710 psi.
We know that the value of n =  at UTS (at necking), n before necking and n after necking.
The value of the work hardening coefficient, n is of major importance for forming operations
since it controls the amount of uniform plastic strain the material can undergo during a tensile
23
test before strain localization, or necking, sets in leading to failure. If the onset of necking occurs
at maximum load, it is easily shown that, to first order, the amount of uniform plastic strain then
equals the work hardening coefficient, n; this relation is known as the consideration criterion.
This then limits the amount of uniform plastic strain that can be applied in a room temperature
under tensile deformation. At room temperature, or more exactly at temperatures below about
0.4Tm (homologous temperature, Tm being the melting temperature in K), the stress-strain curve
experience a minor effect by straining rate, at least for conventional rates. However, at higher
temperatures, the straining rate (έ) has a significant influence on the plastic flow stresses. As
illustrated in Fig.4, higher strain rates lead to higher flow stresses.
Figure 4: Effect of strain rate on hot deformation behaviours of materials.
The material strain rate sensitivity, m is defined as follows:
Here m takes values from about 0.05 at moderate temperatures to 0.5 or higher in some specific
materials at very high temperatures.
1.1 Effect of Cold Working on Mechanical Properties
In Fig.5 are presented the relations between the tensile properties and the percentage reduction of
area by cold drawing for all specimens tested. It will be noted that small amounts of drawing up
to approximately 10%, produced large changes in strength and ductility, but that additional
amounts of drawing (up to at least 50%) caused relatively smaller changes for the range beyond
10% reduction of area. Beyond the initial rapid increase that occurred for reductions of area
below 10%, average curves through the data for the ultimate strength and the yield strength
approximated straight lines, although a slightly curved line would fit the data fully as well. The
24
relations between the compressive strength properties and the amount of cold drawing are also
very similar.
Figure 5: Effect of cold working on properties of sheet steel.
In both tension and compression the amounts of cold drawing of the SAE 1010 steel tubing up to
10 per cent reduction of area caused large increases in strength, whereas additional amounts
caused the ultimate strengths and the yield strengths to vary according to a linear relationship
which can be expressed by the general equation:
S = kSa (1 + R)
Here S = the strength (tensile or compressive, ultimate or yield) in psi k = a constant depending
upon the material and type of test, Sa = the strength (of the same type as S) of the normalized
25
tubing free from cold drawing, R = the reduction of area expressed as a decimal. For this
particular case the values of k for the four of the properties are as follows:
Ultimate tensile strength k = 1.27, Maximum compressive strength, k = 1.33, Tensile yield
strength (0.20 per cent offset) k = 1.67, Compressive yield strength (0.20 per cent offset) k =
1.45.
Problem 2: Design a cold working schedule of an AISI 1030 steel to increase the UTS to 130ksi.
Solution: Calculate the %pearlite and ferrite, then the UTS of the annealed steel. Find out the
UTS of normalized steel from relation between normalized and annealed steels, then calculate
the degree of cold working needed using the above equation.
1.2. Rate of Deformation Effects
We can shape a piece of material in a manufacturing process at different speeds. Some machines,
such as hydraulic presses, form materials at low speeds; others, such as mechanical presses, form
materials at high speeds. To incorporate such effects, it is common practice to strain a specimen
at a rate corresponding to that which will be experienced in the actual manufacturing process.
The deformation rate is defined as the speed at which a tension test is being carried out, in units
of, say, m/s or ft/min. The strain rate, on the other hand, is a function of the specimen‟s length. A
short specimen elongates proportionately more during the same period than does a long
specimen. For example, let‟s take two rubber bands, one 20mm and the other 100mm long,
respectively, and elongate them both by 10mm within a period of 1 second. The engineering
strain in the shorter specimen is that in the longer is thus, the strain rates are 0.5s-1 and 0.1s-1,
respectively, with the short band being subjected to a strain rate five times higher than that for
the long band, although they are both being stretched at the same deformation rate.
Deformation rates typically employed in various testing and metalworking processes and the true
strains involved. Because of the wide range encountered in practice, strain rates are usually
stated in terms of orders of magnitude, such as 102s-1, 104s-1 and so on. The typical effects that
temperature and strain rate jointly have on the strength of metals are shown in Fig.6 and strain
rates used in various practical metal shaping process are given in the Table below.
26
Figure 6: Effect of strain rate on tensile strength of a typical steel.
Note that increasing the strain rate increases the strength of the material (strain rate hardening).
The slope of these curves is called the strain-rate sensitivity exponent, m. The value of m is
obtained from log–log plots, provided that the vertical and horizontal scales are the same. A
slope of 45° would therefore indicate a value of m equal to 1. The relationship is given by the
equation (where C is the strength coefficient and is the true strain rate, defined as the true strain
that the material undergoes per unit time.
27
Note that C has the units of stress and is similar to, but not to be confused with, the strength
coefficient K. From Fig.6, it can be seen that the sensitivity of strength to strain rate increases
with temperature; in other words, m increases with increasing temperature. Also, the slope is
relatively flat at room temperature; that is, m is very low. This condition is true for most metals,
but not for those that recrystallize at room temperature, such as lead and tin. Typical ranges of m
for metals are up to 0.05 for cold-working, 0.05 to 0.4 for hot-working, and 0.3 to 0.85 for
superplastic materials. The magnitude of the strain rate sensitivity exponent significantly
influences necking in a tension test. With increasing m, the material stretches further before it
fails; thus, increasing m delays necking. Ductility enhancement caused by the high strain-rate
sensitivity of some materials has been exploited in superplastic forming of sheet metal.
1.3. Effect of Metallurgical Factors on Forming Processes
The forces required to carry out a forming operation are directly related to the flow stress of the
metal being worked. This, in turn, depends on the metallurgical structure and composition of the
alloy. For pure metals the ease of mechanical working will, in general, decrease with increasing
melting point of the metal. Since the minimum recrystallization temperature is approximately
proportional to the melting point, the lower temperature limit for hot work will also increase with
melting point. (As a rough approximation, this temperature is about one-half the melting point in
degree Kelvin.) The addition of alloying elements to form a solid solution alloy generally raises
the flow curve and the forming loads increase proportionately. Since the melting point is often
decreased by solid solution alloying additions, the upper hot working temperature must usually
be reduced in order to prevent hot shortness. The plastic working characteristics of two phase
(heterogeneous) alloys depend on the microscopic distribution of the second phase particles. The
presence of a large volume fraction of hard uniformly dispersed particles, such as are found in
the class of high-temperature alloys, greatly increases the flow stress and makes working quite
difficult. If the second phase particles are soft, they have only a small effect on the working
characteristics. If these particles have a lower melting point than the matrix, then difficulties with
hot shortness will be encountered. The presence of a massive, uniformly distributed
microconstituent, such as pearlite in mild steel, results in less increase in flow stress than for very
finely divided second phase particles. The shape of the carbide particles can be important in cold
working processes. For annealed steel, a spheroidization heat treatment, which converts the
cementite platelets to spheroidal cementite particles, is often used to increase the formability at
room temperature. An important exception to the general rule that the presence of a hard second
phase increases the difficulty of forming is brass alloys containing 35 to 45 per cent zinc (Muntz
metal). These alloys, which consist of a relatively hard beta phase in an alpha brass matrix,
actually have lower flow stresses in the hot working region than the single phase alpha brass
alloys. In the cold working region the flow stress of alpha beta brass is appreciably higher than
that of alpha brass.
28
Alloys which contain a hard second phase located primarily at the grain boundaries present
considerable forming problems because of the tendency for fracture to occur along the grain
boundaries. As the result of a mechanical working operation second phase particles will tend to
assume a shape and distribution which roughly correspond to the deformation of the body as a
whole. Second phase particles or inclusions which are originally spheroidal will be distorted in
the principal working direction into an ellipsoidal shape if they are softer and more ductile than
the matrix. If the inclusions or particles are brittle, they will be broken into fragments which will
be oriented parallel to the working direction, while if the particles are harder and stronger than
the matrix, they will be essentially undeformed. The orientation of second phase particles during
hot or cold working and the preferred fragmentation of the grains during cold working are
responsible for the fibrous structure which is typical of wrought products. The fiber structure can
be observed after macroetching. Microscopic examination of wrought products frequently shows
the results of this mechanical fibering (Fig.7).
Figure 7: Fibered and banded structure in longitudinal direction of a hot rolled mild steel
plate.
An important consequence of mechanical fibering is that the mechanical properties may be
different for different orientations of the test specimen with respect to the fiber (working)
direction. In general, the tensile ductility, fatigue properties and impact properties will be lower
in the transverse direction (normal to the fiber) than in the longitudinal direction. The forming
characteristics of an alloy can be affected if it undergoes a strain-induced precipitation or straininduced phase transformation. If a precipitation reaction occurs in a metal while it is being
formed, it will produce an increase in the flow stress but, more important, there will be an
appreciable decrease in ductility, which can result in cracking. When brittleness is caused by
precipitation, it usually results when the working is carried out at a temperature just below the
solvus line or from cold working after the alloy had been heated to the same temperature region.
29
Since precipitation is a diffusion-controlled process, difficulty from this factor is more likely
when forming is carried out at a slow speed at an elevated temperature. To facilitate the forming
of age hardenable aluminum alloys, they are frequently refrigerated just before forming in order
to suppress the precipitation reaction. A most outstanding practical example of a strain-induced
phase transformation occurs in certain austenitic stainless steels where the Cr:Ni ratio results in
an unstable austenite phase. When these alloys are cold worked, the austenite transforms to
ferrite along the slip lines and produces an abnormal increase in the flow stress for the amount of
deformation received. While this phase transformation is often used to increase the yield strength
by cold rolling, it can also result in cracking during forming if the transformation occurs in an
extreme amount in regions of highly localized strain.
2. Plastic Anisotropy
Virtually, all large strain shaping and forming operations lead to some form of material plastic
anisotropy such that the mechanical, physical and sometimes chemical properties vary with
testing direction. This is basically due to the formation of directional microstructures (e.g.
particle or grain alignment) and in particular, preferential grain orientations or crystallographic
textures, for example, during rolling deformation and/or eventually subsequent recrystallization.
An example is the variation, with direction in the sheet plane, of the yield strength of an Al–Li
alloy as illustrated in Fig.8.
Figure 8: Effect of grain orientation on deformation behaviours of materials.
A second case concerns the plastic anisotropy during a forming operation such as deep drawing.
A circular blank stamped out of a sheet is drawn down by punching through a die into a cup
30
shape, but the resulting „cup‟ develops irregular wall heights commonly denoted „ears‟ (see
Fig.9).
Figure 9: Ear formation during cupping of a strongly textured aluminium alloy sheet.
The ears are situated at certain angles to the sheet directions according to the plastic anisotropy,
or the texture, of the sheet. Plastic anisotropy of sheet material is measured experimentally by the
contraction ratios of flat tensile samples, taken at angles  to the rolling direction and elongated
by tensile testing. The ratio of the width (plastic) strain w to the through-thickness strain t is
denoted the Lankford coefficient or the R value.
In theory, R varies from 0 (no widening) to
materials.
 (no thinning) and equals 1 for isotropic
3. Work Hardening Stages
3.1. Stage I
During Stage I, which is most easily seen in single crystals oriented for single slip, the
dislocations are usually confined to their slip planes and do not interact with each other so that
the work hardening rate is very low. However, as the crystal rotates by plastic deformation it
tends to reorient towards double slip orientations, which then favour the stronger dislocation
interactions of Stage II. In polycrystals, which begin to deform plastically, Stage I is negligible
since the movement of the first few dislocations is restricted by the grain boundaries at which
31
they often pile-up. The resistance of the grain boundaries to dislocation movement gives rise to
the well-known Hall–Petch grain size (D) hardening relation:
Here  is the flow stress of the material at a very large grain size. This relation is very
important for hardening many polycrystalline alloys particularly when the grain size can be
reduced to 20m or less. Typical values of the k1 coefficient (in MNm-3/2) vary from about 0.7 to
1 for carbon steels, through 0.4-0.2 for the HCP metals and down to 0.1-0.07 for FCC Cu and Al,
respectively. The high value of k1 for carbon containing steels constitutes the physical basis for
the development of high strength low alloy (HSLA) steels with fine grain sizes. Note that the
presence of carbon in solution significantly increases k1 compared with the pure metal case
which is 0.2 for pure iron.
3.2. Stage II
The dislocation interactions on different slip systems give rise to a rapid multiplication of the
dislocations and thereby a high and roughly constant, work hardening rate (d/d) ~30-50x10-4
G. In low SFE metals, networks composed of 3D arrays of dislocation multipoles are formed. In
the higher SFE metals dislocation tangles develop and often adopt a cellular pattern. This Stage
II extends up to strains of 0.05-0.2 (or even more at low temperatures and/or low SFEs) and to
first order is independent of temperature.
3.3. Stage III
Subsequently and up to strains of order unity, the flow curve becomes parabolic as the work
hardening rate decreases progressively down to values almost an order of magnitude lower than
Stage II. In this stage, the dislocation multiplication processes are counterbalanced by local
dislocation annihilations (dynamic recovery due to localized cross-slip, climb and/or annihilation
of segments of opposite sign). These recovery mechanisms and therefore the work hardening
rates are strongly temperature dependent. The microstructure evolves towards a well defined cell
substructure composed of dislocation cell walls which delimit cell interiors of low dislocation
density. The cell walls are initially complex tangles of dislocations but which tend to collapse
into thinner, neater, boundaries during Stage III. The cells have dimensions which decrease
during deformation, typically from a few microns to some tenths of microns. Simultaneously, the
misorientation between adjacent cells increases from about 1 to 3 or 4o (and often higher for
heterogeneous deformations).
3.4. Stage IV
At higher strains 1 typical of many rolling and extrusion processes, many grains break up into
bands of different orientations, separated by transition zones and grain boundaries. Figure 10
shows the onset of this process in cold rolled iron where the TEM micrograph reveals a cell
32
structure which is starting to break up by the formation of microbands more or less inclined to
the rolling direction. At very high strains this develops into a lamellar structure composed of
misoriented microbands parallel to RD. Note that the grain boundary area per unit volume
increases significantly by large plastic deformations. All these features are characteristic of
fibrous microstructures. As noted above, the work hardening rate in Stage IV is relatively low,
but stays at a near constant value over large strains so that at very high strains the flow stress
increase can be considerable.
Figure 10: TEM micrograph of high purity Fe cold rolled 80% showing cells and microbands.
4. Influence of Alloying Elements
The strong influence of alloying elements on the work hardening behaviour is related to the
metallurgical state of the material and depends particularly on whether the elements are in solid
solution or as a dispersion of 2nd phase particles.
4.1. Solute Atom Effects
In solid solution, many elements such as Mg and Cu in Al or C in Fe are attracted to the
dislocation cores and significantly reduce their mobility thereby increasing the stress required for
plastic flow. The solute hardening is expressed in terms of the increment of critical resolved
shear stress s compared with the pure metal flow stress. The effect is ascribed to two major
types of dislocation–solute interactions, respectively atom size and shear modulus. The size
effect is usually the strongest and produces an attractive force between the dislocation core and
the solute atoms as a consequence of the elastic distortion of the core which can accommodate
solute atoms of sizes different from those of the solvent matrix. For example, edge dislocations
are characterized by expanded zones below the extra half plane (and compressed above) which
will attract larger atoms (or smaller above). Rigorously, this is not the case of undissociated
screw dislocations but is true of dissociated screws, which behave like two edge dipoles, so the
same reasoning can be generally applied. The size interaction energy between a dislocation and
an immobile solute atom can be estimated with the assumption of spherical distortions which is
33
valid for substitutional solute atoms, following Table gives some typical values together with
those due to modulus variations. The latter becomes significant when the solvent and solute atom
sizes are similar. In this case, the variation of the shear modulus of the matrix with solute
concentration gives rise to an additional interaction energy as a result of the dependence of flow
stress on shear modulus.
A particular form of the size effect is due to the tetragonal distortion of the lattice by interstitial
atoms in cubic structures, e.g. carbon in BCC iron. Here the carbon atoms occupy the octahedral
interstitial sites and induce elastic displacements, which are larger along the directions of closest
distance to the Fe atoms than along the other two orthogonal directions. The resulting interaction
energy can be very large (see Fig.11).
Figure 11: Solute hardening in ferritic iron.
34
The overall effect of solute hardening has been estimated for these different situations with a
variety of dislocation- solute atom interaction models. Most of them predict a (low temperature
T0.5Tm) hardening which varies with the square root of the solute concentration, e.g. for
spherical distortions Fleischer gives:
Here the parameter s, of order unity, is a function of the fractional change of lattice parameter
and shear modulus (G) with concentration C (expressed as atomic fraction).
After initial yielding and during subsequent plastic deformation, the solute atoms tend to confine
the dislocations to slip planes, reduce their capacity to recover dynamically by local climb and
cross-slip, inhibit the formation of „clean‟ cell structures and thereby increase the dislocation
density for a given deformation. In general, Stage II work hardening is prolonged and Stages III
and IV retarded, so more alloy means more extensive work hardening, Fig.12.
Figure 12: Stress–strain curves of Al–Mg alloys.
At moderate temperatures, which allow local diffusion processes, the solute atoms can begin to
move and can therefore „catch up‟ with slowly moving dislocations so that very strong
interactions are possible (typically between RT and ~300oC). The reduced dislocation mobility
by solute segregation tends to favour heterogeneous deformation by Lüders bands and Portevin
LeChatelier (PLC) serrations in the stress–strain curves (Fig.13).
35
Figure 13: PLC serrations in Al-Mg alloy.
4.2. Second Phase Particles
Alloying elements in the form of 2nd phase particles almost always harden the material by
requiring the dislocations to expend additional energy either by cutting the particle (fine particles
of radius rp≤ 10nm) or by looping around them (rp typically ≥20nm). The effect of these
processes on the yield strength is well documented since they control, in part, the final
properties. As is well known, dislocation cutting of fine particles requires a critical shear stress
which increases with the particle size. The exact relation between p and rp depends upon the
details of the cutting mechanism. There are in fact several basic mechanisms for hardening
crystals by a dispersion of fine particles through which dislocations can pass. The amount of
hardening decreases as the interparticle spacing increases on overaging. The combination of both
the cutting and looping mechanisms means that the particle strengthening goes through a
maximum-the peak hardness as a function of particle radius (or of time during an ageing
treatment).
The effect of 2nd phase particles on work hardening, i.e. after yield, depends critically on the
particle size but in a rather different way. The work hardening rate tends to be rather low for very
fine particles (including the peak hardness distributions) since the dislocations, once they have
cut through one particle, can cut through entire fields of particles at roughly the same stress. This
leads to the formation of shear bands in which plastic deformation is heavily concentrated, e.g.
certain Al-Cu alloys. On the other hand, if the particles have dimensions of ≥1m the
dislocations loop around them and on continued straining build up high local dislocation
36
densities near the particles and therefore relatively high work hardening rates. In fact, a
considerable fraction of the dislocation population is required to accommodate the difference in
plastic strain between the hard particles and the soft matrix. The accumulation of dislocations in
these particle deformation zones creates high local stresses if the particles are sufficiently large
to withstand them (≥1m). This process creates a strongly dislocated substructure with a
dimension characteristic of the interparticle distance and is particularly pronounced if the
particles are non-spherical, e.g. discs (Al-Cu) or fibers (pearlitic steels).
5. Fracture
During the shaping and forming operations typical of many thermo-mechanical processes,
rupture of the material is a constant threat; so, the conditions leading to rupture have been the
subject of a large number of studies. The treatment here is an elementary introduction to the
problem. In the earlier section, it has been introduced that engineering materials may have
different types of stress-strain behaviours. The schematic stress-strain curves of Fig.14 illustrate
the three major, typical, purely elastic stressing before brittle failure (Fig.14a), as occurs, for
example, in ceramics and some brittle metallic alloys at low temperatures. This brittle failure
mode will not be examined here in any detail since we are primarily concerned with the more
ductile failure characteristic of deformation processing methods.
Figure 14: Schematic stress–strain curves for common failure modes (a) brittle, (b) ductile at
room temperature and (c) high temperature.
Figure 14b illustrates the typical behaviour of a metal when deformed at room temperature as in
a forming operation; the material undergoes a certain amount of plastic strain before failure,
37
whereas Fig.14c describes typical ductile stress-strain behaviour during high-temperature
straining; plasticity can take place over larger strains with a gradual stress decrease after the
maximum load, as failure occurs progressively in the material. The ductility that can be obtained
before fracture is usually given by the sample cross-section at failure Af relative to the initial
value Ao, i.e. ductility = ln(Ao/Af). Now, we can make a relationship between work hardening and
strain rate sensitivity on ductility. During tensile straining, one analyses the behaviour of a small,
local, variation in the specimen cross-section, A to determine if this local change in area will be
amplified (leading to failure) or reduced (leading to continued plastic strain). We, therefore, need
the rate of change of the local area compared with the surrounding „average‟ area. The load
transmitted through the specimen is the same everywhere. So, the following relationship can be
made:
Or
Now, in the form of a differential equation and ignoring second-order terms the above equation
be presented as:
Here, as indicated, the second term corresponds to the difference in strain increment (d)
between the local and average sections. The variation in stress d is due to strain hardening and
strain rate effects:
But,
and
Substituting for d and dέ gives a relation for d in terms of A, dA, etc. and the partial derivates
for stress. The latter can be written,
the rate of change of section:
𝟏


 έ
=

, etc to obtain the following expression for
 έ
38
Assuming constant values for the work hardening and strain rate sensitivity coefficients, n and m
as defined in the earlier section, this can be written:
The critical condition between local necking and plastic stability is dώ = 0 so that the uniform
strain to this condition is then simply:
6. Softening Mechanisms
The cold deformation structures developed during cold working are intrinsically unstable so that
on annealing, after deformation processing, substructure evolution often occurs by thermally
activated processes, leading to a reduction of stored energy. These processes usually induce a
significant softening of the plastically deformed material as shown in Fig.15.
Figure 15: Effect of temperature and time on the hardness of cold worked materials.
At low temperatures (in commercial alloys, typically between 0.4–0.5 of the melting
temperatures, Tm), recovery dominates and often leads to a slow, logarithmic, decrease of the
hardness. At high temperatures (more than 0.7Tm), recrystallization can occur very rapidly,
without much prior recovery. At intermediate temperatures, both mechanisms can contribute
significantly to softening. The associated microstructural changes are defined based on the
driving force and the mechanism(s) involved. As shown in the following Table, there are two
39
possible driving forces – (i) the stored energy of deformation and (ii) the surface energy or the
grain boundary energy.
During plastic deformation of crystalline materials, part of the plastic work, typically 1–10%, is
stored as microstructural energy, mostly as increased dislocation density; the rest is dissipated as
heat. The softening processes are usually separated into recovery, recrystallization and
eventually grain growth. The latter two necessarily imply the movement of high-angle
boundaries, but recovery involves a set of micromechanisms for the motion and annihilation of
point defects and dislocations. It is the combination of driving force and mechanism that
differentiates these three „softening‟ processes:
a) Recovery (stored energy and movement of dislocations, either individually or collectively
as low-angle boundaries),
b) Recrystallization (stored energy and movement of high-angle boundaries) and
c) Grain growth (surface energy and movement of high-angle boundaries).
6.1. Recovery
Softening by recovery can occur if a non-equilibrium concentration of lattice defects is
„reduced‟, usually by annealing at an appropriate temperature. The defects can be both, point and
line defects; but the latter, i.e. dislocations, are more relevant. Point defects are usually annealed
out at relatively low temperatures (0.3Tm), i.e. at temperatures below most thermomechanical
processing and can usually be ignored except for very low-temperature deformations. Recovery
by dislocation annihilation often involves a combination of several micromechanisms (see ealier
Table). The ratio of recovery to recrystallization, however, depends on several factors – strain,
annealing temperature and material. The effect of temperature is illustrated schematically in
Fig.10. Recovery dominates the low-temperature regime, while recrystallization usually occurs
rapidly at higher temperatures. Even at higher temperatures, however, there is always some
recovery before recrystallization, recovery kinetics being faster than that of low temperatures.
For single phase materials, the stacking fault energy (SFE) also has a strong influence on the
40
amount of recovery; in deformed high-SFE metals, such as Al and body centred cube (bcc) iron,
dislocation cross slip and local annihilations are sufficiently easy to favour significant amounts
of recovery. A classical example is the recovery of cold-drawn Al beverage cans during curing of
the varnish at 150–200oC. On the other hand, the low SFE metals and alloys, e.g. rolled
austenitic stainless steels and -brass, do not undergo much recovery before recrystallization.
This is also generally true for alloys with high solute contents, which reduce the dislocation
mobility. Though recovery is an important issue, it is often difficult to quantify. It can occur
immediately after deformation, and also dynamically during deformation. Furthermore, recovery
does not affect the optical microstructure or the crystallographic texture. Recovery affects
properties such as hardness and structural features like, dislocation density, subgrain size and
misorientation, but the resolution of such property changes is often poor and statistically
quantifying the changes in the affected structural features is difficult.
6.2. Recovery Mechanisms
The various mechanisms of recovery include (in order of increasing difficulty):
a) Point defect (vacancies and interstitials) annihilation by diffusion to sinks such
as dislocations,
b) Mutual dislocation annihilation (closely spaced dislocations of opposite sign, or
dipoles, which require small amounts of dislocation climb and/or cross slip),
c) Organization of free, random dislocations into dislocation walls or sub-boundaries
(polygonization) and
d) Coalescence of sub-boundary walls during subgrain growth.
The latter three mechanisms are illustrated schematically in Fig.16.
Figure 16: Schematic of successive dislocation annihilation mechanisms; cross-section of a bent
crystal containing both free (edge) dislocations and dislocations, which accommodate the
orientation gradient. During annealing, some dislocations anneal out by climb of opposite sign
segments (encircled pairs) then the remainder rearrange into subgrain boundaries.
41
Figure 17 illustrates an example of stored energy reduction in rolled high purity iron by
differential scanning calorimetry (DSC) (calorimetric) measurements at a constant heating rate.
The diffuse recovery reaction extends over a wide temperature range before the sharper
recrystallization peak. Recovery mechanisms often operate simultaneously, so that there is no
clear demarcation between them. For example, it is impossible to distinguish the collapse of
diffuse dislocation cells into well-defined subgrain boundaries and subgrain growth. This is one
reason why recovery is difficult to treat analytically. Also, the mechanisms of the later stage of
recovery, e.g. the formation of well defined subgrains, are often the first stages of
recrystallization nucleation which can lead to rapid recrystallization, stopping any further
recovery. Finally, these fundamental mechanisms are also very sensitive to a wide variety of
material parameters and processing conditions, such as deformation, temperature, etc. As noted
above, solute atoms play a major role in reducing defect mobility and therefore recovery kinetics.
For example, deformed ultrahigh purity metals can recover at about 0.2Tm and start
recrystallizing at 0.3Tm (see Fig.18). Solute atoms in commercial alloys push recovery and
recrystallization temperatures to 0.4 and 0.6Tm, respectively. This Second phase particles,
particularly as very fine distributions, will also inhibit recovery by pinning dislocations.
Figure 17: DSC plots at 20K/min of ultrahigh purity Fe cold rolled 80%. Negative heat flows
correspond to exothermic reactions, which are estimated at 4J/mol for the recovery region
(100-300oC) and 15J/mol for recrystallization (320–450oC).
42
Figure 18: Schematic diagram showing the temperature dependency of recovery and
recrystallization in cold worked metals.
6.3. Structural Changes in Recovery
Apart from the initial and rapid loss of point defects, the main structural changes taking place
during recovery can be categorized as:
a) Rearrangement of dislocations into cellular structures (for high-SFE materials and most
hot-deformed metals, this occurs simultaneously with deformation).
b) Elimination of free dislocations within the cells.
c) Collapse of the complicated dislocation cell walls into neat subgrain boundaries-mostly
by annihilation of excess or redundant dislocations and rearrangement of the others into
low energy configurations (Fig.19).
Figure 19: Schematics showing dislocation structure changes during recovery-random
dislocation tangles through cell structures to subgrains.
43
d) Subgrain growth. During continued annealing, an increase in subgrain size is
theoretically expected since it leads to a reduction of internal energy. The experimentally
observed kinetic relationships are usually written:
Here d and do are the final and initial subgrain size, n, and k3 are constants. While k3 is strongly
temperature dependent (through the activation energy), values of n between 2 and 7 have been
reported. There is a trend for the lower n values to be found in high purity metals and at high
temperatures, where sub-boundary mobility is the highest.
It should be pointed out that due to experimental difficulties in determining subgrain sizes with
good accuracy and therefore, their exact evolution during recovery before the onset of
recrystallization there have not been many detailed, quantitative studies of subgrain growth.
Another important aspect of recovery, with direct implication to recrystallization, is the issue of
orientation dependence. This is also the least understood. Differences in stored energies, or in
dislocation substructure, are often related to differences in Taylor factor and also to differences
in the so called „textural softening‟. Both are, however, related more to deformation than to
recovery. The quantitative influence of recovery on softening is dependent on the relation
between subgrain size and flow stress. The best fit for available experimental data on
substructural strengthening is obtained through a Hall–Petch type of relationship(s):
Here  is the applied stress, d the subgrain size, o, is the initial yield sress, k5 and c are
constants. The exponent c is equivalent to the classical Hall–Petch exponent; c = 0.5 for
subgrains, which behave like grains, and c = 1 for low-energy dislocation substructure. The
constant k5 is also proportional to ()1/2, where  is the average misorientation. It is, however, fair
to point out that these generalized values or relationships are often not too consistent, making it
difficult to relate recovery-induced structure with properties.
7. Recrystallization
Even after recovery the grains may remain strained. These strained grains of cold worked metal
can be replaced by equiaxed strain free grains by further heating. The temperature where
recrystallization is completed within one hour is the recrystallization temperature. It is typically
1/3 to 1/2 of the melting temperature (can be as high as 0.7 Tm in some alloys). Here it is to be
mentioned that the recrystallization temperature decreases as the %CW is increased. Below a
"critical deformation", recrystallization does not occur, Fig.20.
44
Figure 20: Effects of cold work level on the recrystallization temperature of cold worked metals.
Primary recrystallization (also termed „discontinuous recrystallization‟) is often „viewed‟ as a
nucleation and growth process. Though similar in name and even partly in approach, to the
nucleation and growth of phase transformation or solidification, there are significant differences.
First of all, there is no „classical‟ nucleation- the driving force of recrystallization being usually
much smaller than that of „classical‟ nucleation. The recrystallized nucleus is a part of the
deformed matrix. In other words, any large subgrain or relatively well-recovered region of a
deformed grain can be considered as a potential recrystallization nucleus- purely from the
consideration of driving force, or relative differences in stored energy between the potential
nucleus and its immediate surroundings. Whether such a potential nucleus is real or active will
depend on its growth possibilities, particularly the presence of a growth-favourable boundary.
The velocity of such a boundary can be generalized as:
45
Here V, M and P are respectively, the grain boundary velocity, mobility and the net pressure on
the boundary. P has two components- PSE or pressure due to the driving force or stored energy
and PC or pressure due to boundary curvature. The former can be given in terms of dislocation
density ( = constant close to 0.5,  = dislocation density, G = shear modulus and b = Burgers
vector), while the latter can be obtained from the Gibbs–Thompson relation b and r are
respectively the grain boundary energy and curvature.
A critically important aspect of this subject is the misorientaion dependence of boundary
mobility. Low angle boundaries, such as those between sub-grains formed by
deformation/recovery, have very low mobility, while boundaries with larger misorientations
(>10–15º) have very high mobility. As a result, nucleation occurs by the rapid growth of a very
small minority of sub-grains that evolve into growing new grains. The first necessary condition
for this is that the sub-grain has, or quickly acquires, a local misorientation of more than 15º. The
rapid growth of a very few sub-grains, compared to the slow growth of the remaining sub-grains,
gives this common type of recrystallization its heterogeneous character- described as a
“Nucleation and Growth” process. Experimentally, it is impractical and impossible to exactly
separate nucleation from growth. A region free from strain (e.g. without grain boundaries or
misorientation) and exceeding a certain size (often based on the dimensions of the deformed
grains) is considered as a recrystallized grain. To achieve this size, typically of the order of a
micron, both nucleation as well as local or limited growth can be involved.
To identify the exact nuclei, or potential nuclei just turning active, is very difficult. In typical
metallic systems, the size difference between the original subgrains (potential nuclei) and the
final recrystallized grain is 10-100 times, making the probability of finding the exact nuclei in
the deformed/recrystallizing matrix of the order of 10-3-10-6. Naturally, the focus of experimental
research is often directed at identifying the recrystallization sources and also indexing and
understanding their relative contributions to the recrystallized microstructures, size, shape and
orientations of the recrystallized grains.
8. Sources of Recrystallized Grains
8.1. Deformed Grains
Deformed grain may act as a source of recrystallized grains with more or less the same
orientation as the „mother‟ grain. Recrystallized grains in low-carbon steel also originate from
deformed bands of similar orientation. Such bands are an effective recrystallization source due to
extensive formation of grain interior strain localizations. The selective formation of strain
localization leads to fragmentation of the  bands and correspondingly large variations in stored
energy.
46
8.2. Shear Bands
Shear bands cutting across several grains may also act as a source of recrystallized grains. The
potency is often related to high stored energy and correspondingly large variations in relative
misorientations and the possible presence of growth-favourable boundaries. Shear banding is
particularly strong in low-SFE metals and alloys. The formation of shear bands is often
orientation sensitive and hence, strong developments in recrystallization texture can be
associated with recrystalliztion from shear bands.
8.3. Particle Stimulated Nucleation
Dislocations can be trapped by relatively large non-shearable particles. The dislocation density
() around a particle is represented as:
Here Fv, r, s and b are volume fraction and size of the of the 2nd phase particles, shear strain and
dislocation Burgers vector. The entrapment and corresponding increase in dislocation density
leads to the formation of a deformation zone-region around the 2nd phase particles with large
misorientation developments. Though considerable efforts has been expended for modelling the
deformed zones, a comprehensive physical model remains to be developed. Recrystallization is
favoured from particle-deformed zones due to large differences in the stored energies.
Recrystallization of this type is referred as particle stimulated nucleation (PSN). The particledeformed zones, and correspondingly the PSN grains, are of randomized orientations. In particlecontaining commercial alloys, the annealing behaviour, including recrystallization texture
developments, is strongly influenced by annealing temperature. Low-temperature annealing is
often related to stronger randomization. To explain such behaviour, two approaches have been
proposed. The first approach assumes the presence of inner and outer deformed zones- the
former being more randomized. The annealing temperature is expected to determine the relative
contributions from the zones and in turn decides the recrystallization behaviour. An alternative
approach is that the relative contributions from PSN and deformation bands are responsible for
the overall recrystallization behaviour, including recrystallization texture developments.
8.4. Role of Second Phase
Following Table outlines the possible effects of different types of 2nd phase particles on the
recrystallization behaviour.
47
As shown in the table, the effects of 2nd phase particles can be generalized as (i) nucleation
advantage through PSN and/or nucleation on particle-induced strain localizations and (ii) growth
disadvantage through particle pinning or Zener drag. The latter can be used effectively to control
the grain size in a particle-containing alloy. The „pinning‟ limited grain size (DZener) is often
approximated as:
Here r and F are the particle size and volume fraction, respectively.
v
9. Dynamic Recrystallization
Under certain conditions, the structure can recrystallize during deformation giving rise to
dynamic recrystallization. In principle, this form of recrystallization can also occur during cold
deformation, but in practice, this is only exceptionally observed, e.g. in very pure metals. In this
section, dynamic recrystallization is classified as either discontinuous dynamic recrystallization
or as one of two other types. The latter are geometric dynamic recrystallization and dynamic
48
recrystallization through progressive subgrain rotation and both involve strain-induced
phenomenon with limited or no movements of high-angle boundaries. Following usual practice,
these other types have been included here as part of the present section on dynamic
recrystallization.
9.1. Discontinuous Dynamic Recrystallization
Depending on the temperature during hot deformation, the shape of the flow curve can be
„restricted‟, or work hardening rates counterbalanced, by dynamic recovery or by dynamic
recrystallization (i.e. discontinuous dynamic recrystallization), Fig.21.
Figure 21. Typical flow curves during cold and hot deformation of metals.
Dynamic recovery is typical of high-SFE metals (e.g. aluminium, low-carbon ferritic steel, etc.),
where the flow stress saturates after an initial period of work hardening. This saturation value
depends on temperature, strain rate and composition. On the other hand, as shown in Fig.21, a
broad peak (or multiple peaks) typically accompany dynamic recrystallization.
49
Figure 22. Microstructural development during recrystallization.
Figure 22 illustrates schematically the microstructure developments during dynamic recovery
and dynamic recrystallization. During dynamic recovery, the original grains get increasingly
strained, but the sub-boundaries remain more or less equiaxed. This implies that the substructure
is „dynamic‟ and re-adapts continuously to the increasing strain. In low-SFE metals (e.g.
austenitic stainless steel, copper, etc.), the process of recovery is slower and this, in turn, may
allow sufficient stored energy build-up. At a critical strain, and correspondingly at a
value/variation in driving force, dynamically recrystallized grains appear at the original grain
boundaries – resulting in the so-called „necklace structure‟. With further deformation, more and
more potential nuclei are activated and new recrystalized grains appear. At the same time, the
grains, which had already recrystallized in a previous stage, are deformed again. After a certain
amount of strain, saturation/equilibrium sets (see Fig.22b). Typically equilibrium is reached
between the hardening due to dislocation accumulation and the softening due to dynamic
recrystallization. At this stage, the flow curve reaches a plateau and the microstructure consist of
a dynamic mixture of grains with various dislocation densities.
It is important, at this stage, to bring out further the structural developments and structureproperty correlation accompanying dynamic recovery and dynamic recrystallization respectively.
Both the subgrain size (dsubgrain, from dynamic recovery) and grain size (Drex, dynamic
recrystallization) are increasing functions of temperature and of inverse strain rate. Both follow a
Hall-Petch type relationship.
50
Where  is flow stress and 1, k1, n1, 2, k2 and n2 are constants. Corresponding to dynamic
recovery, 1 has a low value and n1 is close to 1, while k1 depends on alloy composition (being
higher at higher solute content), n2 typically falls within 0.5–0.8. Unlike static and dynamic
recovery, recrystallization includes another classification- a sort of grey area between dynamic
and static: meta-dynamic recrystallization. In this situation, the recrystallized nuclei form or
nucleate dynamically, during hot deformation, but growth takes place during subsequent static
annealing.
10. Hot Working
Plastic deformation of metal carried out at temperature above the recrystallization temperature, is
called hot working. Under the action of heat and force, when the atoms of metal reach a certain
higher energy level, the new crystals start forming. This is called recrystallization. When this
happens, the old grain structure deformed by previously carried out mechanical working no
longer exist, instead new crystals which are strain-free are formed.
In hot working, the temperature at which the working is completed is critical since any extra heat
left in the material after working will promote grain growth, leading to poor mechanical
properties of material.
In comparison with cold working, the advantages of hot working are:
1.
2.
3.
4.
5.
6.
No strain hardening
Lesser forces are required for deformation
Greater ductility of material is available, and therefore more deformation is possible.
Favorable grain size is obtained leading to better mechanical properties of material
Equipment of lesser power is needed
No residual stresses in the material.
Some disadvantages associated in the hot-working of metals are:
1.
2.
3.
4.
5.
6.
Heat energy is needed
Poor surface finish of material due to scaling of surface
Poor accuracy and dimensional control of parts
Poor reproducibility and interchangeability of parts
Handling and maintaining of hot metal is difficult and troublesome
Lower life of tooling and equipment.
We know that hot working is carried out above the recrystallization temperature, which is
approximately 0.4Tm of the metal. So, for calculation of the hot working temperature we need to
know the melting temperature, which is also chemical composition dependent. In order to define
the recrystallization temperature (Trec), it is necessary to know exact percentages of the steel
51
alloy components. Then, at first, melting temperature Tm is calculated from the following
empirical relation:
Tm = 1537 – (88C + 8Si + 5Mn + 5Cu +1.5Cr + 4Ni + 2Mo + 2V + 30P + 25S) °C
Then the Trec will be = 0.4Tm
The starting hot rolling temperature depends on the rate of heat loss by radiation and conduction
and total time of forging.
Note: Get ready to solve related problems for design of forging operation.
11. Warm Working
Metal deformation carried out at temperatures intermediate to hot and cold forming is
called Warm Forming. Compared to cold forming, warm forming offers several advantages.
These include:
a) Lesser loads on tooling and equipment
b) Greater metal ductility
c) Fewer number of annealing operation ( because of less strain hardening )
Compared to hot forming, warm forming offers the following advantages.
a)
b)
c)
d)
e)
f)
g)
Lesser amount of heat energy requirement
Better precision of components
Lesser scaling on parts
Lesser decarburization of parts
Better dimensional control
Better surface finish
Lesser thermal shock on tooling
Shaft joint manufactured using a combination of warm forging and cold sizing. As-forged part
on the left, finished part on the right.
52
Problem 3: A copper bar is to be cold rolled into a section which must have a min. tensile
strength of 390 MPa. If the final cross-sectional area is 20.13 mm2 and assuming the flow
properties of the workpiece material are given as K = 450 MPa, n = 0.33. Calculate the
followings:
a) The tensile strength of the annealed material.
b) The initial diameter of the copper bar.
Solution: It is important to understand the question well. In this question, the copper bar is
annealed first then a cold rolling operation is done on it. Initial diameter of the copper bar is
same before and after the annealing operation.
a) Flow stress of the plastically deformed bar could be shown as  = 4500.33. As shown in
Course Slides at UTS  = n = 0.33.
Then UTS of the original bar (no annealing, no cold working) is found as below:
u = 450 (0.33)0.33
u = 312.12 MPa
Since before necking occurs (< n) area stays constant at the whole bar, the formula below could
be used:
By putting the area ratio into the formula (i) UTS of the annealed material is found as:
b) For this question d0 can be found by using the ratio:
53
If <n (which means necking is not started yet) with the UTScw value given in the question as
UTScw = 390 MPa, to check the value
So  n which means that necking started, then UTScw becomes equal to flow stress of the
deformed material,
54
Chapter Three
Sheet Metal and Superplastic Forming
1. Introduction
Large quantities of thin sheets are produced at a relatively low cost by rolling mills. They are
transformed into familiar products, such as beverage cans, car bodies, metal desks, domestic
appliances, various parts of aircrafts, etc., by sheet metal forming processes. Many of these
processes involve a rather complex deformation path. In most cases, the latter can be considered
as a superposition of some „elementary‟ processes like bending, stretching and deep drawing,
which will be discussed in this chapter. In most sheet metal forming processes, the stress
perpendicular to the sheet surface is small compared to the stresses in the plane. It is often
assumed that this „normal‟ stress can be neglected. When the normal stress is zero, the stress
state is called „plane stress‟.
2. Bending and Folding
Bending is a relatively simple forming operation, which can be achieved in various ways. A
schematic illustration of a bended sheet is shown in Fig.1. During bending, the convex part of the
sheet (the upper part) is in tension and the concave (lower) part in compression.
Figure 1: Illustration of a simple bending operation.
The strain is zero at the neutral axis and maximum at the outer surface. The strain distribution over the
thickness is linear, as illustrated in Fig.2. At a distance y from the neutral axis  = y/r with r the
end radius and at the surface max = t/2r. The strain state during bending of a sheet (with wt) is
approximately plane strain with l = -t and w = 0. The stress state is biaxial with at the surface
with l = (2/3)f with f the flow stress in a simple tensile test and for isotropic materials and
55
w= (l/2) and t = 0. S = (2/3)f is the so called „plane strain flow stress‟. For anisotropic
material it can be calculated from:
Figure 2: Stress and strain distribution over the sheet thickness.
If the width of the sheet is not at least 8–10 times larger than the thickness, the stress ratio w/l decreases
as shown in Fig.3. For practical applications, it is important to know how far a sheet can be bent before
cracks appear at the surface.
Figure 3: Ratio of w /l as function of the width over thickness ratio, the bending limit.
It is difficult to calculate an accurate bending limit. An approximate value can be estimated from
the reduction in area (RA) in a uniaxial tensile test:
According to above equation, a small bend radius can be reached for ductile materials with a
large RA value; for most materials, this means a low yield strength. This rule of the thumb must
56
however be used with some caution because microstructural effects, especially a morphological
texture, can have a big influence on the bendability. The bending limit predicted can only be
reached when the length of the bended zone is sufficiently large. When the length of the bended
zone (l = r) is too small (Fig.4), the maximum strain in the outer surface will not be reached
because the whole length is taken by a transition zone between bended and unbended parts. Only
when l increases by increasing r or increasing , a zone with constant maximum strain in the
outer region will be present.
Figure 4: Effect of bending (r/t) on the strain along the circumference.
2.1. Spring Back and Residual Stress
Spring back is a dimensional change that occurs after plastic forming and unloading, and is a
consequence of the recovery of the elastic part of the deformation (Fig.5).
Figure 5: Spring back as a consequence of the recovery of the elastic part of the deformation. A: end of the
elastic deformation (=f); B: end of the plastic deformation; C: recovery of elastic deformation.
57
For an ideal plastic material it was shown by Hosford and Caddell [1983] that  = 3yS/tE, with
E the Young‟s modulus in plane strain [E =E/(1–2) with  the coefficient of Poisson‟s ratio, t
the sheet thickness and y the distance to the neutral fiber. In this case the following relationship
exists:
In practice, it remains a difficult task to predict the spring back accurately. Formula can be used
as a first estimate and shows which parameters will have an influence on spring back. It appears
that spring back will increase with increasing flow stress, increasing strain hardening coefficient,
decreasing Young‟s modulus and decreasing sheet thickness. After bending and subsequent
relaxation of the elastic stress, an internal stress remains inside the sheet. For an elastic-idealplastic material (Fig.6a), it can be shown that the elastic relaxation can be estimated from = (3y/t)S. Superposition of the total stress during bending and elastic relaxation leads to an internal
stress profile shown in Fig.6c. It means that after unloading a compressive stress (-0.5S) is
present at the outer (convex) surface and a tensile stress (0.5S ) remains at the inner surface.
Figure 6: Bending stress (a), elastic relaxation (b) and residual stress (c) through the sheet thickness.
3. Deep Drawing
In deep drawing, a sheet is pushed through an opening in a die. A blank holder prevents
wrinkling of the sheet but, in contrast to stretching, the material from the flange can more or less
be drawn towards and into the die opening without constraints. The most common example of
deep drawing is the formation of a cylindrical cup (Fig.7). For a constant punch diameter Dp, the
height of the cup wall will increase with increasing sheet or blank diameter (Dbl). There is,
however, a limit to the height that can be obtained in one drawing pass, without fracturing the
cup wall. This limit is called the „limiting drawing ratio‟ or LDR and is defined as:
58
Figure 7: Deep drawing of a cylindrical cup from a circular blank.
During deep drawing, four important zones can be identified: Zone 1: the flange, Zone 2: the
transition between flange and cup wall, Zone 3: the cup wall and zone 4: the bottom of the cup
(Fig.8).
Zone 1: The situation in zone 1, i.e. in the flange is more complicated. The material is drawn
into the die hole by a radial tensile force. An imaginary circle on the flange will shrink during
drawing, so the stress state is tensile in the radial and compressive in the circumferential
directions. In an ideal case, the strain can be considered as „ideal drawing‟ without change in
thickness (point C). At the outer surface, rad = 0 (point C). At the edge of the die hole, using
Tresca‟s yield criterion (Marciniak et al. [2002]), the stress state can be described by:
Where f is the flow stress. Since rad cannot exceed f , the limiting drawing ratio Dblmax/Dp = e
= 2.27. In that case, cir = 0 (point C). In reality, the most deep drawing materials have an LDR
value between 2-2.4, which keeps rad f and cir0. In any case, the strain state will be such that
the material will thin down. In many cases, the blank holder, whose principle task is to prevent
the flange from wrinkling, will prevent (or limit) the thickening of the blank.
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Figure 8: Stress and strain state in various points of the cup during deep drawing. Possible
compressive stresses in flange and wall are not taken into account.
Zone 2: The transition between flange and cup wall is done by bending and unbending. This will
add some extra component to the total force needed for deep drawing, it will increase the work
hardening and it will lead to an extra reduction in thickness. The total force P that has to be
exerted on a blank to draw a cup, depends on many factors. Besides the complicated stress state
described above, the friction between blank holder and flange and between cup wall and die must
be considered, as well as the blank holder force and the force needed to bend the material. An
approximate equation for the total punch force as function of the blank diameter Dbl at any stage
of the process is:
Here Dbl the blank diameter, Dp the punch diameter, t the thickness of the wall, f is the average
flow stress, A the force to bend and unbend the material, B the blank holder force,  the friction
coefficient. The first part of the equation gives the ideal force to draw a cup, the second term
expresses the friction force under the blank holder and the exponential factor brings the friction
between wall and die into account.
Zone 3: The force exerted by the punch is transmitted to the deforming flange by the material in
the cup wall. Hence this material is subjected to a tensile force. Because of the geometry of the
cup and punch, no contraction in the circumferential direction is possible. This results in a plane
strain deformation (an elongation of the cup wall compensated by a reduction in thickness), point
B in Fig.8. The purpose of deep drawing is to concentrate the deformation in the flange and not
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in the cup wall. For this reason, the thinning of the wall must be kept to a strict minimum. As
will be explained in the following paragraph, this is done by choosing materials with a large R̅
value. With the assumption that flange, wall and bottom of the cup retain the initial sheet
thickness, the following expression for the height of the cup can be found:
For a material with a LDR = 2.25, the maximal cup height that can be drawn in one pass is equal
to the cup diameter. It must be noted that the assumption of constant wall thickness is not
completely correct. In reality, the wall will thin down close to the bottom part, while the top is
thickened.
Zone 4: The bottom of the cup, which is formed by the material under the punch, is equibiaxially
stretched (point A). In principle, the material will thin down; but in practice, the strain in the
bottom is not so large and it is often assumed that the bottom of the cup has more or less the
same thickness as the original sheet.
3.1. Redrawing and Ironing
According to earlier section, the cup height that can be obtained in one single drawing pass is
limited. To obtain deeper cups, two techniques are frequently used: redrawing and wall ironing.
Both techniques are illustrated in Fig. In redrawing, several consecutive drawing passes are
applied. After each pass, the cup radius decreases and the cup height increases. When the cup is
turned inside out after each pass, the process is called „reverse redrawing‟. In wall ironing, the
cup passes through a series of ring shaped dies (Fig.9, right). The clearance between the punch
and each die is less than the local sheet thickness, which increases the height and decreases the
thickness of the cup wall.
Figure 9: Redrawing, reverse redrawing and wall ironing to produce deeper cups.
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Problem 1: A 0.5 mm thick sheet is to be drawn with a LDR of 1.9 to produce a container with
an inside diameter of 40 mm and a height of 60 mm. Tensile strength is 150 MPa. Assume the
thickness of the bottom and the walls of the container remain unchanged. (i.e., 0.5 mm).
a) Calculate the diameter of the initial circular blank necessary.
b) For drawing the same initial circular blank, check if single drawing is enough and if not
calculate the smallest possible punch diameter for the first step and estimate the number of
redrawing necessary.
c) Calculate the drawing force. (If single drawing is not enough calculate the drawing force of
the first step).
Solution:
(a) Using volume constancy:
Do = 106.4mm
(b) LDR = 1.9
So, redrawing is necessary.
After first redrawing:
This means single redrawing is sufficient.
(c) Drawing force:
For no friction condition, we just need to consider the first term only. In this respect, the drawing
force will be 16kN.
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3.3. Spinning
In a conventional spinning process (Fig.10a), a circular blank is pushed against a mandrel and
rotated. With a rigid tool (often in the form of rollers), the blank is forced against the mandrel.
Spinning is a useful cold forming technique for shaping relatively simple axisymmetric parts.
Figure 9: (a) Conventional spinning, (b) shear sinning and (c) tube spinning.
Shear spinning is a variant of conventional spinning in which each element of the blank
maintains its distance from the axis of rotation. A direct consequence is a reduction of the part‟s
thickness (Fig.9b): tpart = tblank sin. For many materials, the maximum reduction in wall
thickness is around 80%. Some materials with low ductility can be spun at elevated temperature.
In tube spinning (Fig.9c), the wall thickness of a cylindrical part is reduced by spinning on a
cylindrical mandrel. This operation can be carried out internally or externally.
4. Stretch Forming
In stretch forming, the material is clamped along the edges and stretched over a punch. A simple
case of stretch forming is an equi-biaxial stretch over a hemispherical punch as shown in Fig.10
(left).
Figure 10: Complex stretch-forming operation
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The edges of the sheet are clamped by some groove in the die (the so-called „draw-bead‟). In
many industrial stretch forming operations, the situation is more complex. The sheet is often
rectangular and is clamped along two sides only (Fig.10, right). In this case, the strain is close to
plane strain. The middle section of the sheet is less stretched because of the friction between
punch and sheet. To avoid unstretched regions (without work hardening) uniaxial stretching with
the clamps, before „draping‟ the sheet over the punch can be a solution. In many cases, the
clamps can not only exert a tensile force, but can also rotate in order to maintain the tensile force
tangential to the sheet.
5. Hydroforming
Hydroforming (or fluid forming) is a relatively new technique with an increasing number of
applications in the automotive and aircraft industry. The principle is rather simple: a sheet or
tube is pressed into a die cavity by fluid pressure. In most cases, the fluid is separated from the
material by a flexible membrane. In some cases, the die itself can move, to assist the
deformation. The production rate of hydroforming is smaller than in conventional press forming,
but hydroforming has the advantage that more complex parts can be formed in one pass. Sheet
hydroforming is well suited for prototyping or for low volume production, which is often
required in the aerospace industry. A closer control over the sheet thickness is possible and less
springback is noticed. In the automotive industry, hydroforming is used for shaping alloys with
lower formability (e.g. aluminium alloys and high strength steels). It can be used for both sheet
and tube forming
5.1. Sheet Hydroforming
An illustration of sheet hydroforming is shown in Fig.11. The two principal deformation modes
are stretch forming (the pressure of the blank holder is high and the flange material is not
allowed to flow into the die cavity) and deep drawing (the flange material is allowed to flow into
the die cavity).
Figure 11: Schematic illustration of sheet hydroforming.
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Most practical hydroform operations start with stretching. When the internal pressure increases,
the tensile force on the flange increases and at a certain point the material under the blank holder
is pulled inwards and the deformation becomes a combination of deep drawing and stretching, as
shown in Fig.12. When the internal pressure is too high, two failure modes are possible. For a
relatively low blank-holder force, the sealing between die and blank holder starts leaking. For
high blank-holder forces, the sheet or part will burst open.
Figure 12: Influence of blank holder force and internal pressure on the strain mode and
failure mechanism during hydroforming.
5.2. Tube Hydroforming
Hydroforming can also be used to deform tubes. An example of a fabrication route is shown in
Fig.13. A tube, in some cases pre-bend, is placed in a die. The die is sealed off on both ends and
the tube is put under internal pressure. This pressure may range from 2000 to 10 000 bar,
although 3000 bar will do for many applications. An axial displacement of the seals assists the
material flow into the cavities of the die. A good synchronization between the pressure built-up
and the axial feeding is required. During tube hydroforming, some typical defects can occur.
„Bursting‟ occurs when the pressure in the tube rises too fast and not enough extra material can
flow into the die. It is also the typical failure mode at high blank-holder forces. A too fast „axial
feeding‟ of material, will however lead to buckling or wrinkling of the tube.
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Figure 13: Tube hydroforming; (a) positioning of the tube in the die; (b) sealing off the tube and filling
with fluid; (c) pressurizing combined with axial feeding; (d) opening of the die.
6. Defects in Sheet Metal Forming
6.1. Lüder Bands
Lüderlines or stretcher strain marks become visible after press forming of a sheet and have a
typical „flame-like‟ pattern as shown in Fig.14. This surface pattern is, in most applications,
unacceptable for visible parts.
Figure 14: Lüder band caused surface defects on press formed sheet products.
The phenomenon is well known in most steels and in certain aluminium alloys. It can easily be
detected with a simple tensile test. Materials which are prone to form Lüderlines during press
forming always show a so-called „yield point elongation‟ or „Lüderstrain‟ in the stress–strain
curves obtained in a tensile test. The reason for these Lüderstrains is the pinning of dislocations
by carbon atoms in steel or by substitutional atoms in aluminium. In steel the effect can be
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eliminated by giving a so-called „skin pass‟ (a few per cent cold rolling reduction) or by „roll
levelling‟ (bending–unbending). This liberates the dislocations from their pinning points. In
aluminium the effect can be avoided by grain size control (a grain size above 10-15m is
required).
6.2. Orange Peel
Plastic deformation, for example: stretching, bending and drawing, may develop rough surface,
which is generically termed as „orange peel‟. This has been reported in aluminium and also in
steel. Coarse surface grains are usually considered to have less constraints to plastic deformation.
This, on the other hand, may cause severe non-uniform deformation between the surface grains,
leading to an apparent roughening or an „orange peel‟ condition, Fig.15. The development of
„orange peel‟ or surface roughness is dependent on the surface grain size effect being negligible
at finer grain sizes. Though cluster of small grains of the similar crystallographic orientations
may act as individual coarse grain(s) and create „orange peel‟ effects, no clear relationship
between „orange peel‟ and the crystallographic orientations of the surface grains has been
reported.
Figure 15: Orange peel like surface defect.
6.3. Wrinkling
Wrinkling or the formation of surface roughness/wrinkles (Fig.16) is caused by internal
compressive stresses, plastic as well as elastic. It is usually observed in the flange, but is also
reported in the free forming zone between die and tool, when the minor stress of sheet metal
forming is compressive in nature. Normally, wrinkling is more severe in metals with lower
normal anisotropy. Wrinkling also depends on tooling, elastic modulus and sheet thickness and is
normally considered as a complicated phenomenon, exact initiation and growth of wrinkling
limit being difficult to predict theoretically.
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Figure 16: Wrinkling in deep drawing products.
To avoid wrinkling, usually the blank holder pressure is increased, which, on the other hand,
introduces additional strain in the sheet metal and hence may provide a narrow processing
window between wrinkling limit and failure limit. An alternative exists by forming at elevated
temperatures. Thermal shrinking of sheet metal is attributed to reduce compressive stresses and
the resulting wrinkling, while elevated temperature forming also improves drawability by
reducing the yield strength. Alternate forming technologies, e.g. hydroforming and electromagnetic forming, are often „recommended‟ as techniques with lesser „wrinkling‟.
6.4. Roping
Roping or looper lines (Fig.17), is also a phenomenon of surface roughening, observed during
deep drawing. The name roping is linked to characteristic „roping‟ marks on drawn shapes. The
roping is also caused by non-uniform deformation, non-uniformity linked to irregularities or
heterogeneities in the structure. For example, macro-segregation from the cast structure may
produce striated structure or surface banding or roping marks. Alternatively, the roping may also
develop from deformed grains or bands of fine grains of similar orientations– both may originate
from earlier coarse grains.
Figure 17: Roping in sheet metal forming.
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7. Superplasticity and Superplastic Forming
Superplasticity can be described as „the capability of crystalline materials to undergo very large
plastic deformations under tensile loading‟. We know that the flow stress of materials usually
increases with strain rate. The strain rate effect at constant strain can be approximated by:
Here C is a strength constant that depends upon strain, temperature and material, and m is the
strain rate sensitivity of the flow stress. For most metals at room temperature, the magnitude of
m is quite low (between 0 and 0.03). The ratio of flow stresses, σ2 and σ1, at two strain rates, ε2
and ε1, is:
Taking logarithms of both sides:
If, as is likely at low temperatures, σ2 is not much greater than σ1, earlier can be simplified to:
Problem 2: Find out the increase in the flow stress of a material having the strain rate sensitivity
factor 0.01 if the strain rate is increased by a factor of 10.
Solution: 2% increase in flow stress.
If one wishes to predict forming loads in wire drawing or sheet rolling (where the strain rates
may be as high as 104/sec) from data obtained in a laboratory tension test, in which the strain
rates may be as low as 10–4/sec, the flow stress should be corrected unless m is very small. This
means materials of higher m values are very sensitive to strain rate. A material‟s strain rate
sensitivity is temperature dependent. At hot working temperatures, m typically rises to 0.10 or
0.20, so rate effects are much larger than at room temperature. Under certain circumstances, m
values of 0.5 or higher have been observed in various metals. The higher values of rate
sensitivity at elevated temperatures are attributed to the increased rate of thermally activated
processes such as dislocation climb and grain boundary sliding.
To be superplastic, the m value of the material must be  0.5. Some other conditions also need to
be satisfied as mentioned below.
a) An extremely fine grain size (a few micrometers or less), with generally uniform and
equiaxed grain structure.
b) High working temperatures (T > 0.4 Tm).
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c) Low strain rates (10–2/sec or lower).
In addition to the above conditions, the microstructure should be stable, without grain growth,
during deformation. Under these conditions, extremely high elongations and very low flow
stresses are observed in tension tests, so the term Superplasticity. In super plastic material, the
tensile elongation is more than 100%, which is more than several hundred percents in many
cases, Fig.18.
Figure 18: Strain rate and temperature dependent elongation in superplastic materials
High m values promote large elongations by preventing localization of the deformation as a
sharp neck. This can be seen clearly in the following example.
Problem 3: Consider a bar that starts to neck. Prove that strain rate at the unnecked area is rather
higher than that of the necked area.
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Solution: If the cross sectional area in the neck is An and outside the neck is Ao, F = σoAo = σnAn
or σo/σn = An/Ao. Now from earlier equation we can write:
Since An<Ao, if m is low, the strain rate outside the neck will become negligibly low. For
example, let the neck region have a cross sectional area of 90% of that outside the neck. If m =
0.02, εo/εn = (0.9)50 = 5 × 10−3. If, however, m = 0.5, then εo/εn = (0.9)2 = 0.81, so that although
the unnecked region deforms slower than the neck, its rate of straining is still rather large.
Owing to the large deformation during superplastic forming, significant thinning of the sheet is
unavoidable. In many cases, this thinning will not be uniform throughout the sheet. It can be
calculated and experimentally verified that this will lead to more thinning at the pole than at the
edge. The difference in thickness will be larger when the strain rate coefficient m is smaller,
Fig.19.
Figure 19: Relative wall thickness between edge and pole of a hemisphere, for different values of the
strain rate sensitivity coefficient m (t: actual wall thickness; tm: mean wall thickness.
Metals and their alloys are not only superplastic materials. Composites and ceramics might also
be superplastic. Some of superplastic materials are listed in the following Table.
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7.1. Superplastic Forming
It was mentioned that superplasticity occurs in fine grained materials, deformed at high
temperature and low strain rate. In the present paragraph, the technology of superplastic forming
will be introduced. In most cases, superplastic forming is carried out with one of the following
techniques: blow forming/vacuum forming, thermo forming or superplastic forming combined
with diffusion bonding. Forging and extrusion can also be used to shape superplastic materials.
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7.2. Blow Forming and Vacuum Forming
These are related techniques. In blow forming, a gas (mostly argon) is used to create a pressure
difference over the (warm) superplastic sheet (Fig.20). The sheet is stretched and forced to adopt
the shape of the die. The outer side of the sheet is held in a fixed position and does not draw in as
would be the case in deep drawing. In some cases, a „back pressure‟ is used to prevent cavitation.
In vacuum forming, the pressure difference over the sheet is generated by vacuum in one of the
die chambers. In this case, the pressure difference is limited to 1 atmosphere.
Figure 20: Illustration of the blow-forming technique for superplastic forming.
7.3. Thermo Forming
Thermo forming is a typical forming technique for plastics. In this technique, a moving die is
used in conjunction with a gas pressure. Several configurations are possible, e.g. a male die is
used to stretch form the superplastic sheet. After that, a gas pressure is used to force the sheet
against the die (Fig.21). One of the most important advantages of superplastic forming is that
complex shapes can be produced in one piece and most often in one pass. The absence of welds,
rivets, etc. diminish the risk for fatigue damage and corrosion. An additional advantage is that
little or no residual stresses are present. The low forces acting during superplastic forming reduce
the tooling cost. A disadvantage of superplastic forming is of course the low production rate,
because of the limitations in maximum allowed strain rate.
Figure 21: Illustration of a possible set up for the thermo forming technique.
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7.4. Diffusion Bonding and Superplastic Forming
Superplastic forming is a relatively slow process that yields low production rate. The low
production rate could be turned into an advantage when superplastic forming is combined with
diffusion bonding (the „SPD/DB‟ process). Two or more sheets of superplastic material are
stacked together but make direct contact with each other only at some well-chosen locations
(Fig.22a). At the other contact areas, a diffusion barrier (a so called „stop-off‟ material) is used.
In a first step, the sheets are heated and bonded together at the chosen locations by diffusion
bonding. This bonding process is „assisted‟ by an external gas pressure (Fig.22b). In a
subsequent step, the small clefts at the stop-off material are expanded by an internal gas pressure
(Fig.22c). The outer sheets are forced into the die cavities and the final shape is being formed
(Figure 11.72d). The stop-off material depends on the material of the sheets. For titanium alloys,
yttrium and boron nitride have successfully been used. The SPD/DB technique is well
established for titanium alloys and has many industrial applications, for example, in the aircraft
industry. For aluminium alloys, diffusion bonding is less evident because of the surface oxide
film and solutions have been sought by introducing interlayers in the form of claddings, coatings
or foils.
Figure 22: Combination of superplastic forming with diffusion bonding.
Problem 4: A tensile test on a certain metal is carried out at a temperature of 540oC. At a strain
rate of 10/s, the stress is measured as 160 MPa; and at a strain rate of 300/s, the stress is
measured as 310 MPa.
a) Determine the strength constant C in MPa and the strain rate sensitivity exponent m.
b) If the temperature were 480oC, what changes would you expect in the values of C and m?
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Solution:
a)
b) Since the temperature is lower, the strength constant would be higher whereas the strain rate
sensitivity exponent would become smaller.
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Chapter Four
Forging
1. Introduction
Forging was the first of the compression type process and is probably the oldest method of metal
forming. It involves the application of a compressive stress which exceeds the flow stress of the
metal. The stress can either be applied quickly or slowly. The process can be carried out hot or
cold, choice of temperature being decided by such factors as whether ease and cheapness of
deformation, production of certain mechanical properties or surface finish is the overriding
factor. Over other manufacturing processes, forging provides some benefits some of which are
discussed below.
Stronger Components
Forging provides better mechanical properties, ductility and fatigue and impact resistance
because this process refines and directs the grain flow according to the shape of the piece, Fig. In
most cases, the ingots have been pre-worked and this produces a “grain flow” with important
directional properties.
Figure 1: Grain refinement and fiber flow in forged products.
Usuable for a Wide Range of Metals
Almost all metals such as ferrous and non-ferrous can be forged. Any kind of steel can be used:
carbon, alloy, stainless or superalloy. Here it is to be noted that the forgeability of all metals are
not the same. Following Table shows a list of forgeable metals with decreasing forgeability.
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There is a range of more than 2,500 types of steel from which to choose to achieve the most
economical production process. The forgeability of some of the common steel groups are
presented in the Table below. Note that the forgeability is in decreasing order from top to
bottom.
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Significant Savings
Forging reduces the weight required to manufacture the piece, therefore, there is a real and
significant cost savings. Also, the pieces have less excess so they require less machining hours
and less material to be used to clean the piece at the end. Recently, it has been possible to
produce net shape or nearly net shape products by precision forging.
Wide Range of Shapes and Sizes
The design of shapes (Fig.2) is so versatile that they can be forged from simple bars and rings to
more complex pieces, according to different needs.
Figure 2: Wide range of forged products.
Not only diversive product shape, size and geometry, forging ensure defect free high strength
reliable products. As a result, demand of forged products are increasing every day, especially
where safety is very important in the case load bearing components. Following Fig.3 provides a
view of approximate shares of forged products in various engineering applications.
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Figure 3: Market shares of products.
2. Forging Alloys
2.1. Commonly Forged Light Weight Materials
The commonly used lightweight materials are (i) Aluminum and (ii) Titanium. Another material
of growing interest is magnesium.
2.1.1. Aluminum Alloys
Within the family of structural metals and alloys, aluminum alloys are the material most readily
forged to precise, intricate shapes and proper lubrication are used to prevent galling and seizure.
The significant reasons for this are: (i) the alloys are ductile, (ii) they can be forged in dies
heated to essentially the same temperatures as the workpiece, (iii) the material do not develop
scale during heating and (iv) low forging pressures required.
Research studies shows that deformation rate and solidus temperature play the most vital role
influencing the forgeability for aluminum alloys. Most of these alloys are forged at about 55ºC
(100º F) below the solidus temperature. Where it is known that forging increases the process
temperature, hence leading to too rapid temperature increase for too large forging. To minimize
this risk, forging temperatures are often adjusted downward for increasing amounts or increasing
rates of reduction. The two main factors normally considered in forging of aluminum alloys
would be the grain flow and final grain size. These factors greatly affect the final shape and
properties after forging. Wrought aluminum alloy bars generally exhibit directional ductility, the
highest ductility is seen in the longitudinal direction of the bar and the lowest ductility is
experienced in the transverse direction. The transverse ductility can be improved by forging if
the bar is deformed to produce flow in the transverse or lateral direction. Whilst, the heat
treatable aluminum alloys are generally strengthened slightly by forging in hot working range.
This is due, in part, to the accompanying reduction of grain size and to a certain extent, to
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precipitation hardening that occurs at the working temperatures. Maximum strength is
subsequently attained by solution heat treating, quenching and aging.
2.1.2. Titanium Alloys
Titanium alloys can be readily forged into various shapes, sharing similar forgeability with other
metals such as steel. Titanium alloys of various compositions do exhibit different degrees of
forgeability based on their forging temperature range, forging pressure requirements, sensitivity
to strain rate and susceptibility to cracking. Generally for this material, for the same amount of
metal flow, more forging power is required than that required for alloy steels. Forging experience
indicates that an alloy such as Ti-6Al-4v requires one and one half to two times the machine
capacity needed to forge low alloy steel into comparable shapes. For the above reasons, the
particular forging characteristics of individual titanium alloys need to be considered with care in
order to obtain the preferred shapes and properties. Forging temperature and pressure
considerations must be given a high priority in either the open die or impression die forging of
titanium alloys. The pressure required to forge titanium alloys increases at a faster rate as the
working temperature decreases as compared to the pressure required for forging alloy steel. This
effect of working temperature on the forging pressure is the characteristics of titanium alloys;
there is some variation in this characteristic with alloy content. Also, forging pressure increases
in an approximately linear relationship with the logarithm of the strain rate. Furthermore,
because titanium alloys exhibit rapid increasing strengths with increasing strain rates, more
energy is therefore required, for example, in hammer forging than in press forging at comparable
temperatures. On the other hand, better temperature control of the work piece is possible,
resulting in less heat loss when fast acting, high strain rate machines are used.
2.1.3. Magnesium Alloys
Forgeability of magnesium alloys is influenced by three important factors: solidus temperature,
deformation rate and grain size. Magnesium alloys are usually forged at higher temperatures
within its solidus temperature. The high zinc magnesium alloy (ZK60) will sometimes contain
small amounts of the low melting eutectic that forms during ingot solidification. This eutectic
melts upon heating to temperatures above 300°C (600° F) and can cause severe fracturing when
the alloys are forged above this temperature. To minimize this problem, suppliers generally
homogenize cast ingots at elevated temperatures for extended period to re-dissolve the eutectic
and to restore the higher solidus temperature. The commercial alloys containing aluminium,
zirconium and thorium do not form low melting eutectics and therefore are not subject to
dimensional instability at low temperatures.
Magnesium alloys forged at room temperature exhibit different forgeability as compared to hot
forging. At temperature as low as 100°C, forging of magnesium alloys might not be favourable,
similarly the ductility, are strongly dependent on forging procedures. In general, both
longitudinal and transverse ductility improve with decreasing grain size and with increasing
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amount of works. Although the basic strength properties of magnesium alloys are determined by
alloy composition, forging plays an important role in establishing property uniformity and
maximum ductility. It is important to provide as much flow in the transverse direction as possible
during forging. This is necessary because wrought magnesium alloys bars require high
directional ductility. By providing transverse metal flow, the transverse ductility is improved and
the longitudinal ductility is kept high. The ductility of magnesium alloys not only vary according
to the type of magnesium alloys, it depends on the die temperature as well. The effective control
on the die temperature contributes to the final product properties. If die temperature fall much
below forging temperatures, surface cracking becomes a potential problem. Typically when the
die temperature exceeds forging temperatures, the metal will flow past impression and promotes
under filling.
It has been discussed that all metals and metal alloys, with very few exceptions, are suitable for
forging. Because of variations in yield strength of various forgeable metals and alloys, their
forging loads are also variable as shown in the following Fig.4.
Figure 4: Forging force requirement for various alloys.
3. Types of Forging
There are two kinds of forging process, Impact Forging and Press Forging. In the former, the
load is applied by impact and deformation takes place over a very short time. Press forging, on
the other hand, involves the gradual build up of pressure to cause the metal to yield. The time of
application is relatively long. Over 90% of forging processes are hot. Impact forging can be
further subdivided into three types:
(a) Smith forging
(b) Drop forging
(c) Upset forging
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3.1. Smith Forging
This is undoubtedly the oldest type of forging, but it is now relatively uncommon. The impact
force for deformation is applied manually by the blacksmith by means of a hammer, Fig.5.
Figure 5: Shaping in smith forging process.
The piece of metal is heated in a forge and when at the proper temperature is placed on anvil.
This is a heavy mass of steel with a flat top, a horn which is curved for producing different
curvatures and a square hole in the top to accommodate various anvil fitting. While being
hammered the metal is held with suitable tongs. Formers are sometimes used, these have handles
and are held onto the workpiece by the smith while the other end is struck with a sledgehammer
by a helper. The surfaces of the formers have different shapes and are used to impact these
shapes to the forging. One type of former, called a fuller, has a well-rounded chisel shaped edge
and is used to draw out or extend the workpiece. A fuller concentrates the blow and causes the
metal to lengthen much more rapidly than can be done by using a flat hammer surface. Fullers
are also made as anvil fittings so that the metal is drawn out using both a top and bottom fuller.
Fitting of various shapes can be placed in the square hole in the anvil. The working chisels are
used for cutting the metal, punches and a block having proper-sized holes are used for punching
out holes. Welding can be done by shaping the surfaces to be joined, heating the two pieces are
then hammered together producing welding. The easiest metals to forge are the low and medium
carbon steels and most smith forgings are made of these metals. The high carbon and alloy steels
are more difficult to forge and require great care. Most non-ferrous metals can be successfully
forged.
3.2. Drop Forging
This is the modern equivalent of smith forging where the limited force of the blacksmith has
been replaced by the mechanical or steam hammer. The process can be carried out by open
forging where the hammer is replaced by a tup (die) and the metal is manipulated manually on an
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anvil. Figure 6 shows the drop forging setup, where the tup is operated by gravity. The quality of
the products depends very much on the skill of the forger. Open forging is used extensively for
the cogging process where the workpiece is reduced in by repeated blows as the metal gradually
passes under the forge.
Figure 6: Drop hammer forging operation.
In forging hammers the force is supplied by a falling weight or ram. The two basic types of
forging hammers are the board hammer and the steam hammer (Fig.7). In the board hammer the
upper die and ram are raised by rolls gripping the board. When the ram is released, it falls
owing to gravity. The energy supplied to the blow is equal to the potential energy due to the
weight of the ram and the height of the fall. Board hammers are rated by the weight of the falling
part of the equipment. They range from 400lb hammers with a 35in. fall to 7,500lb hammers
with a 75in. fall.
Load is applied by dropping the hammer (impact load) over the workpiece. Here the potential
energy transfers to deformation energy via kinetic energy. So, from the concept, finally the
following relationship can be made for drop forging.
Here m mass of hammer, g gravitational force, h height of fall, v velocity just before fall, 
required strain, n strain hardening coefficient and K constant. In the case of hot forging, there
will be no strain hardening. In such case the relationship will be:
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Greater forging capacity, in the range from 1,000 to 50,000 lb, is available with the steam
hammer (Fig.7).
Figure 7: Steam drop hammer forging.
Steam is admitted to the bottom of a cylinder to raise the ram and it enters the top to drive the
ram down. Since the falling ram is accelerated by steam pressure, the energy supplied to the
blow is related to the kinetic energy of the falling mass. In this case the available energy is sum
of the potential energy from gravity and the steam or air pressure:
E = (w + PA)H
Here E is the hammer energy, w is the weight of the die and ram, P is the air or steam pressure
on the downward stroke, A is the area of the piston, and H is the drop height. In the case hammer
forging the total blow energy is absorbed by noise creation, heat formation, foundation shock and
workpiece deformation (strain energy). The blow efficiency,  is defined as the fraction of the
hammer energy available that goes into deforming the workpiece:
=
𝐄𝐬𝐭𝐫𝐚𝐢𝐧
𝐄𝐡𝐚𝐦𝐦𝐞𝐫
The value of  depends on types of blow. For hard blow it is 0.3, which is  0.9 for soft blow.
Now, the energy available in the hammer Ehammer = (w + PA)H and the energy necessary for
forging of the workpiece at high temperature Estrain = fV. We know that:
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=
𝑬𝒉𝒂𝒎𝒎𝒆𝒓 =
𝐄𝐬𝐭𝐫𝐚𝐢𝐧
𝐄𝐡𝐚𝐦𝐦𝐞𝐫
𝑬𝒔𝒓𝒂𝒊𝒏

=
𝒇  𝑽

Problem 1: Prepare a board hammer to forge a workpiece of brass of 3″ diameter and 1″
thickness to 1/2″ by one step at 1100oF where the combined die and ram weight is 5000lb. The
flow stress of the brass at 20ksi. Assume  to be 0.8.
Solution: Brass at 1100oF, constant flow stress 20ksi, V = 7.07in3,  = 0.69
Estrain = 25000x7.07x0.69 = 121958 in-lbs, drop height should be 13″.
Open die forging is used extensively for the cogging process where the workpiece is reduced by
repeated blows as the metal gradually passes under the forge. How this is achieved is shown in
Fig.8 with the metal ready to be deformed indicated by the shaded area, the workpiece moving to
the right.
Figure 8: Cogging operation in forging.
The cogging of a prismatic bar can be used to assess the parameters involved and how they are
controlled in the drop forging. The objective is to reduce the thickness of the workpiece in a
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stepwise sequence from end to end. Several passes may be required to complete the work and
edging is usually carried out to control the width. The reduction in thickness is accompanied by
elongation and spreading. The relative amounts of elongation and spread cannot be calculated
theoretically but they have been determined experimentally for mild steel. Actual values were
found to depend upon the ratio of the tool length to the metal width called the bite ratio 𝑏/𝑊0 .
Making use of the true strains (since deformation will be large), the spread and elongation may
be defined as follows:
C𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 𝒐𝒇 𝑺𝒑𝒓𝒆𝒂𝒅 = 𝑺 =
𝑾𝒊𝒅𝒕𝒉 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆
= 𝑰𝒏
𝑻𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 𝒄𝒐𝒏𝒕𝒓𝒂𝒄𝒕𝒊𝒐𝒏
𝑪𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 𝒐𝒇 𝒆𝒍𝒐𝒏𝒈𝒂𝒕𝒊𝒐𝒏 = 𝟏 − 𝑺 =
=
𝑰𝒏
𝑰𝒏
𝑾𝟏
𝑾𝒐
𝑳𝒆𝒏𝒈𝒕𝒉 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆
𝑻𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 𝒄𝒐𝒏𝒕𝒓𝒂𝒄𝒕𝒊𝒐𝒏
𝒍𝟏
𝒍𝒐
𝒉𝒐
𝒉𝟏
Here 𝑙𝑜 and 𝑙1 are the initial and final lengths of the bar and 𝑤𝑜 𝑎𝑛𝑑 𝑤1 its initial and final width.
Clearly if S=1, then the decrease in thickness would all appear as spread, and is S=0 there would
be no spread at all, all of the decrease in thickness appearing as elongation.
3.3. Die Drop Forging
It is one type of close-die forging. Here the tup and anvil of the open die forging are replaced by
lower and upper dies. Matching dies fit into the anvil and the tup. The dies have a series of
grooves and depressions cut into them and the workpiece is passed in sequence through a
shaping series. Figure 9 illustrates the principle of an impact forge.
Figure 9: Die drop type close-die forging.
Nowadays, huge amount of forgings are produced by the die drop forging process. Figure 10
shows an example of the dies used for this process.
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Figure 10: Dies used in drop-die forging.
The stations have names such as fullering, blocking, edging, bending and cut off. Where several
stages are involved, care must be taken to ensure that the metal does not become excessively
chilled before the last station is reached. To ensure that the die cavity is completely filled the
volume of the starting billet is greater than that of the final forging. The excess metal appears as
a “flash” at each stage, this is a thin fin around the perimeter of the forging at the parting line.
The effect of friction in restraining metal flow is used to produce shapes with simple dies.
Edging dies are used to shape the ends of bars and to gather metal, Fig.11. In edging, as shown in
Fig.11, the metal is confined by the die from flowing in the horizontal direction but it is free to
flow laterally to fill the die. Fullering is used to reduce the cross-sectional area of a portion of the
stock. The metal flow is outward and away from the center of the fullering die. An example of
the use of this type of operation would be in the forging of a connecting rod for an internalcombustion engine. The reduction in cross section of the work with concurrent increase in length
is called drawing down, or drawing out. If the drawing-down operation is carried out with
concave dies so as to produce a bar of smaller diameter, it is called swaging. Other operations
which can be achieved by forging are bending, twisting, extrusion, piercing, punching, indenting,
etc.
Figure 11: Various types of forging operations.
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In many case, final products are made in multiple stages by die-drop forging process. Various
stages (cutting of steel blank, making a pre-formed blank, rough shaping of forged part, final
shaping of the crankshaft) of production in die-drop forging are presented below in Fig.12:
Figure 12: Various types of forging operations.
3.4. Upset Forging
Upset forging increases the diameter of the workpiece by compressing its length. Based on
number of pieces produced this is the most widely used forging process. Upset forging is usually
done in special high speed machines; the machines are usually setup to work in the horizontal
plane to facilitate the quick exchange of workpieces from one station to the next, Fig.13.
Figure 13: Upset forging set-up.
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The initial workpiece is usually wire or rod, but some machines can accept bars up to 25 cm (10
in.) in diameter. The standard upsetting machine employs split dies that contain multiple cavities.
The dies open enough to allow the workpiece to move from one cavity to the next; the dies then
close and the heading tool or ram, then moves longitudinally against the bar, upsetting it into the
cavity. If all of the cavities are utilizes on every cycle then a finished part will be produced with
every cycle, which is why this process is ideal for mass production.
A few examples of common parts produced using the upset forging processes are engine valves,
couplings, bolts, screws and other fasteners. The following three rules must be followed when
designing parts to be upset forged:
1. The length of unsupported metal that can be upset in one blow without injurious buckling
should be limited to three times the diameter of the bar.
2. Lengths of stock greater than three times the diameter may be upset successfully provided that
the diameter of the upset is not more than 1.5 times the diameter of the stock.
3. In an upset requiring stock length greater than three times the diameter of the stock and where
the diameter of the cavity is not more than 1.5 times the diameter of the stock, the length of
unsupported metal beyond the face of the die must not exceed the diameter of the bar.
3.5. Press Forging
Press forging is variation of drop hammer forging. Unlike drop hammer forging, press forges
work slowly by applying continuous pressure or force over the workpiece after making contact
with the die, Fig.14.
Figure 14: Press forging set-up.
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The amount of time the dies are in contact with the workpiece is measured in seconds (as
compared to the milliseconds of drop hammer forges). The main advantage of press forging, as
compared to drop hammer forging, is its ability to deform the complete workpiece. Drop hammer
forging usually only deforms the surfaces of the workpiece in contact with the hammer and
anvil; the interior of the workpiece will stay relatively undeformed. There are a few
disadvantages to this process, most stemming from the workpiece being in contact with the dies
for such an extended period of time. The workpiece will cool faster because the dies are in
contact with workpiece; the dies facilitate drastically more heat transfer than the surrounding
atmosphere. As the workpiece cools it becomes stronger and less ductile, which may induce
cracking if deformation continues. Therefore, heated dies are usually used to reduce heat loss,
promote surface flow and enable the production of finer details and closer tolerances. The
workpiece may also need to be reheated. Press forging can be used to perform all types of
forging, including open-die and impression-die forging. Impression-die press forging usually
requires less draft than drop forging and has better dimensional accuracy. Also, press forgings
can often be done in one closing of the dies, allowing for easy automation.
We know that press forging is one version of close-die forging, where workpiece deformation
cannot be seen once the operation is started. In all cases of close-die forging die design is a very
critical job. The reasons of criticality in die deign and some tips for this are discussed below.
4. Design of Finisher Dies
Using the shape complexity and the forging material as guidelines, the forging process engineer
establishes the forging sequence (number of forging operations) and designs the dies for each
operation, starting with the finisher dies. The most critical information necessary for forging die
design is the geometry and the material of the forging to be produced. The forging geometry in
turn is obtained from the machined part drawing by modifying this part to facilitate forging.
Starting with the forging geometry, the die designer first designs the finisher dies by:
a) Selecting the appropriate die block size and the flash dimensions
b) Estimating the forging load and stresses to ascertain that the dies are not subjected to
excessive loading.
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The geometry of the finisher die is essentially that of the finish forging augmented by flash
configuration. In designing finisher dies, the dimensions of the flash should be optimized. The
designer must make a compromise: on the one hand, to fill the die cavity it is desirable to
increase the die stresses by restricting the flash dimensions (thinner and wider flash on the dies),
Fig.15; but, on the other hand, the designer should not allow the forging pressure to reach a high
value, which may cause die breakage due to mechanical fatigue. To analyze stresses, “slab
method of analysis” or process simulation using finite-element method (FEM)-based computer
codes is generally used.
Figure 15: Dies for close-die forging and associated flash in close-die forging.
By modifying the flash dimensions, the die and material temperatures, the press speed and the
friction factor, the die designer is able to evaluate the influence of these factors on the forging
stresses and loads. Thus, conditions that appear the most favorable can be selected. In addition,
the calculated forging stress distribution can be utilized for estimating the local die stresses in the
dies by means of elastic FEM analysis. After these forging stresses and loads are estimated, it is
possible to determine the center of loading for the forging in order to locate the die cavities in the
press, such that off-center loading is reduced.
4.1. Flash Design and Forging Load
The flash dimensions and the billet dimensions influence the flash allowance, forging load,
forging energy and the die life. The selection of these variables influences the quality of the
forged part and the magnitude of flash allowance, forging load, and the die life. The influence of
flash thickness and flash-land width on the forging pressure is reasonably well understood from a
qualitative point of view. The forging pressure increases with:
a) Decreasing flash thickness
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b) Increasing flash-land width because of the combinations of increasing restriction,
increasing frictional forces, and decreasing metal temperatures at the flash gap.
Before designing a flash, forging load increment versus forging stroke should be studied very
carefully. A typical load-versus-stroke curve from an impression-die forging operation is shown
in Fig.16.
Figure 16: Variation in forging load with forging stroke.
Loads are relatively low until the more difficult details are partly filled and the metal reached
the flash opening. This stage corresponds to point P1 in Fig.16. For successful forging, two
conditions must be fulfilled when this point is reached: A sufficient volume of metal must be
trapped within the confines of the die to fill the remaining cavities and extrusion of metal
through the narrowing gap of the flash opening must be more difficult than filling of the more
intricate detail in the die. As the dies continue to close, the load increases sharply to point P 2, the
stage at which the die cavity is filled completely. Ideally, at this point the cavity pressure
provided by the flash geometry should be just sufficient to fill the entire cavity and the forging
should be completed. However, P3 represents the final load reached in normal practice for
ensuring that the cavity is completely filled and that the forging has the proper dimensions.
During the stroke from P2 to P3, all the metal flow occurs near or in the flash gap, which in turn
becomes more restrictive as the dies close. In that respect, the detail most difficult to fill
determines the minimum load for producing a fully filled forging. Thus, the dimensions of the
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flash determine the final load required for closing the dies. Formation of the flash, however, is
greatly influenced by the amount of excess material available in the cavity, because that amount
determines the instantaneous height of the extruded flash and, therefore, the die stresses. The
effect of excess metal volume in flash formation was studied extensively. It was found that a
cavity can be filled with various flash geometries provided that there is always a sufficient
supply of material in the die. Thus, it is possible to fill the same cavity by using a less restrictive,
i.e., thicker, flash and to do this at a lower total forging load if the necessary excess material is
available (in this case, the advantages of lower forging load and lower cavity stress are offset by
increased scrap loss) or if the workpiece is properly preformed.
4.2. Structure and Properties of Forging
Forging are invariably produced by the hot working process and this controls the resultant
structure and properties. There are, however, important differences in forgings produced by
different techniques. The fact that the impact forge applies a stress for a very short period
compared to the long period for the press forge results in totally different structures in the
product. In the case of impact, the mechanical working is concentrated in the surface layers,
since rapid removal of the stress after the blow results in metals relaxation before the effect of
the blow has penetrated into the centre. Impact forging of a large “as cast” piece of metal at high
temperature will result in a very inhomogeneous structure, the outside layers showing a typical
hot worked structure whilst the centre is still as cast, Fig.17. Any attempt to achieve greater
penetration by increasing the impact load usually leads to internal cracking. Impact forging is
therefore limited to relatively small workpieces. Press forging invariably results in total
penetration of the effect of the applied tress into the centre of the workpiece. The process is
generally less severe on the metal than impact. The end result is a more homogeneous product
having very high quality. Since the process is much slower and the equipment used is much
larger, press forged articles are more expensive than impact forged components.
Figure 17: Microstructures developed after hammer (le) and press forging (right).
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4.2.1. Fiber Flow Lines in Forged Products
A single phase metal which has been hot worked has microstructures consisting of equiaxed
grains. The mechanical and physical properties of such a metal will be the same no matter in
which direction the specimen is cut from the worked metal. Such materials which show no
directionality are said to be isotropic. On the other hand, if the metal is duplex then it is possible
that on hot working, some or all the second phases will elongate in the direction of major strain
and the hot worked metal will be anisotropic. The metal used for forging usually comes from
rolling mills. Hot rolling causes the grains to elongate in the rolling direction and small particles
of carbides, sulfide and nitrides segregate and elongate, producing fiber. Thus the metal from
rolling has fiber flow lines, resembling the grain structure in wood, running parallel to the length,
Fig.18.
Figure 18: Elongated grains after rolling.
Like wood, the strength and toughness are greater in the fiber direction than across it. It is
normally considered that anisotropy in metal is detrimental and precautions are taken during
processing to avoid this. However, it is possible to turn this to advantage. Normally metal
components are use in tress environments, and these are usually triaxial with one element of
stress much greater than the others. If it is possible to produce metal with anisotropy to match the
stress environment variation, then efficient use is achieved. An example of this is the production
of high strength bolts in one case due to the risk of shear, a high strength shank is needed, in the
other case due to the presence of tensile stresses there is a risk of the head of the bolt shearing off
and a high strength head is needed. Both of these types of bolts can be produced as shown in
Figs.19.
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Figure 19: Fiber flow lines in cast, machined, cold forged and hot forged products.
The bolt blank is forged to produce a high strength shank which can resist shear. In the case the
forging is upset and a high strength head is formed whilst the shank remains in its original
condition. Here it is important to note that cold press forging is result much complex pattern of
flow lines than hot forging because of dynamic recovery during the forging process.
Damascus steel was a term used by several western cultures from the Medieval period
onward to describe a type of steel created in Asia and used in making sword by hand forging
from about 300 BC to 1700 AD. These swords were characterized by distinctive patterns of
banding and mottling reminiscent of flowing water. Such blades were reputed to be not only
tough and resistant to shattering, but capable of being honed to a sharp and resilient edge.
The patterns of fiber flow vary depending on how the Damascus artist works the billet. The
billet is drawn out and folded (may be up to 300 times) until the desired number of layers
are formed, Fig.20.
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Figure 20: Very complex fiber flow patterns in Damascus swords.
These Damascus swords helped a lot to survive when the crusaders were making massacre in the
Middle East. For making swords in such a delicate way controlling the thermomechanical
parameters that pearlites in the steel transformed into discrete form of carbon nanofibers, which
are thought to be much stronger than the hardened steel.
This control of fibre flow is the principal advantage of forging over all other working processes.
The direction of the flow lines and their intensity depends upon the direction of deformation. In
most processes, the deformation direction is fixed, e.g. rolling (an amount of cross rolling may
be possible), wire drawing, extrusion all have only one main axis of deformation. There are some
challenging load bearing applications where three dimensional stress exists. One of the most
96
challenging application is the crack hook. Crane hooks are highly liable components and are
always subjected to failure due to accumulation of large amount of stresses which can eventually
lead to its failure. Crane hooks are the components which are generally used to elevate the heavy
load in industries and constructional sites. A crane is a machine, equipped with a hoist, wire
ropes or chains and sheaves used to lift and move heavy material. Cranes are mostly employed in
transport, construction and manufacturing industry. Overhead crane, mobile crane, tower crane,
telescopic crane, gantry crane, deck crane, jib crane, loader crane are some of the commonly
used cranes. A crane hook is a device used for grabbing and lifting up the loads by means of a
crane. It is basically a hoisting fixture designed to engage a ring or link of a lifting chain or the
pin of a shackle or cable socket. Crane hooks with trapezoidal, circular, rectangular and
triangular cross section are commonly used. So, it must be designed and manufactured to deliver
maximum performance without failure. It has been proved that forged hooks shows excellent
performance because of its inside three dimensional fiber flow (Fig.21) that are ultimately
capable to resist acting three dimensional stress under service.
Figure 21: Crane hook and its inside fiber distribution.
In many other precision forgings for other high-tech applications amazing grain flow is produced
and maintained, Fig.22. This controlled grain flow ultimately gives the difference in longevity of
service with a great reliability.
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Figure 22: Some precision forging products with their inside fiber flow lines.
98
5. Effects of Friction in Forging
In the case tensile stress, the chance of friction between die and the workpiece is low. However,
for all metal shaping processes under compressive loading friction exists, which is beneficial in
some cases, however, in some other cases it creates a lot of problem. Examination of a forged
specimen reveals that one effect of friction between the workpiece and the tools (tup/anvil or
dies) is to cause the vertical profile to become barrel shaped, because the central portion has
deformed more than the upper and lower surfaces, Fig.23.
Figure 23: Actual deformation of a cylindrical workpiece in open die forging showing pronounced
barrelling due to workpiece-die interface friction.
Deformation is, therefore, inhomogeneous. This requires a higher load and greater total energy
expenditure than for homogeneous deformation. This extra energy is described as Redundant
Work. A second effect is to increase the deformation load due to friction, and to emphasize the
special role of friction in deformation processes. When a press tool is in contact with a
workpiece, it is loaded to below its yield point, but the workpiece load exceeds the yield point
and the conditions are those of elastic/plastic friction. This has a very large effect on the frictionstress pattern which is generated. If it were possible to place small pressure measuring devices at
intervals on the interface between the tool and the workpiece during compression the indications
would be as shown in Fig.24a on the pressure-gauge dials. Figure 24b shows how the interface
pressure varies with position.
Figure 24: Load cell reading and friction in compression test.
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The variation in pressure is symmetrical about the centre line and increases smoothly from the
equivalent of the metal flow stress at the edges to a maximum at the centre. This diagram
illustrates a phenomenon which is called the Friction Hill and is present in all working operations
when friction operates. It is possible to derive a mathematical expression for the friction hill by
considering the forces and stresses operating in the deformation process. A piece of metal
thickness h, width 2a and length l is compressed between a pair of parallel platens. Consider the
state of the forces on a vertical element inside the metal of width dx and distance x from the
centre line. Since this element is stationary the resultant forces acting upon it must be zero
(Fig.25).
Figure 25: Stress distribution between forging platen and workpiece.
𝑸 + 𝒅𝑸 𝒉𝒍 − 𝑸𝒉𝒍 − 𝟐𝑭 = 𝟎 (F friction force at top and bottom)
𝒅𝑸𝒉𝒍 − 𝟐𝑭 = 𝟎
(1)
(2)
Assuming that Coulomb Friction conditions operate (this is usually the case in cold working
when sliding occurs) and  is the coefficient of friction, the following relationship can be
written:
𝑭 = µ𝑷𝒍𝒅𝒙
Then 𝒅𝑸𝒉𝒍 = 𝟐µ𝑷𝒍 𝒅𝒙
or
𝒉𝒅𝑸 = 𝟐µ𝑷𝒅𝒙
(3)
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The above equation can be integrated directly if the relationship between P and Q is known. This
can be found, since it is known that the element is at the point of yielding, therefore Tresca‟s
Yield Criterion must hold. If it is assumed that P and Q are the major and minor principal
stresses for the element, then
𝑷 − 𝑸 = 𝒐 where 𝒐 is the yield stress of the metal then 𝒅𝑷 = 𝒅𝑸
Equation (3) can now be rewritten and integrated as follows:
𝒅𝒑 𝟐𝒖
=
𝒑
𝒉
or
𝑰𝒏 𝑷 =
𝟐µ𝒙
𝒉
+𝒂
𝒅𝒙
−𝒂
+𝒄
(4)
Here C is integration constant. Now, equation (4) can be rewritten as:
𝑷 = 𝑪 𝒆𝒙𝒑
𝟐µ𝒙
𝒉
The value of C can be determined since at 𝒙 = ±𝒂 and 𝑷 = 𝟏. 𝟏𝟓𝟓𝟎 (plane strain conditions)
or
𝑷 = 𝟎 (homogeneous strain conditions), then 𝑷 = 𝟎 𝒆𝒙𝒑
𝟐µ
𝒉
𝒂±𝒙
(5)
When equation (5) is plotted the friction Hill Curve, Fig.26 is obtained.
Figure 26: Friction hill formed in forging.
Equation 5 can be simplified if we make the following approximation. The general series
expansion for expx is:
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Since μ is usually small (<1) we can approximate expx as (1+x) for small x.
So, now it is possible to simplify this equation.
𝒆𝒙𝒑
Now equation (5) becomes
𝟐µ
𝟐µ
𝒂±𝒙 ≈ 𝟏+
(𝒂 ± 𝒙)
𝒉
𝒉
𝑷 = 𝟎 𝟏 +
𝟐µ
𝒉
𝒂±𝒙
(6)
The minimum value of P (at the edges) = 0 . Maximum value at the centre (x=0)
𝑷 = 𝟎 𝟏 +
𝟐µ𝒂
𝒉
If it is assumed that the curved sides of the friction hill can be replaced by straight line then
𝑷𝒎𝒆𝒂𝒏 = 𝑷 = 𝟎 𝟏 +
µ𝒂
𝒉
(7)
In the forging operation, there is a significant influence of the ratio 𝑎/𝑕, which is shown in
Fig.27.
𝑷
𝒂
𝒉
Figure 27: Effect of a/h ratio on the forging load.
102
The value of the coefficient of friction will also affect 𝑷. The rougher the interface the greater
the value of µ and therefore of 𝑷. When µ is equal to or greater than 0.5, then the frictiongenerated shear stress is greater than the shear strength of the metal since this is 𝒐 /𝟐 and 𝑷
must obviously be greater than the value of 𝒐 . Plastic shearing will occur inside the metal, but
the surfaces will stick to the platens. This is the case under hot compression and the conditions
are described as sticking friction (case where the value of  is within 0.5) as opposed to slipping
or Coulomb friction which normally operates during cold working. This phenomenon was
investigated by Capus and Cockcroft for hot rolling. Evidence of subcutaneous shearing cracks
have been obtained both in rolling and forging as shown in Figs.28-29.
Figure 28: Shearing crack on rolled sheet.
Figure 29: Shearing crack on surface of forged product.
103
If sticking friction occurs then equation (1) must be modified, since the friction force, 𝑭𝟏 , must
equal K the critical shear stress of the metal. Then 𝑭 = µ𝑷 = 𝑲 = 𝟎 /𝟐. If this substituted into
equation (1) we get:
𝒉𝒅𝑸 = ±𝟐𝑲 𝒅𝒙.
(8)
Equation (8) is equivalent to equation (3). Using the conditions of yielding again to find a
relationship between P and Q:
𝒉 𝒅𝑷 = ±𝟐𝑲 𝒅𝒙
𝒅𝑷
𝒐𝒓
𝟐𝑲
=±
𝒅𝒙
𝒉
.
(9)
Equation (9) can be integrated and the following relationship is obtained.
𝑷
𝟐𝒌
𝒙
=± +𝑪
𝒉
At the edges 𝒙 = ±𝒂/𝟐 and 𝑸 = 𝟎,  𝒑 = 𝟐𝑲 or 𝒐 , therefore, 𝑪 = 𝟏 + 𝒂/𝟐𝒉 . Now the
equation becomes:
𝑷
𝟐𝒌
𝒂/𝟐 −𝒙
=𝟏+
𝒉
.
(10)
This defines the friction hill for sticking friction. The maximum value at the centre is thus
𝑷
𝟐𝒌
=𝟏+
𝒂
𝟐𝒉
and the mean pressure becomes
𝑷 = 𝟐𝒌 𝟏 +
𝒂
𝟒𝒉
(11)
For sticking friction, this compares with
𝑷 = 𝟐𝒌 𝟏 +
𝒂
𝟐𝒉
(7)
Using different values of 𝑷 it is possible to calculate forging loads for hot (equation 11) or cold
working conditions (equation 7)) once the area of contact and the flow stress of the metal is
known.
Problem 2: A steel billet is to be hot forged. If the billet is 20 m long, 0.9m wide and 0.2m thick,
calculate and compare the loads required at the commencement and the completion of forging.
104
Assume plane strain conditions so that the width remains constant throughout. The tool bite is
0.3m and the tensile yield stress of the steel is 50MN/m2 at the start of forging and 150 MN/m2 at
completion.
0.3
Solution: Forging load at start = 1.115 × 50 × 0.3 × 0.9 1 + 4×0.2
= 21.44𝑀𝑁
Since the total reduction is not stated the value of h is not known. If it is assumed that the
reduction 50% then h is 0.1 m.
0.3
Forging load at completion = 1.115 × 150 × 0.3 × 0.9 1 + 4×0.1
= 81.86𝑀𝑁.
Problem 3: Show that the maximum stress, 𝑃𝑚𝑎𝑥 , required for the forging of a plate of uniform
thickness and unit length under conditions of plane-strain and slipping friction is given by:
𝑏
𝑃𝑚𝑎𝑥 = 2𝐾 1 + 2𝑕 ,
Where K is the critical shear stress,  is the coefficient of friction, b the width and h the
thickness of the plate.
How is the expression modified by forging under conditions of sticking friction?
Calculate the mean instantaneous pressure per unit length during the forging of a steel plate
under sticking friction conditions, when the thickness is 150mm and the width is 600mm.
Assume the plate to be so long that plane strain condition exist and the tensile stress is
460MN/m2.
𝑏
Derivation is already provided. For maximum stress: 𝑃𝑚𝑎𝑥 = 2𝑘 1 + 2𝑕
𝑏
At the same time for sticking friction: 𝑃 = 2𝑘 1 + 4𝑕
𝑏
In the case of plane strain conditions: 𝑃 = 1.115 2𝑘 1 + 4𝑕
=1.115 × 460 1 +
1
4×150
.
This assumes that the bite is one unit length, then 𝑃 = 532 𝑀𝑁/𝑚2 .
6. Forging Defects
If the deformation during forging is limited to the surface layers, as when light, rapid hammer
blows are used, the dendritic ingot structure will not be broken down at the interior of the forging
105
(see Fig.17). Incomplete forging penetration can be readily detected by macroetching a cross
section of the forging. The examination of a deep etch disk for segregation, dendritic structure
and cracks is a standard quality control procedure with large forgings. To minimize incomplete
penetration, forgings of should be carried out slowly. If this does not give solution, instead of
drop forging, forging press should be used.
Surface cracking can occur as a result of excessive working of the surface at too low a
temperature or as a result of hot shortness or due to sticking friction (see Fig.23). A high sulfur
concentration in the furnace atmosphere can produce hot shortness in steel and nickel leading to
cracking in the products, Fig.31.
Figure 31: Cracking due to hot shortness.
So, before doing forging operation, the S or other low melting trace elements should be
identified and proper stock materials should be used. Otherwise, cold forging can be selected for
shaping the materials, if possible.
Cracking at the flash of closed-die forgings is another surface defect, since the crack generally
penetrates into the body of the forging when the flash is trimmed off (Fig.32).
Figure 32: Cracking at flash.
106
This type of cracking is more prevalent the thinner the flash in relation to the original thickness
of the metal. Flash cracking can be avoided by increasing the flash thickness or by relocating the
flash to a less critical region of the forging. Another common surface defect in closed-die
forgings is the cold shut, or fold (Fig.33). A cold shut is a discontinuity produced when two
surfaces of metal fold against each other without welding completely. A cold shut can occur
when a flash or fin produced by one forging operation is pressed into the metal surface during a
subsequent operation. It might also happen if the forging temperature is insufficient or workpiece
of oxidized surface is forged.
Figure 33: Cold shut in forged products.
In the upsetting of bar stock on a forging machine certain precautions must be taken to prevent
buckling of the bar, Fig.34. For upsetting in a single operation the unsupported length should be
no greater than two to three times the diameter of the stock. General rules for the optimum
dimensions for upsetting in forging machines have been developed.
Figure 34: Buckling of workpiece in upset forging.
107
Secondary tensile stresses can develop during forging and cracking can thus be produced.
Internal cracks can develop during the upsetting of a cylinder or a round (Fig.35), as a result of
the circumferential tensile stresses. Proper design of the dies, however, can minimize this type of
cracking. In order to minimize bulging during upsetting and the development of circumferential
tensile stresses, interfacial friction should be reduced. However, it is usual practice to use
concave dies. Internal cracking is less prevalent in closed-die forging because lateral
compressive stresses are developed by the reaction of the work with the die wall. The
deformation produced by forging results in a certain degree of directionality to the
microstructure in which second phases and inclusions are oriented parallel to the direction of
greatest deformation. When viewed at low magnification, this appears as flow lines, or fiber
structure. The existence of a fiber structure is characteristic of all forgings and is not to be
considered as a forging defect. To achieve an optimum balance between the ductility in the
longitudinal and transverse directions of a forging, it is often necessary to limit the amount of
deformation to 50 to 70 percent reduction in cross section.
Figure 35: Buckling of workpiece in upset forging.
Besides the above mentioned forging defects some other defects might be formed such as scale
pits, improper product shape due to die shift, flakes, improper grain flow etc. Scale pits are seen
as irregular depurations on the surface of the forging. This is primarily caused because of
improper cleaning of the stock used for forging. The oxide and scale gets embedded into the
finish forging surface. When the forging is cleaned by pickling, these are seen as depurations on
the forging surface. Die Shift is caused by the miss alignment of the die halve, making the two
halve of the forging to be improper shape Flakes are basically internal ruptures caused by the
improper cooling of the large forging. Rapid cooling causes the exterior to cool quickly causing
internal fractures. This can be remedied by following proper cooling practices. Improper grain
flow is caused by the improper design of the die, which makes the flow of the metal not flowing
the final interred direction.
Problem 4: A cylindrical part is warm upset forged in an open die. The initial diameter is 45mm
and the initial height is 40mm. The height after forging is 25mm. The coefficient of friction at
108
the die-work interface is 0.20. The yield strength of the work material is 285MPa and its flow
curve is defined by a strength coefficient of 600MPa and a strain hardening exponent of 0.12.
Determine the force in the operation (a) just as the yield point is reached (yield at strain = 0.002),
(b) at a height of 35mm, (c) at a height of 30mm and (d) at a height of 25mm.
Solution:
Problem 5: A hot upset forging operation is
performed in an open die. The initial size of the work part is: Do=25mm and ho=50mm. The part
is upset to a diameter=50mm. The work metal at this elevated temperature yields at 85MPa
(n=0). Coefficient of friction at the die-work interface=0.40. Determine the following:
a) Final height of the part
b) Maximum force in the operation.
109
Problem 6: A cold heading operation is performed to produce the head on a steel nail. The
strength coefficient for this steel is 600MPa and the strain hardening exponent is 0.22.
Coefficient of friction at the die-work interface is 0.14. The wire stock out of which the nail is
made is 5.00mm in diameter. The head is to have a diameter of 9.5 mm and a thickness of
1.6mm. The final length of the nail is 120mm. (a) What length of stock must project out of the
die in order to provide sufficient volume of material for this upsetting operation? (b) Compute
the maximum force that the punch must apply to form the head in this open-die operation.
Forged Products in Today’s Challenging High-Tech Applications
1. Engine Gearboxes: Gearboxes are typically used in engines to drive timing, balance shaft or
auxiliary systems. Complex geometry makes these products an ideal application for forged
products. Net or nearest to net shape teeth, weight reduction options and net shape drive features
gives forged products an advantage over other metal working processes. Lots of gears and other
components of different sizes are concealed in a gear box. The high torques in the gearboxes of
today's diesel engines can only be transmitted by heavy duty forgings. The components are cold
or hot-forged or made using a combination of processes.
110
2. Suspensions: When people think of automobile performance, they normally think
of horsepower. But all of the power generated by a piston engine is useless if the driver can't
control the car. That's why automobile engineers turned their attention to the suspension system
almost as soon as they had mastered the four-stroke internal combustion engine.
111
Suspension is the system of tires, tire air, springs, shock absorbers and linkages that connects
a vehicle to its wheels and allows relative motion between the two. Suspension systems serve a
dual purpose; contributing to the vehicle's roadholding/handling and braking for good active
safety and driving pleasure and keeping vehicle occupants comfortable and a ride
quality reasonably well isolated from road noise, bumps, vibrations, etc. These goals are
generally at odds, so the tuning of suspensions involves finding the right compromise. It is
important for the suspension to keep the road wheel in contact with the road surface as much as
possible, because all the road or ground forces acting on the vehicle do so through the contact
patches of the tires. The suspension also protects the vehicle itself and any cargo or luggage from
damage and wear. This challenging job of suspension system became easier because of forged
products.
Cylinder Valves
Internal combustion engines are devices that generate work using the products of combustion as
the working fluid rather than as a heat transfer medium. To produce work, the combustion is
carried out in a manner that produces high pressure combustion products that can be expanded
through a turbine or piston. The valve drive has to withstand extremely high accelerations and
temperatures with a very high level of continuous cyclic stress. In this type challenging portion
of auto body engine most of the components are made by forging for improved operating safety
and performance.
112
Jet
Engine
Alongside their use in jet
engines,
forged
components are also used
in highly loaded areas
such as wings, rudders, control surfaces and landing gear.
113
Cost Analysis
7. Cost Analysis for Forging
It has been clear that forged products ensure best quality and the highest level reliability. So, in
most of the high-tech applications forged products come as the first choice. But the question is
that how much expensive is the forged products compared to products of other shaping process.
Figure shows typical l unit cost (cost per piece) in forging. It is important to note how the setup
and the tooling costs per piece decrease as the number of pieces forged increases, if all pieces use
the same die. From experience, it has been clear that the material costs usually make up around
50% of forging costs and of this material, a significant proportion is waste material in the form of
flash, scale losses, and so on. Die costs represent about 10% of forging costs and the remainder
includes direct labor, equipment operating costs and overhead costs. For the purposes of early
cost estimating, three main cost elements are considered:
1. Material costs, including flash and scale losses,
2. Equipment operating costs, including labor, heating costs, ancillary equipment and overhead,
3. Die costs, including initial tooling costs and maintenance and resinking costs.
114
In Fig. the costs for the production of connecting rod by forging, investment casting, die casting,
sand casting and permanent mould casting are shown. From this figure it is clear that that, for
large quantities, forging is more economical. Sand casting is the more economical process for
fewer than about 20,000 pieces.
115
Chapter Five
Rolling and Roll Pass Design
1. Introduction
Rolling has been used for about 500 years to form flat sections and sheet metal. In fact, it was
probably first developed in the mid-16th century for the production of gold and silver strip of
near-constant dimensions, to be used for coining and minting (and still is employed for this). It
basically involves pushing a metal workpiece into the gap between two rotating rolls, which then
simultaneously draw the workpiece into the rolls and compress it to reduce the thickness and
increase the length. For large components this often requires significant power input, which was
initially supplied by water mills, then steam power, before the advent of modern, electrically
driven and highly automated rolling mills.
From an economic point of view, rolling is the most important metal working and shaping
technique; it can be used to roll large ingots from half a meter thickness down to a few microns
in the case of Al foil (of total length up to a hundred kilometres). Thus, 30 tons of ingots are
rolled down in a succession of rolls, often starting at high temperatures and finishing near room
temperature. Using appropriately shaped rolls, hot rolling is also widely employed to form long
profiles of more complex sections such as I beams and rails (known as „shape rolling‟ as opposed
to flat rolling). A very wide variety of forms, widths and thicknesses can, therefore, be
manufactured, with high productivities, from semi-finished slabs through car body sheet to
packaging foil. Modern rolling mills are extremely efficient units capable of processing over a
million tons of metal per year.
Rolling is an indirect compression process. Normally the only force or stress applied is the radial
pressure from the rolls, Fig.1.
Figure 1: Applied compressive load on workpiece in rolling process.
116
Rolling is carried out in a sequence of rolling passes during which the compressive strain can
vary from a few percent to 50%. Since the deformation is only applied on the part of the
workpiece between the rolls, i.e. a relatively small volume, the loads are reduced to moderate
values even for very large ingots; this is of course the practical origin of the process. A reversible
rolling mill is often used for the first stages of hot rolling of large sections such as ingots and
slabs to reduce their thickness as rapidly as possible and avoid cooling down. Further reductions
are achieved in a series of one way mills known as „stands‟. Cold rolling of sheet is also usually
carried out at high strain rates between roll stands; but for thin foil, reversible rolls are used with
coilers at each end. Both hot and cold rolling can lead to major improvements of the material
properties by refining the microstructure. As-cast ingots are often characterized by large grain
sizes, significant porosity and coarse 2nd phase particles. During hot rolling, porosity can be
closed up, grain size reduced by recrystallization and coarse particles broken up leading to
stronger, tougher alloys, Fig.2.
Figure 2: Microstructural changes in as-cast and wrought materials by hot rolling.
Cold rolling can also be used to increase strength by work hardening; the latter is often sufficient
to limit the amount of achievable rolling strains so that intermediate softening operations by
annealing are necessary to continue rolling. Although the property improvements by hot and cold
working have been known for centuries, their microstructural origin have only been really
understood over the last 50 years and the detailed process-structure-property relations, through
TMP are the current object of intense research and development. Rolling lends itself to TMP
117
because of the large number of variables during the process: temperature, strain and strain rate
per pass and interpass periods, all of which need to be tailored to a specific alloy composition.
2. Rolling Mill for Sheet Metals
The first and still a very common type of rolling equipment is the two-high mill, Fig.3.
Figure 3: Two-high rolling mill.
The two-high mill was the first and simplest but production rates tended to be low because of the
time lost in returning the metal to the front of the mill. This obviously led to the reversing twohigh mill where the metal could be rolled in both directions, Fig.4. Such a mill is limited in the
length that it can handle and if the rolling speed is increased, the output is almost unchanged
because of the increased time spent in reversing the rotation at each pass. There is limitation
concerning length to
be handled.
Figure 4: Two-high reversing rolling mill.
118
This type of reversing mill with large diameter rolls is often used for the first stages of hot rolling
ingots in the primary rolling mill (breakdown rolling in the blooming, slabbing or cogging mill).
Typically, the ingot is reversibly hot rolled down from 500 to 30mm (total average strain of 2.8)
in a series of 10-20 passes. Higher strains per pass are carried out during subsequent rolling
operations down to sheet or foil using smaller diameter rolls to reduce the required power.
The next obvious development was the three-high mill (Fig.5), which has the advantages of both
the two-high reversing and non-reversing mills. Such a mill must, of course, have elevating
tables on both sides of the rolls. The roll gap on a three-high mill cannot be adjusted between
passes, therefore, grooves or passes must be cut into the roll face to achieve different pass
reductions. All three kinds of mill suffer from the disadvantage that all stages of rolling are
carried out on the same roll surface and the surface quality of the product tends to be low. Roll
changes on such mills are relatively frequent and time consuming. Moreover, because of larger
size roll, the power consumption is very high. This type of mill is, therefore, used for primary
rolling where rapid change of shape is required, even at the expense of surface quality.
Figure 5: Three-high rolling mill.
Higher strains per pass are carried out during subsequent rolling operations down to sheet or foil
using smaller diameter rolls to reduce the required power. However, smaller diameter rolls are
less rigid than the large ones and, therefore, tend to bend significantly around the workpiece,
producing camber in the strip particularly during cold rolling of hard metals. This is reduced, or
eliminated, by using larger diameter back-up rolls which support the smaller work rolls. This
type of rolling mill is popularly known as four-high rolling mill, Fig.6.
119
Figure 6: Four-high rolling mill.
The principle of four-high mill has been extended to the development of cluster mills, Fig.7, in
which each roll is supported by two backing rolls. A Sendzimir mill is an example of such a
cluster mill used to roll very thin sheet or foil.
Figure 7: Cluster or Sendzimir type rolling mill.
120
High rates of production can be achieved in a continuous mill using a series of rolling mills often
denoted tandem mills, Fig.8.
Figure 8: Four-high Tandem type rolling mill.
Each set of rolls is placed in a stand and since the input and output speeds of the strip at each
stand are different, the strip between them moves at different (usually rapidly increasing)
velocities. The rolling speeds of each stand are, therefore, synchronized so that the output speed
of stand n equals the input speed of stand n+1, i.e. successive stands work in tandem. The final
output sheet is usually coiled and both the coiler and the uncoiler can be adjusted to provide a
back or a front tension. Continuous 4-high tandem mills are used for rolling strip of typical
thickness 30mm down to a few mm in 3-5 stands; this can be done hot or cold. In the latter case,
the production rates are very high but so are the capital costs and the product is very standardized
(e.g. car body sheet). This type of mill can be reversible also that ensures better productivity.
More flexible cold rolling is performed in 4-high single stand reversing mills with coilers at both
ends, which can also provide front and back tension.A special type of mill for large reductions is
the planetary mill which is made up of two large backing rolls surrounded by several small
planetary rolls (Fig.9).
Figure 9: Planetary type rolling mill.
121
Each of the latter gives a roughly constant reduction to the slab before it meets the next set of
rolls. Thus, during a single pass (at high temperatures), the slab undergoes a large number of
reductions so that it is, in effect, rolled down to strip in one pass.
3. Rolling for Bars, Rods and Profiles
Long products such as beams, rails, rebar and wire rods are manufactured by rolling them
through a series of work rolls of specific shapes, typically grooved rolls, Fig.10. The workpiece
starts as an initial round or square bloom or billet which is then repeatedly passed through the
calibrated work rolls by reversible or non-reversible rolling mills. The pass geometry is generally
established by empirical trials but some numerical methods are being developed. During shape
rolling, in contrast to flat rolling, the cross-section of the metal is reduced in two directions. In
one pass, the metal is compressed in one direction and then rotated 90o for the following pass so
that more „equiaxed‟ sections can be achieved. Thus, a square billet is reduced to bar by alternate
passes through oval and square shaped grooves, which will be discussed in the subsequent topic.
The area of contact, therefore, changes continuously during the rolling process. The total
reduction per pass is expressed in terms of the change in cross-sectional area, since there are both
thickness reductions and width increase. Shape rolling involves significant amounts of lateral
spreading, which is difficult to control so the more complex shapes require very experienced
designers.
Figure 10: Form rolling processes.
122
4. Thread Rolling
Thread rolling is a commonly used manufacturing process for threading round workpieces,
illustrated in Fig.11. It is by nature a forming process, thus no material is removed during
threading of the blank. Production rates can be high, approaching 8 pieces per second for smaller
diameter parts, with slower cycle times for large diameter pieces. Multiple styles of machines are
available, with the differences resulting from the types of dies and die motion used. The
underlying process is the same for all machines; a blank is passed through moving dies and the
thread shaped dies progressively intrude on the workpiece to be formed. Flat die rolling is
common, especially in smaller diameter fasteners. In this process, the blank is rolled across the
face of a stationary die with a reciprocating opposing die. Cylindrical die thread rolling is also
used where two or three rotating cylindrical dies are fed into a centrally located part.
Figure 11: Form rolling process.
4.1 Advantages and Disadvantages
This type of processing has advantages and disadvantages, so that its adoption should be
carefully considered. Compared to conventional thread cutting system, there are some basic
advantages as given below:
a) The thread rolling process is undoubtedly the fastest to execute threads in a wide range,
and in fact, in some cases production is over a thousand pieces per minute. The
appropriate use of autoloaders also allows a single operator to control multiple machines
with a considerable saving of manpower.
b) Since there is no generation of chips, so there is a slight economy of material. They are
also not ecological problems related to disposal of oil soaked chips.
c) The fibers of the material are not cut as in conventional methods, but plastically
deformed and forced to follow the contours of the thread. So, there is a general
improvement of all the technological characteristics. The tensile strength, in rolled
123
products in general, is about 10% higher than the normal . The resistance to torsion is
significantly increased and finally the resistance to stress, given the greater smoothness of
the surfaces of the threads, which ensures a better grip, increase of about 75%.
d) By rolling one can get high precision threads, suitable for every application, but only if
that the roller dies are carefully constructed and that the blanks are properly prepared.
blanks have constant diameters and that the material always has the same characteristics.
Compared to conventional thread cutting, thread rolling equipments are significantly expensive.
Another technical problem is that if the die alignment is not proper, then wrong thread cutting
will be performed.
5. Forces in the Roll Gap
Consider a rolling operation, where a piece of metal of thickness h1 and width W1 is passing into
a pair of rolls (Fig.11) at a velocity v1. The gap between the rolls is such that the thickness is
reduced to h2 at the point of nearest approach and the velocity of the metal leaving the rolls is v2.
The width is assumed to be constant for simplicity, but in practice there is always some spread
and W2 is greater than W1.
Figure 11: Schematic diagram showing rolling stress distribution in a typical rolling operation.
The velocity of the roll surface, which is normally constant, must lie between v1 and v2. Figure
12 shows how the velocity of the workpiece varies in the roll gap. Between the point of entry, A
and C, the rolls are travelling faster than the metal, tending to drag it into the gap. Between C and
B, the exit, the rolls are travelling more slowly than the metal, tending to hold it back. There is
only one point, C, where the rolls and the metal are travelling at the same speed, this is the
Neutral Point or the Point of No Slip. The friction force between the rolls and the metal must,
therefore, be exercised towards the neutral point.
Velocity
124
Rolls
Metal
Roll Gap
Figure 12: Schematic diagram showing workpiece velocity variation with roll gap.
Capus and Cockcroft in an elegant experiment showed that state of affairs does indeed exist in
the roll gap. They agreed that if relative slip occurred between metal and rolls firstly in a forward
direction and then in a backward direction, this could lead to scratching of the surface of the
metal. If metal spread occurred, then the scratches would gradually lie at an angle the direction
of rolling. Their findings are shown in Fig.13. So, it is better to set the neutral point closer to the
neutral point as much as possible.
Figure 13: Scratch marks formed on the finished sheet product.
125
5.1. Friction Force in the Arc of Contact
It is possible to derive an expression for this friction force. Consider in Fig.14 a vertical element
of metal, height h1, width W1, thickness dx, located in the roll gap at a position  from the line
joining the roll centers. Pressure P acts radially on the ends of this element and if the element is
located between the point of entry and the neutral point a frictional force acts toward the neutral
point (Fig.14).
O

O
d
O
h1
dx
O
B
h2
Figure 13: Stress distribution in rolling.
126
The radial pressure has a horizontal component which tends to reject the metal and prevent it
from entering the rolls, whilst the friction force has a horizontal component dragging the metal
inward. Whether the metal passes through the rolls depends upon the values of the two horizontal
force components as rejecting force Psin and pulling force µPcos.
The variation of these components with  is given in Fig.15. The maximum angle possible in the
roll gap before the rejecting force exceeds the pulling-in force is max where
µPcosmax - Psinmax=0
i.e.,
µ=tanmax
(1)
max is the maximum angle of bite or the friction angle and decides the maximum reduction
possible for a given mill. It will be noticed that this depends only on the coefficient of friction
between the surfaces of the work piece and the rolls.
Figure 15: Variation of various active forces with roll gap.
Let us consider the basic geometry of rolling to obtain the relationship between roll diameter and
maximum draft possible in the rolling process shown in Fig.16.
127
O
R 
max
A
𝑹 𝒉
𝒉
𝟐
B
Figure 16: Basic geometry of flat rolling.
Geometrically tanmax =
𝑹∆𝒉
∆𝒉
𝑹−( )
𝟐
≈
∆𝒉
𝑹
So, the maximum draft ∆𝒉max ≈ µ2R
Primary rolling is a process where large maximum reductions are required in order that the metal
can be deformed quickly and cheaply. Such mills have large diameter rolls with surfaces that are
roughened or ragged to increase the coefficient of friction.
It is possible to calculate an approximate rolling load from the following relationship:
Rolling Load = 𝟎 𝑾 𝑹∆𝒉
This equation yield an approximate value the, however, the effect of friction is ignored and this
can result in a large error if the metal being rolled is relatively thin. It is, therefore, necessary to
consider the effect of friction in the roll gap.
128
Problem 1. Determine the maximum reduction possible on a piece of steel 250mm thick during
cold rolling when µ=0.1 and during hot rolling when µ=0.6. What would be the effect on the
maximum draft if the roll diameter was changed from 500mm to 1.5m?
Solution:
µ = tanmax‟
max = tan-1 0.1 = 6
𝑅∆𝑕
Sinmax = 𝑅
0.1045 =
When
500∆𝐻
500
∆𝑕 = 5.46 mm
µ = 0.6 then max = tan-1 0.6=31,
sinmax= 0.5145 =
500∆𝐻
500
, ∆𝑕 = 132.35 𝑚𝑚
Maximum draft in hot rolling = 132.35/250×100 = 53.9%. If the roll diameter is increased from
500m to 1.5m the maximum drafts possible are:
Cold rolling 0.1045 =
1500∆𝐻
1500
∆𝑕= 16.4 mm.
16.4
=
Hot rolling 0.5145 =
1500 ∆𝐻
1500
250
× 100= 6.6%
∆𝑕 = 397 mm
=
397
250
× 100= 100%+
Theoretically the mill could achieve 100% reduction by hot rolling but this is, of course,
impossible in practice since there are other limitations which will be referred to later. It can be
seen that the maximum draft possible depends upon two factors, the coefficient of friction, µ,
and the roll radius R (Fig.15).
In reality, the roll pressure varies significantly along the arc of contact and a typical distribution
is shown in Fig.17 The pressure goes through a maximum close to the neutral point and the
general form of the curve is known as the „friction hill‟, Fig.18.
129
O
Friction Hill
Hill
Roll
Metal
Rolling
Figure 17: Distribution of friction along the arc of contact of roller.
Figure 18: Variation of roll pressure along the length of contact.
The total area under this curve is proportional to the rolling load. The area under the dotted line
represents the force required to deform the metal in plane strain compression. The area above
this line is related to the force required to overcome the friction between roll and workpiece,
130
hence the name of friction hill. The height of the friction hill depends upon the value of the
friction coefficient, but both the peak height and position can be shifted by the application of
front or back tensions to the workpiece. A back tension will significantly reduce the rolling load
and shift the peak towards the exit side so this is often applied industrially.
Similar type of friction hill can also be observed in forging. However, there are two differences,
in the relative friction hills caused in rolling and forging. Firstly the maximum pressure in
forging always occurs at the centre line of the platen, whereas in rolling the maximum occurs at
the neutral point, which can be located anywhere in the arc of contact, depending upon the stress
situation. Secondly, the value of the pressure at the two extremes of the metal in forging is the
same and equal to 𝑜 . In rolling the metal is deformed as it passes from entry to exit and the
yield stress increases. Siebel confirmed the existence of the friction hill by measuring pressures
in the roll gap using radially drilled holes in one roll which contained steel pins pressing on
piezo-electric quartz crystals.
Using the analogy between forging and rolling an approximate expression can be developed for
the effect of friction on the rolling load.
𝒑
In forging
𝟐𝒌
=exp
𝑷𝒎𝒂𝒙
and
𝟐𝑲
𝒑
𝟐𝒌
𝟐µ(𝒂±𝒙)
𝒉
≈𝟏+
≈𝟏+µ
(2)
𝒂
𝟐𝒉
𝒂
𝒉
(3)
These equations apply for conditions of slipping friction. For the case of sticking friction they
become:
𝑷𝒎𝒂𝒙
𝒂
≈𝟏+
𝟐𝑲
𝟐𝒉
𝒑
𝟐𝒌
and
𝒂
≈ 𝟏 + 𝟒𝒉
(4)
In rolling 𝟐𝒂 = 𝑹∆𝒉 𝒂𝒏𝒅 𝒉 = 𝒉𝒎𝒆𝒂𝒏 = 𝒉𝟏 − (∆𝒉/𝟐) then we get for slipping friction:
𝑷𝒎𝒂𝒙
𝟐𝒌
𝒑
𝟐𝒌
=𝟏+
=𝟏+
µ 𝑹∆𝒉
{𝒉𝟏 −(∆𝒉/𝟐)}
µ 𝑹∆𝒉
𝟐{𝒉𝟏 −(∆𝒉/𝟐)}
(5)
(6)
131
For sticking friction:
𝑷𝒎𝒂𝒙
𝟐𝒌
=𝟏+
𝒑
𝟐𝒌
𝑹∆𝒉
(7)
𝟐{𝒉𝟏 −(∆𝒉/𝟐)}
=𝟏+
𝑹∆𝒉
(8)
𝟒{𝒉𝟏 −(∆𝒉/𝟐)}
The 𝑝 values can be used to determine the rolling load. For sticking friction and homogeneous
deformation
R.L.=∗𝑜 𝑅∆𝑕 𝑊 ∗ 𝟏 +
𝑹∆𝒉
(9)
𝟒{𝒉𝟏 −(𝒉/𝟐)}
Where 𝑜∗ is the mean yield stress and W* is the mean width. For sticking friction and plane
strain deformation:
R.L. = 1.55∗𝒐 𝒘 𝟏 +
𝑹∆𝒉
𝟒{𝒉𝟏 −(𝒉/𝟐)}
𝑹∆𝒉
(10)
And for slipping friction appropriate loads would be:
R.L = 1.55𝑜 𝑊 𝑅∆𝑕 1 +
µ 𝑹∆𝒉
𝟐{𝒉𝟏 −(∆𝒉/𝟐)}
Problem 2: Calculate the rolling load to reduce steel 600mm wide 30mm thick by 20%. Roll
diameter 800 mm. Flow stress of steel 150MPa. Assume µ = 0.15. What would be the effect on
the rolling load if there was sticking friction?
Solution:
The answer is based on a number of assumptions, relating condition of deformation, whether it is
homogeneous or plane strain. This is related to the ratio of the arc of contact to the thickness (h).
If the ratio is low, the deformation tends to be homogeneous, if it is large, it is plane strain. For
above problem the ratio is:
𝑅∆𝑕
=
𝑕
400 × 6
1.81: 1
27
which is relatively small, so deformation can be assumed to be homogeneous. The second
assumption refers to the value of the flow stress ∗𝑜 . In the case of any further information the
value given o must be taken to be the value 𝑜∗ . If further information was supplied, e.g. the
equation of the stress-deformation curve of the metal, an accurate value for rolling load was
calculated. The same is true for W*.
132
R.L.= ∗𝑜 𝑊 ∗ 𝑅∆𝑕 𝑊 ∗ 1 +
µ 𝑅∆𝑕
2{𝑕 1 −(∆𝑕/2)}
= 150×600 400 × 6 1 +
0.15 400×6
2 30− 6/2
= 4.43 MN
With sticking friction the appropriate equation is:
R.L.= ∗𝑜 𝑊 ∗ 𝑅∆𝑕 𝑊 ∗ 1 +
𝑅∆𝑕
4{𝑕 1 −(∆𝑕/2)}
= 150×600 400 × 6 1 +
400×6
4 30− 6/2
= 6.41 MN
5.2. Factors Affecting Rolling Load
The value of µ and R as shown in the earlier equation affect the maximum angle of bite and
therefore the maximum reduction possible in one pass. The rolling load is directly proportional
to o and 𝑊. It also depends upon 𝑅∆𝑕. The greater the reduction the greater the rolling load,
1
i.e. R.L is proportional to ∆𝑕2 . In the same way the larger the roll diameter the greater the rolling
1
load, i.e. R.L. is proportional to 𝑅 2 . The greater the value of µ the larger the rolling load. It is,
however, inversely related to h1, in that the thinner the original gauge the greater the rolling load.
These factors greatly influence mill design, since too high a rolling load can have an adverse
effect on mill behaviour as explained in the next section. The metals most likely to give high
rolling loads are of high yield stress and thin gauge and this is particularly the case in foil rolling.
An examination of the above parameters will illustrate the possibility of altering mill design in
an attempt to minimize rolling load. The two parameters which can be altered at the design stage
are µ and R.
The rolling load can be minimized by making the radius as small as possible and the roll surface
as smooth as possible. This principle is used in the design of cluster mills which are used
extensively for foil rolling and consist of small work rolls supported by larger back-up rolls to
prevent bending. Even with such mills the rolling loads can still be excessive and recourse is
made to devices which apply front and back tension to the metal being rolled. This operates
according to the stress diagram for an element of metal in roll gap given in Fig.19.
133
2
1 RL
3
o
3
o
2
1 RL
Figure 19: Effects of front and back tension on rolling load.
The applied major stress 1 induces the two compressive stresses 2 and 3. According to
Tresca‟s Yield Criterion are given by:
i.e.
1 -3 = o
 1 =  o + 3
The rolling load as shown in Fig.19 is proportional to 1, i.e. to o + 3. If back tension b is
applied to the strip entering the roll gap as shown then the conditions become:
 1 =  o + 3 -  b
Here b acts in a direction opposite to 3 and therefore lowers the value of the rolling load.
Tension is achieved by using braked coilers on each side of the mill stand.
6. Roll Flattening
The workpiece passing between a pair of rolls is compressed by the radial stress in them, but the
reaction is transferred to the mill bearings and housing, which are capable of only limited yield
because of their large dimensions. If an attempt is made to compress thin hard material further,
the reaction becomes so large that the rolls deform elastically and the radius of curvature of the
arc of contact is increased, Fig.20.
134
Figure 20 Effect of roll flattening on the radius of curvature.
The extent of this flattening depends on the magnitude of the reaction stress and the elastic
constants of the rolls. Attempts to determine R, the deformed radius of curvature is now the
target. Concerning this, it has been proposed that the arc of contact did not remain circular, but it
gets deformed and flattened to some extent. In such case, the relationship between the initial roll
radius R and deformed roll radius R becomes:
𝑹′
𝑹
𝑪𝑷′
= 𝟏 + 𝑾∆𝒉
𝑪 = 𝟏𝟔
and
(11)
𝟏−𝟐
𝑬
= Poisson‟s ratio 0.35 for steel, E is Young‟s Modulus 1.01 MN/mm2. P′ the rolling load based
on the radius R′ , W the width of the metal and ∆h the reduction. To calculate a value for R′
successive approximations are necessary.
Problem 3: Determine the deformed radius of curvature of steel rolls 500mm diameter, rolling
copper strip 800mm wide, 75mm thick, given 20% reduction, if the yield stress of the copper is
675 N/mm2.
Solution:
We know that 𝑃′ = 𝑜 𝑊 R∆h for the undeformed radius
= 675 × 800 ×
𝐶=
𝟏𝟔
𝟏−𝟎.𝟑𝟓𝟐
 𝒙 𝟐.𝟎𝟏
250 × 15 = 33.0681𝑀𝑁
= 2.2234𝑀𝑁
135
𝑹′
𝟐𝟓𝟎
= 1+
𝟐.𝟐𝟑𝟒×𝟑𝟑.𝟎𝟔𝟖𝟏
𝟖𝟎𝟎×𝟏𝟓
= 1.006 24
𝑹′ = 251.5599 mm
A new value of 𝑅 ′ must now be calculated using this derived value for 𝑅′.
P = 0𝒘 𝑹∆𝒉 = 𝟑𝟑. 𝟏𝟕𝟏𝟏 𝑴𝑵.
𝑹
𝟐𝟓𝟏.𝟓𝟓𝟗𝟗
= 1+
𝟐.𝟐𝟐𝟑𝟒×𝟑𝟑.𝟏𝟕𝟏𝟏
= 1.006 146
𝟖𝟎𝟎×𝟏𝟓
R = 253.106 mm
By progressive approximations the error between the derived deformed radii of curvature
becomes negligibly small and this value is accepted. Using this technique for steel, chilled iron
and cast iron rolls the attached curves have been plotted relating 𝑅/𝑅 to 𝑃/𝑊∆𝑕 (Fig.21).
1. Steel rolls
𝐸 = 2.01 𝑀𝑁/𝑚𝑚2  = 0.35
𝑅
𝑅
= 1+
2.2234𝑃
𝑤∆𝑕
2. Chilled-iron rolls
𝐸 = 1.74 𝑀𝑁/𝑚𝑚2  = 0.35
𝑅
𝑅
= 1+
2.5683𝑃
𝑤∆𝑕
3. Cast-iron rolls
𝐸 = 1.005 𝑀𝑁/𝑚𝑚2  = 0.35
𝑅
𝑅
= 1+
4.4468𝑃
, 𝑃 𝑖𝑛 𝑀𝑁.
𝑤∆𝑕
Problem 4: A 0.1% carbon steel strip 50mm wide and 5mm thick was rolled in one pass to
3.5mm at 1060C when the homogeneous yield stress was 1.05 kN/mm2. The roll diameter was
340mm. Find the magnitude of the rolling load, taking into account roll flattening, if the rolls
were made of cast iron.
136
Solution: Rolling load for under formed radius = 0 𝑊 R∆h
= 1.05×50 170x1.5
= 838.4 kN.
To correct this nominal value of the load for the effect of roll flattening, the following procedure
should be used:
Firstly determine
𝑃
𝑊×∆𝑕
=
83.84
50×1.5
=
83.84×10 −3
50×1.5
= 0.00112
and then read off curve 3 in Fig.21. Unfortunately in this case the curve is not accurate enough so
the formula must be used:
𝑅
𝑅
giving
= 1+
𝑅
4.4468𝑃
when
= 1.004 97
𝑤∆𝑕
𝑅
𝑅 = 170 × 1.004 97 = 170.8449
P = 0𝑤 𝑅∆𝑕
= 1.05 × 50
170.8449 × 1.5 = 840.44 𝑘𝑁
Figure 21: Curves for determining /𝑅 , the roll-flattening factor 𝑅 equals effective radius of the
roll. R equals nominal radius of the roll.
137
Further approximations could be carried out to give a closer reading. Roll flattening has another
effect in that for a given mill there is a minimum gauge below which it is not possible to roll.
Any attempt to do so results in greater deformation of the rolls, without any plastic deformation
of the strip. With thin gauges as already seen the friction hill becomes very large producing
reaction stresses in the arc of contact which exceed the yield stress of the rolls, therefore, it is
easier to deform the rolls than the metal. As long as the mill is running the rolls will remain
circular, but if the load is not removed when it is stopped, deformation will take place to flatten
the surface over the area of contact between the rolls. The limiting thickness is found to be very
nearly proportional to the following parameters:
𝒉𝒍𝒊𝒎 𝜶 𝒄µ𝑹𝒐 ,
𝑪 = 𝟏𝟔
𝟏−𝟐
𝑬
(12)
= 𝟐. 𝟐𝟐𝟑𝟒 𝒎𝒎𝟐 /𝑴𝑵
Now for steel rolls 𝒉𝒍𝒊𝒎 = 𝟐. 𝟐𝟐𝟑𝟒 µ𝑹𝒐
(13)
R is measured in mm and 0 in N/𝑚𝑚2 .
Problem 5: Calculate the minimum gauge of steel, with a flow stress when fully hard of 530N
mm-2, which can be rolled on a mill with steel rolls of diameter 560 mm, µ = 0.135.
Solution: From equation (13):
𝑕𝑙𝑖𝑚 = 2.2234 × 0.135 × 280 × 530 × 10−6 = 0.0445𝑚𝑚.
6.1. Roll Bending or Camber
Four-high, cluster and Sendzimir mills have been developed in attempts to eliminate roll bending
because any deflection results in the metal produced being thicker along its centre line than at the
edges. Whilst it is possible that such a shape would result in the product being outside gauge
tolerance the greater problem is that of loss of shape. The metal elongates more along the edges
than the centre line, resulting in different lengths across the width, as shown in Fig.22.
Figure 22: Uniform and non-uniform section of rolled metal sheet.
138
This can only be accommodated by puckering of wrinkling with the resultant loss of flatness.
Once metal strip has lost its shape in this way, it can never be recovered and must be scrapped.
Attempts to avoid or limit roll bending have involved ways of decreasing the rolling load. This
has resulted in small work rolls and four-high mills. But even with these mills a certain amount
of roll bending still occurs and is accommodated by cambering the rolls, i.e. making them barrel
shaped. The rolling load still bends the rolls but the profile adjacent to the material being rolled
is straight. It must be realized, however, that there is only one value of the rolling load which
produces this flat profile, Fig.23.
Figure 23: Use of cambered rolls to compensate for roll bending. Proper camber (left) and no camber (right).
7. Mill Spring or Plastic Distortion
The reaction to rolling load is called the roll separating force and if the rolls were not held in the
mill housing they would indeed separate and reduction of metal would not be possible. The
upper roll pushes the top of the housing upwards whilst the bottom roll pushes the base of the
housing downwards. The housing is, therefore, subjected to a tensile stress, which is obviously
below the yield stress of the steel normally used, but there is a measurable elastic deformation.
The extent depends upon (a) the rolling load, (b) the cross sectional area of the housing and (c)
the height of the housing. If the extent of this deformation is small the mill is said to be hard or
rigid, whilst if it is large, the mill is said to be soft or springy. This housing deformation will
obviously affect the gauge of the metal produced. For example, if the mill gap is set to 3mm
before feeding the material to be rolled, entry of the metal provides the force which causes the
mill to stretch and the gap to increase to say, 3.05mm. The metal produced will be 3.05mm thick
instead of 3.00mm. The setting of the rolls before metal is entered is called the passive roll gap,
while the actual gap produced when metal passes through is called the active roll gap. It is
important to know the relationship between the active and the passive roll gaps. This relationship
is called the mill Modulus. It is a characteristic of the mill and can be determined in the
following way. The mill is set to constant roll gap and a series of different pieces of metal are
rolled. These produce different rolling loads which are measured. The rolling loads can be varied
either by using different gauges of the same metal or by using different metals. A graph is drawn
relating rolling load to gauge, the gauge being found by measuring the thickness of the rolled
pieces. A typical curve is shown in Fig.24.
139
Figure 24: Relation between rolling load and product gauge.
Extrapolation back to where the rolling load is zero gives the passive roll gap (Gp). The mill
modulus is 1/m where m is the tangent of the above curve. The units of mill modulus are mm/kN
and by using this information it is possible to calibrate any given mill so that accurate gauge
control can be achieved. The law of the above curve is:
𝑮𝒂 = 𝑮𝒑 +
𝟏
𝒎
𝑳
(13)
Here 𝐺𝑎 is the active roll gap, 𝐺𝑝 the passive roll gap, 1/m the mill modulus and L is the rolling
load. When a particular metal is being rolled another relationship is required before accurate
gauge control can be achieved, this is the plastic deformation curve for the metal. This gives the
relationship between the final thickness of the rolled metal 𝐺𝑎 rolled from initial thickness 𝐺𝑜
and the rolling load generated. Such a curve is obtained by rolling a series of identical pieces of
metal through a mill with varying roll gaps. A typical curve in shown in Fig.25.
Figure 25: Relation between rolling load and deformation.
140
Combination of the two curves given in Figs.24 and 25 allow a system of gauge control to be
achieved. Such a composite curve for a given mill rolling a specific metal is shown in Fig.26. In
order to roll metal from incoming gauge 𝐺𝑜 to 𝐺𝑎 , the passive roll gap must be set at 𝐺𝑝 , which
generates a rolling load L1. Because mill spring increases the difficulty of achieving accurate
gauge control, the best type of mill this purpose would be one with zero spring or “fully hard”.
Such mills are not yet possible although some modern hydraulic mills are approaching this
situation. It is, however, possible to capitalize on the disadvantages of soft mills and use this for
automatic gauge control.
Figure 26: Setting of passive roll gap for targeted gauge.
Problem 6: Metal strip, 4.0mm thick, is cold rolled in one pass under the conditions given
below:
Rolling Load (kN)
225
360
450
600
700
Roll Gap Setting (mm)
3.63
3.36
3.10
2.48
1.78
Rolled Gauge of Strip (mm)
3.83
3.68
3.50
3.02
2.40
(i) Calculate the mill modulus and show how it is used to determine the roll setting required to
produce strip of 3.25mm thickness.
(ii) Discuss the sources of error that can arise when applying this type of calculation to practical
rolling mill situations.
141
Solution:
The mill modulus can be calculated from equation (21), i.e.
𝐺𝑎 = 𝐺𝑝 +
1
𝑚
𝐿. A calculation of 1/m can be made for each of the above situations giving
Rolling Load (kN)
225
360
450
600
700
Mill Modulus (1/m) (µm/kN)
0.889
0.889
0.889
0.900
0.971
True mill modulus 0.889 µm/kN. It will be noticed that a slight drift occurs in the determined
values with the higher rolling loads. This is probably due to roll flattening. Eventually if the
rolling load is increased a point is reached where no reduction is possible due to so much roll
flattening and the mill modulus will be infinite.
7.1. Automatic Gauge Control
The gauge of a rolled piece of metal can vary across its width or along its length. Normally
variation across the width is associated with shape control. Variation along the length is
associated with gauge control which is becoming an increasingly urgent factor in modern strip
rolling. The demand by customers for closer and closer gauge tolerances coincides with everincreasing mill speeds and, to avoid the production of large quantities of “off-gauge” material,
modern high-speed strip mills invariably include automatic gauge control. Such equipment
corrects the mill whenever “off-gauge” material is being produced. Since the corrections cannot
be applied until off-gauge material has passed through the sensing devices, a proportion so such
material is always present in the product. This is a corrective system, a far better system would
be one based on anticipation by placing sensors before the mill and using the signals to vary the
gap in such a manner as to produce “on-gauge” material all the time. In practice it has not been
possible to devise such a system, since all the metal parameters which can affect the active roll
gap must be continuously monitored and interpreted. These include yield stress, and incoming
gauge, width, surface condition and to achieve this on strip travelling art speeds up to 50m/s is
impracticable at the moment. Because of this the corrective system is used even with its inherent
disadvantage of always producing some off-gauge material, but it has the practical advantage
that only one parameter, i.e. outgoing gauge, needs to be monitored.
8. Roll Torque
An examination of the friction hill in the arc of contact indicates that the resultant roll separating
force acts, not along the line joining the roll centers but rather at a position which is between the
point of entry and the point of exit. The resultant forces are acting in a direction opposing the
142
revolving rolls which must, therefore, be supplied by a torque to overcome this resistance. The
distance between the line of action of the roll separating force and the line joining the roll centers
is called the lever arm, indicated by a, in Fig.27.
Figure 27: Roll torque acting in rolling operation.
It can be seen that the lever arm is a fraction of the arc of contact, which is denoted by 
=
𝑎
𝑅∆𝑕
(14)
A typical value for  is about 0.5 for hot rolling and 0.45 for cold rolling. Mill torque, T, is then
equal to Pa.
8. Mill Power
Power, which is usually supplied by an electric motor, in necessary to drive the mill and
overcome the mill torque. The work done to turn one roll one revolution is aP. But since there
are two rolls the total work done for 1 rev = 2aP. If the rolls turn at n rev/s then the rate of
doing work, i.e. power = 2aPn watts.
Problem 7: A trip 185mm wide, 2.5mm thick is reduced 30% in a cold rolling mill with 650mm
diameter rolls. Given that the coefficient of friction of the rolls is 0.15 and the mean yield stress
of the steel for the reduction is 675N/mm2.If the mill runs at 100 rpm, calculate the theoretical
power required.
Solution: Since the problem dealt with cold rolling  can be assumed to be 0.45 then
143
𝑎 =  𝑅∆𝑕 = 0.45 342.6 × 0.51 = 5.95 𝑚𝑚
Power =
2×5.95×10 −3 ×6.22×10 6 ×100
60
𝑤𝑎𝑡𝑡𝑠
= 388 kW
The above question deals with the theoretical power required by the mill; in practice a greater
amount is required since power is needed to run the mill empty and this must be added to the
above figure.
9. Rate of Deformation with Sticking Friction
Consider the element AB in the roll gap subtending an angle  with the line joining the roll
centres, Fig.28.
Figure 28: Schematic diagram showing the rate of deformation in rolling.
As the clement is deformed, A approaches B with velocity 𝑣, and B must also approach A with
the same velocity 𝑣 = 𝑓sin where 𝑓 is the speed of the rolls, therefore, the average rate of
deformation per unit thickness 𝑕 is:
𝑘 =
2𝑓𝑠𝑖𝑛 
𝑕
But 𝑕 = 𝐴𝐵 = 𝑕𝑎 + 𝐷 1 − 𝑐𝑜𝑠 which gives
𝑘 = 𝑕
2𝑓𝑠𝑖𝑛 
𝑎 +𝐷
1−𝑐𝑜𝑠 
(15)
144
9.1. Rate of Deformation with Slipping Friction
When slipping friction occurs the velocity of the metal cannot be assumed equal to the peripheral
velocity of the rolls. There is only one place where this occurs, at the neutral point and use can
be made of this fact to drive a relationship for 𝑝 . For doing this, consider once again a vertical
element AB height h subtending an angle  in Fig.29.
Figure 29: Schematic diagram showing the rate of deformation in rolling.
Let the neutral point be C subtending an angle α. By law of constancy of flow:
𝑕𝑏 𝑣𝑏 = 𝑕𝑐 𝑣𝑐 = 𝑕𝑎 𝑣𝑎
𝑕 𝑐 𝑣𝑐
then
𝑣=
But
𝑣𝑐 = 𝑓𝑐𝑜𝑠𝛼
So
𝑣=
𝑕
𝑕𝑐
𝑕
𝑓𝑐𝑜𝑠𝛼
Point A moves towards B with a velocity of 𝑣 tan, 𝐵 also moved upwards towards A with the
same velocity therefore the average rate of deformation per unit thickness h is:
𝑝 =
which is
2𝑣 tan 
𝑕
𝑕𝑐
𝑝 = 2𝑓 𝑕 2 𝑐𝑜𝑠αtan
145
but as before
𝑕 = 𝑕𝑎 + 𝐷 1 − cos  ,
therefore
𝑝 =
2𝑓𝑕 𝑐 𝑐𝑜𝑠 𝛼 tan 
𝑕 𝑎 +𝐷 1−cos 
2
(16)
10. Rolling Defects
Roll bending would produce sheets with varying thickness. To counter this effect, rolls are
usually cambered (crowned) as shown in Fig.30. The degree of cambering varies with the width
of the sheet, the flow stress, and reduction per pass. The results of insufficient camber are shown
in Fig.33. This type of insufficient camber will cause thicker center and thinner edges. This can
cause edge wrinkling or warping of a plate. The center is left in residual tension and center
cracking can occur.
Figure 29: Possible effects of insufficient camber (a): edge wrinkling (b), warping (c), centerline cracking
(d), and residual stresses (e).
If the rolls are over-cambered, as shown in Fig.30, the residual stress pattern is the opposite.
Centerline compression and edge tension may cause edge cracking, lengthwise splitting and a
wavy center.
146
Figure 30 : Effects of over-cambering (a): wavy center (b), centerline splitting (c), edge
cracking (d), and residual stresses (e).
With multistand continuous rolling, interstand tension is adjusted to maintain the rolling load to a
constant value and so achieve a flat surface. This is an important aspect of shape control in the
rolling of strip. A recent development has been the introduction of hydraulic jacks onto the roll
necks thereby altering the roll camber by actually bending the rolls. Results to date indicate that
this method will be very successful in controlling strip shape. All the methods described so far
have involved continuous rolling where front and back tension or interstand tension can be used.
With single sheet rolling this technique for controlling rolling load cannot be used and therefore
the problem of shape control is tackled in another way. Cook and Parker devised a technique for
computing rational rolling schedules, i.e. a sequence of rolling passes for a given metal which
will produce the same rolling load for each pass and it has been used successfully in industry for
the rolling of copper alloy sheet and plate.
10.1. Fins and Laps
Fins are caused by trying to push too much metal into the rolling groove, i.e. attempting too large
a reduction, so that the rolls are forced apart and the excess metal is squeezed out sideways,
Fig.31. If the fins are subsequently rolled into the rod, they become laps that form planes of
weakness and they can open up at later stages, particularly under torsion or a twisting motion.
Such defects can be prevented by avoiding excessively large reductions and by rotating the rod
through 90o between each successive pass.
147
Figure 31: Fins and laps formed on rolled products.
10.2. Defects by Roll Misalignment
Misalignment of the rolls leads either to curvature of the strip to one side as it comes out of the
roll gap, if it is relatively thick, or to a wavy edge on one side if it is thin strip, Fig.32. To avoid
this type defect proper adjustment of the roll screws to give a parallel roll gap is essential.
Figure 32: Rolling defects caused by roll misalignment.
148
10.3. Alligatoring
A pipe is the funnel like depression at the top of a cast ingot that results from shrinkage during
solidification. When the ingot is subsequently rolled, this will give a centre line defect along
sheet, strip or wire, particularly if the pipe surface is oxidized. This can lead to a splitting apart
of strip and sheet during subsequent rolling, a defect known as 'alligatoring', Fig.33. To avoid
such problem, the region containing the pipe should be dropped off before working and recycled
as scrap of known quality.
Figure 33: Alligatoring type defect in rolling.
10.4. Blistering
Blistering on the surface of sheet and strip may be caused by gas porosity trapped in the cast
stock or arising from reactions with the atmosphere during annealing treatments. The problem
can be avoided by control of casting or annealing conditions, including factors such as the
dissolved gas or base metal oxide content in feedstock materials through good de-oxidation
practices in melting, annealing temperature and avoiding the use of hydrogen-rich annealing
atmospheres. Evolution of lamination to blister for the mild carbon steel with banded ferriticpearlitic structure having minimal non-metallic inclusions, Fig.34
Figure 34 Blistering in rolled sheet.
10.5. Inclusions
Inclusions in the cast stock are insoluble particles such as oxides and silicides. These can lead to
problems of cracking during working or to the formation of hard spots that can affect the quality
of final polished surfaces ('comet tail' effect). Inclusions may be pieces of crucible or furnace
lining which have fallen into the metal or they may be formed by chemical reaction, e.g. between
149
absorbed gas and an alloy constituent. Regular inspection of crucibles and furnace linings,
cleanliness of working surroundings and a consideration of possible reactions is important if
inclusions are to be kept to a minimum. Many examples of defects due to inclusions are given in
Fig.35. It can cause fish eye, dimple, voids leading to porous products, scratches, line caused by
elongated roe like inclusions, light areas with contrast colour differences, dimples, coating skip
or lamination by rolled thin inclusions, orange peel or bump like defects and so on.
Figure 35: Inclusion related various defects in rolled sheet.
Problem 8: Determine how the rate of deformation changes when a slab 100mm thick is reduced
to 75mm in one pass on a hot mill having 600mm diameter rolls operating at 3m/s. Compare the
results with those obtained when 100mm strip is reduced to 7.5mm. Roll flattening can be
ignored and in one case sticking friction operates whilst in the other case there is slipping friction
with the neutral point occurring at an angle of 10 for the slab and 3 for the strip.
Solution: The angle of contact 𝑚 , Now cos 𝑚 = 1 −
For the slab cos 𝑚 = 1 −
100−75
600
; 𝑚 = 16.6°,
𝑕 𝑏 −𝑕 𝑎
𝐷
150
𝑘 =

2𝑓𝑠𝑖𝑛 
2 × 300 sin 
=
𝑕𝑎 + 𝐷 1 − cos 
75 + 600 1 − cos 
sin 
6000 sin 
cos 
75 + 600 1 − cos 
𝑘 𝑠𝑒𝑐 −1
2°
0.0349
209.40
0.999 39
75.3655
2.78
4°
0.0698
418.54
0.997 56
76.4616
5.47
6°
0.1045
627.17
0.994 52
78.2869
8.01
8°
0.1392
835.04
0.990 27
80.8392
10.33
10°
0.1736
1041.89
0.984 81
84.1153
12.39
12°
0.2079
1247.47
0.978 15
88.1114
14.16
14°
0.2419
1451.53
0.970 30
92.8226
15.64
16.6°
0.2857
1714.13
0.958 32
100.0065
17.14
For the strip cos 𝑚 = 1 −
10−7.5
𝑚 = 5.23°
600
𝑘 =

sin 
2 × 3000 sin 
75 + 600 1 − cos 
6000 sin 
cos 
75 + 600 1 − cos 
𝑘 𝑠𝑒𝑐 −1
0
2
0.0349
209.40
0.999 39
7.8660
26.62
4
0.0698
418.54
0.997 56
8.9640
46.69
5.23
0.0912
546.92
0.995 84
9.9979
54.70
For the slab
𝑘 =
2𝑓𝑕 𝑐 cos 𝛼 tan 
[𝑕 𝑎 +𝐷 1−cos  ]2
But
𝑕𝑐 = 𝑕𝑎 + 𝐷(1 − cos 𝛼) = 75 + 600(1 − cos 10°) = 84.12 𝑚𝑚
𝑝 =
2×3000 ×84.12 cos 10° tan 
[75+600 1−cos 
]2
=
497,052.17 tan 
[75+600 1−cos  ]2
Value for [75 + 600 1 − cos  ]2 can be obtained from the previous table.
151

tan 
497.0521 𝑡𝑎𝑛
75 + 600 1 − cos 
[75 + 600(cos )]2
𝑝 𝑠𝑒𝑐 −1
2°
0.0349
17,357.44
75.3655
5679.96
3.06
4°
0.0699
34,757.27
76.4616
5846.38
5.95
6°
0.1051
52,242.29
78.2869
6128.84
8.52
8°
0.1405
69,856.13
80.8392
6534.98
10.69
10°
0.1763
87,643.71
84.1153
7075.38
12.39
12°
0.2126
105,651.70
88.1114
7763.62
13.61
14°
0.2493
123,929.02
92.8226
8616.04
14.38
16.6°
0.2981
148,117.69
100.0065
10,001.3
14.82
For strip 𝑕𝑐 = 7.5 + 600 1 − 𝑐𝑜𝑠 3° = 8.32 𝑚𝑚
𝑝 =
2×3000 ×𝑐𝑜𝑠 3° 𝑡𝑎𝑛 
[7.5+600(1−𝑐𝑜𝑠 )]2
=
49,851.59 𝑡𝑎𝑛 
[7.5+600(1−𝑐𝑜𝑠 )]2

tan 
49,851.59 𝑡𝑎𝑛
75 + 600 1 − cos 
[75 + 600(cos )]2
𝑝
2
0.0349
1740.856
7.8660
61.8740
28.14
4
0.0699
3485.963
8.9640
80.3533
43.38
5.23
0.0915
4563.169
9.9979
99.9580
45.65
Figure 36 shows that the strain rate varies as the metal passes through the arc of contact, being
high at the point of entry and decreasing to zero at the point of exit, the strain rate of the strip
being very much higher than that of the slab. There is difference between sticking and slipping
friction in the rolling mill, where sticking tends to be the higher. If it is desired to use the graphs
produced by Alder and Phillips it is necessary to calculate a mean strain rate. This can be derived
by integrating the strain rate equations with respect to  between the limits  = 0 and  = 𝑚 and
dividing by 𝑚 ; all angle be expressed in radians.
152
Figure 36: Change of rate of deformation throughout the length of the arc of contact. Slab 4 in.
thick, strip 0.4 in. thick; roll diameter 24 in. reduction 25%.
The arc of contact, given by 𝑅𝑚 =
then
𝑚𝑘 =
𝑚𝑘 =
𝑅∆𝑕 𝑜𝑟 𝑚 =
𝑚
2𝑓
2∆𝑕
𝐷
0
2
𝐷∆𝑕
𝐼𝑛
sin 
𝐷(1−𝑐𝑜𝑠 )
2∆𝑕
𝐷
𝑑,
𝑕𝑏
𝑕𝑎
Problem 9. Calculate the mean strain rate with sticking friction for the slab and the strip in the
last example.
Solution: For the slab 𝑕𝑎 = 100 𝑚𝑚, 𝑕𝑎 = 75 𝑚𝑚, 𝐷 = 600 𝑚𝑚,
= 3 𝑚/𝑠,
153
2
𝑚𝑘 = 3000
𝐼𝑛
600×25
−1
100
75
= 9.97 𝑠𝑒𝑐
For the strip
𝑕𝑎 = 10 𝑚𝑚, 𝑕𝑎 = 7.5 𝑚𝑚, ∆𝑕 = 2.5 𝑚𝑚, 𝐷 = 600 𝑚𝑚,
= 3 𝑚/𝑠,
2
𝑚𝑘 = 3000
𝐼𝑛
600×2.5
10
7.5
= 31.51 𝑠𝑒𝑐
Only the equation for mean sticking friction strain rate has been developed above since most hotworking processes involve sticking friction. The next exercise applies the above formula to hot
rolling.
Problem 10: Determine the mean constrained yield stress when a copper slab is hot rolled at
750℃, in one pass from 100 mm thick to 75 mm thick on a mill with 600-mm-dimeter rolls
turning at 3 m/s. What would be the mean constrained yield tress if it was copper strip rolled
from 100 mm to 7.5 mm? gave 𝑚𝑘 = 10 𝑠𝑒𝑐 −1 for the slab and ≈ 30 𝑠𝑒𝑐 −1 for the strip.
Solution: The percentage reduction was the same in both cases:
𝑠𝑙𝑎𝑏 =
100−75
𝑠𝑡𝑟𝑖𝑝 =
× 100 = 25%,
100
100−75
100
× 100 = 25%
By reading off the appropriate diagram, i.e. Copper 750℃ the slab 25% red‟n  = 10 𝑠𝑒𝑐 −1 .
Homo. Y.S = 87 N/mm2, therefore the constrained yield stress = 1.115×87 = 100N/mm2, the strip
25% red‟n  = 30𝑠𝑒𝑐 −1 . Homo.Y.S = 100N/mm2 constrained yield stress = 115.5 N/mms.
Problem 11: Determine the mean homogeneous yield stress when a 0.7% carbon steel is rolled
in one pass from 5mm to 3mm at a temperature of 1020℃ on a mill having 700mm rolls running
at a speed of 150rpm.
Solution:
𝑚𝑘 =
𝑓 = 𝐷 × 𝑛 =
2
𝐷∆𝑕
×700×150
60
𝐼𝑛
𝑕𝑏
𝑕𝑎
= 5498 𝑚𝑚/𝑠,
154
𝑚𝑘 = 5498
2
700×2
5
𝐼𝑛 = 106 sec-1
3
5
%𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = × 100 = 40%
2
For 1020℃ diagram is not available, so it is necessary to interpolate between 1000℃ and
1060℃. At a strain rate of 100sec-1 and a deformation of 40% at 1000℃ the yield stress is
182N/mm2 whilst at 1060℃ it is 171N/mm2. By proportion the homogeneous yield stress at
1020℃ is 176.5N/mm2. Once the homogeneous yield stress has been determined by the method
outlined it can now be used to calculate the hot rolling.
155
Chapter Six
Roll Pass Design
1. Introduction
Sections and flat products are usually rolled in several passes, whose number is determined by
the ratio of the initial and final cross sections. The cross sectional area is reduced in each pass
and the form and size of the stock gradually approach the desired profile. Plates, sheets and flats
are rolled in plain-barreled rolls with a cylindrical (actually slightly convex or concave) working
surface, Fig.37. Here the thickness of the metal being rolled is reduced in each pass by
decreasing the distance between the rolls.
Figure 37: Rolling of sheet products.
Rolling between plain rolls is characterized by uniform reduction across the full width of the
stock and is accompanied by free or unrestricted spread. This lateral flow or spread is hindered
only by the contact friction. The side edges of the stock are subject to a tensile stress which is
often the cause of cracks. Steel sections and shapes are rolled in grooved rolls, i.e. rolls on
whose working surface special grooves have been turned to suit the profile of the stock being
rolled. Rolling in passes partly or completely restricts lateral spread, increases the plastic
properties of the metal and enables the draught to be increased in each pass. Rolling in passes is
also characterized by non-uniform deformation. The rolling of various steel sections in modern
mills involves exceptionally large deformation of the metal.
Roll pass design comprises the calculation and design of the rolling schedule to obtain a given
rolled section, as well as the design of the rolls. Expedient roll pass design should ensure that an
156
accurate profile is obtained with a suitable surface finish and with the specified mechanical
properties; it should provide for the highest possibility of mechanising and automating the
complete rolling process, thus considerably increasing the output of the mill and eliminating
manual labour in rolling. As a rule, roll passes are designed on the basis of certain specified
conditions. Chief of these are:
a) Characteristics of the finished product (dimensions of the section, tolerances and
specifications concerning the mechanical properties and surface finish of the rolled
product).
b) Characteristics of the initial material (dimensions and weight of the ingot or billet, grade
of steel and the metal temperature before and in the course of rolling);
c) specifications of the rolling mill (number of stands, roll diameters, rolling speed,
available horsepower of the drive motor, strength of the rolls and other components of the
mills, available mill equipment, etc.).
Sound roll pass design must be based upon the actual prevailing production conditions and the
principal technological factors involved. Only a reduction in the cross section of the stock occurs
in rolling blooms and billets. The same is true for the first passes in rolling of many profiles of
section steel. Passes designed only for reducing the cross section of the stock are called
breakdown passes. The most widely employed breakdown passes are the box, square, diamond
and oval passes (Fig.38).
Figure 38: Possible rolling sub-sequence in the breakdown rolling.
The subsequent passes in rolling section steel are called roughing passes. In addition to reducing
the cross-section, these passes change the form so that it gradually approaches the final profile
required. The great variety of profiles rolled requires a great variety of roughing passes. The next
157
to the last pass is called the leader or leading pass or intermediate pass. The final or finishing
pass imparts the final size and form to the rolled stock. In its form and size, a finishing pass
corresponds to the profile it rolls. The only difference is that a finishing pass is designed with
regard to the linear coefficient of expansion of the metal and to the tolerances on the lateral
dimensions of the section. In rolling production, the main types of passes mentioned above are
employed in a great variety of combination.
The starting point in roll pass design is to draw up the pass schedule which indicates the forms of
the passes required to obtain the given profile. At the same time, the number of passes is
established, as are the draught (or elongation) for each pass, the sequence and number of turns,
distribution of the passes among the mill stands, etc. Various pass schedules may be applied to
the same profile depending on the actual rolling conditions.
2. Total and Mean Draught (Elongation)
The size of the ingot or billet and finished section are usually known when the pass schedule is
drawn up. Consequently, the total deformation is also known. Let us consider the rolling of a
rectangular ingot into a square billet (Fig.39).
B
1
2
5
6
A
a
3 4 7
a
Figure 39: Various breakdown passes.
The total draught in this case will be: Δh = [(A - a ) + (B - a)]k
Where k is a coefficient, which accounts for the spread in rolling. The mean draught per pass will
equal:
∆𝒉𝒎 =
∆𝐡
𝐧
158
Where n is the number of passes. The total deformation may also be expressed through the total
elongation. If we denote the cross sectional area of the billet as Fo and η that of the finished
section as Fn the total coefficient of elongation ηΣ will be equal to:
𝑭
η𝚺 = 𝑭𝒐
𝒏
If the total and mean coefficients of elongation (ηΣ and ηm, respectively) are known, the number
of passes required to roll the finished stock from the given billet or ingot may be determined
from the following formula:
𝒏=
𝐥𝐨𝐠 𝚺
𝐥𝐨𝐠 𝒎
=
𝐥𝐨𝐠 𝑭𝒐 −𝐥𝐨𝐠 𝑭𝒏
𝐥𝐨𝐠 𝒎
The output of open train mills depends largely on the amount of draught in each pass. The more
the draught, the fewer passes and less time will be required for rolling in each stand and the
higher the mill output will be. Therefore, to raise the output of an open train mill, it is necessary
to apply the maximum possible draught and, consequently, the maximum possible elongation.
The principal factors limiting the draught per pass are:
a)
b)
c)
d)
Plasticity of the metal
Angle of bite, roll strength
Available power of the mill drive motor
Roll wear and spread (when rolling in passes)
In many cases, in rolling practice, the angle of bite is the chief factor limiting the draught per
pass. This may be observed, for instance, in rolling blooms and slabs in blooming and slabbing
mills, billets in billet mills, plate in the first passes, etc. In leading and finishing passes, roll wear
becomes a vital factor. For example, in rolling rails and other complex shapes, to which strict
requirements are made as to shape accuracy and surface finish, it is more expedient to apply low
draught in the finishing passes to reduce roll wear. It should be noted that in assigning the
draught for finishing passes, the required structure and mechanical properties of the finished
product must be taken into consideration, as well as the final rolling temperature.
3. Basic Concepts and Symbols in Rolling
The case of longitudinal rolling as shown in the following Fig.1 will be discussed. The height h
of the rolled stock is measured to the roll axis. The breadth b is measured parallel to the roll axis.
The dimension of metal in the direction of rolling is denoted as the length l (Fig.40).
159
Figure 40: Showing dimension change in rolling.
passes.
In the successive stages of rolling, the dimensions of the rolled bars are expressed as follows:
𝑽𝒐 = 𝒉𝒐 𝒃𝒐 𝒍𝒐 − initial value of volume in terms of initial height, breadth and length of stock
when rolling starts.
𝑭𝟎 = 𝒉𝟎 𝒃𝟎 − initial cross-sectional area of stock;
𝑽𝟏 = 𝒉𝟏 𝒃𝟏 𝒍𝟏 −volume, height, breadth and length of stock after first pass;
𝑭𝟏 = 𝒉𝟏 𝒃𝟏 − cross-sectional area of stock after first pass;
𝑽𝒏 = 𝒉𝒏 𝒃𝒏 𝒍𝒏 −volume, height, breadth and length of stock after n passes (n denotes the number
of passes);
𝑭𝒏 = 𝒉𝒏 𝒃𝒏 − cross sectional area of stock after n passes.
The increase in length of stock after a pass in rolling is usually greater than the increase in
breadth. The above notations are given for rectangular or flat sections, i.e. squares, flat bars,
band steel or strip rolled between the plain cylindrical horizontal rolls. For rolling of nonrectangular sections such as bars, shapes, rails, etc., an additional term, the mean height of stock,
is introduced (Fig.41). This mean height of stock is expressed as:
𝒉𝒎 =
𝑭
𝒃
(1)
Where F is cross sectional area and b is the maximum breadth of the filled section. Following
Fig.5 illustrates the methods of determining the mean height of stock in rolling regular sections
such as squares, ovals, diamonds etc., having two axes of symmetry. The method of determining
mean height for non-rectangular profiles having only one axis of symmetry is shown in Fig.41b.
A similar method of determining 𝑕𝑚 is employed for profiles having no axis of symmetry.
160
Figure 41: Methods of determining the average height of passes (a) three successive regular passes
for rolling bars and (b) pass for rolling a section.
The concept of mean height has been introduced to maintain the principle of constancy of
volume. For sections with:
𝑭
𝑭
𝒉𝒐𝒎 = 𝒃𝒐
𝒉𝟏𝒎 = 𝒃𝟏
𝒐
𝟏
𝑭
𝒉𝒏𝒎 = 𝒃𝒏 (Figs.5)
𝒏
Now the following relationships are obtained from the condition of constancy of volume:
𝑽𝒐 = 𝑭𝒐 𝒍𝒐 = 𝒉𝒐𝒎 𝒃𝒐 𝒍𝒐
= 𝑽𝟏 = 𝑭𝟏 𝒍𝟏 = 𝒉𝟏𝒎 𝒃𝟏 𝒍𝟏
= 𝑽𝒏 = 𝑭𝒏 𝒍𝒏 = 𝒉𝒏𝒎 𝒃𝒏 𝒍𝒏
(2)
On the above dividing these relations we get:
𝒉𝟐𝒎 𝒃𝟐 𝒍𝟐
𝒉𝟏𝒎 𝒃𝟏 𝒍𝟏
where
𝒉𝟐𝒎
𝒉𝟏𝒎
= 𝜸𝒎 𝜷𝜶 = 𝟏
𝑭 𝒃
= 𝒃𝟐 𝑭𝟏 = 𝜸𝒎
𝟐
𝟏
(3)
(4)
Here m denotes the mean coefficient of draught and the mean absolute draught hm is given by:
161
𝑭
𝑭
𝒉𝟏𝒎 − 𝒉𝟐𝒎 = 𝒃𝟏 − 𝒃𝟐 = ∆𝒉𝒎
𝟏
𝟐
(5)
The following relationship can also be made:
𝒉𝟏𝒎 −𝒉𝟐𝒎
𝒉𝟏𝒎
𝒉𝟏𝒎 −𝒉𝟐𝒎
𝒉𝟏𝒎
= 𝜺𝒎 − mean relative draught
𝟏𝟎𝟎% = 𝒎 𝟏𝟎𝟎% − mean percentage draught
Where, according to Fig5a, the terms 𝒉𝟏𝒎 , 𝒉𝟐𝒎 and 𝒉𝟑𝒎 are equal to 𝒉𝒊 and 𝒉𝒊 = 𝑭𝒊 ̸𝒃𝒊 .
In rolling non-rectangular sections, the term maximum draught is sometimes used (Fig.5b):
𝒉𝟐𝒎𝒂𝒙
𝒉𝟏𝒎𝒊𝒏
= 𝜸𝒎𝒂𝒙 − maximum coefficient of draught,
𝒉𝟏𝒎𝒂𝒙 − 𝒉𝟐𝒎𝒊𝒏 = ∆𝒉𝒎𝒂𝒙 − maximum absolute draught,
𝒉𝟏𝒎𝒂𝒙 −𝒉𝟐𝒎𝒊𝒏
𝒉𝟏𝒎𝒂𝒙
𝒉𝟏𝒎𝒂𝒙 −𝒉𝟐𝒎𝒊𝒏
𝒉𝟏𝒎𝒂𝒙
= 𝜺𝒎𝒂𝒙 − maximum ralative draught, and
𝟏𝟎𝟎% = 𝒎𝒂𝒙 𝟏𝟎𝟎% − maximum percentage draught.
In rolling, the coefficient of elongation is also expressed as follows:
𝑭
𝒉
𝒃
𝒍
 = 𝑭𝟏 = 𝒉𝟏𝒎 𝒃𝟏 = 𝒍𝟐 =
𝟐
𝟐𝒎 𝟐
𝟏
𝒘𝟐
𝒗𝟏
(6)
Where, 𝑣1 = entry speed, 𝑤2 = exit speed.
This method of calculation is convenient since to find the area, height or breadth of pass it is
sufficient to multiply or to divide by appropriate coefficients of elongation draught and spread. If
the applied reduction or the coefficients of elongation in rolling are known, each can be easily
calculated from the other using the following formula:
𝟏
𝟏𝟎𝟎%
 = 𝟏−𝑼 = 𝟏𝟎𝟎−𝑼%
Where,
𝑈 = relative reduction,
𝑈% = percentage reduction
(7)
162
𝑼=𝟏−𝟏∕
𝑼% = 𝟏𝟎𝟎 − 𝟏𝟎𝟎 ∕ 
(8)
Problem 12: A bloom with having the dimensions: 𝑕1 = 200𝑚𝑚, 𝑏1 = 250𝑚𝑚, 𝑙1 2000 𝑚𝑚
is rolled in one single pass to dimensions: 𝑕2 = 150𝑚𝑚, 𝑏2 = 262𝑚𝑚, 𝑙2 = 2545𝑚𝑚.
Calculate various parameters of rolling and check it volume constancy.
Solution: Area and volume before pass:
𝐹1 = 𝑕1 𝑏 ≔ 200 × 250 = 50,000𝑚𝑚2
𝑉1 = 𝑕2 𝑏2 𝑙2 = 150 × 262 × 2545 = 100,000,000 𝑚𝑚3
The coefficient of deformation are calculated as follows:
𝑕2
Coefficient of draught:
𝑕1
𝑏2
Coefficient of spread:
𝑏1
𝑙2
Coefficient of elongation:
𝑙1
150
= 𝛾 = 200 = 0.750
262
= 𝛽 = 250 = 1.048
2545
=  = 2000 = 1.2725
Checking of volume constancy:
𝑕2 𝑏2 𝑙2 150 262 2545
=
×
×
= 𝛾𝛽𝜆 = 0.750 × 1.048 × 1.2725 = 1.0000
𝑕1 𝑏1 𝑙1 200 250 2000
i.e. the calculation is correct. Further parameters can now be calculated:
relative reduction:
absolute draught:
∆𝑕 = 𝑕1 − 𝑕2 = 200 − 150 = 50 𝑚𝑚
relative draught:
𝜀𝑕 =
percentage draught:
𝐺𝑕 % =
absolute spread:
∆𝑏 = 𝑏2 − 𝑏1 = 262 − 250 = 12 𝑚𝑚
absolute elongation:
∆𝑙 = 𝑙2 − 𝑙1 = 2545 − 2000 = 545 𝑚𝑚
absolute reduction:
∆𝐹 = 𝐹1 − 𝐹2 = 50,000 − 39,300 = 10,700 𝑚𝑚2
𝑈=
𝐹1 −𝐹2
𝐹1
=
50,000−39,000
50,000
𝑕 1 −𝑕 2
𝑕1
=
𝑕 1 −𝑕 2
𝑕1
= 0.214
200−150
200
50
= 200 = 0.25
100% =
200−150
200
= 100% = 25%
163
percentage reduction: 𝑈% =
𝐹1 −𝐹2
𝐹1
100% =
50,000−39,000
50,000
100% = 21.4%
The relative reduction can be calculated in terms of the coefficient of elongation and vice versa
from formulae:
𝑈=
𝐹1 −𝐹2
𝐹1
𝑙
1
1
= 1 −  = 1 − 1.2725 = 1 − 0.786 = 0.216
𝐹
1
2545
50,000
1
𝛼 = 𝑙2 = 𝐹1 = 1−𝑈 = 2000 = 39,300 = 1−0.214 = 1.2725
1
2
Problem 1: Three passes of a breaking down system square-oval-square are considered. The
ingoing profile is a square with 𝑕1 = 𝑏1 = 17.7𝑚𝑚 and 𝐹1 = 314𝑚𝑚2 . This square is entered
flat into the horizontal oval pass. The outgoing oval has dimensions: 𝑕2 = 10𝑚𝑚, 𝑏2 =
30𝑚𝑚 𝑎𝑛𝑑 𝐹2 = 200𝑚𝑚2 . This oval on turning through 90𝑜 enters into the square pass, as a
diagonal pass. The oval dimensions after turning are: 𝑕2 = 30𝑚𝑚, 𝑏2 = 10𝑚𝑚, 𝐹2 = 200𝑚𝑚2 .
The outgoing square has sides 𝑎3 = 12𝑚𝑚.
Solution: The outgoing square has sides 𝑎3 = 12𝑚𝑚 has the following dimensions:
𝑕3 = 𝑎3 × 1.414 = 17.0𝑚𝑚
𝑏3 = 𝑎3 × 1.414 = 17.0𝑚𝑚
𝐹3 = 𝑎3 𝑎3 = 144𝑚𝑚2
Pass I
The maximum absolute draught:
The max. % draught: 𝐺𝑚𝑎𝑥 =
∆𝑕𝑚𝑎𝑥 = 𝑕1𝑚𝑎𝑥 − 𝑕2𝑚𝑖𝑛 = 17.7 − 10.0 = 7.7𝑚𝑚
𝑕 1𝑚𝑎𝑥 −𝑕 2𝑚𝑖𝑛
𝑕 1𝑚𝑎𝑥
100% =
17.7−10.0
𝑕
10.0
17.7
100% = 43.5%
The maximum coefficient of draught: 𝛾𝑚𝑎𝑥 = 𝑕 2𝑚𝑖𝑛 = 17.7 = 0.565
1𝑚𝑎𝑥
164
The mean absolute draught:
𝐹
𝐹
314
∆𝑕𝑚 = 𝑏1 − 𝑏2 = 17.7 −
1
The mean percentage draught: 𝐺𝑚 =
200
2
𝑕 1𝑚 −𝑕 2𝑚
𝑕 1𝑚
𝑕
30
= 17.7 − 6.7 = 11.0𝑚𝑚
17.7−6.7
100% =
17.7
100% = 62.1%
6.7
The mean coefficient of draught: 𝛾𝑚 = 𝑕 2𝑚 = 17.7 = 0.379
1𝑚
From these calculations it may be seen that the values of the mean draught are greater than those
calculated from maximum dimensions.
Pass II
The oval enters on edge into the diagonal square pass.
Maximum absolute draught: ∆𝑕𝑚𝑎𝑥 = 𝑕2𝑚𝑎𝑥 − 𝑕3𝑚𝑖𝑛 = 30 − 17.0 = 13.0𝑚𝑚
Maximum percentage draught: 𝐺𝑚𝑎𝑥 =
𝑕 2𝑚𝑎𝑥 −𝑕 3𝑚𝑖𝑛
𝑕 2𝑚𝑎𝑥
𝑕
Maximum coefficient of draught: 𝛾𝑚𝑎𝑥 = 𝑕 3𝑚𝑖𝑛 =
100% =
17.0
30
2𝑚𝑎𝑥
𝐹
𝐹
Mean absolute draught: ∆𝑕𝑚 = 𝑏2 − 𝑏3 =
2
Mean Percentage draught: 𝐺𝑚 =
200
3
𝑕 2 −𝑕 3𝑚
𝑕 2𝑚
𝑕
10
30−17.0
30
100% = 43.3%
= 0.566
144
− 17.0 = 20.0 − 8.5 = 11.5𝑚𝑚
100% =
20−8.5
20
100% = 57.5%
8.5
Mean draught coefficient: 𝛾𝑚 = 𝑕 3𝑚 = 20.0 = 0.425
2𝑚
4. Calculation of Rolling Temperature
In drawing up a rolling programme for an existing or newly designed mill there is always the
problem of correct determination of rolling temperature. The roll pass designer when designing
the roll passes, their sequence and layout in the roll stands, must also determine the rolling
temperatures.
In practice, the temperature of stock on removing from the heating furnace is usually known.
Knowing the time of travel from the furnace to the first roll stand, then the temperature of metal
in the first pass can be determined or measured directly. The temperature of stock in the
following passes is assumed from experience, as lack of time and the position of the roll guides
prevents accurate measurement.
The factors affecting the cooling of stock during rolling include heat losses by radiation,
convection, conduction, scale formation and descaling, temperature increase due to partial
conversion of deformation work into heat and heat losses resulting from scale formation and
165
descaling. If most of these factors are disregarded and only the radiation loss is considered, heat
loss can be calculated from Stefan-Boltzmann‟s relation:
𝑄𝑠 = 𝜀𝐶𝑠
𝑇1
100
4
−
𝑇𝑎𝑚
100
4
𝑧𝐹
(9)
Where
𝑄𝑠 = quantity of heat lost in radiation, kcal,
𝜀 ≏ 0.8 = emissivity of different rolled products,
𝐶𝑠 = 4.96 = radiation constant of black body, kcal/𝑚2 𝑕 𝑜 𝐾 4 ,
z = radiation time, hrs,
F = radiation surface of product, 𝑚2 ,
𝑇1 = absolute temperature of the radiating product at the beginning of radiation
time z,
𝑇𝑎𝑚 = absolute ambient temperature (273+20) =293𝑜 K).
At the ambient temperature of 20𝑜 C the expression
𝑇𝑎𝑚 4
100
≏ 74
The heat lost by radiation should amount to
𝑄𝑠 = 𝑀𝑠∆𝑡
10
where
M = weight of rolled stock, kg,
s = average specific heat (for steel above 8000 𝐶) 𝑠 = 0.166 kcal/𝑘𝑔0 C,
∆𝑡 = difference in metal temperature at the beginning and at the end of radiation time, z, or
𝑄
T1 − T2 = ∆t. Hence ∆𝑡 = 𝑀 𝑠 𝑆 .
Substituting equation (3.31) into equation (3.30) gives for steel
166
4.0𝑧𝐹
∆𝑡 = 𝑀×0.166
𝑇1
100
4
− 74 𝐶 𝑜
11
In this way the drop of temperature in each pass can be calculated, if only the radiation loss is
taken into account. Knowing 𝑇1 as the initial temperature, the required value of 𝑇2 can be
calculated. Then the temperature change after each pass can be calculated when the cross-section
area F and the pass time z are known.
Problem 2: A bar of length 11m, perimeter 18cm, weight 300kg is rolled for 10sec from initial
temperature 1000𝑜 𝐶. Find out the final temperature.
Solution
Temperature drop ∆𝑡 = 12.5oC.
Final temperature of bar will be 1000-12.5=987.50 C.
Problem 3: A steel round billet of 100mm diameter and 6 m long is rolled to 20mm diameter rod
with 6 passes. The sequences of passes are:
No. of Passes
0
1
2
3
4
5
6
Diameter, mm
100
80
60
50
40
30
20
The initial temperature of the billet was 1000oC and rolling time for the first pass was 5 seconds.
For subsequent passes, the rolling time was proportional to the length of the product. Find out
the final temperature of the rolled steel bar. The average specific heat of steel at high temperature
is 0.166 Kcal/kgoC. Densities of various metallic alloys are listed in the Table given below.
Metal or Alloy
Kg /Cu. Mtr
Aluminium
2600
Brass
8580
Phosphor Bronze
8850
Cast Iron
7300
Copper
8930
Steel
7850
Titanium
4500
Tungsten
19600
167
Solution: Volume of steel: 0.047 cubic meter, weight of metal = 369 kg.
From following equation and supplied data, temperature decrease in first pass is 3oC
𝑄𝑠 = 𝜀𝐶𝑠
𝑇1
100
4
𝑇𝑎𝑚
−
100
4
𝑧𝐹
No. of Passes
0
1
2
3
4
5
6
Diameter, mm
100
80
60
50
40
30
20
3
5
?
?
Temperature Drop, oC
60
5. Work Done During Deformation
When a metal is deformed the external energy is absorbed for elastic and plastic work necessary
for deforming the metal. For elastic deformation, the stress-strain relation is:  = 𝐸
Where , E and  are respectively, stress required for elastic deformation, Young‟s Modulus and
the work done for elastic deformation will be dW = Vd. Here V is the volume of metal.
So, Wel = VE 𝑑. = 𝑉𝐸
2
2
2
= 𝑉 2𝐸
The elastic of the work done is usually negligible. In this case, another parameter the strain
hardening exponent influences the work done. In the stress-strain curve  = 𝐾 𝑛 . The plastic
component of the work done will be:
𝑑𝑊𝑝𝑙 = 𝑉𝐾𝑛 𝑑
𝑊𝑝𝑙 = 𝑉𝐾 𝑛 𝑑 =
𝑉𝐾 𝑛 +1
𝑛+1
or 𝑊𝑝𝑙 =
𝑉 
𝑛 +1
During metal working, supplied energy is expended through two different changes in the metal
which are (i) remains in the metal as residual stress and (ii) by producing heat energy. This
thermal energy may cause increase in the temperature of the metal to be deformed and influences
the overall process parameters. It has been found that about 95% of the expended energy is
converted into heat energy. In the case of very high rate of deformation (adiabatic deformation),
i.e. high speed rolling almost all expended energy causes temperature rise. In this case:
Work done = Heat energy absorbed by metal
= Mass of metal x Specific heat x Temperature rises
= Metal volume x Density x S.H. x T
168
= VCpT
Use the following Table, if necessary.
Temperature, K:
300
600
1200
Strain Hardening Exponent:
0.22
0.32
25
Note: Specific heat of steel at the temperature range 800-1200oC is about 0.62kJ/kgK
Problem 4: A mild steel billet 0.3% carbon of diameter 60mm is rolled to 32mm diameter rod.
The starting hot rolling temperature was 900oC. If the length of the initial stock is 40m,
determine the temperature rise due to the corresponding deformation.
Solution: Work done in adiabatic process Wad = VCpT
We also know, 𝑊𝑝𝑙 =
𝑉
𝑛 +1
= VCpT

Now, T = {𝑛+1}/ Cp = (450x0.15x0.72)/(1.25x7.8x0.6) = 10oC rise in temperature.
6. Calculation of Rolling Speed
Rolled stock enters the gap with a speed less than the peripheral roll speed and that the exit speed
of the product is greater than the peripheral speed of rolls. Since on the entry side the stock
passes through with a speed less than the horizontal component of the peripheral speed of rolls,
there must be a place in the roll gap at which this horizontal component of peripheral speed is
169
equal to the speed of rolled stock. This place is called the neutral line or plane. This relation can
be expressed mathematically as:
𝜗𝑁 = 𝜗𝑟 𝑐𝑜𝑠𝛿
(12)
Where 𝜗𝑁 = speed of rolled stock at neutral plane, 𝜗𝑟 = peripheral speed of rolls,  = Included
angle from roll center to neutral point
𝜗𝑟 =
𝜋𝐷𝑤 𝑛
60
𝑚/𝑠𝑒𝑐
(13)
𝐷𝑤 = working roll diameter, or 𝐷𝑚𝑤 = mean working roll diameter.
n = roll revolutions, rpm.
At the neutral plane another phenomenon occurs, the frictional resistance forces change their
directions. The entry speed of stock is denoted as 𝜗1 (m/sec) and the exit speed as 𝜗2 (m/sec). As
the speed of stock and the horizontal component of peripheral speed of rolls are equal at the
neutral plane only, slip occurs between the stock and rolls at every other point. At the plane of
exit the speed of stock is greater than the peripheral speed of rolls. This difference of speed is
called the forward slip. Mathematically the forward slip is expressed as:
𝑆𝑓 =
𝜗2 − 𝜗𝑟 𝜗2
=
−1
𝜗𝑟
𝜗𝑟
or as a percentage 𝑆𝑓 =
𝜗 2 −𝜗𝑟
𝜗𝑟
14
100%
Or as a coefficient of forward slip
15
𝜗
𝑠 = 𝜗2
𝑟
16
Backward slip at the entry side of the roll gap is defined as difference between the horizontal
component of peripheral speed of rolls and speed of entry of the stock, relative to the horizontal
component of peripheral speed of rolls, i.e.
𝑆𝑏 =
𝜗𝑟 𝑐𝑜𝑠𝛼 − 𝜗1
𝜗𝑟 cos 𝛼
17
When neglecting spread, the value of coefficient of forward slip can be found from Fink‟s
formula
𝜗2 𝐷 1 − cos 𝛿 + 𝑕2
=
cos 𝛿
𝜗𝑟
𝑕2
18
170
Where 𝛿 = neutral angle. From the law of constant volume, two basic relations for metal passing
through the roll gap are obtained:
(1) 𝑕1 𝑏1 𝑙1 = 𝑕𝑥 𝑏𝑥 𝑙𝑥 = 𝑕𝑁 𝑏𝑁 𝑙𝑁 = 𝑕2 𝑏2 𝑙2
(19)
(2) Equations of speed of metal flow.
Assuming the time of stock transference through the roll gap to be equal to t seconds, 𝑉𝑠 the
volume/second of metal passing through the roll gap, i.e.
𝑉𝑖
𝐹1 𝑙1 𝐹2 𝑙2 𝐹3 𝑙3
𝐹𝑛 𝑙𝑛
= 𝑉𝑠 =
=
=
=⋯=
𝑡𝑖
𝑡1
𝑡2
𝑡3
𝑡𝑛
(20)
Problem 5: Rolling speed is to be calculated for a bloom of cross-sectional area b1h1 =
250x200mm is rolled to bfhf = 262x150mm, where the roller is very smooth and included angle
at neutral point is 20o. Other rolling conditions are: working roll dia. = 700mm, rotation of roller
= 85rpm, temperature of stock 1000oC, forward slip = 10%. Consider, the linear expansion of
steel roll is 0.000016m/moC.
Solution: Peripherial speed of the roller = 𝜗𝑟 =
Forward slip 𝑆𝑓 =
𝜗 2 −𝜗𝑟
𝜗𝑟
𝜋𝐷𝑤 𝑛
60
𝑚/𝑠𝑒𝑐 = 3113mm/sec
100% = 0.1
𝑊2 = 1.1𝜗𝑟 = 3.4m/sec,
𝜗1 = 𝜗𝑟 𝑠𝑖𝑛 = 3.11x0.8 = 2.5m/s
7. Slitting Technology in Rolling
Nowadays, the production of rebars is getting highly sensitive to cost of production. So, selection
of technology must meet the client's requirement of capital cost, operational cost and simplicity
of its adoption. These requirements are also possible to be fulfilled in a conventional bar mills,
already in operation, by making a few changes for introduction of slit rolling technology. It is
found that the production of smaller sizes bars, in many steel rolling mills, is a bottleneck in the
capacity utilization as compared to the bigger sizes. This results in uneconomical operation of
the plant and underutilization of reheating furnaces and melting units.
Slit rolling technology was developed in beginning of 20th century for slitting of rail sections
into head, web and flange and subsequent rolling to various sections. During sixties Swedish
engineers adopted this technology for increasing the production of simple sections. Slitting
technology adds many benefits to the rolling industries some of which are listed below:
171
7.1.1 Higher Production Rates in Smaller Sizes
Slit rolling technology was initially developed for production of rebars in two strand rolling and
later developed to multi-strand rolling up to five strands. Obviously for a given speed the
production rate for two strands is almost doubled compared to single strand. When the number of
strands are more (like three, four or five strands) production rates are multiplied.
7.1.2. Low Speed Mill Operation with Higher Productivity
There are many underlying reasons to operate a rolling mill with a very high speed. This may be
to reduce the per unit production cost using same man power and machineries. It may also be to
fulfill the market demand when the low speed production rate cannot coup. What may be the
reasons, it must note that rolling at higher speed ensures higher production, but the rate of wear
and tear of the moving parts will be significantly higher because of the excessive momentum of
the products. Moreover, the cyclic vibrations of the machineries will be higher that means there
will be more break down and maintenance requirements. Finally, it will be very difficult to
maintain the overall quality and dimensions of the products, especially for the deformed bars
where correct impression of rib geometry over the bars is essential. If it is possible to utilize the
slitting technology, then low to medium speed production rate to coup with the market demand.
7.1.3. Better Utilization of Reheating Furnace Capacity
For all rolling mill, the production rate of higher diameter bar is always higher than lower
diameter bars. It is general practice to set a reheating furnace that ensures sufficient billet
reheating for higher diameter bar production. As the production rate of lower diameter bar is
lower, so the full capacity utilization cannot be possible. As a result, there will be energy loss
leading to expensive products for lower diameter bars. When the production rates are same for
each size, the furnace can be utilized in the most optimum manner. The most important cost
parameter fuel cost is thus controlled to optimum level.
7.1.4. Low Investment
Very high speed mills are exceptionally expensive, which will usually not required if slitting
technology is used. All these factors make rebar rolling economical from the point of view of
initial investment as well as operating cost.
7.2. The Slitting Processes
7.2.1. Separation into 2 and 3 Strands
The slitting schedules are shown below in Fig.42. Similar to non-slitting rolling, here the billet
may be round or square.
172
Figure 42: Various stages of 2, 3, 4 and 5 slitting for the production of deformed bars.
In the case of slit rolling, breakdown and roughing operations are similar to conventional, i.e.
non-slitting type rolling. However, in the intermediate rolling section, the workpiece is rolled to
a rectangular section of thickness slightly higher than the targeted diameter of final rebars and
width will be slightly higher than the targeted diameter time the number to slits, which is called
flat pass, Fig.6. After flat pass there will be start of forming pass. At the end of forming pass,
targeted numbers of bar will be preformed but they will remain attached through a small strip of
metal. In the separating or slitting pass, the small strip of metal that connects the preformed bars
are divided into separate bars, which is very round called false round as it is not the final shape.
The slitting technique is that the separating wheels apply diagonal forces to the section to be
separated (Fig.43), resulting into lateral forces splitting or dividing the small strips of material
between the rounds. In the case of two slitting process, sections 1 and 2 are divided and delivered
to the finish rolling mill as two separate bars (Fig.44), whereas for three slitting process, three
individual round bars will be produced at a time, Fig.45.
173
Figure 43: Diagonal force applied
for separating the joined bars.
Figure 44: Single strand two slitter.
Figure 45: Double strand three slitter.
For more than 3 strand slitting a multiple strand separating guide is used. This guide differs from
the 2 and 3 strand slit guide by having two sets of separating wheels incorporated in one unit,
Fig.46.
Figure 46: Multiple strand four slitter.
Figure 47: Multiple strand five slitter.
In principle, the 4 strand slit guide is a combination of two 2 strand slitting operations in one
unit. In the first stage sections 1 and 4 will be separated from the slitting pass and in the second
stage sections 2 and 3 are divided, Fig.46. As a result, four separate strands are delivered and
spread into the correct strand distance by delivery channels situated at the end of the separating
guide. In 5 strand slitting, the multiple strand separating guide a combination of a 2 and a 3
strand slitting system, again incorporated in one unit, is used. In this case, firstly, sections 1 and
5 are separated and in stage two sections 2, 3 and 4 are separated; resulting in five separate bars
of false round to be delivered to the finishing section of the rolling mill.
174
After the slitting operation the stock continues rolling with multiple strands, Fig.48. All guide
equipment, either entry or exit guides are mounted in multiple strand cassettes. Such cassettes
can be made for 2, 3, 4 and 5 strand rolling. Cassettes allow rapid guide changes for correctly
pre-set guides. The pass line is kept and the new guide will take up its correct position. For the
positioning of the roller entry guides in the finishing stand laterally adjustable cassettes are
recommended to guarantee a correct position of the oval into the pass.
Figure 48: Subsequent finishing rolling after slitting operation.
8. The Rolling Sequence in the Finishing Mill
The slit section is a false round, which is guided into the oval stand by static entry guides
(Fig.42) for further deformation and property enhancement. The oval produced has to be twisted
90° and enters the finishing stand through roller guides. In most cases roller guides with a single
pair of rollers will be used in finishing stands.
Problem 6: A 0.2% carbon steel square billet (120x10mm) of length 12m is to be rolled from
1140oC for the production of 12mm deformed bars in several passes consisting of 4 roughing
passes and intermediate passes. Note that 4 slitting process will be used and considering the mill
condition, in any pass, more than 30% reduction will be possible. Design the rolling schedule.
175
Solution
Change in Roughing Passes
The cross-section of the initial billet = 14400mm2.
After first pass X-section: 10080mm2
After second pass X-section: 7056mm2
After third pass X-section: 5040mm2
After forth pass X-section: 3457mm2
Change in Intermediate Passes
Initial X-section 3457mm2.
This is four slitting process for production of 12mm bar.
So, before slitting X-section will be rectangular of dimensions  60x15mm (900mm2)
Suppose 30% reduction will be in first pass, after first pass X-section: 2420mm2
After second pass X-section: 1694mm2
After third pass X-section: 1186mm2
After third pass the x-section is still higher than the required target. So, we need forth
intermediate pass to reduce 24% X-section, so after forth pass X-section 901mm2.
Change in Finishing Passes
After end of intermediate pass, X-section = 901mm2
X-section of one 12mm bar = 113.2mm2.
False round bar size: 225mm2 (16mm bar).
So, we still need to reduce minor X-section.
The final product dimension will be possible if we use three finishing pass and we reduce the
section by 20% in each pass.
RP-1
RP-2
RP-3
RP-4
IP-1
IP-2
IP-3
IP-24
FP-1
FP-2
FP-3
30%R
30%R
30%R
30%R
30%R
30%R
30%R
30%R
20%R
20%R
20%R
176
Problem 7: In problem 7 the stock material will be 0.2% carbon steel billet. If similar rolling
schedule is used, what will final rolling temperature, microstructures and properties of the rolled
bars? Ignore the grain size effect.
Problem 8: In problem 7 what will be the increase in the productivity of the slitted rolling
system compared to that of the conventional rolling process? Assume that each pass, before
slitting, is completed within 10 seconds and after slitting rolling time in each pass is proportional
to the length of the rolled workpiece.
177
Chapter Seven
Wiredrawing and Extrusion
1. Introduction
Prior to the adoption of continuous drawing practices, little attention was given to the
understanding of the wiredrawing theory. This can be largely attributed to the fact that, until the
introduction of steam power, the single, largest problem facing wiredrawers was obtaining the
necessary motive force required for the drawing process. As developments and improvements in
mechanization developed during the industrial revolution, little emphasis was placed on
understanding the physical process, as satisfactory results were generally obtainable with the
moderate drawing speeds and drafting that were used. In any event, wire could be processed only
in low volume as short die life limited any further increases in productivity and quality.
However, commercial introduction of cemented carbide dies in Germany during the 1920s
resulted in an increase in drawing speeds and sophistication in wire mills to handle the larger
volumes that could be drawn. Therefore, it was soon apparent that a more detailed understanding
of the wiredrawing process was needed. While an impressive body of knowledge has
accumulated that affords a comprehensive picture of single hole wiredrawing, additional detail is
needed, particularly for multi hole processes. Modern wiredrawing is a highly competitive global
business where product requirements are continuously changing and the traditional evolutionary
techniques, which characterized technology development in the past, are no longer viable.
Furthermore, given the limited resources that are available in the industry as well as the rapidly
changing technical requirements, it is clear that personnel at all levels need an in-depth
understanding of wiredrawing theory. It is also clear that such an understanding is a prerequisite
for controlling and optimizing existing processes and the sustainable development of new
technology.
2. Wire Drawing Unit
In the conventional drawing process a stable die called drawing unit is used. To assist the
drawing die and for good quality surface finish on back-up or pre-drawing die is used, Fig.1. The
surfaces of material and die in drawing cone of the die during dry drawing process have a direct
contact that increases the friction and required drawing force. Disadvantageous influence of
friction during drawing processes results nonuniform distribution of strain and by the redundant
strain, it causes the non-uniform distribution of internal residual stress that influence the
mechanical and technological properties of the wire produced. To avoid such a technical
problem, in many cases low friction is targeted by avoiding the direct contact between wire and
die surface by proper lubrication. For continuous process the back-up die and the working die are
placed in a closed chamber, which is then set into another chamber containing the lubricant,
Fig.1.
178
Figure 1: Wiredrawing die sealed in a closed chamber with lubricant.
3. Mechanics of Wiredrawing
Deformation in wiredrawing is influenced by a number of factors; wire chemistry, approach
angle, lubrication, drawing speed and amount of reduction per pass as well as total reduction are
the most significant. The primary emphasis in wiredrawing mechanics is on understanding and
defining the relationships that exist between these process conditions and the resulting
thermomechanical response of the wire. Many of the technological developments that have taken
place in wiredrawing over the past 20 years have been the result of an increased understanding of
these relationships.
3.1. Constancy of Volume
Although the fact that volume is not changed during deformation may seem obvious, it is in fact,
a highly useful concept that forms the basis for analyzing a number of wiredrawing problems.
One of the most common applications involves the determination of wire speed at different
stands and the necessary capstan speeds that should be used. Simply stated, constancy of volume
states that the volumetric rate of wire entering a die must be the same as that exiting. Because the
cross sectional area is reduced during drawing, it is necessary that a wire must increase in speed
for the same volumetric rate of material to enter and exit the die. Volumetric rate is defined as
the cross sectional area of the wire multiplied by the wire velocity. This can be expressed
mathematically as:
179
Here Vi and Vf represent the wire velocities (feet or meters per minute) and di and df are the wire
diameters (inches or millimeters) entering and exiting the die, respectively. For circular wire, the
above equation can be simplified and reduced to:
In multi-pass drawing, wire speed exiting each die must increase so that the volumetric rate of
metal flow is equal at all dies. Therefore, capstans, having an angular velocity equal to the
exiting wire speed, are used to pull the wire through the die after each reduction. If this is not
done, the wire will break due to unequal wire tension between dies. Because the volumetric rate
must be the same at all points, wire velocity can be calculated at any intermediate stand
once the incoming wire speed at the first stand is known.
Problem 1: A 0.100 inch (2.5 mm) wire paid off from a spool at 1,200 feet/minute and reduced
to 0.090 inch (2.286 mm) by using two passes. Determine the velocity of the wire as it exits the
last die.
Solution:
Wire diameter increases as drawing dies wear in actual production; therefore, based on constancy
of volume, wire speed will decrease as the dies increase in size. If the linear speed of the pulling
capstan is matched to the wire size of a new die, capstan speed will be faster than the wire speed
as the wire diameter increases. This increased capstan speed will apply high tensile stress on the
wire, often breaking the wire. Therefore, capstans in multi-pass drawing machines are designed
so that the wire slips on the capstan as the dies wear and the wire speed decreases. Slip is
facilitated by limiting the number of wraps around the pulling capstan and wetting the wire and
capstan surfaces with drawing lubricant. Otherwise, each drum is powered by an independent dcmotor and the speed of each motor is adapted to the actual speed of the wire by a tension arm,
located between the drums. In other machines, several drums are driven by one single motor and
the rotation speed of drum cannot be changed independently from the others. However, the
increased speed of the drawn wire from each drawer is accommodated by the variable diameter
of the drum, Figs.2 and 3.
180
Figure 2: Automatic control of capstan speed in wiredrawing.
Figure 3: Accommodation of wire of from different drawing stands.
4. Calculation of Deformation in Wiredrawing
A schematic of a classical wire drawing die is shown in Fig.4. The core of the die is made from a
wear resistant material and fits into a steel frame. The entrance angle  permits the lubricant to
enter the die and adhere to the wire. The deformation takes place in zone b. The deformation
zone is characterized by two important parameters: the length Lp and the semi die angle . In
most dies, the latter takes values from 4o to 12o. A shorter die reduces the friction, but increases
the redundant deformation as shown schematically in Fig.5.
181
Figure 4: Metal deformation in wiredrawing process.
Figure 5: Illustration of (a) homogeneous, (b) frictional and (c) redundant work in wiredrawing.
Now the relation between applied compressive force P and the effective drawing force F
becomes as follows:
P=Fsin
In zone c, called the bearing surface, the final sizing of the exit diameter is performed. Finally,
zone d is the exit zone. The reduction r and the true strain  in wire drawing are defined as:
182
From chapter 1: 𝒕 = 𝑰𝒏
𝒍𝟏
𝒍𝟎
= 𝑰𝒏 𝟏 + 𝒆𝒆 , so we can write:
The semi die angle  and the reduction r can be combined in one parameter , which will be
used to express the degree of redundant deformation as per Hosford and Caddell:
Here Dg the mean wire diameter in the deformation zone and  expressed in degrees.
5. Die Materials
The inner core of a drawing die is fabricated from a wear resistant material, usually cemented
tungsten carbide or, for fine wires, from diamond. Hardened tool steel (HRC around 60) is only
used for small series. Dies made from diamond are very expensive, but can outperform the
cemented tungsten carbide dies by a factor of 10-200. When a die is worn out, it can be reworked
and used again for thicker wires.
6. Lubricants
Friction between wire and die is not required in a drawing process. It causes wear of the die,
possible damage to the wire surface and an increase in drawing force and temperature. Proper
lubricants have to be used to minimize friction and in some cases to cool the wire. In dry
drawing, the surface of the wire is coated with dry soap powder by passing the wire through a
box filled with the lubricant and the wire is cooled, while it resides on the bull blocks or by
cooling the die holder with water. High strength materials are often coated with a softer material
that acts as a lubricant, e.g. steel with brass. In wet drawing, the die is completely immersed in
oil or in an emulsion. In this case, the lubricant also serves as cooling medium. In general, the
friction coefficient in wire drawing ranges from 0.01 to 0.1.
7. The Drawing Force
Although wire drawing seems to be a rather simple deformation, a precise calculation of the
drawing force is not so easy task. In the simplest approach, factors such as friction, redundant
deformation and work hardening are neglected. If the effective strain is considered to be a pure
uniaxial elongation [ = ln(Do/D1)2] and the material as ideal plastic (with constant flow stress
f), the drawing force F can be estimated from:
183
𝑜𝑟 𝐹 = 𝑓 𝑙
𝑓 𝑑
𝑜𝑟 𝐹 =
Several attempts have been done to incorporate the influence of friction and redundant
deformation. Two of the more elegant formulas have been proposed. The formula of Siebel
simply adds a friction and a redundant deformation term:
The formula of Hoffman and Sachs adds a friction term and a correction coefficient  which, can
be expressed as a function of the  factor:
7.1. Ideal Work
To calculate the ideal force F, it is necessary to envision an ideal process for achieving the
desired shape change. It is not necessary that the ideal process be physically possible. For
example the axially symmetric deformation in the extrusion or wire drawing of a circular rod or
wire can be simulated by tension test. The ideal work is:

𝐹=
0
𝑓 𝑑
In general, when metallic materials are deformed below recrystallization temperature, then they
get strain hardened. With power law, the strain hardening effect can be expressed by the
following equation:
𝐹 = 𝐾 𝑛 +1 /(𝑛 + 1)
184
Problem 2: The strain hardening behaviour of a metal is approximated by σ = 140ε0.25MPa. Find
the total load required to reduce a round bar from 12.7 to 11.5mm diameter in tension. Consider
an ideal case.
Solution: The drawing load needed is 14.7MPa.
In a conventional wire drawing process, the diameter of a wire is reduced by pulling it through a
conical die (Fig.1). In industrial production lines, a large reduction is obtained by pulling the
wire or rod through a series of consecutive dies. In some cases, an intermediate annealing
treatment may be necessary. For most metals, drawing is carried out at ambient temperature,
although the temperature inside the die can rise considerably due to heating associated with
deformation and friction. Some materials (e.g. tungsten wire for incandescent lamp filaments)
are drawn at high temperature.
Tubes and straight rods with diameters above 20mm are usually drawn with draw benches
(Fig.6). These machines contain a single die and the pulling force is provided by a drawing
trolley. The drawing speed is relatively low (0.1–1 m/s) and the length of the tube or the rod is
limited (typically less than 30m). Longer rods and wires are drawn by a rotating drum, called a
„bull block‟ or „capstan‟. In most commercial wire drawing plants, several die/capstan
combinations are mounted in series to form a continuous wire drawing machine. Since the wire
diameter D is reduced in each pass, the wire speed v increases after each die.
Figure 6: Bench top type wide/rod drawing setup.
7.2. Deformation Efficiency
In addition to the ideal work, there is work against friction between work and tools, Wf, and work
to do redundant or unwanted deformation, Wr. Expressed on a per volume basis these are wf and
wr. Figure 7 illustrates the redundant work in drawing or extrusion.
Figure 7: Homogeneous and redundant deformation in wiredrawing process.
185
If the deformation is ideal, plane sections would remain plane. In real processes, the surface
layers are sheared relative to the center. The material undergoes more strain than required for the
diameter reduction and consequently strain hardens more and is less ductile. Thus, in the
wiredrawing process, the actual work is the sum of the ideal, frictional and redundant works:
It is often difficult to find wf and wr explicitly, but the need to do this can be avoided by defining
a deformation efficiency, η, where:
Experience allows one to make reasonable estimates of η. For wire and rod drawing, it is often
between 0.5 and 0.65 depending on lubrication, reduction and die angle. Using the deformation
efficiency term, the extrusion pressure or drawing stress can be expressed as:
𝑃=
1

𝑓 𝑑
Problem 3: Calculate the drawing load to draw the bar in earlier problem through a die, reducing
its diameter from 12.7 mm to 11.5 mm, if the efficiency is 70%.
Solution: 21MPa
7.3. Maximum Drawing Reduction
For drawing, there is a maximum possible reduction per pass because the drawing stress cannot
exceed the strength of the drawn wire or rod. Once drawing has started, it is a steady state
process. The maximum reduction corresponds to the stage when the applied drawing stress (f) is
equal to the ultimate tensile strength () of the material, i.e. f =  .Here it is to be mentioned
that at fully strain hardened condition ultimate tensile strength is very similar to that of the yield
strength of the material. If the effect of hardening caused by redundant strain is neglected, the
limiting strain, ε can be calculated. We know:
𝐾 𝑛+1
 
𝑓 =
=
 𝑛+1
(𝑛 + 1)
We also know that
σ = Kεn
186
At the point maximum drawing
So, max
Again we know that 
On the other hand
= ln
𝐴𝑜
𝐴1
𝑟 =1−
or
𝐴1
𝐴𝑜
𝐴𝑜
𝐴1
f = 
= (n+1)
𝑚𝑎𝑥 = 𝑒  = 𝑒 (𝑛+1)
𝑜𝑟 𝑟𝑚𝑎𝑥 = 1 − 𝑒 −(𝑛+1)
For an ideally plastic metal (n = 0) and perfect efficiency (η = 1), the maximum strain would be ε
= 1 which corresponds to a reduction.
1
So, 𝑟𝑚𝑎𝑥 = 1 −
𝑒
We know e = 2.71, rmax or the maximum reduction possible per pass is 0.63 or 63% and with a
more reasonable value of η = 0.65 and rmax = 48%.
7.4. Effects of Die Angle and Reduction
Figure 8 shows schematically the dependence of the friction and redundant work terms on die
angle. For a given reduction, the contact area between the die and material decreases with
increasing die angle. The pressure the die exerts on the material in the die gap is almost
independent of the die angle, so the force between the die and workpiece increases with greater
area of contact at die angles. With a constant coefficient of friction, wf increases as α decreases.
The redundant work term, wr, increases with die angle. The ideal work term, wi, doesn‟t depend
on the die angle. For each reduction, there is an optimum die angle, α*, for which the work is a
minimum. The efficiency and optimum die angle are functions of the reduction. In general the
efficiency increases with reduction. The optimum die angle increases with reduction.
Figure 8: Effects of die angle various work done in wiredrawing.
187
Problem 4: A pearlitic wire should be drawn from 5mm till 2.6mm diameter, using a wire
drawing machine with a maximal pulling force of 15.5kN. The desired reduction scheme is:
5mm → 4mm → 3mm → 2.6mm. Three types of dies are available with die angle 4, 8 and 16o.
The friction coefficient is always 0.05. Calculate for each pass and each die angle the pulling
force. Choose for each pass the best (available) die and discuss your answer.
The pulling force is the product of the pulling stress and the wire cross section after the die. The
pulling stress can be estimated using previous equations. Since pearlite shows a large work
hardening during drawing, an appropriate work hardening law should be used the estimate the
actual material flow stress after each die. The results are shown in Table.
In
the first drawing pass, the die with a semi die angle of 4o leads to a pulling force that exceeds the
capacity of the drawing machine. The dies with angles of 8o and 16o can both be
used, but the die of 8o leads to a more homogeneous deformation (lower  factor) and a slightly
lower pulling force. In the second pass, the pulling force is lower, but another problem occurs for
the die of 4o: although the flow stress of the wire has considerably increased, the pulling stress in
the wire is higher than the flow stress, which would lead to deformation and fracture of the wire
after the second die. The two other dies can in principle be used, but the die of 16o could be
preferred because it requires the lowest pulling stress, although it gives a somewhat less
homogeneous deformation compared to the 8o die. In reality, most production lines operate with
a pulling stress of maximum 60–70% of the flow stress of the material, so an adaptation of the
proposed pass schedule is advisable. In the third pass, the pulling stresses and forces are lower,
because of the smaller reduction, but the homogeneity of the deformation in the 16o die is
questionable. In this step, a die of 4o seems to be the best choice.
188
8. Dieless Wiredrawing
As the name implies, the principle behind dieless wiredrawing (see Fig.9) involves heating and
then stretching the wire in simple tension through differential capstan velocities, rather than
reducing the cross section by pulling it through a sequence of dies. Normally, the wire must be
rapidly cooled immediately after exiting the heating zone to strengthen the reduced area and to
suppress necking. Applied tensile force determines the final wire diameter, so process conditions
must be monitored and controlled rigorously. The purported advantages of this process are: a
broad range of wire diameters can be prepared in a single pass from a small number of starting
rod sizes, minimal labour is required to operate the mill and the need for large die inventories is
eliminated. It is envisioned that this process could lead to flexible “mini-mills” that could serve
the needs of regional customers with greatly reduced physical plant requirements. While several
attempts have been made to commercialize the process, a number of concerns have been
expressed with regard to the equipment cost and ability to control finish diameter.
Figure 9: Die-less wiredrawing process.
9. Some Important Metallurgical Factors
During wire drawing of FCC metals, classical strain hardening of the wire takes place. This
hardening is related to the substructural developments. But during drawing of bcc materials, such
as hypo and eutectoid steels, some unexpected hardening behaviour can be observed. During
wire drawing, grains should elongate in the drawing direction and contract in all directions
perpendicular to the wire axis. In reality this is observed in FCC materials, but in bcc materials,
such as low carbon and pearlitic steels, peculiar effect occurs. The grains do not only elongate in
the direction of the wire axis, but also get a kind of folding, visualized in Fig.10. This is called
the curling effect.
Figure 10: Curling in drawn wire.
189
In order to fold the grains over each other, some extra dislocations have to be generated. The
cementite lamellae in pearlitic is hard and brittle which is generally difficult to have plastic
deformation. It is guessed that the cold drawing deformation can make not only the ferrite layers
become thinner/bending, but also the cementite to some extent. This creates the extra dislocation
both in ferrite and cementite. The increase of the cementite interface energy that ultimately
forces the relatively soft ferrite lamellae to be folded. It is also believed that with increase in the
carbon percent, the proportion cementite increases as well as the cementite interface energy. As a
result, with increase in the carbon percentage, the degree of folding also increases. As the degree
of folding increases with increase in carbon content in cold drawn steel wire, the strength of
higher carbon content steel wire increases exponentially, whereas linear strengthening effect is
observed in low carbon steel, Fig.11.
Figure 11: Effects of carbon content on the strain hardening of behaviours of cold drawn wire.
10. Drawing of Metal Fibres
Ultrafine wires (50m) and fibres have interesting applications such as filter, anti-static textiles,
magnetic shielding, medical products, bonding wires in microelectronics, etc. Metal fibres can be
produced in many ways such as conventional drawing, bundle drawing, shaving and melt
spinning. Most ductile metals can be drawn into ultrafine wire by pulling them through thinner
and thinner dies. In most cases, drawing conditions have to be selected with care: low drawing
speeds, low per pass reductions and diamond dies with low approach angles are recommended.
Unfortunately, productions costs are very high and increase exponentially as the diameter
decreases. An alternative technique to produce fine fibres is the so called „bundle drawing‟.
Instead of drawing a single wire, several (in some cases up to a few thousand) are bundled,
tightly packed into a tube and drawn simultaneously. The challenge is to separate the individual
wires with a suitable material prior to bundling. This separating material must be easily
removable after drawing, e.g. by leaching. Stainless steel fibres can be drawn to a diameter of
1m with this method. Most metals can be drawn up to 8–12m in diameter and even brittle
190
superconductor alloys like NbTi and Nb3Sn are processed in this way. Another alternative is
„coil shaving‟. The material is first rolled into foil, which is coiled. A sort of big razor blade cuts
thin slices of material from the side of the coil. A fibre with rectangular cross-section, one
dimension being the thickness of the foil (typically 25-100m) is obtained. Ribbons of glassy
metals, typically 20-60m thick, can be obtained by melt spinning. A jet of molten metal is
poured onto a cool, fast rotating wheel. The solidification is very fast and amorphous or semicrystalline materials can be obtained.
Extrusion
Extrusion is the process by which a block of metal is reduced in cross section by forcing it to
flow through a die orifice under high pressure, Fig.12. In general, extrusion is used to produce
cylindrical bars or hollow tubes, but shapes of irregular cross section may be produced from the
more readily extrudable metals, like aluminum. Because of the large forces required in extrusion,
most metals are extruded hot under conditions where the deformation resistance of the metal is
low. However, cold extrusion is possible for many metals and is rapidly achieving an important
commercial position. The reaction of the extrusion billet with the container and die results in
high compressive stresses which are effective in reducing the cracking of materials during
primary breakdown from the ingot. This is an important reason for the increased utilization of
extrusion in the working of metals difficult to form, like stainless steels, nickel base alloys, and
molybdenum.
Figure 12: Metal extrusion process.
Extrusion is classified in general into four types. They are: Direct extrusion, indirect extrusion,
impact extrusion and hydrostatic extrusion.
11. Direct Extrusion
Figure 13 illustrates the process of direct extrusion. It is also called forward extrusion. In this
case, the metal billet is placed in a container and driven through the die by the ram. A dummy
191
block or pressure plate is placed at the end of the ram in contact with the billet. Friction between
the container and billet is high. As a result, greater forces are required. Hollow sections like
tubes
can
be
extruded by direct
method, by using
hollow billet and a
mandrel attached to
the dummy block.
Figure 13: Direct extrusion process.
12. Billet-on-Billet Extrusion
Billet-on-billet extrusion is a special method of extrusion for that metals and alloys that are
easily welded together at the extrusion temperature and pressure. Using this process, continuous
lengths of a given geometry (shape) can be produced by different methods. Billet-on-billet
extrusion is also a viable process in the production of coiled semifinished products for further
processing, such as rod and tube drawing production. Perfect welding of the billet in the
container with the following billet must take place as the joint passes through the deformation
zone. For this process the following requirements have to be fulfilled:
a)
b)
c)
d)
e)
Good weldability at the temperature of deformation
Accurate temperature control
Clean billet surface
Clean billet ends free from grease
Bleeding of air from the container at the start of the extrusion using taper-heated billet as
shown in Fig.14 to avoid blisters and other defects.
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Figure 14: Bleeding out air during upsetting
12. Indirect Extrusion
Figure 15 illustrates the indirect-extrusion process. A hollow ram carries the die, while the other
end of the container is closed with a plate. Frequently, for indirect extrusion, the ram containing
the die is kept stationary, and the container with the billet is caused to move. Because there is no
relative motion between the wall of the container and the billet in indirect extrusion, the friction
forces are lower and the power required for extrusion is less than for direct extrusion. However,
there are practical limitations to indirect extrusion because the requirement for using a hollow
ram limits the loads which can be applied.
Figure 15: Bleeding out air during upsetting
Simple hollow sections such as rounds, squares and ovals can be produced from a hollow billet
using a mandrel of required geometry (Fig.16). Here the product has a uniform structure across
the section. For hollow product extrusion the stock materials may be hollow or pierced billet.
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Figure 16: Bleeding out air during upsetting
More complex sections as shown in Fig.17 are made by extrusion process. The design of such
dies requires a great deal of experience although the use of C.A.D and the understanding of metal
flow is helping to add "science" to what is in effect an "art".
Figure 17: Some complex shaped extruded parts.
13. Hydrostatic Extrusion
Normally this is a cold extrusion process and usually carried out at room temperature. In
hydrostatic extrusion the container is filled with a fluid and the extrusion pressure is transmitted
through the fluid to the billet, Fig.18. Friction is eliminated in this process because of there is no
contact between billet and container wall. Also, there is no possibility of surface oxidation, so
extrusion ratios from 20 (for steels) to as high as 200 (for aluminium) can be achieved in this
process. Pressure involved in the process may be as high as 1700 MPa. However, applicable
pressure is limited by the strength of the container, punch and die materials. Vegetable oils such
as castor oil are used. Brittle materials can be extruded by this process. Greater reductions are
possible by this method. A couple of disadvantages of the process are: leakage of pressurized oil
and uncontrolled speed of extrusion at exit, due to release of stored energy by the oil. This
problem is overcome by making the punch come into contact with the billet and reducing the
quantity of oil through less clearance between billet and container. Ceramics can be extruded by
this process. Cladding is another application of the process.
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Figure 18: Hydrostatic extrusion process.
In addition to cold hydrostatic extrusion, attempts have been made to extrude conventional
metals at elevated temperatures for intermetallics. This has been shown to be beneficial for
materials difficult to extrude at room temperature such as titanium alloys, refractory metals and
alloys, bimetallic products and multifilament superconductors. The hot process has also been
used for the production of copper tubing at extrusion ratios on the order of 500 to 1. The pressure
media used in cold or warm processes (e.g., castor oil or other vegetable oils) ignite and burn at
high temperatures. The use of a viscoplastic pressure medium for hot hydrostatic extrusion
provides an alternative as these materials are soft solids at room temperature. This enables the
pressure medium to be introduced into the container without the need for a charging pump,
thereby simplifying machine design. Viscoplastic pressure media used for hot hydrostatic
extrusion include a variety of waxes, such as beeswax, carnauba wax, mountain wax, lanolin,
complex waxes, polyethylene, some metal oxide, non-grease, etc are used.
14. Impact Extrusions
Impact extrusion is the pressing out of a workpiece (e.g. rod section, sheet sections) placed
between tool parts, through an orifice with the help of a punch, Fig.19. It is used mainly to
produce single components. Impact extrusion is an important bulk forming process and offers a
range of special advantages, like:
a) optimal usage of material
b) high production rates with short piece-production times
c) accurate reproduction of dimensions and forms coupled with a good surface
quality
d) good static and dynamic properties of the components due to the favourable
fibre structure and work hardening.
Impact extrusion is similar to the other extrusion methods described, but is a much faster
process. Using shorter strokes and shallower dies, punch impact moves the feedstock slug either
up, down, or in both directions at once, without being completely confined by either the punch or
die walls. Ductile and low melting point metals such as tin, aluminium, zinc and copper are well
suited for impact extruding.
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Figure 19: Impact extrusion process.
The impact extrusion process is a far superior process over the deep drawing process when the
part design requires: (a) the base to be thicker than the side walls; and (b) when the shell length
is more than twice the diameter. Deep-drawn parts are typically limited to a 1:1 wall/bottom ratio
and a length width ratio of 2:1. The impact extrusion process typically has a wall/bottom ratio of
1:2 and is typically limited to a length/width ratio in aluminum of 8:1 and a 4:1 ratio in steel in a
single operation. Further processing can triple these ratios. Cost savings are realized through the
elimination of excess handling, lower tooling costs, and reduced labor costs. Additionally,
material yields are much greater when using the impact extrusion process. Material yields
typically are greater than 90% when using the impact extrusion process versus 80% or less using
the deep draw process.
14.1. Impact Extrusion versus Forging
When the design of a part requires that it be strong, lightweight with minimal draft angles and
the need to maintain close tolerances is necessary, the impact extrusion process is a better choice
over a forging. Impacted parts have a surface area/mass ratio of 16:1 versus 6:1 for forgings.
This allows impacts to have a much thinner wall section than a forging, resulting in a lighter
weight part that exceeds or is comparable in strength to a forging. Another advantage of the
impact extrusion process is its capability to consistently maintain tolerances in the 0.005” range
versus 0.060” for forgings. The close tolerance capability of impacting in many cases eliminates
the need for costly secondary machining operations.
15. Extrusion Variables
The principal variables which influence the force required to cause extrusion are: (1) the type of
extrusion (direct vs. indirect), (2) the extrusion ratio, (3) the working temperature, (4) the speed
of deformation and (5) the frictional conditions at the die and container wall. In Fig.20 the
extrusion pressure is plotted against ram travel for direct and indirect extrusion. Extrusion
pressure is the extrusion force divided by the cross sectional area of the billet. The rapid rise in
pressure during the initial ram travel is due to the initial compression of the billet to fill the
extrusion container.
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Start of Actual Extrusion
Redundant Work Start
Figure 20: Effect of ram travel on extrusion force in three different processes.
For direct extrusion the metal begins to flow through the die at the maximum value of pressure.
As the billet extrudes through the die, the pressure required to maintain flow Ram travel
progressively decreases as the frictional forces decrease with decreasing length of the billet in the
container. For indirect extrusion there is no relative motion between the billet and the container
wall. Therefore, the extrusion pressure is approximately constant with increasing ram travel and
represents the stress required to deform the metal in the die. On the other hand, no friction is
experienced between billet and extrusion chamber in hydrostatic extrusion, so the required
extrusion pressure is required, Fig.20. Among the three extrusion processes, hydrostatic process
needs the minimum energy. From the figure, it is also clear that, for direct extrusion, the curve
approaches the curve for indirect extrusion when the billet length approaches zero. For both
processes the curves turn upward at the end of the ram travel as the ram attempts to extrude the
thin disk of the billet which remains in the die. It is generally uneconomical to develop enough
pressure to force the billet completely through the die, and therefore a small discard, or butt,
must be removed from the container. However, it is exceptional for hydrostatic extrusion where
full length extrusion is possible. The curve for direct extrusion will be dependent on the length of
the billet and the effectiveness of lubrication at the billet container interface.
Extrusion ratio is the ratio of the initial cross sectional area to the cross sectional area after
extrusion, R = Ao/Af. The extrusion pressure is an approximately linear function of the natural
logarithm of the extrusion ratio. Therefore, the extrusion force P is given by:
𝑨𝒐
𝑷 = 𝒐 𝑨𝒐 𝒍𝒏
𝑨𝒇
The above equation can also be written in the following form:
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Here k is extrusion constant, an overall factor which accounts for the flow stress, friction and
inhomogeneous deformation. The values of k are temperature dependent and different for
different materials, some of which are shown in the following Fig.21.
Figure 21: Variations of extrusion constant of several metals with extrusion temperature.
For any particular metal, the hot extrusion temperature is not a fixed value rather than a range.
The ranges of hot extrusion temperatures for several common metals are presented in the Table
below.
If o is taken as the uniaxial flow stress at the conditions of temperature and strain rate used
during extrusion, above equation will predict an extrusion force which is at least 50% lower than
the observed extrusion force. This is because this equation does not take into consideration such
factors as nonhomogeneous deformation of the billet (which results in redundant work), die
friction, and friction between the billet and the container (for direct extrusion). A complete
analytical treatment of these factors is difficult, which prevents the accurate calculation of
extrusion force and extrusion pressure.
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Increasing the ram speed produces an increase in the extrusion pressure. A tenfold increase in the
speed results in about a 50% increase in pressure. Greater cooling of the billet occurs at low
extrusion speeds. When this becomes pronounced, the pressure required for direct extrusion will
actually increase with increasing ram travel because of the increased flow stress as the billet
cools. The higher the temperature of the billet, the greater the effect of low extrusion speed on
the cooling of the billet. Therefore, high extrusion speeds are required with high strength alloys
that need high extrusion temperatures. The temperature rise due to deformation of the metal is
greater at high extrusion speeds, and therefore problems with hot shortness may be accentuated.
The selection of the proper extrusion speed and temperature is best determined by trial and error
for each alloy and billet size. The interdependence of these factors is shown schematically in
Fig.22. For a given extrusion pressure, the extrusion ratio which can be obtained increases with
increasing temperature. For any given temperature a larger extrusion ratio can be obtained with a
higher pressure. The maximum billet temperature, on the assumption that there are no limitations
from the strength of the tools and die, is determined by the temperature at which incipient
melting or hot shortness occurs in the
extrusion. The temperature rise of the extrusions will be determined by the speed of extrusion
and the amount of deformation (extrusion ratio). Therefore, the curve which represents the upper
limit to the safe extrusion region slopes upward toward the left. The worst situation is for
extrusion at infinite speed, where none of the heat produced by deformation is dissipated. At
lower extrusion speeds there is greater heat dissipation, and the allowable extrusion ratio for a
given preheat temperature increases. The allowable extrusion range is the region under the curve
of constant pressure and extrusion speed.
Figure 22: Schematic diagram showing interdependence of temperature, pressure,
and extrusion speed.
There is a great effect of temperature on the extrusion behaviours of the metals. With increase in
extrusion temperatures, the flow stress or deformation resistance decreases. However, optimum
temperature should be selected that can provide suitable plasticity for the metal to be extruded.
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Here it is to be noted that the top working temperature should be safely below the melting point
or hot shortness range. High temperature also causes oxidation of billet and extrusion tools and
die/tool softening, which also need to consider in high temperature extrusion. For selection of
high temperature extrusion temperature, the following should be considered:
a. The initial temperature of the tools
b. Heat generated due to plastic deformation
c. Heat generated by friction at the die/material interface (highest).
d. Heat transfer between the deforming material and the dies and surrounding
environment.
16. Deformation in Extrusion
The pressure required to produce extrusion is dependent on the way the metal flows in the
container and extrusion die. Also, certain defects which occur in extrusions are directly related to
the way the metal deforms during the process. A fairly large number of investigations of the flow
characteristics of the softer metals, lead, tin and aluminum, have been made by using the split
billet technique. Both the deformation of the metal in the container and in the die must be
considered. Figure 23 illustrates the flow patterns produced by the deformation caused by the
direct extrusion process through a flat die.
Figure 23: Deformation patterns in extrusion; (a) at low friction or in indirect extrusion, (b) at
high friction, (c) with high cooling rate of the outer regions of the billet in the chamber.
Figure 23a represents the extrusion of a well-lubricated billet in which the billet slides along the
container wall. Deformation in the billet is relatively uniform until close to the die entrance. Here
the center part of the billet moves more easily through the die than the metal along the container
wall. At the corners of the die there is a dead zone of stagnant metal which undergoes little
deformation. Elements at the center of the billet undergo essentially pure elongation in the
extruded rod, which corresponds to the change in cross section from billet to extrusion. Elements
near the sides of the billet undergo extensive shear deformation. The shear deformation which
occurs over much of the cross section of the extruded rod requires an expenditure of energy
which is not related to the change in dimensions from the billet to the extrusion. This redundant
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work is chiefly responsible for the large discrepancy between the actual extrusion pressure and
the extrusion pressure calculated on the basis of ideal deformation.
If there is high friction between the billet and the container wall, severe shear deformation will
occur in the billet as well as in the flow pattern of the metal through the die (Fig.23b). Since the
velocity of the metal at the center of the billet is higher than along the container wall, there is a
tendency for metal to pile up along the wall and eventually it will move toward the center of the
billet. This gives rise to the extrusion defect. Alternatively, if the shear resistance of the metal
along the container wall is lower than the frictional stress, the metal will separate along this
region and a thin skin of metal will be left in the container. Similar behaviour of deformation
might also be observed for extrusion process where the heat loss from surface is very high. In
some cases, more complex metal flow pattern might also be observed, Fig.23c. The
nonhomogeneous flow through an extrusion die can be modified by changing the die angle.
Decreasing the die angle of a conical die so that it approaches the natural angle for flow through
a flat die results in less shear deformation. However, even though more uniform flow results
from smaller angle dies, the friction forces are higher. Therefore, it does not necessarily follow
that the extrusion pressure is lower when
the deformation is more uniform. In indirect extrusion there is no friction between the billet and
the container wall. With a flat die a dead metal zone exists.
17. Calculation of Extrusion Load
17.1. Ideal Conditions
An estimate of the pressure required for extrusion under ideal conditions can be made from an
analysis of the dimensional changes produced in the extrusion operation. Consider the extrusion
of a cylindrical billet of length Lo and cross sectional area Ao into a rod of length Lf
Cross sectional area Af. On the assumption of no friction and of uniform deformation, so that
there are no regions of high shear deformation and hence no redundant work, the work per unit
volume required to increase the length of the extrusion by an increment dL is given by:
The total work required in deforming the metal is:
Where V = AL is the volume of the metal. Therefore, from the above equation we can write:
The work produced by the ram in moving through a distance L is given by:
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Where P is force on ram and p is extrusion pressure. Equating the work required in deforming
the metal to the work produced by the extrusion ram gives the equation for the extrusion pressure
as given below:
Actually, above equation will predict an extrusion pressure approximately 50% lower than is
required, because it does not consider friction and nonhomogeneous deformation. In this
equation it is assumed that the maximum shear stress law is the criterion of yielding. If it is
assumed that the deformation starts on the basis of distortion energy yield criterion, the yield
stress for plane strain would be used in the equation as given below:
Extrusion with Friction and Nonhomogeneous Deformation
The flow of metal during extrusion under practical conditions is too complex to permit a precise
analytical solution of the forces involved. For the case of extrusion through a flat die an
expression can be developed for the effect of friction between the billet and the container on the
same basis as was used in case of forging.
Where R is extrusion ratio, f is coefficient of friction, L is length of unextruded billet,  is form
factor to account for redundant work 1.5.
The coefficient of friction can be evaluated by measuring the pressures required to extrude two
billets of different lengths, since
Extrusion of Tubing
With modern equipment, tubing may be produced by extrusion to tolerances as close as those
obtained by cold drawing. To produce tubing by extrusion, a mandrel must be fastened to the end
of the extrusion ram. The mandrel extends to the entrance of the extrusion die and the clearance
between the mandrel and the die wall determines the wall thickness of the extruded tube.
Generally, a hollow billet must be used so that the mandrel can extend to the die. In order to
produce concentric tubes, the ram and mandrel must move in axial alignment with the container
and the die. Also, the axial hole in the billet must be concentric, and the billet should offer equal
resistance to deformation over its cross section. One method of extruding a tube is to use a
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hollow billet for the starting material. The hole may be produced either by casting, by machining,
or by hot piercing in a separate press. Since the bore of the hole will become oxidized during
heating, the use of a hollow billet may result in a tube with an oxidized inside surface. A more
satisfactory method of extrusion of hollow pipe is to use a solid billet and pierce it, then extrude
to the final specification of the pipe, Fig.24.
Figure 24: Piercing of solid billet and then extrusion for seamless pipe production.
18. Extrusion Defects
18.1. Internal Oxide Stringers
Because of the inhomogeneous deformation in the direct extrusion of a billet, the center of the
billet moves faster than the periphery. As a result, the dead metal zone extends down along the
outer surface of the billet. After about two-thirds of the billet is extruded, the outer surface of the
billet moves toward the center and extrudes through the die near the axis of the rod. Since the
surface of the billet often contains an oxidized skin, this type of flow results in internal oxide
stringers, Fig.25. This type of defect can be considered to be an internal pipe, and it is known as
the extrusion defect. On a transverse section through the extrusion this will appear as an annular
ring of oxide. The tendency toward the formation of the extrusion defect increases as the
container wall friction becomes greater. If a heated billet is placed in a cooler extrusion
container, the outer layers of the billet will be chilled and the flow resistance of this
region will increase. Therefore, there will be a greater tendency for the center part of the billet to
extrude before the surface skin, and the tendency for formation of the extrusion defect is
increased. One way of avoiding the extrusion defect is to carry out the extrusion operation only
to the point where the surface oxide begins to enter the die and then discard the remainder of the
billet. This procedure may have serious economic consequences since as much as 30% of the
billet may remain at the point where the extrusion defect is encountered. An alternative
procedure, which is frequently applied in the extrusion of brass, is to use a dummy block which
is slightly smaller than the inside diameter of the extrusion container. As the ram pushes the
dummy block forward, it scalps the billet and the oxidized surface layer remains in the container.
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Figure 25: Oxide stringer and circular lubrication film in extruded components.
18.2. Axial Hole
When extrusion is carried to the point at which the length of billet remaining in the container is
about one-quarter its diameter, the rapid radial flow into the die results in the creation of an axial
hole or funnel in the back end of the extrusion, Fig.26. This hole may extend for some distance
into the back end of the extrusion, and therefore this metal must be discarded. The length of this
defect can be reduced considerably by inclining the face of the ram at an angle to the ram axis.
Figure 26: Axial hole formation at the back end of the extruded part.
18.3. Surface Cracking
Surface cracking can result from extruding at too rapid a rate or at too high a temperature. A
severe form of surface serrations, called the "fir-tree defect," results from the momentary sticking
of the extrusion in the die land. The pressure builds up rapidly as the metal tries to extrude
internally to overcome the high friction at the die wall, subsequently surface cracking results by
shearing, Fig.27. This type of defect can be avoided by using proper lubrication.
Figure 27: Fir-tree type surface cracking in extrusion.
In hot extrusion, this form of cracking usually is intergranular and is associated with hot
shortness. The most common case is too high ram speed for the extrusion temperature.
18.4. Nonuniform Deformation
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Because of high friction between the billet surface and internal surface of extrusion chamber,
nonuniform deformation might take place. Sometimes, billet surface may be cooled excessively
that result significant increase in the yield strength of the surface layer materials. This also
causes nonuniform deformation. Usually more deformation takes place at the central zone than
the surface area, Fig.28. Nonuniform deformation is also depends of the die angle. With increase
in die angle, more energy is needed for deformation of materials at the surface area. This type of
nonuniform deformation produced in extrusion also causes a considerable variation in structure
and properties from the front to the back end of the extrusion in the longitudinal direction and
across the diameter of the extrusion in the transverse direction.
Figure 28: Nonuniform deformation in extrusion.
18.5. Chevron Cracking
It can obviously be observed that extruded product breakage due to inclusions. The
inclusion/metal system may be simplistically considered as a composite material with the
inclusions acting as the aggregate and the metal as the matrix. It is apparent that there are number
of factors that affect the performance of the whole. Among these are the volume percentage,
shape, orientation and mechanical properties of the inclusions and the direction of the principal
stresses with respect to this orientation. The failure of the inclusion interface can be attributed to
ductile fracture that initiates after necking begins. This type of fracture is known to be multistep
process as void initiation, growth and coalescence. The coalescence of the voids forms a
continuous fracture surface. Voids can initiate at inclusions or secondary phase particles by
decohesion of the particle-matrix interface or fracture of the particle in the center of the neck
region. The internal or chevron cracks as shown in Fig.29.
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Figure 29: Chevron cracking in extrusion.
The chevron cracking that is also called center-burst may also result due to hydrostatic tensile
stress at center line of deformation zone (similar to necking in a tensile test specimen).
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Chapter Eight
Thermo Mechanical Control Process
1. Introduction
In the earlier days, hot rolling was the only option to give required dimensions. Thermo
Mechanical Control Process (TMCP) steels have higher strength and better toughness. TMCP
technology was developed in Japan in the 1980‟s. With the use of the TMCP process, very fine
and uniform acicular ferrite is attained as microstructure and therefore, TMCP steels have higher
strength and better toughness. Also according to the TMCP process, lower hardenability, less
susceptibility for cold cracking and the availability for the extra high heat input welding have
been improved. The overall consequence is that the quality level as well as mechanical property
of TMCP steels is quite high, which also remains stable over a quite high temperature and time.
2. What is TMCP?
In the past, the role of hot rolling was only to achieve the nominal dimensions like thickness,
width and length. If the quality requirement was somewhat high, an off-line heat treatment such
as normalizing or quenching and tempering would be added. As the quality requirements
increased, a new process for rolling had been developed called TMCP. With the TMCP process,
the total control during reheating of slab, rolling and cooling after rolling is critical. According to
the exact definition of TMCP, it includes TMR (Thermo Mechanical Rolling) and accelerated
cooling (AcC), Fig.1. Commonly, however, when people speak of TMCP, they usually think of
AcC as TMCP.
Figure 1: Schematic diagram showing the difference between conventional
rolling and TMCP
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2.1. Aim of TMCP
The aim of TMCP is to achieve, for example, in the case of hypoeutectoid steel a fine and
uniform acicular ferrite microstructure instead of a ferrite/pearlite banded structure of
conventional steels, Fig.2.
Figure 2: Hypoeutectoid steel with various ferrite and pearlite morphologies.
Acicular ferrite (top left) is the term used to describe a microstructure comprising an interwoven
ferrite laths or plates, first recognized in high strength, low alloy (HSLA) steel weld metals. This
interlocking structure was found to be a desirable microstructure in low carbon steel weldments,
because it showed improved toughness over that of other transformation products, such as
conventional bainite. According to this fine and uniform acicular ferrite, TMCP steels have a
higher strength and superior toughness, Fig.3.
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Figure 3: Tensile properties of steel after various types of rolling operations.
Above Fig.3 also shows an example of the relation between tensile strength and Ceq. It can be
understood that TMCP brings about further improvement in strength. The increment of tensile
strength for TMCP steel comes from the refinement of the microstructure, which can be
predicted by Petch‟s law. As per the figure, we can make steels with low Ceq, by TMCP
compared with conventional process. As for ship structures and offshore structures 320, 360, 400
and 500 MPa yield strength class, which have experience to be used for actual ship hull.
Obviously, AcC type TMCP steel has quite less Ceq than conventional steel. Since TMCP steel is
characterized by its low Ceq, it reduces the requirement of alloying elements. Therefore, it can be
summarized that TMCP can help to achieve steels of better toughness and weldability without
the addition of expensive alloying elements.
3. Metallurgical Aspects of TMCP
The concept of microstructural control by TMCP is schematically presented in the following
Fig.4. This enhances toughness mainly by refinement of the ferrite microstructure, TMCP
achieves high strength by utilizing the transformation to ferrite and bainite in addition to
enhanced toughness. TMCP consists of two stages in series: controlled rolling and a subsequent
accelerated cooling process. During the rolling stage, the austenite grains are elongated into a
pancake shape (Fig.4), which introduces crystallographic discontinuities such as ledges and
deformation bands. These ledges and deformation bands remain until accelerated cooling starts
when the rolling temperature is sufficiently low (below about 800oC).
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Figure 4: Schematic diagram showing the microstructural control during TMCP.
Recrystallization occurs when the temperature is sufficiently high (above about 900oC) and most
of the ledges and deformation bands induced by deformation disappear. The retaining
deformation ledges and bands can act as potential heterogeneous nucleation sites for the
austenite to ferrite transformations and contribute to grain refinement. It is also worth to note that
the heterogeneous deformation of austenite increases the grain surface area and the length of
grain edges per unit volume, while there is no change in the number of grain corners per unit
volume. The other feature of TMCP is its cooling process. During the accelerated cooling the
growth of transformed products is effectively suppressed and grain refinement is achieved by
transformations where the aforementioned nucleation sites are introduced. The decrease in the
transformation temperature caused by accelerated cooling induces strong changes in the
intragranular structure. The transformation driving forces also contribute to grain size refinement
through low temperature rolling followed by water quenching. The tensile strength can be widely
controlled (from 500 to over 800MPa). It is also important to note that steelmaking and slab
reheating processes have to be carefully controlled to achieve steels with high strength and
toughness.
The microalloying elements control the microstructure. Trace amounts of elements such as
niobium and titanium in concentrations on the order of 0.01 mass% allow the microstructure to
be refined from the slab reheating to controlled rolling and accelerated cooling processes and
enhance the strength of the final products. The effects of niobium, as an example of a
microalloying element, are schematically illustrated in the following Fig.5
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Figure 5: Effects of microalloying element on steel after TMCP.
The size of the niobium precipitates formed during each process is roughly 300nm at the slab
reheating temperature before rolling (1000oC or higher), 50nm during controlled rolling (about
800oC) and 1nm at the transformation temperature (about 600oC) during cooling. In summary,
the size of newly formed precipitates decreases with decreasing in temperature as the process
progresses. This is useful for microstructural control because the precipitates formed in the
earlier processes are too large and thus useless for the subsequent processes. It is, therefore,
necessary to maintain niobium in a solid solution so that it can be precipitated in sufficient
amounts in the subsequent processes. The general solubility of microallying element products
can be expressed by the following equation:
−log10[Nb][C + (12/14)N] = −6770/T + 2.26
Here the concentrations are expressed as weight percents and T is the absolute temperature.
Niobium precipitates during slab reheating and prevents austenite grain growth via the pinning
effect. During the subsequent rolling process, at below the recrystallization temperature (about
900oC), the driving force generated by the strain energy introduced by such rolling facilitates the
precipitation of fine niobium carbides and/or nitrides. These fine precipitates prevent austenite
grain recrystallization and therefore coarsening.
Because of the nonrecrystallized nature of austenite, there is a plentiful supply of heterogeneous
ferrite nucleation sites (ledges and deformation bands) for the subsequent cooling process.
Recent in situ observations by neutron diffraction have also demonstrated that niobium addition
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and austenite deformation increase the ferrite transformation temperature. Niobium also induces
other effects: during the austenite to ferrite transformation upon cooling, it precipitates in the
ferrite matrix and enhances its strength via the precipitation strengthening mechanism.
4. Applications of TMCP Steels
The relationship between market requirements and the role of TMCP is summarized in the Fig.6.
Figure 6: Relationship between market requirements and role of TMCP.
Since the first application of TMCP in the shipbuilding industry, TMCP steel has found uses in
many plate markets. The popularity of TMCP reflects the advantages of TMCP steel such as
enhanced strength and toughness coupled with excellent weldability. Another key issue that
might explain the success of TMCP is that alloy design, impurity control during the steelmaking
process, segregation reduction, hydrogen removal, slab reheating and the rolling and cooling
processes are considered in both the upstream and downstream processes. Some examples of
successful applications of TMCP steels in various industries are introduced below.
Comparison of HAZ microstructures between TMCP and conventional steels after electroslag
welding is shown in Fig.7. The microstructure of top one is clearly finer than the conventional
one, which subsequently ensures a very low heat affected zone.
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Figure 7: Microstructures and HAZ of steel plates made by TMCP (top) and
conventional way (bottom).
Using the TMCP process, highly crack resistant steel plates with a very high strength ultrafine
grain surface layer have been developed. The crack arrestability of these plates is significantly
improved by the ultrafine microstructure in the surface layer as shown in Fig.8 given below.
Figure 8: Macro and microstructures of highly crack arrestable high strength
plate developed by TMCP.
These plates exhibit high crack arrestability of over 6000MPam0.5 at a temperature of -10oC even
when subjected to a plastic strain of 10% to simulate damage due to collision or grounding.
These plates have already been incorporated in the liquefied petroleum gas (LPG) tankers and
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bulk carriers. The production method for these plates differs from conventional TMCP in that
accelerated cooling is performed during rolling. For safety of large tankers the requirements are:
(i) Brittle crack initiation must be avoided
(ii) If a brittle crack occurs, it must be arrested in the weldment and
(iii) Any crack that propagates beyond the weldment must be arrested within the base metal.
The safety of structures can be enhanced by employing TMCP by improving the base metal
toughness. In recent years, the exploitation of offshore oil and gas resources has moved into
deeper waters and colder regions, such as the northern part of the North Sea and the Arctic
Ocean. Offshore structures have increased in size to meet recent requirements of the energy
industry. As these structures are exposed to extremely low temperatures, the steels used need to
be thicker and tougher. The yield strength required for most uses has increased from 355 to
500MPa. On fracture mechanics has been adopted in addition to that represented by the Charpy
impact value to improve safety. In short, high-strength heavy plates, which can be welded with a
high heat input and have sufficiently high fracture toughness at low temperatures, are now
required for offshore structures. Toughness after high heat input welding has a trade-off
relationship with strength, however and the conventional method of quality design based on
alloying has certain limitations. In contrast, TMCP and other related
metallurgical technologies can solve for these problems. Other requirements include a lower
preheating temperature.
In cryogenic tanks, high crack arrestability is required for both the base plate and welded joints.
To satisfy such requirements, 3.5 mass% nickel steel is used for LPG tanks operating at -50oC.
Low cost plates with reduced nickel content (1.5 mass% nickel) and sufficiently high crack
arrestability have been developed by applying TMCP and put to commercial use. Steel with even
lower nickel content (0.5 mass% and excellent crack arrestability has developed using TMCP.
The application of TMCP steel as a high strength material in building construction has gradually
increased since the early 1990s. At present, TMCP plates account for more than 10% of the plate
steel used in building construction. This steel has been widely accepted in Japan because it
readily meets the requirements for high rise buildings and large span structures owing to its
higher welding efficiency. Since Japan is subject to frequent earthquakes, steels, which absorb
seismic energy through plastic deformation, have been widely applied to high rise buildings.
TMCP steel is also used for line pipes, including pipes for sour gas services, owing to its high
strength and excellent low temperature toughness. To prevent hydrogen induced cracking in
acidic environments, the hardened microstructure area should be reduced. TMCP can reduce
the amount of hard structures and markedly improve the resistance to hydrogen induced
cracking.
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The formation of hard structures can be explained by the diffusion of carbon, which results from
the  to  transformation. In the case of conventional air cooling, carbon readily diffuses from
the nonsegregation zone with a higher transformation temperature (Ar3) to the central segregation
zone with a lower Ar3 during the austenite to ferrite transformation, forming a hardened structure
in the center zone. In accelerated cooling, carbon diffuses slowly as the cooling rate is very high
and consequently the formation of the hardened structure is suppressed. TMCP is thus beneficial
for improving resistance to hydrogen induced cracking. Consequently, TMCP steels have been
used for many pipeline projects involving sour gas services.
TMCP is also applicable to nonferrous alloys. Here TMCP for Zn-22Al-0.15Cu is discussed.
This alloy exists as a solid solution α′ phase above eutectoid temperature (275°C), Fig.9. The α′
phase decomposes into two phases, α and β, where α is Al-rich, FCC structure and β is Zn-rich,
HCP structure below eutectoid temperature. Pure Al (99.99%), pure Zn (99.99%) and Al-40%Cu
alloy were melted in a graphite crucible and then cast into ingots of 27mm in thickness, 32mm in
width and 200mm in height. Two different ingots in as cast condition were cut and scalped into
specimens with 20mm in thickness, 30mm in width and 60mm in length.
Figure 9: Al-Zn binary phase diagram.
Conventional rolling mill without a heating device was used for hot rolling. In order to obtain the
final sheet of 2mm in thickness from a 20mm thick ingot, i.e. a total rolling reduction of 90%,
the hot rolling process was conducted. In conventional process, the specimen was air cooled after
homogenization and heated to 250°C in 30min, hot rolled to underlined thickness. In TMCP, the
specimen was immediately hot rolled after homogenization to underlined thickness, reheated to
250°C in 10 min and then subjected to repetitive hot rolling and reheating steps. Following
Fig.10 shows the final microstructures obtained after conventional (left) and TMCP.
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Figure 10: Microstructures of Al-Zn alloy after conventional (left) and TMCP (right).
The tensile strength of the sheet formed by TMCP was better with around 30% more elongation
compared to that of the conventional hot rolled sheet.
4. Importance of TMCP in Steels for Some Common Applications
4.1. Applications in Car Body Making
For many decades, steel has been the most widely used material for the fabrication of car bodies.
Although lighter materials like aluminium, polymers and composites are gradually taking an
important share at the expense of steel, for the time being, the latter remains the principal
material in cars. A steel sheet for car body applications must comply with a number of
requirements, such as a very good formability, sufficient strength, good weldability, corrosion
resistance or suitable for corrosion protection, good surface quality, etc. These requirements can
only be met by low carbon steel, since medium or high carbon steels are not ductile enough and
are difficult to weld. Within the family of low carbon steels, several variants like Al-killed steel,
interstitial-free (IF) steel, etc., have been developed and will be discussed in the present chapter.
The formability of sheets cannot be expressed with one single parameter, but important
quantities are: the deep drawability, the planar anisotropy and the strain hardening coefficient n
(resistance against strain localization). Although a high n-value is very important for a car body
sheet, the present case study will mainly focus on the processing parameters that will lead to a
good deep drawability. Since the deep drawability is closely related to the crystallographic
texture of the material, the present study is a good example of „texture control‟ during
thermomechanical processing.
4.2. Batch Annealed Al-killed low-carbon steel
A traditional Al-killed low-carbon steel has a typical composition of about 0.05 wt% C, 0.3 wt%
Mn, 0.05 wt% Al and 0.006 wt% N. It is processed in a rather conventional way, involving the
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following production steps: basic steelmaking, continuous casting in slabs, soaking above
1200ºC, hot rolling with a finishing temperature around 900ºC, coiling below 600ºC, cold rolling
(70-90% reduction) and finally batch annealing. The latter is a fairly slow process carried out
around 650–700ºC for several hours. The heating rate towards the annealing temperature varies
between 20 and 200ºC/h. During annealing the cold-deformed sheet will recrystallize, but this
process interacts with the precipitation of fine AlN particles. This interaction turns out to be the
key to a successful texture control!
It is commonly observed that cold deformed of low carbon steel grains with 111 orientation,
have a much stronger tendency to recrystallize than grains of other orientations and that those
recrystallized grains have again a 111 orientation, which is a favourable orientation for deep
drawing. The basic idea of texture control in Al-killed low carbon steels is to enhance the
balance between „favourable‟ and „detrimental‟ grains by an interaction of fine AlN precipitates
with recrystallization. The nucleation and growth of 111 type grains is somewhat hindered by
the presence of fine AlN, but remains possible, due to the high driving force present in these
grains. The appearance of nuclei in the other grains, however, is seriously hampered. This
„filtering‟ of recrystallization nuclei increases the amount of „favourable‟ grains in the
recrystallized sheet. An important prerequisite for this processing is that the AlN precipitates are
small enough when the material starts recrystallizing. For this, they have to be formed during
during the slow heating towards the annealing temperature, just before the recrystallization starts.
From these requirements, some general processing conditions for batch annealed Al-killed are:
I. The soaking temperature must be high enough to bring all Al and N in solid solution after
casting. A relation between the Al and N content and the minimum solution temperature (T in
Kelvin) is:
where wt% Al and wt% N refer to atoms in solid solution. Most N atoms are dissolved, but some
Al may combine with O atoms to form Al2O3. The wt% Al in solid solution can be estimated
from the following relationship:
Problem: Calculate the amount of N in wt% that will ensure full utilization of Al at a
solution temperature of 1200ºC where the total Al and O contents in the system are,
respectively, 0.05 and 0.005 wt% .
Precipitation of AlN during and after hot rolling must be avoided because in that case the
precipitates would already be too coarse and no longer effective during batch annealing. The
schematic CCT curve in Fig.11 illustrates that after hot rolling, a fast cooling till about 600ºC is
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necessary. From that point, the material can be coiled since further slow cooling will not induce
any
AlN
precipitation.
Figure 11: Schematic CCT curve for AlN precipitation in an Al-killed low-carbon steel.
The reheating rate towards the recrystallization temperature may not exceed a critical value.
When the material is cooling too fast, the sheet will recrystallize before the fine AlN have been
formed and hence the „filtering‟ of nuclei cannot take place. A formula to calculate the optimal
heating rate Top has been proposed by Takahashi and Okamoto:
Top =18.3 + 2.7log[wt% Al][wt% Mn][wt% N]/%CR
Where %CR the cold-rolling reduction.
4.3. Trend Towards Higher Strength Steels
The need to reduce the fuel consumption and the emissions of passenger cars has driven the
automobile manufacturers towards an increasing use of high strength steels. This allows to
down-gauge the body panels and to reduce the weight of the car. Unfortunately, an increase in
strength goes in general hand in hand with a decrease in formability. This is illustrated in Fig.12,
where the deep drawability is plotted as a function of the tensile strength for a number of steel
grades. Another problem is that thinner sheets and higher strength also increase the spring back.
It is a continuous challenge for the steel industry to develop steel grades that combine a high
strength with an acceptable ductility. In the following paragraphs the most important higher
strength grades used in car body applications will be discussed.
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Figure 12: Deep drawability as a function of the ultimate tensile strength (UTS) for
several steel grades used in car body applications.
4.4. Bake Hardening (BH) Steels
One of the most important objectives in the development of automotive steel sheet is the
combination of strength and formability. Formability is required when the sheet is shaped into an
automobile body panel by cold pressing and high strength is required after assembly. Bakehardenable steel sheet was developed by exploiting the fact that these two properties are not
needed simultaneously. The lowest possible strength in an automotive steel sheet is desirable for
good formability when the sheet is subjected to press forming, therefore, the carbon or nitrogen
atoms in the steel sheet are kept in the solid solution condition. This can be accomplished by
rapid cooling of the steel sheet from high temperature during the sheet production process and
this rapid cooling has become industrially possible by the development of the continuous
annealing technique for strips. Before the development of the continuous annealing technique,
rapid cooling was impossible because annealing of heavy coil with big heat capacity was
conducted as a batch process. The overall industrial production process for this type of steel is
shown schematically in Fig.13.
Figure 13: Schematic diagram showing the steps for production of bake hardenable steel.
Steel producers take care up to the annealing treatment for production of bake hardenable steel.
In the final stage of sheet steel production, i.e. after annealing the cooling rate is maintained
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intentionally higher that enables the interstitial solute carbon atoms to remain distributed in
within the matrix in relatively higher concentration compared to that of ideal level, Fig.14.
Figure 14: Schematic diagram showing the distributed excess solute carbon in the
annealed steel sheet.
Auto body makers collect the specially annealed highly deformable and relatively soft sheet from
steel producers. Afterward, auto body panel shape is given by press forming. Extra dislocations
are introduced by press forming a steel sheet and strength is increased by the action of work
hardening in which accumulated dislocations prevent the movement of other dislocations, Fig.15.
After panel formation and assembly, painting and baking are carried out. These processes
involve heating the steel body panels to about 443K (170 ) for 20–30 min. At this temperature,
the excess carbon atoms that were remained dissolved in the solid solution of the steel matrix
diffuse by jumping between lattice points, which occurs 103 to 105 times a second, segregating in
the regions around dislocations. This results in locking of the dislocations which is called strain
aging, Fig.16. This mechanism makes the steel panels harder after baking than after press
forming and is referred to as bake hardening. The utilization of this bake hardening phenomenon
has made it possible to utilize steel sheet that has good formability during press forming and that
can withstand severe working, while being hard and less prone to denting when assembled in the
automobile body.
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Figure 15: Dislocation formation by press forming and locking of dislocation by baking process.
During press forming of the car part, a large number of new dislocations are created and during
the paint baking cycle, these dislocations are locked by the carbon atoms. This increases the YS
of the part by roughly 50MPa along with change in tensile behaviours, which is shown
schematically in Fig.16. In IF steels the interstitial atoms are combined with elements like Ti,
Nb, Al, etc. and hence no paint baking effect can be anticipated. Because, all interstitial carbon
atoms get exhausted by the formation of various types of carbides.
Figure 16: Tensile behaviours of steel sheet after pain bake hardening.
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4.5. Dual Phase and Trip Steels
In the previous section, some important developments concerning the use of higher strength
steels in car body applications have been briefly discussed. An important emerging family of
steel grades is the „multi-phase‟ or „transformation strengthened‟ steels. These grades contain a
significant proportion of a hard phase (e.g. bainite and/or martensite) mixed with soft ferrite. The
„dual phase steels‟ have a typical structure of ferrite and martensite. Further developments have
led to „TRIP‟ steels, which consist of ferrite, bainite and retained austenite. The TMCP, needed
to obtain these new steels, will be discussed in the following paragraphs.
4.5.1. Dual phase steel
Dual phase steels are low carbon steels with some Mn and Si and in most cases alloyed with
other elements. An example of a possible composition (in wt%) is given in the following Table.
Dual phase steels are produced by soaking in the intercritical (+) region, mostly around 800ºC
and by subsequent rapid cooling. In order to avoid the transformation from austenite into pearlite
or bainite, the cooling rate T/s must be faster than:
In principle, both hot and cold rolled grades can be produced, but cold rolling followed by
continuous annealing seems to be the most flexible route and the processing is schematically
shown in Fig.17.
Figure 17: Processing of dual phase (DP) steel by cold rolling and a two-step annealing treatment.
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After conventional hot and cold rolling, the sheet is reheated into the (+) region, for example
around 800ºC. At this temperature the structure consists of ferrite and 10–20% austenite,
depending on the composition. After annealing, mostly carried out on a continuous annealing
line with fast cooling possibilities, the sheet is rapidly cooled and austenite transforms into
martensite. In some grades some retained austenite may still be present at room temperature. The
UTS of such steel grades can vary roughly between 500 and 1000 MPa according to the exact
steel composition and seems mainly to be proportional to the amount of martensite.
Dual phase steels combine a high strength with an excellent work hardening (high UTS/YS
ratio), but with a low formability. Most grades show a bake hardening effect. An additional
advantage is the absence of yield point elongation (Lüderlines). A sufficient amount of
dislocations is generated in the ferrite near the martensite plates at the onset of plastic
deformation. These dislocations, formed by the induced stresses, are not locked by interstitials
and hence no yield point elongation occurs. These steel grades can, for example, be used for
energy absorbing elements in car body parts. Dual phase steels can in principle also be produced
in the hot rolled condition. In this case, the steel can develop a suitable ferrite austenite structure
immediately after hot rolling and must be cooled fast enough to avoid formation of bainite or
pearlite. A major problem is, however, that coiling must be done above martensite start
temperature (Ms) but at a relatively low temperature (e.g. 250ºC), because when slow cooling in
the coil at higher temperatures, bainite would be formed (Fig.18). In most production lines it is
not possible to use such a low coiling temperature because the steel would be too strong to be
coiled. Another possibility is to shift the start of pearlite and bainite formation towards longer
times by suitable alloying (more Mn and Si and addition of Mo). A high Si content leads
however to a poor surface quality of the hot-rolled product. In practice, most dual phase steels
are cold rolled and annealed grades.
4.5.2. TRIP Steel
TRIP steels can be considered as a further development of dual phase grades. The starting
structure is again a mixture of ferrite and austenite, formed during a first annealing treatment in
the (+) region. A second annealing step is carried out, usually between 350 and 400ºC, so that
the austenite is partially transformed into a mixture of bainite and retained austenite. The
presence of this retained austenite is of utmost importance because during further cold
processing it will gradually transform into martensite and this transformation assists the
deformation. This is called the „TRIP effect‟. The reason that retained austenite does not
transforms into martensite during cooling is due to its stabilization by carbon atoms. For some
TRIP steel grades, the Ms can, however, remain above room temperature and in that case, with
the martensite finish temperature (Mf) below room temperature, the final structure is a mixture of
four phases: ferrite, bainite, martensite and some retained austenite. The grades of TRIP steels
are very limited. Based on the published literature, the main ingredients of TRIP steels are:
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Carbon: As will be discussed below, a minimal amount of carbon is necessary to stabilize the
austenite during processing; too much carbon would however impair the weldability of the steel,
so most TRIP steels have a carbon content between 0.1 and 0.2 wt%, although variants with
higher carbon content (up to 0.4 wt%) have been studied.
Silicon: The addition of Si to steel retards the formation of carbides; this is important because the
carbon atoms, rejected by the transforming austenite should be absorbed by the retained austenite
and may not precipitate as carbides. Si helps to delay this precipitation reaction; a second benefit
is that it gives some solid solution hardening; most TRIP steels have a Si content between 0.7
and 1.5 wt%; larger amounts give rise to hot shortness problems and to the formation of oxide
scales during hot rolling.
Manganese: The addition of Mn increases the relative stability of austenite towards martensite
and helps to retain a sufficient amount of austenite at room temperature; Mn also shifts the start
of the pearlite nose towards longer times and helps to avoid pearlite formation during cooling.
Aluminium: Al has been proposed as a substitute for Si. Some compositions of experimental
TRIP grades are shown in the following Table.
5. Thermomechanical Processing
5.1. Cold Rolling Route
The main target in the processing of TRIP steels is to obtain a mixture of ferrite, bainite and a
sufficiently large amount of retained austenite (~10% in low-carbon TRIP steels) at room
temperature. In most cases these steels are hot and cold rolled as for a normal low-carbon steel
and then annealed in two steps, as illustrated in Fig.18. During reheating towards the first
annealing temperature, the ferrite in the cold-deformed sheet will recrystallize. During
subsequent soaking in the intercritical region, pearlite transforms into austenite. The soaking
temperature is kept just above Ac1 because this gives the highest carbon content in the austenite
and limits the austenite grain growth.
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Figure 18: Processing scheme and structural evolution during the two-step heat treatment of
TRIP steel.
For a low carbon high Si steel, a typical soaking temperature is 750ºC. The soaking time must be
long enough to dissolve all carbides, but not too long to avoid grain growth. A typical soaking
time at 750ºC is 4 min. After the first soaking treatment, the material is rapidly cooled to avoid
the formation of additional ferrite and/or the formation of pearlite (Fig.19). A second heat
treatment is carried out in the upper bainite range, usually between 350 and 400ºC. During this
second treatment some important transformations take place, which are schematically illustrated
in the Fig.19. The residual austenite inherited from the intercritical annealing treatment, will
transform into bainite. Since bainite has a very low solid solubility for carbon, the carbon atoms
from the transforming austenite are rejected from the transformation product into the residual
austenite. Due to this increase in carbon content, the residual austenite becomes more and more
stable against martensite and a decrease in the Ms temperature can be noticed (Fig.18). After
some soaking the residual austenite is so loaded with carbon that the transformation into bainite
ceases. Nevertheless, the remaining austenite is in metastable condition and after prolonged
annealing it will decompose in carbides and ferrite (called „secondary‟ ferrite). Silicon is known
to delay this decomposition.
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Figure 19: Illustration of the structural changes in TRIP steel during the second isothermal
treatment (above) and transformation products after rapid cooling (below).
After this second heat treatment, the material is rapidly cooled to room temperature. The final
structure obtained at room temperature, depends on the previous soaking time. If no second
annealing is applied (t=0 in Fig.19) austenite transforms into martensite, although some retained
austenite will be present because for most TRIP steels the Mf temperature is below room
temperature. After a short time (t1), the residual austenite still transforms into martensite, but
larger parts of austenite do not transform. After a time t2 the residual austenite
present at the soaking temperature is completely retained during cooling. During further cold
deformation of these alloys, the retained austenite will gradually transform into martensite by a
strain-induced transformation. An illustration of this TRIP effect for some of the alloys
mentioned in the previous Table is shown in Fig.20.
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Figure 20: Consumption of retained austenite during a uniaxial tensile test.
5.2. The Hot Rolling Route
TRIP steels can also be produced in a hot rolled condition. The TMP scheme follows the same
principles as the one from the cold rolling route. The material is hot rolled in the austenite region
or in the intercritical (+) region and must be adequately cooled to a „quench finish‟
temperature, mostly around 400ºC. During cooling, ferrite can be formed, but the formation of
pearlite must be suppressed. During annealing in the bainite region the residual austenite will
partially transform into bainite and the rejected carbon atoms stabilize the remaining austenite.
After further cooling some austenite will be retained at room temperature. A very important
aspect of this processing is the fact that austenite can be deformed (hot rolled) below the
recrystallization temperature. This leads to an elongation of the austenite grains and the
formation of shear bands in austenite. During subsequent cooling more nucleation centres for
ferrite are present, leading to more, finer ferrite and to smaller bainite plates. It has been reported
that the stability of retained austenite, at room temperature, increases with prior austenite
deformation. During further cold deformation this retained austenite transforms more gradually
into martensite and better mechanical properties are observed: higher strength, increased work
hardening and higher fracture strain. A disadvantage of the hot rolling route is that the processing
conditions are somewhat difficult to control and the low coiling temperature is often problematic.
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6. TMCP of Steels for Pipeline Applications
The problem of transportation of fluids over large distances emerged as soon as people began to
live in large communities, creating the need to divert water from its natural course. The first
aquaducts were constructed from clay, wood or lead. None of these materials was really
satisfactory, and a first significant improvement was made in the 16th and 17th century with the
introduction of cast iron pipes. One of the first full-scale cast iron pipe systems was built in 1664
to carry water from Marly-on Seine to the castle of Versailles, France over a distance of about
25km.
Drilling of the first commercial oil wells in the middle of the 19th century, created new demands.
The first specification for pipeline steel, issued by the American Petroleum Institute (API) in
1948, prescribed a weldable low carbon high manganese steel, grade X42, which means that it
has a YS of 42 ksi or 290 MPa. Since that time higher strength steels have been developed up to
grade X80 (80 ksi or 552 MPa). These high strengths are reached by grain refinement obtained
by a special TMCP scheme, called „controlled rolling‟ and by precipitation hardening.
Besides a minimal strength, structural steels need an excellent weldability and a high toughness
(low ductile to brittle transition temperature). The general weldability of a steel can be expressed
by its carbon equivalent (CE): the lower the CE, the better the weldability. Several equations can
be found in literature to calculate the CE. Traditionally, the following equation has been used,
although, but some authors also prefer other equations.
CE (wt%) = wt%C + wt%Mn/6 + wt%(Cr+Mo+V)/5 + wt%(Ni+Cu)/15
Before World War II a fine ferrite grain was obtained using a normalized Al killed steel.
Stimulated by the bad experience with the break-up of welded Liberty ships and guided by the
work of Hall and Petch in the 1950s, new processing routes for fine grained material were
investigated. In a number of European countries (Sweden, Holland and Belgium), the concept of
„controlled rolling‟ was established (see next paragraph). In the 1970s, stronger steel grades were
developed, using small amounts of Nb, Al, Ti and V. Most of these HSLA steels were hot rolled
using the concept of controlled rolling. A last improvement in structural steels was obtained in
Japan with the introduction of accelerated cooling.
7. Conventional and Modern TMCP
Traditional hot rolling of steel takes place in the austenite region. As long as the temperature
stays above a critical value, called „the temperature of no recrystallization, (TNR), the austenite
grains remain more or less equiaxed, due to subsequent waves of recrystallization. After hot
rolling the austenite grains transform into ferrite and some pearlite during cooling of the hot
rolled plate. Since most ferrite grains nucleate on the former austenite grain boundaries, a finer
austenite grain size results in finer ferrite. In conventional hot rolling the reheating temperature
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before entering the roughing mill is usually around 1200–1250ºC. In this temperature range it is
difficult to prevent the growth of austenite. Finishing, rolling is carried out above TNR to avoid
high rolling forces as a result of accumulation of strain hardening due to the absence of
recrystallization.
In controlled rolling the reheating temperature is limited in order to avoid excessive austenite
grain growth (e.g. 1100ºC). The final rolling passes are carried out below TNR. This results in
pancaked austenite with an increased grain boundary fraction/volume and hence in more ferrite
nuclei and smaller ferrite grains. The consequence is of course an accumulation of strain
hardening in the last rolling passes, leading to high rolling forces. A common practice is to apply
more reduction in the first passes (roughing mill) and to reduce the strain in the final passes.
Accelerated cooling starts above A3 and is maintained till about 500ºC. It activates additional
ferrite nuclei inside the austenite grains and hence contributes to additional ferrite grain
refinement. A faster cooling can however also lead to the formation of some bainite. This
contributes to the strength of the material but it impairs the toughness. Accelerated cooling
should be limited to 10–15ºC/s. The main differences between conventional and controlled
rolling are the lower reheating temperature of the latter and the larger reduction during roughing.
The time between roughing and finishing mill is much higher in controlled rolling
in order to cool down the thick plate. This is considered as one of the drawbacks of controlled
rolling because it decreases the productivity. In spite of the lower plate thickness, more rolling
passes are needed in the finishing mill during controlled rolling, because the reduction per pass is
limited due to the high rolling forces required at this temperature. After controlled rolling, an
accelerated cooling of 8ºC/s is applied. The combined effect of controlled rolling and accelerated
cooling is an increase of 50 MPa of the YS and a decrease by 70ºC of the fracture appearance
temperature.
Until 1950, pipelines for oil and gas transport were made from conventionally hot rolled C–Mn
steels, as in rolled or normalized condition. They had a YS up to 360 MPa. New developments
including a reduction of the carbon content and alloying with Nb and/or V increased the YS to
420 MPa by grain refining and precipitation hardening. Thanks to controlled rolling and further
adjustments of micro alloying elements, the YS was raised to 552 MPa (grade X80). New grades
(X100 with YS ~700 MPa) are currently being developed.
The chemical composition of HSLA steels must be well balanced. The carbon content is kept
low (usually below 0.1 wt%) and only Mn is added in larger quantities (usually 1.4–1.9 wt%)
because it has been shown to improve notch toughness. Micro alloying elements such as Nb, V,
Ti and Al form carbides, nitrides and carbonitrides. They play a three fold role:
● Fine precipitates prevent the excessive growth of austenite during reheating towards the
starting rolling temperature. Especially, TiN remains stable up to temperatures above 1200ºC.
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● Nb in solid solution retards the recrystallization. In the case of recrystallization controlled
rolling the use of Nb will thus be avoided or restricted, but in case of conventional controlled
rolling, it will increase TNR and this allows to carry out the last passes at higher temperature
and hence with lower rolling force. Vanadium is reported to show only a weak retardation effect.
● During the last low-temperature rolling passes and during cooling, fine precipitates will form
and will contribute to the strength of ferrite. Vanadium is especially effective because it is
completely in solid solution above 1000ºC. It re-precipitates on cooling and contributes
significantly to the strengthening of ferrite.
8. TMCP for High Strength Wire Used in Bridges and Radial Tyres
Steel wires are used extensively throughout the world for many critical engineering applications;
high strength cables for bridges (Fig.21), cable and ski lifts, general haulage, e.g. ship moorings
and on a large scale, for reinforcing radial tyres. They are also widely used for more cultural
activities such as piano and violin strings. In all cases, their properties of very high strength and
toughness are just about unique. In applications where high corrosion resistance is necessary,
special stainless steel wires are employed but otherwise for high strength requirements, as in
vehicle tyres, patented steel wires are essential. As detailed below, patenting consists of heating
carbon steel rods into the austenite phase region, cooling to pearlite and then wire drawing down
to thin wire. The resulting work hardened pearlite is extremely strong, probably the strongest
material known which possess some ductility and therefore toughness. It is this strength that
enables architects to design spectacular suspension bridges and engineers to make reliable tyres
for vehicles and aircraft, such as the jumbo jets.
Figure 21: High strength steel wires in bridge and tyre.
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8.1. The Patenting Process
The steel composition is basically a fully eutectoid 0.8%C steel containing some Mn and Si
(more exactly the carbon content is between 0.7 and 0.9%C) designed to develop the maximum
amount of pearlite. To produce fine wire it starts as coiled rod of diameter around 5mm. In this
condition, the strength is about 1100-1200MPa and the aim of the patenting process is to
multiply this by a factor of about 3. The rod is first given a preliminary drawing reduction down
to 1-2mm diameter without lubrication. It is then passed into a furnace and heated in the range
950–1000ºC, i.e. in the single phase austenite domain for transformation into homogeneous
austenite with all the carbon in solid solution. It is then very carefully cooled to transform into
fine pearlite. This can be done isothermally by cooling in liquid lead or in a fluidized bath but
can also be carried out by controlled air cooling. The cooling rate is one of the critical parameters
in the process. Figure 22 shows that according to the cooling rate one can form pearlite, bainite
or even some ferrite mixed with pearlite. Also during cooling the austenite to pearlite, the
exothermic transformation gives off sufficient heat, as indicated, to significantly increase the
temperature in the range of transformation. The cooling rate allows for the heat of transformation
to follow a finely judged path into the pearlite domain that leads to the formation of a very fine
pearlite, i.e. in the range of 500-600ºC. The microstructure is then basically 100% pearlite with a
spacing of about 0.25m (Figs.23-24). Before wire drawing the rod is coated with a fine layer of
brass which acts as a lubricant. The important feature is that the material should work harden
sufficiently during each drawing pass so that the extra hardening compensates for the reduced
section to avoid rupture during pulling through the dies. In practice, reductions of 15-25% per
pass is possible for in drawing of this type of steel. To produce wire for tyre reinforcements, the
rod is drawn down to thicknesses of about 0.3mm or less.
Figure 22: Continuous cooling transformation diagram of eutectoid steel for wire production.
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Figure 23: TEM microstructure of fine 0.7%C pearlitic steel before wire drawing (left) and
after cold drawing to a strain of 2.9 (right).
Figure 23 shows the concomitant lamellar alignment and pearlite spacing reduction which
ultimately decreases to values of order 20-50nm. This is in fact a composite nanomaterial used
on a large scale before the word came into fashion! Unlike most other nanomaterials it is also not
very expensive. Here the interlamellar spacing eventually becomes much smaller than the typical
dislocation cell size giving unusual hardening effects at very high strains. The wires can fail
during the drawing operation if they contain defects such as inclusions. The inclusion content
must therefore be reduced to very low levels in the initial steel casts. These very fine wires are
then usually twisted together into strands, which are used in practice (Fig.25). The twisting
operation is also quite critical since if the material has insufficient ductility it can fail by
localized shear, often initiated at surface defects.
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Figure 24: SEM microstructure (longitudinal section) of fine 0.7%C pearlitic steel after cold
drawing strains of 0 (a), 1 (b), 2 (c) and 3.5 (d).
Figure 25: Patented high strength wire.
Figure 25: Successive wire-twisting operations into strands.
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8.3. The Mechanical Properties
The material can harden from about 1200 to 4000 MPa. The strength is also inversely
proportional to the square root of the lamellar spacing in accordance with the Hall–Petch law It
is also worth pointing out that the cementite phase, unlike most carbides, must possess extensive
ductility during the wire drawing to maintain some compatibility. It appears to deform plastically
by dislocation slip under the high hydrostatic pressures of the drawing operation, as for the bcc
iron. Patented steel wires are usually drawn up to strengths of about 3000 MPa for use in tyre
reinforcements. However, there is a trend to develop even higher strength wires by increasing the
drawing strain and, in some cases, the carbon content (Fig.26). These wires, aimed to attain 4000
MPa, could be used in a new generation of tyres for heavy duty trucks and personal vehicles. At
these levels of strain, and even before, the cementite layers break up and, surprisingly begin to
dissolve locally so that excess carbon goes into solution in the ferrite. This behaviour is the
object of current research topic for many researchers in this field.
Figure 26: The UTS of drawn pearlitic wire as a function of drawing strain. The two plots for
the 0.8%C steel refer to different initial lamellar spacings. Note the higher strength of the 0.9%C
steel.