Sheet metal forming process Chapter 7

Sheet metal forming process
Chapter 7

Introduction
• Sheet metal forming operations produce a wide range of
consumer and industrial products, such as metal desks,
appliances, aircraft fuselages, car bodies, and kitchen utensils.
• Sheet-metal forming also called press working, press forming
or stamping, is among the most important of metalworking
processes, dating back to as early as 5000 B.C., when
household utensils, jewelry, and other objects were made by
hammering and stamping metals such as gold, silver, and
copper.
• Compared to those made by casting or forging, sheet metal
parts offer the advantages of light weight and shape
versatility.
Chapter 7

Introduction
• Sheet forming, unlike bulk deformation processes,
involves work pieces with a high ratio of surface area
to thickness such as cookie sheet hubcaps.
• Sheet metal is produced by rolling process.
• If the sheet is thin, it is generally coiled after rolling, if
thick, it is available as flat sheets or plates, which may
have been decoiled and flattened prior to forming
them.
• In a typical forming operation, a blank of suitable
dimensions is first cut from a large sheet, this usually
done by a shearing process.
Chapter 7

TABLE 16.1
Process Characteristics
Roll forming Long parts with constant complex cross-sections; good surface finish; high production rates; high
tooling costs.
Stretch forming Large parts with shallow contours; suitable for low-quantity production; high labor costs; tooling
and equipment costs depend on part size.
Drawing Shallow or deep parts with relatively simple shapes; high production rates; high tooling and
equipment costs.
Stamping Includes a variety of operations, such as punching, blanking, embossing, bending, flanging, and
coining; simple or complex shapes formed at high production rates; tooling and equipment costs
can be high, but labor cost is low.
Rubber forming Drawing and embossing of simple or complex shapes; sheet surface protected by rubber
membranes; flexibility of operation; low tooling costs.
Spinning Small or large axisymmetric parts; good surface finish; low tooling costs, but labor costs can be
high unless operations are automated.
Superplastic
forming
Complex shapes, fine detail and close tolerances; forming times are long, hence production rates are
low; parts not suitable for high-temperature use.
Peen forming Shallow contours on large sheets; flexibility of operation; equipment costs can be high; process is
also used for straightening parts.
Explosive
forming
Very large sheets with relatively complex shapes, although usually axisymmetric; low tooling costs,
but high labor cost; suitable for low-quantity production; long cycle times.
Magnetic-pulse
forming
Shallow forming, bulging, and embossing operations on relatively low-strength sheets; most
suitable for tubular shapes; high production rates; requires special tooling.
Characteristics of Sheet-Metal
Forming Processes

• Forming of sheet metals is generally carried out by
tensile forces, as otherwise the application of external
compressive forces could lead to buckling, folding and
wrinkling of the sheet.
• In some bulk deformation processes, the thickness of
the work piece is changed to produce part, whereas in
sheet –forming process, any change in thickness is
typically due to stretching of the sheet under tensile
stresses.
• So sever thickness decreases in sheet metal forming
should generally be avoided as they can lead to necking
and failure, as occurs in a tension test.
Sheet Metal - Characteristics and
formability

The mechanics of all sheet forming basically consists
of stretching and bending, certain parameters
significantly influence the overall operation. These
are:
1. Elongation
2. Yield point elongation
3. Anisotropy
4. Grain size
5. Residual stress
6. Springback
7. wrinkling
Sheet Metal - Characteristics and
formability

Elongation :
• When a specimen is subjected to tension it is first
undergoes uniform elongation up to the UTS, after
which it begins to neck. This elongation is then
followed by further nonuniform elongation until
the specimen fractures.
• Because the sheet will be stretched during forming
process, high uniform elongation is thus desirable
for good formability,
Forming Processes

Elongation :
• For a material that has a true-stress-true-strain curve
represented by the equation:
• The strain at which necking begins is given by ϵ = n.
• Thus, the true uniform strain in a simple stretching
operation is numerically equal to the strain-hardening
exponent, n.
• A high value of n indicates large uniform elongation and
thus is desirable for sheet forming.
Forming Processes

Yield point elongation
 Low carbon steels exhibit a behavior
which is called yield point elongation,
involving upper and lower yield
points.
 This yield point elongation is usually
on the order of a few percent.
 In yield point elongation, a material
yields at a given location; subsequent
yielding occurs in adjacent areas
where the lower yield point is
unchanged.
 When the overall elongation reaches
the yield point elongation, the entire
specimen will undergo a uniform
deformation
Characteristics of Sheet-Metal Forming Processes

• This behavior of low carbon steel
produces Lueder’s band (Also
called stretcher strain marks or
worms) on the sheet.
• These bands consist of elongated
depressions on the surface of the
sheet and can be objectionable
in the final product because of its
uneven surface appearance.
• These bands also can cause
difficulties in subsequent coating
and painting operation.
Forming Processes

• Stretcher strain marks can
be observed on the curved
bottom of the steel cans
for common household
products.
• Aluminum cans don’t
exhibit this behavior
because aluminum alloys
do not demonstrate yield
point elongation.
Forming Processes

• The magnitude of the yield point elongation
depends on:
1. The strain rate (with higher rates, the
elongation generally increase).
2. The grain size of the sheet metal (as the grain
size decreases, the yield point elongation
increases.
Forming Processes

• The usual method of a voiding these marks is to
eliminate or to reduce yield-point elongation by
reducing the thickness of the sheet 0.5 to 1.5% by
cold rolling , a process known as temper rolling or
skin rolling (preferred grain orientation , or
directionality, of sheet metal).
• Because of the strain aging. The yield-point
elongation reappears after a few days at room
temperature. Thus, the sheet metal should be formed
within a certain period of time (such as from one to
three weeks for rimmed steel) to avoid the
reappearance of stretcher strain.
Forming Processes

Temper rolling
Skin rolling
Forming Processes

Anisotropy
 Another important factor influencing sheet-metal forming is
anisotropy (preferred grain orientation) , or directionality, of
sheet metal.
 Anisotropy is acquired during the thermo mechanical processing
history of the sheet.
 There are two types of anisotropy:
1. Crystallographic anisotropy (preferred grain orientation)
2. Mechanical fibering ( alignment of impurities, inclusions and
voids.
 These behaviors are particularly important in deep drawing of
sheet metals.
Forming Processes

 Grain size
 Grain size of the sheet metal is important for two reasons:
1. Because of its effect on mechanical properties of the
material (larger size grain is different from smaller size
grain) how??? [smaller grain size exhibit more formability
than larger grain size]
2. Because of its effect on surface appearance of the formed
part
 The coarser the grain, the rougher the surface appears
(orange peel)
 An ASTM grain size of No. 7 is typically preferred for general
sheet-metal forming
Forming Processes

Residual stresses
Residual stresses can develop in sheet-metal parts
because of the nonuniform deformation that the
sheet undergoes during forming . (Residual stresses
are stresses that remain within a part after it has
been deformed plastically non uniformly and all
external forces have been removed).
Disturbing the equilibrium of residual stresses, such
as by bending or stretching of it, the part may
distort.
We should remove residual stresses prior to
forming.
Forming Processes

Springback
• Because they are generally thin and are subjected to
relatively small strain during forming, sheet-metal parts
are likely to experience considerable springback
• Because all materials have a finite modulus of elasticity,
plastic deformation is always followed by elastic recovery
upon removal of the load. In bending, this recovery is
known as springback.
• This effect is particularly significant in bending and other
forming operations where the bend radius-to-sheet-
thickness ratio is high, such as in automotive body parts.
Forming Processes

Wrinkling
In the sheet metal forming the metal is typically subjected
to tensile stresses, the method of forming may be that
compressive stresses are developed in the plane of the
sheet.
An example in sheet metal forming is the wrinkling of the
flange in deep drawing because of the circumferential
compressive stresses that develop in the flange.
Other terms used to describe this phenomena are folding
and collapsing.
Forming Processes

Wrinkling
• The tendency for wrinkling in sheet metals increases
with:
1. Decreasing thickness
2. Nonuniformty of the thickness of the sheet
3. Increasing length or surface area of the sheet that is
not constrained or supported.
4. Lubricants that are trapped or are not distributed
evenly at the die-sheet metal interfaces can also
contribute to the initiation of wrinkling
Forming Processes

Coating sheet
• Sheet metals, especially steel, are precoated with a
variety of the organic coating, films and laminate.
• Coatings are used primarily for appearance as well
as for corrosion resistance.
• Coatings are applied at thicknesses generally range
from 0.0025 to 0.2mm.
• Coatings are available with wide range of properties,
such as flexibility, durability, color, and gloss,
resistance to abrasion and chemicals.
• Zinc is used extensively as a coating on sheet steel
(galvanized steel by hot dipping) to protect it from
corrosion, particularly in the automotive industry
Forming Processes

• High strength
• Good dimensional accuracy
• Good surface finish
• Relatively low cost
Advantages of Sheet Metal Parts
Sheet Metal Processes
1. Cutting
– Shearing to separate large sheets; or cut part perimeters or
make holes in sheets
2. Bending
– Straining sheet around a straight axis
3. Drawing
– Forming of sheet into convex or concave shapes

Cutting Operations
Shearing
side view front view
Typically used to cut large
sheets into smaller sections
for subsequent operations

shearing
• The shearing process involves cutting sheet metal, as well
as plates, bars, and tubing of various cross section, into
individual pieces by subjecting it to shear stress, typically
using a punch and a die, similar to action of paper punch.
• The punch and die may be of any shape, such as circular
or straight blades, similar to a pair of scissors.
• Important variables in the shearing process are:
1. The punch force.
2. The speed of the punch
3. The edge condition of the sheet.
4. The punch and die materials.
5. The punch-die clearance.
6. Lubrication.

Shearing (Cutting)
punch begins to push
into work, causing
plastic deformation
punch penetrates
into work causing a
smooth cut surface
fracture is initiated at
both cutting edges
just before the punch
contacts work
C, is the clearance

The overall features of a typical sheared edge for the
two sheared surfaces are illustrated
Shearing (Cutting)
Note that the edges are neither smooth nor
perpendicular to the plane of sheet.

The clearance, c, is the major parameter that determine
the shape and quality of the shear edges
Shearing (Cutting)

• As the clearance increases, the sheared edges become rougher and
the deformation zone becomes larger. The material is pulled into
clearance area into the die rather than be sheared, and the sheared
edges become more and more round. In fact, if the clearance is too
large, the sheet metal is bent and thus subjected to tensile stresses
Effect of the clearance, c, between punch and die on the deformation zone in shearing. As
the clearance increases, the material tends to be pulled into the die rather than be sheared
Shearing process

 As clearance decreases, the deformation zone is subjected to high
shear strain. The width of this zone depends on the rate of
shearing, that is, the punch speed.
 With increasing punch speed, the heat generated by plastic
deformation is confined to smaller zone, and consequently the
sheared surface is smoother
Shearing process

 In practices, clearances usually range between 2 and 8% of the sheet
thickness.
 In general, clearances are smaller for softer materials, and they are
higher as the sheet thickness increases.
 As indicated in the figure below, the sheared edges can undergo
sever cold working, which, in turn, can adversely affect the
formability of the sheet during subsequent operation.
Shearing process

• Observation of the shearing mechanism reveals that shearing
usually starts with the formation of cracks on both the top and
bottom edges of the sheet (at A and B). These crack eventually
meet, resulting in complete separation and a rough fracture surface
Shearing process

 The smooth, shiny, and burnished surfaces are from the contact and
rubbing of the sheared edges against the punch and the die as shown.
1. The burnished surface is in the lower region, because this region is the
section that rubs against the die wall.
2. The burnished surfaces (on the sheet it self ) is on the upper region and
results from rubbing against the punch.
 The ratio of the burnished-to-rough areas on the sheared edge increases
with increasing ductility of the sheet metal and decreasing with increasing
sheet thickness and clearance.
Shearing process rough and smooth, shiny
edges

 Note also the formation of burr. Burr height increases with:
1. Increasing clearance
2. Increasing ductility
3. Tooling with dull edges is also a major factor in burr formation.
Shearing process

Small clearance
– ………………
– ………………….
– …………………….
Large clearance
– ………………………
– ……………………..
– ………………………
As clearance increases,
the material tends to be
pulled into the die rather
than be sheared.
More punch and die wear
Higher cutting force
Better edges
Rougher edges
Larger deformation zone
Larger burrs
Clearance:
The clearance determines the shape and quality of the sheared edge, so
the control of the clearance is important!
Burr:
Burr length increases with clearance & ductility of metal.
Tools with dull edges create burrs.
Shearing process

Clearance in Sheet Metal Cutting
• Recommended clearance can be calculated by:
c = at
where c = clearance; a = clearance allowance; and t = stock thickness.
• Allowance a is determined according to type of metal.
Clearance Allowance for Three Metal Groups a
1100S and 5052S aluminum alloys, all tempers 0.045
2024ST and 6061ST aluminum alloys; brass, soft cold rolled steel,
soft stainless steel
0.060
Cold rolled steel, half hard; stainless steel, half hard and full hard 0.075
Low “c” for soft materials
High “c” for hard materials

Punch force
• An approximate empirical formula for estimating the maximum
punch force, is given buy:
• UTS: is the ultimate tensile strength of sheet metal.
• t : is the thickness.
• L : is the total length of the sheared edge. For round hole of
diameter D, L=πD
tLUTSF )(7.0max

F=S*t*L
Where:
S= Shear strength
t= Sheet thickness
L= Length of cutting edge
 If shear strength is not known, cutting force can be estimated as:

Example
• Estimate the force required in punching a 25
mm diameter hole through a 1.8 mm thick
5052 –O aluminum sheet at room
temperature. UTS is 190 Mpa.
• Solution : Force = 1.8793 * 10^6 N

Various operations that are based on the shearing process.
First it should be noted that in punching, the slug is
discarded (the sheared slug is scrap, or may be used for
some other purpose).
In blanking, the slug is the part it self, and the rest is scrap.
Shearing operations
Slug

1. die cutting
• Die cutting typically consists of various operations where the
parts produced have various uses, particularly in their
assembly with other components of a product
Shearing operations
• The following processes are common shearing operation

1. Die cutting
a) Perforating : that is punching a number of holes in the
sheet metal
b) Parting : shearing the sheet into two or more pieces,
usually when the adjacent blanks do not have a matching
contour
c) Notching : removing pieces or various shape from the
edges.
d) Slitting and lancing : leaving a tab on the sheet without
removing any material
Shearing operations

2. fine blanking
 Very smooth and square edges can be produced by fine blanking.
 The basic die design involves a V-shaped stringer that locks the sheet
tightly in place and prevents the type of distortion of the material
(Prevents distortion at sheared edges).
 Fine blanking involves clearances on the order of 1% of the sheet
thickness, as compared with as much as 8% in ordinary shearing
operations. Very tight (<1%) clearances), Therefore tight tolerances
.possible• Therefore tight tolerances possible
Shearing operations

2. fine blanking
 The thickness of the sheet may typically range from 0.5 to 13 mm
 A suitable sheet hardness is typically in the range of 50-90 HRB
Shearing operations

3. slitting
• Slitting is a shearing operation carried out with a pair of circular
blades, similar to those on a can opener. The blades follow either
a straight line or curved path.
• There are two types of slitting equipment:
a) In the driven type, the blades are powered
b) In the pull-through type, the strip is pulled through idling blades
Shearing operations

Slitting operations
Straight slitting is commonly used in cutting wide sheet, as delivered
by rolling mill, into narrower strips for further processing into
individual parts.

4. Nibbling
• In this operation, a machine called a nibbler moves a straight punch
up and down rapidly into a die. The sheet is fed through the punch-
die gap, making a number of overlapping holes.
• An intricate notches can thus produced using standard punches.
• The process is economical for small production runs since no
especial dies are required.
Shearing operations

Scrap in shearing
• The a mount of scrap produced in shearing
operation can be significantly, being as high as 30%
of the original sheet for large pieces.
• It is an important factor in manufacturing costs
• Scrap can be reduced significantly by proper
arrangement of shapes on the sheet to be cut,
called layout and nesting.
• Computer-aided design techniques are now
available for minimizing scrap.

 Because the formability of a sheared part can be directly
influenced by the quality of its sheared edges, clearance control is
important.
 In practice, clearances usually ranged between 2 and 8%.
 Generally the thicker the sheet, the larger is the clearance, to as
much as 10%, however, the smaller the clearance, the better is the
quality of the sheared edge.
 In a process called shaving, the extra material from a rough
sheared edge is trimmed by cutting
Shearing dies

Schematic illustration of shaving on a sheared edge.
(a) Shaving a sheared edge. (b) Shearing and shaving combined in one
punch stroke.
Shearing dies

Punch and dies shape
 The area being sheared at any instant can be controlled by
beveling the punch and die surfaces
 The beveled geometry is particularly
suitable for shearing thick sheets because
1. it reduces the total shearing forces and
also
2. reduces the noise level during punching

 Some parts requiring multiple operations such as punching and
blanking are made at high production rates using progressive dies.
 In which the coil strip is fed through the dies, and a different
operation is performed at the same station with each stroke of a
series of punches
Progressive dies

Miscellaneous methods of
cutting sheet metal
1. The sheet or plate may be cut with a band saw uses
a blade consisting of a continuous band of metal with teeth along
one edge to cut various workpieces.
2. Oxyfuel-gas (flame) cutting : may be employed particularly for thick
plates, as widely used in shipping and heavy-construction industries
(it can cut thicknesses from 0.5mm to 2,500mm).
3. Friction sawing : involves the use of blade, that rubs against the
sheet or plate at high surface speed. ( a type of band sawing that
uses high speed to generate heat to soften the metal in front of the
blade)
4. Water-jet cutting : are effective operations on sheet metals as well
as on nonmetallic materials
5. Laser beam cutting : is now widely used, with computer controlled
equipment, for high productivity, cons

Oxyfuel-gas (flame) cutting
• A mixture of oxygen and the fuel gas is
used to preheat the metal to its
'ignition' temperature which, for steel,
is 700°C - 900°C (bright red heat) but
well below its melting point.
• A jet of pure oxygen is then directed
into the preheated area instigating a
vigorous exothermic chemical reaction
between the oxygen and the metal to
form iron oxide or slag.
• The oxygen jet blows away the slag
enabling the jet to pierce through the
material and continue to cut through
the material.

Friction sawing
Friction sawing :a type of band sawing that uses high speed to
generate heat to soften the metal in front of the blade)

Water-jet cutting
• Water jet cutting: is an industrial tool capable of
cutting a wide variety of materials using a very high-
pressure jet of water, or a mixture of water and
an abrasive substance. The term abrasivejet refers
specifically to the use of a mixture of water and abrasive
to cut hard materials such as metal or granite, while the
terms pure waterjet and water-only cutting refer to
waterjet cutting without the use of added abrasives,
often used for softer materials such as wood or rubber.
• It is the preferred method when the materials being cut
are sensitive to the high temperatures generated by
other methods.
• Most high-pressure pumps at this time, though,
operated around 500–800 psi (3–6 MPa), some
reaching 1600 psi (11 MPa).

Laser beam cutting
• The laser beam is focused for cutting. All
its power is bundled onto one point,
usually with a diameter of less that half a
millimeter. Where the focused beam
strikes the workpiece, the metal
immediately begins to melt. It even
partly burns or evaporates.
• The highly focused, high-density energy
melts and evaporates small portions of
the workpiece in a controlled manner.
 Laser converts electrical energy into a
highly coherent light beam with the
property of :
 Monochromatic (single wave length)
This property allow laser light to be focused, using optical lenses, onto a very small
spot with resulting high power densities.
Reflectivity and thermal conductivity of the workpiece are important factors in LBC.
The lower these quantities, the more efficient is the process

In sheet metal forming operations, the blank is
typically supplied in one piece, usually cut from a
large sheet, and has a uniform thickness.
An important technology in sheet-metal forming,
particularly in the automotive industry, involves laser
butt welding of two or more pieces of sheet of
different thicknesses and shapes (Tailor -welded
blanks, or TWB).
The welded sheet is subsequently formed into a final
shape buy using any of the processes of sheet metal
forming.
Tailor – welded blanks: Laser Welding

• Advantages:
1. Productivity is increased.
2. The need for subsequent spot welding of the product is
reduced or eliminated
3. Scrap is reduced
4. Dimensional control is improved
• It should be noted,
that because the
sheet thicknesses
involved are small,
proper alignment
of the sheet prior
to welding is
essential
Tailor – welded blanks: Laser Welding

• One of the most common metal working is
bending, a process that is used not only to form
parts such as flanges, and corrugations, but also
to impart stiffness (by increasing the moment of
inertia). Example a flat strip of metal is much less
rigid than one is formed into a V cross section
Bending of sheet and plate

 Straining sheet metal around a straight axis to take a permanent
bend.
Bending
Bending of sheet metal
Metal on inside of neutral plane is compressed, while metal on
outside of neutral plane is stretched.
A + A’ = 180˚

• Bend allowance : is the length of the neutral axis in the bend
area and is used to determine the blank length for a bent part.
It depends on
1. Bend radius
2. Bend angle
• an approximate formula for
the bend allowance. Lb, is given
α is the bend angle in radians,
R is the bend radius,
k is a constant, values usually range from
0.33 for R<2t to 0.5 for R>2t
t is the sheet thickness.
Bending of sheet and plate
)( ktRLb


 The outer fibers of a part being bent
are subjected tension, and the inner
fibers to compression
 Theoretically, Engineering Strains at
the outer and inner fibers are equal in
magnitude and they are:
 Due to shifting of the neutral axis
toward the inner surfaces, the length
of bend L, is smaller in the outer region
than in the inner region ( bending a
rectangular eraser).
 Consequently, the outer and inner
strains are different, with the
differences increasing with decreasing
R/t ratio. (decreasing bend radius)
Minimum bend radius
1)/2(
1


tR
ee io

• As the ratio R/t decreases, the tensile strain at the outer fiber
increases, and the material may crack after a certain strain is
reached.
• The bend radius, R, at which crack appears on the outer surface
of the bend is called the minimum bend radius.
• The minimum bend radius to which a part can be bent safely is
normally expressed in terms of its thickness, such as 2t, 3t, 4t.
• For example, a bend radius of 3t indicates that the smallest
radius to which the sheet can be bent without cracking is three
times its thickness
1)/2(
1


tR
ee io
Minimum bend radius

The minimum bend radii for various materials have been determined
experimentally; some typical results are give in the table below
Minimum Bend Radius for Various
Materials at Room Temperature

 Studies have been conducted to establish a relationship between the
minimum R/t ratio and a particular mechanical property of the material.
 Based on the assumption that : The true strain at cracking on
the outer fiber in bending is equal to the true strain at fracture,
εf , of the material in a simple tension test.
)
100
100
ln()ln(
rA
A
f
o
f


 Where r is the percent reduction of area of
the sheet in a tension test.
)
)2/(
ln()
1)/2(
1
1ln()1ln(
tR
tR
tR
eoo





T
 the true strain at fracture, εf , of the material in a simple tension test.
Minimum bend radius
 The true strain at cracking on the outer fiber in bending
 By equating the above expressions Minimum R/t= (50/r) -1

Minimum Bend Radius and
Ductility
• There is a relationship between
R/t and ductility, expressed as the
tensile reduction in area, r
• Not that as R/t ratio approaches
zero (complete bendability; that
is the material can be folded over
itself, like apiece of paper) at a
tensile reduction of area of 50
• The lower the ductility (smaller
reduction in area) the larger the
R/t [large bend of radius]
Minimum R/t= (50/r) -1

Factor affecting bendability
 Bendability depends on the edge condition of the sheet being bent.
1. Rough edges, because rough edges have various locations of stress
concentration. Bendability decreases as edges roughness increases.
 Removal of the rough edges by shaving, or machining, greatly improves
the resistance to edge cracking during bending
2. The amount of cold working the edges undergo during shearing is
another important factor. Removal of the cold worked regions such as
by annealing, greatly improves the resistance to edge cracking during
bending.

3. Another important factor in edge cracking is the amount
and shape of inclusions in the sheet metal. Inclusions in the
form of stringers are more detrimental than globular-
shaped inclusions; consequently, anisotropy of the sheet is
also important in bendability, cold rolling of the sheets
results in anisotropy because of the alignment of the
impurities, inclusions, and voids (mechanical fibering).

Stringers inclusions globular-shaped inclusions.

Forming by Bending
• Advantages
– Easy to perform
– Simple, low cost tooling
– Fairly precise
• Disadvantages
– Limited in the shapes it can produce
– Spring back difficult to estimate
– Some material difficult to bend without tearing
or necking

• Because all materials have a
finite modulus of elasticity,
plastic deformation is always
followed by elastic recovery
upon removal of the load. In
bending, this recovery is known
as springback.
Springback

Springback
a) The final bend radius is larger than radius to which it is bent.
b) The final bend angle after springback is smaller than the angle to
which it is bent
• This phenomena can easily be observed and verified by bending a
piece of wire or short strip metal.
• This phenomena can easily
be observed and verified by
bending a piece of wire.
• Note that springback will
not occur only in bending
flat sheets or plate, but also
in bending bars and rods

 Where Ri and Rf
are the initial and
final bend radii
Springback
A quantity characterizing springback is the springback factor , Ks:
 Because the bend allowance is the same before and after bending, the
bend allowance is as follow for pure bending:
ffii
t
R
t
R  )
2
()
2
( Bend allowance =
 From this relation Ks is defined as :
1)/2(
1)/2(



tR
tR
K
f
i
i
f
s


 From the above expression that Ks depend on the ratio R/t
 The condition of Ks =1 indicates that there is no springback,
and ks =0 indicates that there is a complete elastic recovery.
 For the case
that k=0.5

The amount of elastic recovery
depends on the stress level and
the modulus of elasticity, E, of
the material.
Thus, elastic recovery increases
with the stress level and with
decreasing elastic modulus
 based on this observation an
approximate formula has been
developed to estimate springback
as:
Springback
1)(3)(4 3

Et
YR
Et
YR
R
R ii
f
i
Y is the yield stress of the material.

1. Overbending : can be achieved by rotary
bending technique in which the upper die has
a cylindrical rockers and is free to rotate.
Compensation for Springback

2. Coining : is a accomplished by subjecting a
high localized compressive stresses between
the tip of the punch and the die surface.

3. Because springback decreases as yield stress
decreases. Bending at elevated temperatures
will decrease the yield stress of the material.
Decreasing the yield stress of the material
decreases the springback. (recall the effect of
elevated temperature on the yield point)

4. Stretch bending : in which the part is subjected
to tension while being bent, consequently
decreasing springback

 Bending force can be estimated by assuming that the process is that
of the simple bending of a rectangular beam.
 Thus bending force is a function of the material’s strength, length and
thickness of the part (L and t). Excluding friction, the general
expression for the maximum bending force, Fmax, is
Force in bending
 Where the factor k include various factors, including friction:
 K values for V-dies ( 1.2 - 1.33 ), for wiping dies ( 0.3 - 0.34 )
UTS: the ultimate tensile stress of the material.
W: part width in direction of bend axis
L: length of the part.
t: thickness of the part

Common bending operations
1.Press-brake forming : sheet metal or plate can be bent with simple
fixtures, using a press.
• Parts that are long (7m or more) and relatively narrow are usually bent
in a press brake.
• This machine uses long dies in a mechanical or hydraulic press is
suitable for small production runs

2. beading : in this operation, the edge of the sheet is bent
into cavity of a die.
Beading improves
1. The appearance of the part and
2. Eliminates exposed sharp edges, which may be a safety
hazard.
3. Also the bead impart stiffness to the part by virtue of
the higher moment of inertia of the edges
a) Bead forming with a single die. (b)-(d) Bead forming with two dies in a press brake.

3. Flanging : is a process of
bending the edges of the
sheet metals, typically to
90o, for the purpose of :
1. imparting stiffness,
2. appearance,
3. or for assembly with
other component

4. Hemming.
• In the hemming process (also
called flattening), the edge of
the sheet is folded over itself
• Advantages:
1. Hemming increase the
stiffness of the part
2. Improves its appearance
3. Eliminate sharp edges
5. Seaming.
• Involves joining two edges of
sheet metal pieces by hemming

Tube bending
• The oldest and simplest method of bending a tube or a pipe
is to pack the inside with loose particles (typically sand) and
bend it in a suitable fixture.
• The packing prevents the tube from buckling inward.
• Tubes also can be bulged with various flexible internal
mandrels.

Stretch Forming
Sheet metal is stretched and simultaneously bent to achieve shape change
(1) start of process
(2) die is pressed into the work with
force Fdie, causing it to be stretched and
bent. F = stretching force
 The shape is produced entirely by tensile stretching so the limiting strain is
that at necking.
 Sheet is gripped by two jaws at its edges.
 Form block is slowly raised by the ram to deform sheet above its yield point.
 The sheet is strained plastically to the required final shape
 Controlling the mount of stretching is important to avoid tearing.

 Stretch forming
• Forming by using tensile forces to stretch the material over a tool or form
block.
• In this operation, the sheet metal is clamped around its edges and
stretched over a die.
• In most stretch-forming operations, the blank is clamped along its
narrower edges and stretched longwise.
Loading
Pre-Stretching
Wrapping
Release
Miscellaneous forming process

• Used most extensively in the aircraft industry to
produce parts of large radius of curvature.
(normally for uniform cross section). Also for
automobile door panels.
• Required materials with appreciable ductility,
Aluminum skins for Boeing 767 and 757 fuselages,
for example, are made by stretch forming.
Stretch forming

Stretch Forming: equipment
Stretch Forming with Reconfigurable Tool

Stretch Forming: Products
Cowlings
Courtesy
of:www.evanscomposites.com

Force Required in Stretch Forming
fLtYF 
where
F = stretching force
L = length of sheet in direction perpendicular to
stretching
t = instantaneous stock thickness
Yf = flow stress of work metal
Calculate the force required to stretch form a wing span from a sheet of
2219 aluminum having a cross-sectional area of 13x305 mm, a strength
coefficient strength of 250 MPa and strain hardening exponent 0.3.
Example

 Bulging
 The basic process of bulging
involves placing a tubular part in a
split female die and expanding it
with the rubber or polyurethane
plug.
 The punch is the retracted, the
plug returns to its original shape,
and the part is removed by
opening the split die.
 Typical product made by this
process includes: bellows,coffee
and water pitchers.
 Polyurethane plugs are very
resistant to abrasive, sharp edges
and wear Bulged tube

Manufacturing of Bellows
 Bulging

 This process consists of forming a number of shallow shapes
(numbers, letters) or designs on sheet metal.
 The part may be embossed with male and female dies
 The female die is replaced with a rubber pad.
 The pressure is applied is typically on the order of 10 Mpa
 The outer surface of the sheet is protected from damage or scratches
because it is not in contact with hard metal surface during forming
 Embossing
Figure 16.38 Examples of the bending and the embossing of sheet metal with a metal punch
and with a flexible pad serving as the female die. Source:

 In this process, one of the dies in a die set is made of flexible
material such as rubber membrane or polyurethane
 In hydroforming, or fluid forming process, the pressure applied over
a flexible membrane with a maximum pressure reaching 100 Mpa.
 Deeper draws are obtained than in conventional deep drawing, the
reason being that the pressure around the rubber membrane forces
the part being formed against the punch
 Hydroforming (fluid forming process)

 Advantages:
1. The capability to form complex shapes.
2. Flexibility and ease of operation.
3. The avoidance of damage to the surfaces of the sheet.
4. Low die wear.
5. Low tooling cost.
Hydroforming (fluid forming process)

Spinning involves the forming of axisymmetric
parts over a rotating mandrel, using rigid tools
or rollers. The equipment used is similar to lath
with various special features
Three types of spinning:
1. Conventional spinning
2. Shear spinning
3. Tube spinning
 spinning

• Spinnability: the maximum reduction in
thickness of the material to which a part can
be subjected by spinning without fracture.
Spinning

Conventional spinning
 In conventional spinning, a circular blank of a flat sheet metal is held
against a rotating mandrel while a rigid tool deforms and shapes it
over the mandrel.
 The tool may be actuated either manually or by a hydraulic
mechanism.
 The operation involves a sequences of passes and requires
considerable skill.
 The process is suitable for conical and curvilinear shapes, which
would otherwise be difficult to form by other methods.
 Most spinning is performed at room temperature
 For thick parts or metals with low ductility or high strength require
spinning at elevated temperature.
 Part diameter may range up to 6 m in diameter

 In shear spinning, also called power spinning or flow turning, an
axisymmetric conical or curvilinear shape is generated in a manner
whereby the diameter of the parts remains constant.
 Parts typically made by this process include rocket-motor casings
and missile nose cones.
 The operation is completed in a relatively short time
 If the operation is carried out at room temperature, the spun part has
relatively a higher yield strength than original material, but lower
ductility.
 Parts typically up to about 3 m in diameter can be spun to close
dimensional tolerances.
Shear spinning

Tube spinning
In tube spinning, tubes or pipes are reduced in thickness
by spinning them on cylindrical mandrels, using rollers.
The operation may be carried out externally or internally.
The reduction in wall thickness results in a longer tube,
because of volume constancy.
Thickness is
reduced

HERF describes sheet-metal forming process
that use chemical, electrical, or magnetic
sources of energy.
They are called high-energy-rate processes
because of the high amount of energy is
released in a very short time.
 High-Energy-Rate Forming (HERF)
 Processes to form metals using large
amounts of energy over a very short time.

(1) Explosive Forming
 Use of explosive charge to form sheet (or plate) metal into a die
cavity
 Explosive charge causes a shock wave whose energy is transmitted
to force part into cavity.
 Applications: large parts, typical of aerospace industry.
 High-Energy-Rate Forming (HERF
setup explosive is
detonated
shock wave
forms part

 The rapid conversion of the explosive into gas generates a shock wave.
 The pressure of this wave is sufficiently high to force the metal into die cavity
1. In this process, the sheet is clamped over a die
2. The air in the die is evacuated
3. Then the whole assembly is lowered into a tank filled with water
4. An explosive charge is the placed at a certain distance from the
sheet surface, and detonated
setup
explosive is
detonated
shock wave
forms part

Detonation speeds are typically 6700m/s, and the
speed at which the sheet metal is formed is to be
estimated on the order of 30 to 200m/s.
Safety is an important aspect in explosive
forming.
Suitable for low-quantity production runs of lager
parts (steel plates 25 mm thick and 3.6 m in
diameter have been formed by this method)

Electro Hydraulic Forming
“Electric Discharge forming”
 Electrical energy is accumulated in
large capacitors and then released to
the electrodes.
 The source of energy in this process
is the spark from two electrodes.
 The rapid discharge of this energy
through the electrodes generates a
shock wave; which is strong enough
to form the part.
 This process is Similar to explosive
forming except:
1. That it utilizes a lower level of
energy, therefore, its safer.
2. And is used for smaller workpiece
(2) Electro Hydraulic Forming:

 The energy stored in a capacitor
bank is discharged rapidly through
a magnetic coil, produces two
magnetic fields, which in turn
produces forces.
 The forces produced by the two
magnetic fields oppose each other;
thus there is a repelling force
between the coil and the tube.
 These high forces generated
collapse the tube over the inner
side of the die - Presently the most widely used HERF process.
- Applications: tubular parts (i.e. swaging)
(3) Electromagnetic Forming:
Electromagnetic Forming
“Magnetic Pulse forming”

 Superplasticity
Superplasticity:
 Conventional metals elongate 10 to 30%.
 Ultra-fine grained materials reach 100-3000%.
 Used to form complex parts at high temperature.
 Large deformations possible, something that would
normally fracture parts, but large deformation + low
strain rate = long time to perform deformation.

 The superplastic behavior of some very
fine grained alloys ( 10-15µm), where
very large elongations (up to 2000%)
are obtained at certain temperatures
and low strain rates
 Superplasticity
Superplastic deformation of an Al alloy
These alloys are : Zinc alloys, Titanium alloys (Ti-Al-V alloys), Aluminum alloys (Al-
Zn-Mg and Al-Cu), Inconel 718 (Ni-Cr alloy), and stainless steels (Fe-Cr-Ni alloy ) can be
made superplastic.
 These alloys can be formed into
complex shapes by employing
traditional metal working or polymer-
processing techniques
 Superplasticity is the ability of a material to withstand very large amounts
of uniform elongation without the occurrence of necking prior to
fracture.

Superplasticity
 Important elements in superplastic properties to attain such deformation:
1. Low strain rate (~3*10-4/s) (so it is not
practical).
2. High temperature (above 0.4Tm).
3. Small grain size (less than 20μm for metallic
alloys).
 In the past, Superplastic forming was available at relatively low strain
rates, typically about 1% per min. At this strain rate, about 1 hr is
needed to form an advanced structural component; too long to be
economically effective.
 Superplasticity at higher strain rates, however, can be expected to
stimulate broad commercial interest in superplastic forming.
 Example: a strain rate higher than 100% per minute is considered
economically practical. Such a strain rate would allow the forming of
relatively complex structures in less than three minutes, including
set-up time.
where
C = strength constant
m = strain-rate sensitivity
exponent (0.3-0.85 for
superplastic materials).
m
C 

Superplastic Forming Process
 The SPF process uses
superplastic materials to form
very complex sheet metal parts.
 Dies are heated in a press
(900°C for
titanium alloys) and inert gas
pressure is applied at a controlled
rate.
 SPF can produce parts that are
impossible to form using
conventional methods.

 Benefits...
 The high ductility and relatively low strength of superplastic alloys
present the following advantages:
1. Lower Tooling cost:
 because of low strength of the material at forming temperatures, and
hence lower strength of tooling
2. Producing complex shape :
 the ability to form complex shape in one piece, with fine detail, close
dimensional tolerance, and eliminating secondary operation.
3. Material saving ;
 because of the good formability of superplastic materials, thus, no
waste in the material.
4. Little or no residual stresses in the formed parts

A superplastically formed
Al-Li alloy component
 Elimination of unnecessary joints, fasteners, welding or
adhesives.
 Reduction of subsequent machining.
 Minimization of materials waste.
 An integrated aluminum structure, for example, traditionally
manufactured by welding four pieces of metal, can be
manufactured in a single operation through superplastic forming.
Courtesy of www.accudyneeng.com
An Al-alloy component

Superplastic Forming with Diffusion Bonding
 An important aspect of superplastic forming
is the ability to fabricate sheet-metal
structures by combining diffusion bonding.
 SPF/DB parts are produced by joining
several sheets in a specific pattern and then
superplastically expanding the sheets to
produce an integrally-stiffened structure
[Typical structures in which flat sheets are
diffusion bonded and then formed into
desired structures]
 These structures are relatively thin and high
stiffness-to-weight ratios; consequently, they
are particularly important in aerospace
applications
.
Courtesy of www.spfintl.com
A Ti-alloy aircraft

Superplastic Forming with Diffusion Bonding

Deep drawing first developed in
1700s, is an important sheet-
metal forming process.
Typical parts produced by this
method include beverage cans,
pots and pans, containers of all
shapes and sizes, and
automobile body panels.
The process, is generally called
deep drawing (meaning forms
deep part), the basic operation
also produces parts with
moderate depths.
Deep drawing

The basic parameters in deep
drawing a cylindrical cup are:
A circular sheet blank with a
diameter Do and thickness to
is placed over a die opening
with a corner radius Rd. the
blank is held in the place with
blankholder under a certain
force. A punch with a
diameter Dp and a corner
radius Rp moves downward
and pushes the blank into die
cavity, thus forming a cup.
Deep drawing

Steps in Deep Drawing:
1) Initial contact
2) Bending
3) Straightening
4) Friction and compression
5) Final shape
Deep Drawing

• The significant variables in deep drawing:
1. Properties of the sheet metal
2. Ratio of the blank diameter to the punch diameter
3. Sheet thickness
4. Clearance between the punch and the die
5. Corner radii of the punch and die
6. Friction at the punch, die, and workpiece interfaces
7. Blankholder force
8. Speed of the punch
Deep drawing

Cup Bottom:
- Near Zero Strain
- No Friction
Cup Flange:
- Compression and
- Friction Zone
Cup Wall:
- Fracture Zone*
- No Friction
Die Radius:
- Bending and
- Friction Zone
Punch Radius:
- Bending and
- Friction Zone
Deep Drawing - Variables
*Failure may result from
thinning of the cup wall.
Deformation of an
element in the flange
Deformation of an
element in the
wall

Deep Drawing - Variables and Defects
Die radius too small Punch radius too small
During drawing, when the blank
moves into the die, compressive
circumferential stresses are induced in
the flange.
– This causes flange to wrinkle.
- Using beads to control contraction in
the flange and the movement of the
material into die cavity
– Eg: try forcing a circular sheet of paper
into a drinking glass.
Effect of die and punch radii on deep drawing:

 At an intermediate stage during the deep drawing operation, the
work piece is subjected to state of stress indicated in the figure
below
• On element A (flange) in the blank, the radial tensile
stresses is due to the blank being pulled into the cavity.
• The compressive stresses is due to the pressure applied
by the blank holder.
Deep Drawing - Mechanism -Variables

 With a free body diagram of the blank along its diameter, it can be
shown that the radial tensile stresses lead to compressive hoop
stresses on element A (flange). Under this state of stress, element A
(flange) contracts in the compressive hoop stress and elongates in
the radial direction.
 It should be noted that it is the compressive hoop stresses in the
flange that tend to cause the flange to wrinkle during drawing, thus
it is necessary to provide a suitable balnkholder force
Deep Drawing - Mechanism -Variables

 The punch transmits the drawing force, F, through the walls of the
cup and to the flange that is being drawing into die cavity.
 The cup wall, which is already formed, is subjected principally to
longitudinal tensile stresses as shown in the figure.
 The tensile hoop stress on the element shown in the figure is caused
by the cup being held tightly on the punch because of its
contraction under the longitudinal tensile stresses in the cup wall
(cup of coffee and plastic bag)
Deep Drawing - Variables and Defects
 And because the cup is constrained by the
rigid punch, the element shown in the
figure dose not undergo any width
change, but elongates in the longitudinal
direction.

 If the thickness of the sheet as it enters the die cavity is more than
the clearance between the punch and die, it has to be reduced by
a deformation called ironing.
 By controlling the clearance, C, ironing produce a cup with a
constant wall thickness.
 Because of the volume constancy, an ironed cup will be longer
than a cup produced with a large clearance.
 Thus, ironing can correct earing that occurs in deep drawing.
Ironing
Ironing to achieve a more uniform wall thickness in a drawn cylindrical cup.

Shapes other than Cylindrical Cups
• Square or rectangular boxes
(as in sinks)
• Stepped cups
• Cones
• Cups with spherical rather
than flat bases
• Irregular curved forms (as
in automobile body panels)
Each of these shapes
presents its own
unique technical
problems in drawing
Very important commercial process.

Methods to reduce diameter of drawn cups:
• Redrawing: For parts with high DR, they require more than one drawing.
• Reverse Redrawing: Metal is bent in opposite direction.
Reverse Redrawing
Redrawing
Methods for Reducing the Diameter of Drawn Cups
p
b
D
D
DR 

Methods for Reducing the Diameter of Drawn Cups
Conventional Redrawing

Steps in
Manufacturing an
Aluminum Can

-Produces lueder’s bands (also called
stretch-strain marks).
-Exhibited by low carbon steels.
-These marks can be eliminated by
reducing thickness of sheet from 0.5%
to 1.5 % by cold rolling process.
Lueder’s bands in a low-carbon steel sheet:Yield-point elongation in a sheet-
metal specimen.
Deep Drawing - Defects
‘Orange peel’-grainy surface appearance.
-Due to overly large grains or uneven flow.
-Coarser grains, the rougher the appearance.
-ASTM grain size of No. 7 or finer is
preferred for sheet metal forming.

Defects in Drawing
(a) Wrinkling in the flange occurs due to compressive buckling in the
circumferential direction (blank holding force should be sufficient to prevent
buckling from occurring).
(b) Wrinkling in the wall takes place when a wrinkled flange is drawn into the cup
or if the clearance is very large, resulting in a large suspended (unsupported)
region.
(c) Tearing occurs because of high tensile stresses that cause thinning and failure
of the metal in the cup wall. Tearing can also occur in a drawing process if the die
has a sharp corner radius.
(d) Earring occurs when the material is anisotropic, i.e. has varying properties in
different directions.
(e) Surface scratches can be seen on the drawn part if the punch and die are not
smooth or if the lubrication of the process is poor.

Analysis of DrawingMosteasilydefinedforcylindricalshape:
Guidelines to Assess Feasibility (3):
(1) Drawing ratio:
p
b
D
D
DR  feasible if DR < 2
(2) Reduction
b
pb
D
DD
r

 feasible if r < 0.5
Draw Force:
  







 7.0
p
b
p
D
D
TStDF 
(3) Thickness-to-diameter ratio = t/Db
As t/Db decreases, tendency for wrinkling increases
Desirable for t/Db ratio
to be greater than 1%

Deep drawability (limiting drawing ratio)
 An important parameter in drawing is the limiting drawing ratio
(LDR), defined as, the maximum ratio of the blank diameter to
punch diameter that the blank can be drawn without failure .
 Deep Drawability is expressed by the limiting drawing ratio (LDR)
where
𝐷 𝑜
𝐷 𝑝
LDR = = Maximum blank diameter /punch diameter
 By observing the movement of the material into the die cavity, we
note that the material must be capable of undergoing a reduction
in width (being reduced in diameter), yet it should resist thinning
under longitudinal tensile stresses in the cup wall
 Failure generally occur by thinning of the cup wall under high
longitudinal tensile stresses

Anisotropy
Metal sheets are produced by rolling, the properties in the rolling
direction, across the sheet width and through the sheet thickness are
different, therefore the sheet metal is anisotropic, that is the properties
are different in different directions.
Important in Deep Drawing.
Normal Anisotropy (R): Ratio to compare strengths in the plane and
thickness direction (or ratio of reducing in the width & thinning in
thickness direction).[ tensile test]
Courtesy of J. Beddoes, 1999
The sheet is rolled and test specimen
can be cut in different directions to the
rolling.
Tensile test specimens are pulled
beyond its yield strength and the strains
in the width (εw-in the plane of the
sheet) & thickness (εt-normal to the
plane of the sheet) are measured.

The ratio of width strain to thickness strain is defined
as:
Normal Anisotropy
)ln(
)ln(
f
o
f
o
t
w
t
t
w
w
R 


 Where:
 R is known as the normal anisotropy of the sheet (strain ratio)
 Subscripts o and f refer to the original and final dimension,
respectively
 R=1 indicates that the width and thickness strains are equal to
each other; that is the material is isortopic

Because errors in the measurement of small thicknesses are
possible, the previous equation is modified, based on volume
constancy
Normal Anisotropy
 Where:
 l refers to length of the sheet specimen
 The final length and width in test specimen are usually
measured at an elongation of 15% to 20% and for materials
wilth lower ductility
)ln(
)ln(
oo
ff
f
o
lw
lw
w
w
R 

Normal Anisotropy
Strains on a tensile-test specimen
removed from a piece of sheet
metal. These strains are used in
determining the normal and
planar anisotropy of the sheet
metal.
 Determines thinning behavior (strain ratio)
of sheet metals during stretching; important
in deep-drawing operations.
 In drawing, we want the sheet to resist
thinning while its under tensile load so we
can do a deeper draw.
 Normal anisotropy: R = w / t
– Remember: l + w + t = 0
– Simple tension, R =1.0-sheet is
isotropic (width & thickness strains are
equal)
 Tensile tests determine normal anisotropy
(from initial & final dimensions).
R = w/t = ln (wo/wf)/ln (to/tf)
R>1, metal is more resistant to thinning
(good thickness strength).
R<1, metal is less resistant to thinning.
εw :The strain in the width (εw-in
the plane of the sheet)
εt :The strain in the thickness (εt-
normal to the plane of the sheet)

Average Normal Anisotropy
 Sheets generally have planar anisotropy, Thus the R value of
specimen cut from a rolled sheet will depend on its
orientation with respect to rolling direction of the sheet.
 An average R value is then calculated
R varies with rolling direction, so an average R-value (Ravg) is determined for a sheet metal.
Ravg = (R0 + 2R45 +R90)/4
R 0
o
R 45
o
R 90
oRolling
Direction
Normal
anisotropy (R)

Average Normal Anisotropy Vs Limiting Drawing Ratio
The relationship between
average normal anisotropy
and the limiting drawing ratio
for various sheet metals.
Limiting Drawing Ratio (LDR) = D0/Dp
Where,
D0: Maximum Blank diameter
Dp: Punch Diameter
FCC BCC HCP
Low c/a ratio
High average
R-values are
ideally suited for
sheet forming.
Drawability can also be expressed in terms of a limiting draw ratio.
HCP
high c/a ratio

Average Normal Anisotropy, Ravg
Zinc alloys
Hot-rolled steel
Cold-rolled rimmed steel
Cold-rolled aluminum-killed steel
Aluminum alloys
Copper and brass
Titanium alloys (a)
Stainless steels
High-strength low-alloy steels
0.4–0.6
0.8–1.0
1.0–1.4
1.4–1.8
0.6–0.8
0.6–0.9
3.0–5.0
0.9–1.2
0.9–1.2
Typical Range of Average Normal Anisotropy, Ravg, for
Various Sheet Metals
Ravg

Planar Anisotropy
R = (R0 -2R45 +R90)/2
Planar Anisotropy (Earing Tendency)
R 0
o
R 45
o
R 90
oRolling
Direction
Normal
anisotropy (R)
 Planar anisotropy causes ears to form in drawn
cups, When R=0, no ears form
 The height of the ears increases as R increases
 Number of ears: 4, 6, or 8
 For better deep drawability: Ravg and R
 Alloying elements and rolling reduction affect
these values.
 Planar anistropy Is the variation in normal anisotropy (R) in the plane of the sheet.
 The sheet metal may be stronger in one direction then in other directions.
ΔR is the difference between the
average of the R values in th 0o
and 90o directions to rolling and
the R value at 45o

R 0
o
R 45
o
R 90
oRolling
Direction
Normal anisotropy (R)
Calculated R-values for various directions:
Annealed steel:
Rolling direction (0˚) R=1.3
45 degree R=1.0
90 degree R=1.4
Ravg=1.2
R =0.35
Planar Anisotropy (Earing Tendency)

Maximum punch force
 The punch force, F, supplies the work required in deep drawing.
 As in other deformation process, the work consists of ideal work of
deformation, redundant work and friction work. Because of many
variables involved in this operation and because deep drawing is
not a steady-state process, accurately calculating the punch force
can be difficult.
 Several expressions have been developed; one simple and
approximate formula for maximum punch force is
]7.0)/)[((max  pop DDUTSTDF 
 The above equation dose not specifically include parameters such as
friction, the corner radii of the punch and die or blankholder force;
however, this empirical formula makes approximate provisions for
these factors.

Formability of sheet metals
Sheet metal formability is generally defined as the
ability of a sheet to undergo the desired shape change
without failure such as necking and tearing.
Three factors have a major influence on formability:
1. Properties of the sheet metal as discussed before
2. Friction and lubrication at various interfaces in the
operation
3. Characteristics of the equipment, tools, and dies
used

Several techniques have been developed to test the
formability of sheet metals, including the ability to
predict formability by modeling the particular forming
operation
1. Cupping test
2. Tension test
3. Bulge test
4. Forming-limit diagrams
Formability of sheet metals

Cupping test
 The earliest tests developed to predict formability of sheet metal
were cupping tests, namely, the Erichsen tests
1. In the Erichesn test, a sheet-metal specimen is clamped over a flat die
with a circular opening and a load of 1000 kg
2. A 20 mm diameter steel ball is then hydraulically pressed into the
sheet until a crack appears on the specimen
3. The distance d, in mm, is the Erichsen number
Erichsen test
The greater the value of d the greater is the formability
d = Erichsen number
 Simple to perform.
 Approximate indicator of formability.
 Do not simulate exact conditions of
actual operations, WHY?
Because the stretching under the ball is
axisymmetric, they do not at all simulate
the exact conditions of actual forming
operations

 In this test, a circular blank is clamped at its periphery and is
bulged by hydraulic pressure, thus replacing the punch.
 The operation is pure biaxial stretching, and no friction is
involved, as would be the case in using a punch.
 The bulge limit (depth penetrated prior to failure) is a
measure of formability
Cupping test
Bulge-test results on steel sheets of various widths.
The specimen farthest left is subjected to, basically, simple tension.
The specimen farthest right is subjected to equal biaxial stretching.

Forming Limit Diagrams
Procedure:
 Blank sheet is marked with a grid of circles (2.5-5mm).
 The blank is then stretched over a punch, until the grid
pattern deforms where necking and tearing occur.
 The deformed circles are measured in the failed region,
that is the major strain, and miner strain are obtained:
that is after stretching, the original circle has
deformed into ellipse shape
 typically 10 data points taken.
 A series of tests on a certain metal produces the FLD.
Major Strain: (5-4)/4 * 100 = 25%
Minor strain: (3.2-4)/4 * 100 = -20%
Example:
Before punch stretch test:
Original circle diameter: 4mm
After punch stretch test:
Major ellipse axis : 5mm
Minor ellipse axis :3.2mm

Major Strain and Minor Strain
• During stretching in sheet
metal, volume is constant:
l + w + t = 0
• Major strain always larger
than minor strain
If the surface area of ellipse after stretching is larger than the original circle, we know
the thickness of the sheet has changed, its thinner due to stretching.
Although the major strain is always positive (because forming sheet metal takes
place by stretching in at least one direction), the minor strain may be either
positive [strain occur in the transvers direction greater than the original] or
negative or shrinking [strain occur in the transvers direction smaller than the
original] or zero [ No strain occur in the transvers direction ]in the transverse
direction

#1
+ε1
-ε2
+ε1
+ε2
+ε1
ε2=0
#3
#4
#2
Courtesy of Roy A. Lindberg, 1983
After sheet metal deformation,
the major and minor axes of the
circles on the grid pattern are
used to determine the coordinates
on the forming limit diagram.
Forming Limit Diagrams
ε1 Major strain
ε2 Miner strain
because the
minor planar
strain is zero
When normal isotropy R=1 ( that is, the width and thickness strains
are equal. ϵw = -05. ϵl )

Tension Tests
The most basic and common test used to evaluate formability.
It determines important properties of the sheet metal such as:
- total elongation of the sheet specimen at fracture.
- strain hardening exponent, n.
- the normal anisotropy (R) and
-the planar anisotropy (delta R).

Sheet metal forming process Chapter 7

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