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1. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Bulk Deformation - 1
ME 206
Manufacturing Processes 1

2. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
2
Outline
• What is bulk deformation?
• Cold vs hot working
• Forging introduction
• Forging analysis
• Forging defects

3. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
3
What is bulk deformation?
• Bulk deformation (or forming): processes
characterized by large amount of plastic
deformation (large strains) carried out at
elevated or room temperature
• Bulk plastic flow of material under uniaxial or
multi-axial stresses dominated by
compression
• Mass conserving processes à volume is
constant

4. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
4
Bulk Deformation Processes
• Examples include: forging, rolling, extrusion, rod
drawing etc.
Forging (heading)
Extrusion Rod Drawing
Rolling

5. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
5
Cold vs Hot Working
• Many bulk deformation processes carried out
at elevated temperatures
• Cold working: T < 0.3Tm
– Usually a finishing step
• Warm working: T = 0.3~0.5Tm
– Intermediate or final step
• Hot working: T > 0.5Tm
– Initial step

6. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
6
Cold Working
Advantages
– Better dimensional control
– Superior surface finish
– Strain hardening of surface layer can be
beneficial
Limitations
– Greater material strength à higher forces
– Stronger tooling required
– Lower ductility à small deformations
– Lower malleability à harder to shape material
– Anisotropic surface properties

7. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
7
Hot Working
Advantages
– Lower yield strength à lower forces
– High ductility à larger strains possible
– Higher malleability à easy to shape metal
Limitations
– Easily forms oxide layers (scales) on surface à
poor surface finish
– Harder to control dimensions

8. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
8
• Shape change via compressive forces
• Types of forging processes
– Open die forging (upsetting)
– Closed or impression die forging
Forging
hi hf
flash

9. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
9
• Carried out between flat dies
• Parts weighing few lbs ~ 150 tons e.g. solid
shafts, spindles/rotors, rings, etc.
• Often carried out in steps
• Wide range of ferrous and non-ferrous metals
Open Die Forging
Stepped shaft Spindles
Source: http://www.forging.org

10. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
10
• Carried out between shaped dies
• Parts weighing few ounces ~ 25 tons e.g.
crankshafts,connecting rods, aircraft parts etc.
• Most engineering metals: carbon steels,
stainless steels, aluminum, bronze, etc.
Closed Die Forging
Aircraft bulkhead Connecting rods
Source: http://www.forging.org

11. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forgings
• Coins
• Landing gear
• Crank shafts
• Turbine shafts

12. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging presses
• Large machines
– hold dies
– form parts

13. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Press types
• Servo-hydraulic presses
• Servo-electrical presses
• Mechanical presses
• Screw presses
• Hammers
– gravity drop
– power drop
– counter blow (two rams)
– high pressure gas

14. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
50,000 ton
press

15. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forges
Schematic illustration of the principles of various forging machines. (a) Hydraulic
press. (b) Mechanical press with an eccentric drive; the eccentric shaft can be replaced
by a crankshaft to give the up-and-down motion to the ram. (continued)

16. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forges
Schematic illustration of the principles of various forging machines. (c) Knuckle-joint
press. (d) Screw press. (e) Gravity drop hammer.

17. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging steps
• Prepare slug
– saw
– flame cut
– shear
• Clean slug surfaces
– shot blast
– flame

18. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging steps
• For hot forging
– heat up and descale forging
– make sure press is hot
• Lubricate
– oil
– soap
– MoS2
– glass
– graphite

19. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Lubrication purposes
• Reduce friction
• Reduce die wear
• Thermally insulate part
– to keep it warm

20. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging steps
• Forge
• Remove flash
– trim
– machine
• Check dimensions
• Post processing, if necessary
– heat treat
– machine

21. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Effect on grain structure
• Large grains are broken up.
• Grains can be made to flow.

22. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Dies
• Final part shape determined by die
accuracy
• Multiple parts can be made in one die
• Progressive shaping can be done in one
die set
• Need to be stronger than highest
forging stress

23. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
23
• Simple stress analysis possible for open die
forging process
• Analysis method called “slab” analysis
• Applicable to plane strain compression with
low sliding friction
Forging Analysis
Source: http://www.forging.org
hi hf

24. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Slab analysis assumptions
• Entire forging is plastic
– no elasticity
• Material is perfectly plastic
– strain hardening and strain rate effects later
• Friction coefficient (µ) is constant
– all sliding, to start
• Plane strain
– no z-direction deformation
• In any thin slab, stresses are uniform
• Three conditions exist: All sliding; Sliding-
sticking transition and Fully sticking

25. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Open die forging analysis –
rectangular part
F
F
h
w
dx
y
x
unit depth
into figure

26. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Expanding the dx slice on LHS
• p = die pressure
• sx, dsx from material on
side
• tfriction = friction force = µp
p
p
sx sx + dsx
tf
tf

27. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Force balance in x-direction
p sx
k
dx
h
d
dx
hd
friction
x
friction
x
t
s
t
s
2
0
2
-
=
=
+
Mohr’s circle
(distortion energy (von Mises) criterion,
plane strain)
flow
flow
x k
p s
s
s ×
=
=
=
+ 15
.
1
3
2
2
N.B. all done on a per
unit depth basis

28. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Force balance
Differentiating, and substituting into Mohr’s
circle equation
noting: tfriction = µp
pdx
h
dp
µ
2
= dx
h
p
dp µ
2
=
( ) ( )
dx
h
dp
dx
h
d
d
dp
p
d
k
d
friction
friction
x
x
x
÷
÷
ø
ö
ç
ç
è
æ
=
-
=
-
=
+
=
t
t
s
s
s
2
2
2

29. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Sliding region
• Noting: @ x = 0, sx = 2k = 1.15 sflow
dx
h
p
dp
x
p
k
x
ò
ò =
0
2
2µ

30. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging pressure – sliding
region
( )
÷
ø
ö
ç
è
æ
×
×
=
÷
ø
ö
ç
è
æ
=
=
-
h
x
p
h
x
k
p
h
x
k
p
flow
x
x
x
µ
s
µ
µ
2
exp
15
.
1
2
exp
2
2
2
ln
ln
Sliding region result (0 < x < xk)
N.B done on a
per unit depth basis
Increasing µ
X
÷
÷
ø
ö
ç
ç
è
æ
f
y
Y
15
.
1
s
0
1

31. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging pressure –
approximation
• Taking the first two terms of a Taylor’s
series expansion for the exponential
about 0, for
÷
ø
ö
ç
è
æ
+
=
h
x
k
px µ
2
1
2
1
£
x
yields
( ) å
=
=
+
+
+
+
+
=
n
k
k
n
k
x
n
x
x
x
x
x
0
3
2
!
!
!
3
!
2
1
exp !
0
0
÷
ø
ö
ç
è
æ
+
×
×
=
h
x
p flow
x
µ
s
2
1
15
.
1

32. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Average forging pressure –
all sliding approximation
• using the Taylor’s series approximation
2
2
2
2
2
1
2
2
2
2
0
2
2
0
2
0
w
h
x
x
w
dx
h
x
w
dx
k
p
k
p
w
w
w
x
ave
÷
÷
ø
ö
ç
ç
è
æ
+
=
÷
ø
ö
ç
è
æ
+
=
=
ò
ò
µ
µ
N.B done on a
per unit depth basis
÷
ø
ö
ç
è
æ
+
=
h
w
k
pave
2
1
2
µ
÷
ø
ö
ç
è
æ
+
×
×
=
h
w
p flow
ave
2
1
15
.
1
µ
s

33. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging force –
all sliding approximation
depth
w
h
w
F flow
forging ×
×
÷
ø
ö
ç
è
æ
+
×
×
=
2
1
15
.
1
µ
s
depth
width
p
F ave
forging ×
×
=

34. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
34
Example Problem
A rectangular workpiece has the following
original dimensions: w = 100 mm, h = 25 mm,
and depth d= 20 mm and is being open die
forged in plane strain. The true stress-true
strain curve of the metal is given by
MPa and the coefficient of friction is µ = 0.3.
Calculate the forging force required to reduce
the height by 20%. Use both the “exact” and
the average pressure methods.
5
.
0
400 t
t e
s =
w
h

35. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Slab - die interface
• Sliding if tf < tflow
• Sticking if tf ³ tflow
– can’t have a force on a material
greater than its flow (yield) stress
– deformation occurs in a sub-layer just
within the material with stress tflow
sliding
region
sticking
region

36. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Sliding / sticking transition
• Transition will occur at xk
• using k = µp, in:
• hence:
µ
µ 2
1
ln
2
1
=
h
xk
÷
ø
ö
ç
è
æ
=
h
x
k
px µ
2
exp
2
÷
ø
ö
ç
è
æ
=
h
x
k
k k
µ
µ
2
exp
2

37. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Sticking region
• Using p = k/ µ
pdx
h
dp
µ
2
=
( )
k
x
x x
x
h
k
p
p k
-
=
-
2
dx
h
k
dp
x
x
p
p k
x
k
x
ò
ò =
2
dx
k
h
dp
µ
µ
2
=

38. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Sticking region
We know that
• at x = xk, pxk
= k/µ
• and
µ
µ 2
1
ln
2
1
=
h
xk

39. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging pressure - sticking
region
h
x
k
px
+
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
-
=
µ
µ 2
1
ln
1
2
1
2
Combining (for xk < x < w/2)
ú
ú
û
ù
ê
ê
ë
é
+
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
-
×
×
=
h
x
p flow
x
µ
µ
s
2
1
ln
1
2
1
15
.
1

40. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging pressure –
all sticking approximation
• If xk << w, we can assume all sticking,
and approximate the total forging force
per unit depth (into the figure) by:
x=0 x=w/2
0
pedge
Dp

41. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging pressure –
all sticking approximation
k
pedge 2
=
÷
ø
ö
ç
è
æ
+
×
×
=
÷
ø
ö
ç
è
æ
+
=
h
x
p
h
x
k
p
flow
x
x
1
15
.
1
1
2
s
( )
x
h
k
k
px
2
2 =
-
dx
h
k
dp
x
p
k
x
ò
ò =
0
2
2

42. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Average forging pressure –
all sticking approximation
2
2
2
1
2
2
2
2
0
2
2
0
2
0
w
h
x
x
w
dx
h
x
w
dx
k
p
k
p
w
w
w
x
ave
÷
÷
ø
ö
ç
ç
è
æ
+
=
÷
ø
ö
ç
è
æ
+
=
=
ò
ò
÷
ø
ö
ç
è
æ
+
=
h
w
k
pave
4
1
2
÷
ø
ö
ç
è
æ
+
×
×
=
h
w
p flow
ave
4
1
15
.
1 s

43. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging force –
all sticking approximation
depth
w
h
w
F flow
forging ×
×
÷
ø
ö
ç
è
æ
+
×
×
=
4
1
15
.
1 s
depth
width
p
F ave
forging ×
×
=

44. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Sticking and sliding
• If you have both sticking and sliding, and you
can’t approximate by one or the other,
• Then you need to include both in your
pressure and average pressure calculations.
( ) ( )sticking
ave
sliding
ave
forging A
p
A
p
F ×
+
×
=
sticking
sliding
forging F
F
F +
=

45. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Material Models
n
flow K
Y e
s =
=
Strain hardening (cold – below recrystallization point)
Strain rate effect (hot – above recrystallization point)
( )m
flow C
Y e
s !
=
=
height
ous
instantane
velocity
platen
h
v
dt
dh
h
1
ε =
=
=
!

46. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-1
• Lead 25 mm x 25 mm x 900 mm
• sy = 6.89 MPa
• hf = 6.25 mm, µ = 0.25
• Show effect of friction on total forging force.
• Use the slab method.
• Assume it doesn’t get wider in 900 mm
direction.
• Assume cold forging.
25
25
900

47. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-2
• At the end of forging:
hf = 6.25 mm, wf = 100 (conservation of mass)
• Sliding / sticking transition
"
347
.
0
25
.
0
2
1
ln
25
.
0
2
25
.
0
2
1
ln
2
1
=
´
´
=
=
k
k
x
h
x
µ
µ

48. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-3
• Sliding region:
( )
x
h
x
p
f
flow
x
2
exp
1150
2
exp
15
.
1
×
=
÷
÷
ø
ö
ç
ç
è
æ
×
×
=
µ
s

49. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-5
0
2000
4000
6000
8000
10000
12000
0 0.5 1 1.5 2 2.5 3 3.5 4
Distance from forging edge (in)
Forging
pressure
(psi)
P(sticking)
P(sliding)
sticking
sliding sliding
friction
hill
xk
xk

50. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-6
• Friction hill
– forging pressure must be large (8.7x) near the
center of the forging to “push” the outer
material away against friction

51. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-7
• Determine the forging force from:
• since we have plane strain
dA
p
Force òò ×
=
dx
p
depth
unit
F
x
x
ò
=
0

52. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-8
• We must solve separately for the sliding
and sticking regions
sticking
w
x
x
sliding
x
x
forging depth
dx
p
depth
dx
p
F
k
k
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
+
÷
÷
ø
ö
ç
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
= ò
ò .
2
.
2
2
/
0

53. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-16
or since the part is 36” deep:
F(both) = 337 Tonnes
F(all sticking) = 363 tonnes
F(all sliding) = 496,800 lbs = 218 tons
Can we use exact solution for this???
All sticking over-estimates actual value.
depth
w
h
w
F flow
forging ×
×
÷
ø
ö
ç
è
æ
+
×
×
=
4
1
15
.
1 s
depth
w
h
w
F flow
forging ×
×
÷
ø
ö
ç
è
æ
+
×
×
=
2
1
15
.
1
µ
s

54. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging – Effect of friction
• Effect of friction coefficient (µ) – all sticking
• Friction is very important
Friction coefficient Fmax (lbf/in depth) xk Stick/slide
0 4600 2 slide
0.1 11365 2 slide
0.2 19735 0.573 both
0.25 21331 0.347 both
0.3 22182 0.213 both
0.4 22868 0.070 both
0.5 23000 0 stick

55. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-17
Forging force vs. stroke – all sticking
0
5000
10000
15000
20000
25000
0 0.2 0.4 0.6 0.8
Stroke (in)
Forging
force
(lbf/in
depth)
mu=0
mu=0.1
mu=0.2
mu=0.25
mu=0.3
mu=0.4
mu=0.5

56. Prof. Ramesh Singh, Notes by Dr.
Singh/ Dr. Colton
Forging - Ex. 1-19
Maximum forging force vs. friction coefficient (µ)
all sticking
0
5000
10000
15000
20000
25000
0 0.1 0.2 0.3 0.4 0.5 0.6
Friction coefficient
Max
forging
force
(lbf/in
depth)

57. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
57
Deformation Work
In general, work done in bulk deformation processes has three
components
Total work, W = Wideal + Wfriction + Wredundant
Work of ideal plastic deformation, Wideal
= (area under true stress-true strain curve)(volume)
= (volume)
For a true stress-true strain curve :
÷
÷
ø
ö
ç
ç
è
æ
ò t
t d
t
e
s
e
0
n
t
t Ke
s =
( ) ( ) t
f
n
t
ideal Y
n
K
W e
e
volume
1
volume
1
=
÷
÷
ø
ö
ç
ç
è
æ
+
=
+
stress
flow
Avg.
=
f
Y

58. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
58
Deformation Work
Friction between dies and workpiece causes
inhomogeneous (non-uniform) deformation
called barreling
Barreling
Effect
Frictional Forces

59. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
59
Deformation Work
Internal shearing of material requires redundant
work to be expended
Ideal Deformation Redundant Deformation

60. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
60
Redundant Zone

61. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
61
Closed/Impression Die Forging
• Analysis more complex due to large variation in
strains in different parts of workpiece
• Approximate approaches
– Divide forging into simple part shapes e.g. cylinders,
slabs etc. that can be analyzed separately
– Consider entire forging as a simplified shape

62. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
62
Closed/Impression Die Forging
Steps in latter analysis approach
• Step 1: calculate average height from volume V
and total projected area At of part (including
flash area)
• Step 2:
Lw
V
A
V
h
t
avg =
=
÷
÷
ø
ö
ç
ç
è
æ
=
=
avg
i
avg
h
h
ln
strain
avg.
e
avg
avg
h
v
=
= rate
strain
avg.
e
!

63. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
63
Closed/Impression Die Forging
• Step 3: calculate flow stress of material Yf for
cold/hot working
• Step 4:
Kp = pressure multiplying factor
= 3~5 for simple shapes without flash
= 5~8 for simple shapes with flash
= 8~12 for complex shapes with flash
t
f
p
avg A
Y
K
F =
=
load
forging
Avg.

64. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
64
Other Analysis Methods
• Complex closed die forging simulated using
finite element software
Source: http://nsmwww.eng.ohio-state.edu/html/f-flashlessforg.html

65. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
65
Forging Defects
• Surface cracking due to tensile stresses
• Internal cracking in thick webs
Surface
Crack

66. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
66
Forging Defects
• Laps due to buckling of thin webs
• Cold shuts due to small radii fillets in die

67. ME 4210: Manufacturing Processes &
Engineering
Instructor: Ramesh Singh Notes by Prof.
67
Summary
• What is bulk deformation?
• Cold vs hot working
• Forging analysis
– Slab analysis
• Forging defects