Forming – Metallurgical Basics in
Plastic Deformation
Manufacturing Technology II
Lecture 3
Laboratory for Machine Tools and Production Engineering
Chair of Manufacturing Technology
Prof. Dr.-Ing. Dr.-Ing. E. h. F. Klocke
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Seite 1
Outline
„ Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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1
Introduction
What is Manufacturing Technology?
Manufacturing Technology is the teachings of economical production
of finished products from raw materials according to given
geometrical properties.
raw material
Manufacturing Tech.
geometrically undefined
finished product
geometrically defined
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Introduction
What is Forming?
semi-finished product
forming
finished product
plastic forming
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Outline
Introduction
„ Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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Seite 5
Chemical Constitution of Metals
4 Basic Chemical Bonds
„ metal bond
„ ionic bond
„ covalent bond
metal bond
„ Van-der-Waals bond
positive charged
metal ions
electron gas (e-)
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Chemical Constitution of Metals
The Metal Bond
„ metal atoms basically emit electrons
positive charged ions
„ in pure metals no electron-absorbing atoms do exist
un-combined electrons (outer electrons) form an electron gas
„ outer electrons in metals can freely move
good electrical and thermal conductivity
„ in absolute pure metals all Atoms are totally equal
plastic deformation
metal bond
positive charged
metal ions
electron gas (e-)
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Chemical Constitution of Metals
Lattice Types of an Unit Cell
face-centred
cubic
(fcc)
body-centred
cubic
(bcc)
hexagonal
(hex)
γ-Fe, Al, Cu
α-Fe, Cr, Mo
Mg, Zn, Be
sliding planes:
4
6
1
sliding directions:
3
2
3
sliding systems:
12
12
3
very good
good
poor
examples:
formability:
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Chemical Constitution of Metals
Atomic and Macroscopic View of Metal Structures
unit cell
crystal lattice
ideal
crystal
structure
a
Real
crystal
structure
microstructure
2D – Cut
of the microstructure
section plane
schematically
special agglomeration of crystals
photograph
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Chemical Constitution of Metals
load
Comparison of Load-displacement Curves of Mono- and Multi-Crystal
multi-crystal
mono-crystal with
unfavourable
orientation
mono-crystal with
favourable
orientation
body-centred cubic
lattice
favourable loading direction
displacement
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unfavourable loading direction
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Chemical Constitution of Metals
Punctual Lattice Errors
vacancy
intermediate-lattice atom
FRENKEL-matching
„ The foreign atoms induce
stress to the crystal lattice.
This stress effects crystal
strengthening of the
material.
substituting atom
emplacement atom
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Chemical Constitution of Metals
Dislocations
edge dislocation
screw dislocation
„ dislocations are linear errors in the lattice.
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6
Outline
Introduction
Chemical Constitution of Metals
„ Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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Seite 13
Elastic Deformation
Tensile Test – Load-Displacement Diagram
load
specimen 1
F1
specimen 2
F2
A1 = 2 • A2
follows:
F1 = 2 • F2
tensile specimen
l1 =l1l2
displacement
relate force to cross section surface
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Elastic Deformation
Stress-Strain Curve of Elastic Behaviour
stress
F
Re
engineering stress:
specimen
1=2
engineering strain:
∆l
A
l
F
A0
σ =
l0
∆σe
A0
dε =
dl
l0
l1
dl
∫l
⇒ ε =
l1 − l0
∆l
=
l0
l0
=
l0 0
α
∆εel
strain
For elastic behaviour:
∆σe
∆ε el
tan α =
F
E =
σ
ε el
σ ≤ Re
E = Young‘s Modulus
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Seite 15
Elastic Deformation
Stress Determination Depending on Load
tensile test
shear test
compression test
F
A1
F
l1
A0
F
a
θ
A1
l0
l0
l
l1
A0
σ=
F
A
tensile stress
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F
F
σ=
−F
A
compression stress
F
τ=
A
F
A
shear stress
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Elastic Deformation
Atomic Representation of Pure Elastic-Tensile Deformation
unloaded
tensile-loaded
σ
l0
l
σ
E =
σ
ε el
ε =
„ elastic strain based on tensile load
l1 − l0
∆l
=
l0
l0
σ - nominal stress
ε - strain
E - Young‘s Modulus
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Elastic Deformation
Atomic Representation of Pure Elastic-Shear Deformation
unloaded
shear-loaded
τ
γ
τ
G =
τ
γ el
υ =
E
-1
2G
„ elastic shearing based on shear load
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γ - shear angle
τ - shear stress
G - shear modulus
ν - Poisson‘s ratio
E - Young‘s modulus
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9
Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
„ Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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Seite 19
Plastic Deformation
Stress-Strain Curve up to the Uniform Elongation
true tensile stress:
F
stress
(related to real section)
σ‘
σ
Rm
σ′ =
F
A
∆l
A
l
l0
Re ,σe
A0
engineering stress:
load
relieving
(related to starting section)
reload
σ =
εpl
εel
F
A0
strain
F
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Plastic Deformation
Types of Plastic Deformation
sliding
before
dislocation movement
after
high power requirements
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low power requirements
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Plastic Deformation
Sliding and Dislocation Movement
sliding
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dislocation movement
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Plastic Deformation
Video Clip – Recordings of Dislocation Movements on Infrared Camera
„ tensile specimen of tempered aluminium
with reflective surface
F
F
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Plastic Deformation
Plastic Deformation Based on Twinning
twinning
Inconel 718,
austenitic structure
200 µm
twinning
„ Mechanical twinning especially appears, if the
use of sliding systems is no longer possible or if
deformation velocity reaches a critical value.
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Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
„ Flow Stress
Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
© WZL / IPT
Seite 25
Flow Stress
Using the Tensile Test as an Example of Flow Stress Determination
σ‘
stress
F
uniaxial stress
σ1
triaxial stress
σ1, σ2, σ3
Rm
∆l
A
l
l0
σ
Re ,σe
lateral contraction
A0
fracture
εel
elastic
ϕ / εpl
Ag – uniform elongation
strain
plastic strain ϕ
strain ε
F
„ true flow stress increases with increasing plastic deformation
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Flow Stress
Using the Tensile Test as an Example of Flow Stress Determination
σ‘
useable region to
determinate flow stress
stress
F
kf
Rm
∆l
l
l0
σ0
Re ,σe
A
A0
fracture
εel
F
ϕ / εpl
true tensile stress: σ´=
Ag
F
A
strain
flow stress:
kf =
F
F
=
⋅ eϕ
A A0
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Flow Stress
flow stress
Flow Curve
required strain to break
the strain hardening
required strain for
plastic deformation
effective strain
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14
Flow Stress
Strain Hardening Depends on Dislocations
schematic diagram
dislocation movement
grain boundary
dislocation origin
sliding planes
moving direction
dislocation structure of little-formed copper
piled up dislocations at boundary grains
grain boundary
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Flow Stress
Yield Conditions According Tresca and von Mises
τ
τ
τmax
σIII
σII
σIII
Tresca:
von Mises:
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σI
σ
σII
σI σ
1 σ = 1 max (I σ – σ I;I σ – σ I;I σ – σ I)
I
II
I
III
II
III
2 v 2
σv = 1 [(σI – σII)² + (σI – σIII)² + (σII – σIII)²]
2
τmax =
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Flow Stress
Strain Determination of an Idealized Upsetting Process
true strain (plastic)
l
dϕ =
1
dl
dl
l
⇒ ϕ = ∫ = ln 1
l
l
l0
l0
ϕ x = ln
l1
;
l0
ϕ y = ln
b1
;
b0
ϕ z = ln
h1
h0
including of volume constancy
l0 ⋅ h0 ⋅ b0 = l1 ⋅ h1 ⋅ b1 = konst.
ϕ x + ϕ y + ϕz = 0
engineering strain (elastic)
l
dε =
1
∆l
dl
dl l − l
⇒ ε =∫ = 1 0 =
l
l
l0
l0
l0 0
connection between true strain - engineering strain
l 
 l + ∆l 
 ∆l l 
 = ln  + 0  = ln ( ε +1)
ϕ = ln  1  = ln  0
l
l
 0
 0 
 l0 l0 
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Flow Stress
Why is it Important to Distinguish Plastic and Elastic Strain?
„ as an example a cylinder has to be halved and/or doubled around its length
compression forming
tensile forming
l1 − l0
l0
-0.5
+1.0
l1
l0
-0.693
+0.693
l1 = l0 / 2
elastic
strain
plastic
strain
ε=
ϕ = ln
l1 = 2 l0
Advantage: By using the plastic strain it is possible to sum deformation
values of successive forming steps.
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Flow Stress
Strain Calculation of Successive Forming Steps
H0 = 30mm
H1 = 25mm
H2 = 20mm
H3 = 15mm
0
1
2
3
1Æ2
-20%
2Æ3
-25%
0Æ2
-33,3%
0Æ3
-50%
1Æ2
-0,22
2Æ3
-0,29
0Æ2
-0,40
0Æ3
-0,69
elastic strain
H − H0
ε= 1
H0
0Æ1
-16,6%
plastic strain
ϕ = ln
H1
H0
0Æ1
-0,18
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Seite 33
Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
„ Occurring of fractures
Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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Occurring of Fractures
Fracture as a result of Radial Extrusion
„ fractures depending on passing a critical deformation value
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Occurring of Fractures
Fracture Shape in Longitudinal Direction
Effective strain detected by the simulation
„ The fracture shape depends on the present stress conditions.
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Occurring of fractures
Fracture Shape in Crossing Direction
Effective strain detected by the simulation
„ The fracture shape depends on the present stress conditions.
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Occurring of Fractures
Ductile Fracture
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Occurring of Fractures
Brittle Fracture
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Seite 39
Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
„ Recrystallisation
Influences on Flow Stress
Typical Materials in Forming Technologies
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Recrystallisation
Grain Origin and Grain Deformation Regarding Primary Shaping and Forming
primary shaping
1. nucleation
2. nucleic growth
3. grain origin
forming
grain deformation
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Recrystallisation
Static Recrystallisation
- ϕv > 0
- T > T recrystallisation
crystal
regenatation
requirements:
ductile yield
tensile strength
schematic course of recrystallisation of cold formed structure
- impact time
temperature
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Recrystallisation
ϕvBr
ϕvBr - effective strain
at time of fracture
annealing for
recrystallisation
annealing for
recrystallisation
flow stress
Stress Curve of Cold Forming as a Result of Static Recrystallisation
ϕvBr
effective strain
„ annealing for recrystallisation increases strain hardening and decreases flow stress
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Recrystallisation
Recrystallisation of Brass
starting conditions
3 s at 580°C
4 s at 580°C
„ recrystallisation decreases material‘s
mechanical properties
to the values of
unformed materials
8 s at 580°C
15 min at 580°C
imwf Stuttgart
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Recrystallisation
Dynamic Recrystallisation
hot extrusion
T >> T recrystallisation
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Recrystallisation
flow stress
Forming Temperature and Velocity Influences the Flow Stress
forming temperature below
recrystallisation temperature
high forming velocity
forming temperature above
recrystallisation temperature
low forming velocity
effective strain
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Recrystallisation
grain size
Effective Strain and Temperature Influences the Grain Size
e
ur on
at ati
r
p e l is
m stal
e
t y
cr
re
range of
recrystallisation
strain
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Seite 47
Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
„ Influences on Flow Stress
Typical Materials in Forming Technologies
© WZL / IPT
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Influences on Flow Stress
Flow Curves – Material Influence
carbon content
normalized
normalized
MPa
normalized
800
steel
stress
flow stress kf
1200
soft annealed
malleable
cast iron
grey cast iron
soft annealed
600
soft annealed
strain
400
200
C15
0
0
0,4 0,8
1,2
16MnCr5
0
0,4
0,8
1,2
carbon content
C35
0
0,4
0,8 1,2
1,6
effective strain ϕ
flow stress
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Influences on Flow Stress
Flow Curves – Forming Velocity Influence
flow stress kf
300
ϕ = 1000 s-1
MPa
250
ϕ = 360 s-1
200
forming velocity
ϕ = 40 s-1
150
flow stress
100
0
0,4
0,8
1,2
1,6
2,0
effective strain ϕ
C15 at 1100 °C
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Influences on Flow Stress
Flow Curves – Temperature Influence
flow stress kf
200
MPa
20°C
200°C
100
60
250°C
40
300°C
20
400°C
10
500°C
6
temperature
4
2
flow stress
0
Al 99,9 at 10 s-1
1,5
3,0
4,5
6,0
7,5
9,0
effective strain ϕ
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Seite 51
Outline
Introduction
Chemical Constitution of Metals
Elastic Deformation
Plastic Deformation
Flow Stress
Occurring of fractures
Recrystallisation
Influences of Flow Stress
„ Typical Materials in Forming Technologies
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Typical Materials in Forming Technologies
The Iron-Carbon Diagram
perlite
0,1 % C
martensite
ferrite
perlite
0,4 % C
bainite
ferrite
perlite
0,8 % C
perlite
1,2 % C
austenite
cementite
Quelle: www.metallograf.de
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Seite 53
Typical Materials in Forming Technologies
Steels and Their Industrial Use
Quelle: CIS
steel
16MnCr5
(case-hardened steel)
100Cr6
Quelle: BOIE
(heat-treated steel)
X5CrNi1810
(austenite steel)
lattice
C
Cr
Mn
Si
Ni
bcc
0,16
0,95
1,15
0,25
-
bcc
1,0
1,5
0,35
0,25
-
fcc
0,05
18
-
-
10
„ Because of the face-centred cubic lattice of austenite austenitic
steels can be cold formed very easy.
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Typical Materials in Forming Technologies
Non-Iron Metals and Their Industrial Use
„ aluminium- and aluminium forgeable alloys
(e.g. EN AW-AL99,98Mg1)
– fcc
very good hot and cold forming
properties
– alloying elements to increase mechanical
strength (e.g. Cu, Mg, Si, Zn)
„ titan alloys
(e.g. Ti6Al4V)
– bcc/hex
moderate cold forming properties
– alloying elements to favour hexagonal structure
(e.g. Al, Sn, O)
– alloying elements to favour bcc structures (e.g. V, Cr, Fe)
„ more non-iron metals:
copper, nickel, magnesium, zirconium, tin, zinc, lead
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