mech

Fundamental
metalworking

Subjects of interest

• Introduction/objectives
• Classification of meta
• Mechanics of metalwo
• Flow curves
• Effects of temperature

- Hot working
- Cold working
• Effects of metallurgica
• Effects of speed of de
• Effects of friction and

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Chapter 1

ls of
g

s
al processes
orking

e on metalworking

al structure on forming processes
eformation on forming processes

lubricant

Tapany Udomphol Jan-Mar 2007

Objectives

• This chapter provides clas
processes based on types o
• Mechanics of metal formin
stress criterion for plastic de
• Differences between hot a
and advantages-disadvanta
given.
• Effects of deformation spe
process will be included.

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ssification of metal forming
of forces applied onto metals.
ng will be outlined to understand
eformation.
and cold working will be highlighted
ages of hot and cold working will be

eed and friction on metal working

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Classification of
processes

(based on the type of force ap
it is formed into shape).

• Direct-compre
• Indirect-comp
• Tension type
• Bending proc
• Shearing proc

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f metal forming

pplied on to the work piece as

ession-type processes
pression processes
processes
cesses
cesses

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• Direct-compression
type processes:

the applied force is normal to
the direction of the metal flow
in compression, i.e., forging
and rolling processes.

• Indirect-compression type

the primary forces are frequently ten
forces developed by the reaction of
therefore under the combined stress
tube drawing.

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processes:

nsile, with indirect compressive
the work piece. The metal flow is
s state, i.e., extrusion, wiredrawing,

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• Tension type processes

the applied force is tensile, i.e.,
stretching forming.

• Bending processes:

the applied force involves the
application of bending moments
to the sheet.

• Shearing processes:

the applied force involves the
application of shearing forces of
sufficient magnitude to rupture th
metal in the plane of shear.

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s:

s Jan-Mar 2007

f
he

Tapany Udomphol

Classification of meta

Metal fo

Compressive Combined tensile T
forming and compressive f

forming

•Rolling •Pulling through a die •S
•Open die forming •Deep drawing •E
•Closed die forming •Flange forming •R
•Indenting •Spinning
•Pushing through a die •Upset bulging

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al forming by subgroups

orming

Tensile Forming by Forming by
forming bending shearing

Stretching •Bending with •Joggling
Expanding linear tool •Twisting
Recessing motion •Blanking
•Coining
•Bending with
rotary tool
motion

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Mechanics of me

• Metal working occurs due to p
associated with analysis of com
require simplification.

Only (large) plastic strain is c
very small and can be negle

Strain hardening is often ne

Metal is considered to be iso

Normally plastic deformation
frictions, but we need to simp
to determine the force requir
deformation to obtain a prod

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metal working

plastic deformation which is
mplex stress distribution.

considered while elastic strain is
ected.

eglected.

otropic and homogeneous.

n is not uniform and also have
plify the stress analysis in order
red to produce a given amount of
duct in a required geometry.

Tapany Udomphol Jan-Mar 2007

• Required theory of plasticity, an
plastic deformation a constan
relationship is required.

ε1 + ε2 +

In metalworking, compressive

If a block of initial height ho is
compressive strain will be:

For true strain ∫ε = h1 dh = ln h1
hho ho

For conventional strain e = h1 −
h

Note: the calculated strain is neg

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nd for σ
nt-volume ho
Deformation

h1

+ε3 = 0 σ
…Eq. 1

e stress and strain are predominated.
compressed to h1, the axial

= − ln ho , ho > h1 …Eq. 2
h1 …Eq. 3

− ho = h1 −1
ho ho

gative compressive strains.

Tapany Udomphol Jan-Mar 2007

• However the convention is rev
that compressive stresses and
Note: ec is used as strain in defo

εc = ln ho , e
h1

And the fractional reduction
(reduction of area) in metal worki
deformation is given by

From the constant-volume rela

Ao Lo

σ A1 L1

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versed in metalworking problems so
d strains are defined as positive.
ormation process.

ec = ho − h1 =1− h1 …Eq. 4
ho ho

ing r = Ao − A1 …Eq. 5
Ao

ation A1L1 = Ao Lo

r = 1− A1 or A1 = 1− r
Ao Ao

σ ε = ln L1 = ln Ao = ln 1 1 r
Lo A1 −

…Eq. 6 Jan-Mar 2007

Tapany Udomphol

Example: Determine the engine
reduction for (a) a bar which is d
which is halved in length.

(a) For a bar which e = L2
is double in length,
L2 = 2L1 ε = ln

r = A1

(b) For a bar e = L1 /
which is halved in
length, L2 = L1/2 ε = ln L

r =1−
L

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eering strain, true strain, and
doubled in length and (b) a bar

2 − L1 = 2L1 − L1 = 1.0
L1 L1

L2 = ln 2L1 = 0.693
L1 L1
1 − A2 = 1− A2 = 1− L1 = 1− L1 = 0.5
A1 A1 L2 2L1

2 − L1 = −0.5 or ec = L1 − L1 / 2 = 0.5
L1 L1

L1 / 2 = ln 1 = − ln 2 = −0.693
L1 2

L1 = −1.0
L1 / 2

Tapany Udomphol Jan-Mar 2007

Yield criteria and s

• Yielding in unidirectional
tension test takes place when

the stress σ = F/A reaches the

critical value.

• Yielding in multiaxial
stress states is not
dependent on a single stress
but on a combination of all
stresses.

•Von Mises yield criterion
(Distortion energy criterion)
• Tresca yield criterion
(maximum shear stress)

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stress-strain relations

F σ=F
A
A
F
…Eq. 7
Uniaxial stress

Triaxial stresses Jan-Mar 2007

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Von Mises yield criterion

Yielding occurs when the secon
> critical value k2.

[(σ1 −σ 2)2 + (σ 2 −σ

In uniaxial tension, to evaluate the co

σ2 - σ3 = 0, where σo is the yield stress

Therefore 2σ 2 = 6k 2 ,then
o
k

[Substituting k from(σ1 −σ 2)2 + (σ 2 − σ
Eq.9 in Eq.8;

In pure shear, to evaluate the constan

where σo is the yield stress; when yiel

By comparing with Eq 9 we then

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nd invariant of the stress deviator J2

]σ 3 )2 + (σ 3 − σ1)2 = 6k 2 …Eq. 8

onstant k, note σ1 = σo,

s;

k = σo …Eq. 9

3

1 …Eq. 10

]σ 3 )2 + (σ 3 − σ1)2 2 = 2σ o

nt k, note σ1 = σ3 = τy , σ2 = 0,
lds: τy2+τy2+4τy2 = 6k2 then k = τy

n have τ y = 0.577σ o …Eq. 11
***

Tapany Udomphol Jan-Mar 2007

Tresca yield criterion

Yielding occurs when the maxim

the value of the shear stress in th

τ max = σ1 −σ3 …Eq.17 W
a
2 p

For uniaxial tension, σ1 = σo, σ2 = σ
and the shearing yield stress τo = σo

Therefore the maximum - shear
stress criterion is given by

In pure shear, σ1 = -σ3 = k , σ2 = 0,
τmax = τy

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mum shear stress τmax reaches
he uniaxial-tension test, τo .
Where σ1 is the algebraically largest
and σ3 is the algebraically smallest

principal stress.

σ3 = 0, τ = σ1 −σ3 =τo = σo …Eq.12
max
o/2. 2 2

σ1 −σ3 = σo …Eq.13
…Eq.14
τ y = 0.5σ o ***

Tapany Udomphol Jan-Mar 2007

Therefore, from von Mises an

Von Mises yield criterion

Tresca yield criterion

• The differences in the maxim
both criteria lie between 0-15%
• However experiments confirm
is more accurate to describe t

• Once the metal has reached i
flow under the influence of stre
where stress is not directly prop
• The manner of flow or deform
state.

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nd Tresca yield criteria we have

τ y = 0.577σ o ***

τ y = 0.5σ o ***

mum shear stress prediction from
%.

med that the von Mises criterion
the actual situations.

its yield point, the metal starts to
ess state. This is in the plastic regime
portional to strain.
mation is dependent on the stress

Tapany Udomphol Jan-Mar 2007

FEM analysis

• Finite element method
(FEM) is used in
metalworking plasticity
where stresses are
complex.

• FEM is a very powerful
technique for determining
stress-strain distributions in
plane strain or plane stress
conditions.

Distor

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rtion of FEM grid in forging of a compressor disk.

Tapany Udomphol Jan-Mar 2007

Flow curves

• Flow curve indicates whethe
conditions, i.e., strain rate, tem
• Flow curve is strongly depen
temperature.

Flow curves of some met

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er metal is readily deformed at given
mperature.

ndent on strain rate and

tals at room temperature Jan-Mar 2007

Tapany Udomphol

Determination of f

Stress-strain curve

σA

σο

ε2 ε1 ε

Ture stress-strain curve of a ductile
metal under uniaxial tensile loading.

• Hook’s law is followed up to

• Beyond σo, metal deforms

• Unloading from A immedia

ε1 to ε2 = σ/E the strain decr

elastic strain.

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flow curve

σ = Kεn

σ is ture stress
ε is true strain

K is constant
n is work hardening exponent

(this is valid from the beginning of plastic
flow to the maximum load at which the
specimen begins to neck down.)

o the yield point, σo.

plastically (strain hardening).

ately decreases the strain from

rease ε1-ε2 is the recoverable

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Flow curve

Flow curve

True stress

0 10 20 30 40 50

Reduction of area by drawing, %

Flow curve constructed from stress-
strain curves after different amounts
reduction.

Temperature Flo

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True stress, σ σy

True strain, ε εf
Method of using average flow
of stress to compensate for strain
hardening.

ow stress

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Flow curve
• Strain hardening occurred w
drawn to a specific true strain.

True stress-strain curve for iro
wiredrawing at room temperat

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when an iron wire had been
.

on wire deformed by Jan-Mar 2007
ture.

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Working proces

• The methods used to mechan
product forms are called Worki

Working processes

Hot working (0.6-0.8Tm)
Definition : deformation unde
strain rate such that recrysta
simultaneously with the defo
Examples : rolling, forging, e

Cold working (< 0.3Tm)
Definition : deformation carri
recovery processes are not e
Examples : rolling, forging, e
swaging, coining

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sses

nically shape metals into other
ing Processes.

Hot working T ~ 0.6−0.8Tm

Cold working T ≤ 0.3Tm

er conditions of temperature and
allisation process take place
ormation.

extrusion

ied out under conditions where
effective.

extrusion, wire/tube drawing,

Tapany Udomphol Jan-Mar 2007

• The products resulting from the
metals are called Wrought Prod
sheet, plate, bar, forging.
• Plastic working processes ca
divided into:

Primary mechanical working proces

Designed to reduce an ingot or billet
a standard mill product of simple
shape, i.e., sheet, plate, bar.

Secondary mechanical working pro

Primary sheets, plates or
bars are formed into final
finished shapes, i.e., wire &
tube drawing, sheet metal
forming operation.

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e working of www.magnesiumextrusions.com
ducts. such as
Magnesium bars
an also

ss

t to

ocess Steel plates

Tapany Udomphol Drawn wires

Jan-Mar 2007

Hot working

• Hot working involves deforma
recrystallisation can occur (0.6-

Examples of hot working tempe

Metal Melting p
(oC)

Iron 1535
Copper 1083
Aluminium (alloys) 660
420
Zinc

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ation at temperatures where
-0.8 Tm).

eratures for each metal

point Recrystallisation Hot working
temperature range
(oC) (oC)

5 450 900-1200
3 200 650-900

150 350-500
20 110-170

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PropertiesEffects of tempera
processes

Strength

Cold worked and New grains
recovered

Recovery Recrystallis
~0.3Tm ~0.5

Annealing mechanisms in cold worked metals

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ature on metal forming

Ductility
Hardness

Temperature

sation Grain growth
5Tm

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Recrystallisation durin

• The minimum temperature at w
occurs is called Recrystallisatio
• Above the recrystallisation tem
increases and therefore they are
newly formed nuclei which in tur
process continues until all the di
transformed.
• Hot working results in grain re

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ng hot working

Deformed in
direction of work

Nuclei form at grain boundaries at
points of max stress

Nuclei grow into new grains

which reformation of the crystals
on Temperature.

mperature the kinetic energy of atoms
e able to attach themselves to the
rn begin to grow into crystals. This
istorted crystals have been

efining. Jan-Mar 2007

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Recrystallisation

• Recrystallisation takes place at hig
temperatures than recovery which le
a new formation of grains.

• The process includes 1) primary
recystallisation and 2) secondary
recrystallisation and grain growth.

Primary recrystallisation

- Primary recrystallisation
new grain formation process

- Recrystallisation tempera
metal alone, but on a whole
temperature, strain and minim
available (amount of deforma

- Small impurities in pure m
increase the recrystallisation

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www.msm.cam.ac.uk

gher Deformed matrix
eads to

Recrystallised grains with
annealing twins

Recrystallised grain with annealing twins
surrounded by deformed matrix with high
density of dislocations.

occurs at the beginning of the
s.

ature does not depend on the
number of variables
mum dislocation density
ation)

metals can considerably
n temperature.

Tapany Udomphol Jan-Mar 2007