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THEORY OF PLASTICITY
and ITS APPLICATIONS
INSTITUTE OF METAL FORMING
This Script has been given for Master Course “Mold and Die Engineering” in KUAS.
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Content
Chapter I: Introduction
Chapter II: Metallurgical Fundamentals
Chapter III: Strain
Chapter IV: Stress
Chapter V: Yield Criteria
Chapter VI: Flow Rule
Chapter VII: Flow Curve
Chapter VII: Analysis Methods
Extra Chapt. FEM Simulation
Chapter IX: Bulk Forming Processes
Chapter X: Sheet Forming Processes
TOTAL LECTURE PERIOD: 8 W
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Content
• Classification of Manufacturing Processes
• Advantages of Metalforming Processes
• Classification of Metalforming Processes
• Examples of Metalforming Processes
• Metalforming Machines
• Metal Forming System
Chapter I: Introduction
Chapter I: Introduction


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Questions about production…
Crankshaft
CV Joint
Rear part of TOYOTA
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Manufacturing Processes
Manufacturing processes produce solid bodies with given
geometry and given properties.
Chapter I: Introduction
Creation of
Cohesion
Maintenance of
Cohesion
Destruction
of Cohesion
Increase of Cohesion
1. Primary
Forming
(Form
generation)
Shape (Form) Modification
5. Coating
2. Deforming 3. Separating 4. Joining
6. Changing Material Properties
Rearrangement
of Particles
Removal of
Particles

Addition of
Particles
Maintenance of Cohesion: Duy trì sự liên kết
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Manufacturing Processes
1. Primary Forming: Casting, Powder Metallurgy
2. Deforming: Metal Forming Processes
(Bulk and Sheet Forming)
3. Separating: Machining (with Cutting Tool
or with Abrasive Tool),
Non-Traditional Machining (Laser)
4. Joining: Welding, Joining
5. Coating: Various
6. Changing Material Properties: Heat Treatments
(temper, blank a fire)
Chapter I: Introduction
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7
Casting of Stator made of gray iron
Milling on Milling-machine with 5 axes
Lathe
Drilling
Manufacturing Processes
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Jioning with rivet
Coating of TiN by method PVD
Thremal treatment
Welding
Manufacturing Processes
5

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Drawing of car body parts Car body parts
Parts of machines
Hollow parts used in conduit of oil or gas
Manufacturing Processes
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Basic Question of Manufacturing
Chapter I: Introduction
How can we manufacture a technical product with given
specific dimensional and shape tolerances, given surface
structure and given material properties most economically?
Primary Forming:
Casting
Metal Forming
Joining:
Welding
Separation:
Turning
Weld
Waste
Example Step-shaft ?
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Comparision of Machining and
Metalforming
• Forces and stresses in metalforming are high
– Metalforming: stresses between 50 to 2500 MPa,
forming forces are upto 75,000 tons
– Metal cutting: Forces about 2 to 20 tons
• Tools are large, heavy and expensive

• Minimum workpiece quantities are necessary
Chapter I: Introduction
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Advantages of Metalforming
• High material utilization [,ju:təlai'zei∫n] tận dụng (no waste,
shavings by manufacturing)
• High productivity with short production times
• High dimensional and shape accuracy within
certain tolerances
• Superior [su:'piəriə] tốt hơn mechanical material
properties of the product (especially for
dynamic loadings)
Chapter I: Introduction
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13
Grain Flow Comparison
(a) casting, (b) machining, (c) forging
Fiber/Structure of a Drive Shaft
after the Extrusion
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Definition of Metal Forming
Chapter I: Introduction
Metalforming bases on plastic deformation
of metal.
Metalforming is the manufacturing by
plastic (permanent) change of the form of a
solid body by preserving (duy trì) both the
mass and the cohesion.
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Classification Metal Forming Processes
Chapter I: Introduction
By the primary stress
in the deformation zone.
Further classification by kinema-
tics, tool geometry and workpiece
geometry leading to more than 200
basic processes!
Rolling
Open-Die
Forming
Closed-Die
Forming
Indenting
Pushing
through a Die
Compressive
Forming
Pulling
through a Die
Deep
Drawing
Spinning
Flange
Forming
Upset
Bulging
Combined Tensile
and Compressive
Forming

Stretching
Expanding
Recessing
Tensile
Forming
B. w. Linear
Tool Motion
B. w. Rotary
Tool Motion
Forming by
Bending
Joggling
Twisting
Forming by
Shear
Metalforming
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Classification Metal Forming Processes
Chapter I: Introduction
Metal Forming Processes
Bulk Forming Processes Sheet Forming Processes
• Spatial workpieces
• Large changes in cross-section
& large changes in thicknesses
• Material flows in all directions
• Generally multi-axial compressive
stress states
• Larger relative forces
• Planar workpieces (sheets, plates)
• Hollow pieces with almost constant

wall thickness
• Generally two-axial stress states:
tensile-tensile/tensile-compressive
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Classification Metal Forming Processes
Chapter I: Introduction
Bulk Forming Processes
Steady-State Processes Non-Steady-State Processes
Deformation patterns are
independent of time
Deformation patterns are
dependent of time
Examples:
Extrusion, rolling, drawing
Examples:
Upsetting, forging, extrusion
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Classification Metal Forming Processes
Chapter I: Introduction
Metal Forming Processes
Cold Forming Warm Forming Hot Forming
Forming at room
temperature
(everyday sense)
Forming below the recry-
stallization temperature
Steel: Room Temperature
Forming above room
temperature

(everyday sense)
Forming above the recry-
stallization temperature
Steel: 1150-1250
o
C
Forming above room
temperature
(everyday sense)
Forming below or around
the recrystallization
temperature
Steel: 750-950
o
C
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Recyrstallization Temperatures
Chapter I: Introduction
Material
Recrystallization
Temperature
Material
Recrystallization
Temperature
C-Steel 550
o
C tin 0 to 40
o
C

Pure-Al 290 to 300
o
C zinc 50 to 100
o
C
Dur-Al 360 to 400
o
C Mo 870
o
C
Cu
200
o
C
(changes drastically with alloying
elements)
W 900-1000
o
C
Lead (chì) -50 to 50
o
C Ni 400-600
o
C
Recrystallization temperatures depend on prior plastic strain
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Temperatures
• Room temperature
• Initial temperature of workpiece before forming
• Average temperature of workpiece after forming

• Surface temperature of workpiece after forming
• Highest temperature of workpiece during forming
• Average temperature of tools
• Highest temperature of tool-interface during forming
• Initial temperature of tool
Chapter I: Introduction
Notice temperature by forming process!!!
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Heating Processes
Chapter I: Introduction
Heating Processes:
• Heating before forming (a)
• Self-heating of workpiece due to
forming (b)
• External-heating the workpiece
during forming (c)
• Cooling of the workpiece during
forming (d)
• Cooling of the workpiece after
forming (e)
• Cooling before forming (f)
Process Time
Time
T
e
m
p
e
r

a
t
u
r
e
RT
a
f
b
e
d
b
c
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Examples of Metalforming Processes:
Compressive Forming
Chapter I: Introduction
Upsetting:
Impression Die Forging:
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Examples of Metalforming Processes:
Compressive Forming
Open die forging:
Chapter I: Introduction
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Open die forging
Impression Die Forging
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Free form Upsetting
Upsetting of Head’s Bolt
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Examples of Metalforming Processes:
Compressive Forming
Chapter I: Introduction
01.020
07.09.2001
Heading (Upsetting)
Forward
Extrusion
Backward Can
Extrusion
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Examples of Metalforming Processes:
Compressive Forming
Chapter I: Introduction
Spiders: Cold Lateral Extrusion
Courtesy of Nichidai
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Examples of Metalforming Processes:
Compressive Forming
Chapter I: Introduction
Courtesy of Nichidai
Inner Race:
Cold Lateral Extrusion
Bevel Gears:
Cold Lateral Extrusion
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Examples of Metalforming Processes:
Compressive Forming
Chapter I: Introduction
Rotor Case: Cold combined forward-backward extrusion
Courtesy Nichidai
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Chapter I: Introduction
Courtesy Niels Bay & Thyssen-Krupp Presta
Examples of
Metalforming
Processes:
Compressive
Forming
Steel Workpieces
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Examples of
Metalforming
Processes:
Compressive
Forming
Chapter I: Introduction
Courtesy Niels Bay and Alutec
Aluminum
Workpieces
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Chapter I: Introduction
Examples of Metalforming Processes:
Compressive Forming

Ring Rolling
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Examples of Metalforming Processes:
Compressive Forming
Flow Turning,
Spinning:
Chapter I: Introduction
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Chapter I: Introduction
Design a model of spinning machine to producing of bottles
for high pressure gas
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Spinning:
Chapter I: Introduction
1. Disc Blank 2. Spinning Roller 3. Mandrel 4. Clamping Plate 5. Blank Support Unit
6. Trimming Plate 7. Spindle 8. Cross Slide 9. Tailstock
Orbit motion of Spinning roller
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Spinning:
Chapter I: Introduction
Axis-symmetric Parts
See some movies !

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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Chapter I: Introduction
d
1
d
0
α
F
total
d
0
z
r
Wire Drawing:
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Chapter I: Introduction
Deep drawing:
Wash basin
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Products by deep drawing
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Deep drawing:

Courtesy of University of Munich
Chapter I: Introduction
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Deep drawing examples (Sidepanel – ULSAB)
Chapter I: Introduction
Courtesy Niels Bay
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Deep drawing examples
Chapter I: Introduction
Courtesy Niels Bay
Products: pot, pan, basin
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Chapter I: Introduction
Flange Forming:
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Chapter I: Introduction
Hydro-
forming:
1. Closing of the press 2. Filling the water
3. Pressurizing/compressing 4. Opening the press

Courtesy
of Schuler
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Cap for pump housing (IPL, Grundfos)
Camera housing
Parabolas (IPL)
Chapter I: Introduction
Courtesy Niels Bay
Hydroforming
Examples
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Examples of Metalforming Processes:
Combined Tensile & Compressive Forming
Chapter I: Introduction
Courtesy Niels Bay
Hydroforming
Examples
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Examples of Metalforming Processes:
Tensile Forming
Chapter I: Introduction
Stretch-forming:
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Metalforming Machines
Chapter I: Introduction
Rolling

Machines
Drawing
Machines
Energy Driven
Force Driven
Displacement
Driven
Presses
Linear Relative Motion
of the Tools
Longitudinal
Lateral
Oblique
Rolling
Machines
Bending
Machines
Stretching
Machines
Nonlinear Relative Motion
of the Tools
Forming
Medium
Forming
Energy
Special Machines
Forming Machines
by K. Lange
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Metalforming Machines: Examples (1)

Compressed air hammer
Hydraulich hammer

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