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Deep Drawing, Formability

Deep Drawing, Formability

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Deep Drawing, Formability

Deep drawing

1

Principle

punch, blankholder ring, blank, die ring

Deep drawing of metal sheet is used to form containers

A flat blank is formed into a cup by forcing a punch

against the center portion of a blank that rests on the

die ring

Tooling: punch, blankholder ring, blank, die ring

2

Redrawing

blankholder

blank

workpiece

die ring

punch for redrawing

Final shape of a container can be reached by more

drawing steps, these operations are called as

redrawings

3

Combined drawings

First drawing

Second drawing

More drawing operations can be combined into one

tool using multiple ram system in a hydraulic press

4

Other characteristics of deep

drawing

• Easiest way is to draw cylindrical parts

from circle disc, but…

• The process is capable of forming box

(rectangular) shapes or shell-like

containers

• Special variants are liquid pressure

forming and rubber die forming

• These processes result in near net

shapes for many purposes.

5

Deep drawing ratio

• Limiting Drawing Ratio (LDR) –

β= D o /d n

• where D o is the diameter of the first (largest) blank

and d n is the smallest cup diameter that can be

successfully drawn

Drawing Ratio in general:

β i = d i /d i+1

• First drawing β 1 =2,2…1,8

redrawing β i =1,4…1,1

(copper, aluminium, mild steel)

6

Calculation of blank diameter

• In case of cup-like

components the blank

is circular

• Area of blank equal to

theareaofcup:

D

D

2

0

4

0

π

=

d π

= 1 + d πh

1

4

d

2

1

2

+

4d

1

h

h

d 1

D o

7

Calculation of drawing force

Drawing force: Fd,max = n*π*d*t*UTS

Example:

Cup diameter: d= 45,7 mm

Sheet thickness: t = 0,5 mm

Ultimate Tensile Strength: UTS = 320 MPa

Drawing coefficient: n = 0,7…0,95

F d,max = 0,9*π*45,7*0,5*320 = 20 674 N

8

Drawing tool

Húzógyűrű

Die ring

Bélyeg

punch

Ráncgátló

blankholder

alakítás

közbeni

állapotban

workpiece

9

Drawing errors (1)

Earing Stress corrosion cracks

Other errors:

Buckling and wrinkling

Fracturing

10

Drawing errors (2)

Buckling and wrinkling, causing fracturing

11

Drawing errors (3)

Fracturing

12

Deep Drawing

Example

13

Analysis of a cup drawing

• The cup to be drawn:

– Diameter: 60,3 mm

– Height: 104,8 mm

• Blank diameter (earing is eliminated):

D =

d + 4d

h

n n n

D

D

0

0

0

=

=

2

60,

3

170,

1

2

+

mm

4⋅

60,

3

⋅104,

8

14

Calculation of drawing ratio

• Suggested drawing ratio

– First drawing ~2

– Second drawing 1,2…1,25

– Third drawing 1,15…1,18

– Further drawings 1,1…1,12 etc.

• Calculations by approximative

(iterative) way

15

Nr. of

operations

0. blank

1. Cup drawing

2. Redrawing

3. Redrawing

Results

Height

in mm

-

65,1

85,7

104,8

Diameter

in mm

170,1

85,7

69,9

60,3

Drawing

ratio

-

1,98

1,23

1,16

16

Drawing force

• Cup drawing (first drawing)

– Diameter: 85,7 mm

– Thickness: 2 mm

– UTS: 320 MPa

F

F

F

d

d

d

max

max

max

=

=

=

n

π

0,

9

⋅d

π

155079

⋅t

N

⋅UTS

85,

7

⋅ 2⋅

320

155kN

17

Fluid forming

„hidromec” process

Seal, fluid,

fluid holder

Punch,

blankholder

Fluid forming uses only one solid die half.

Forming pressure is applied by the action of hydraulic fluid, which

forces the blank to assume the shape of the rigid tool

Sometimes a flexibile membran is used to separate blank and the

fluid

18

die

Strech drawing

Used for drawing car body panels

Blank is clamped, rigid die gives the shape of sheet

metal

Change in thickness: s 1

Formability Testing of Sheet

Metals

20

Representation of Strain

• True or logarithmic strain: ϕ

• The integral of the incremental change

in length dL, divided by the actual

length L:

d ϕ =

dL

L

ϕ

=

L

1

L

0

dL

L

=

ln

L1

L 0

21

Equivalent strain

• Strain in the direction of 3 axes:

φ 1= φ L φ 2= φ w φ 3= φ th

• Equivalent strain:

2 2 2 2

ϕ = ( ϕ −ϕ

) + ( ϕ −ϕ

) + ( ϕ −ϕ

)

e

3

1 2 2 3 1 3

22

True stress-strain

(flow stress) curve

• Flow stress curve: σ f = σ f (φ e )

if temperature (T) and strain rate,

is constant.

• In general

(n: strain hardening exponent;

m: strain rate sensitivity)

σ

σ

σ

f

f

f

= σ

=

=

f

n

c ⋅ϕ

n

c ⋅ϕ

( ϕ ; &

ϕ ; T )

e

e

e

( if

⋅ & ϕ

e

m

e

( if

& ϕ =

e

& ϕ ; T

e

T

dt

=

=

const.)

const.)

23

• Tensile test:

Plastic strain ratio (r)

Measurement

L 0

w 0

φ L= ln(L 1/L 0);

φ w= ln(w 1/w 0);

φ th = - (φ L + φ w) ( as φ L+ φ w + φ th = 0 )

24

= w; s = th

25

Plastic strain ratio (r)

Evaluation

• Calculation: r = φw / φth • Definition: ratio of the true width strain

devided to the true thickness strain

• The r value frequently changes with

direction in the sheet

• Test specimens should be machined

parallel (0o ), perpendicular (90o ), and

(45o ) related to the rolling direction

26

Measure of anisotropy

Test

27

Measure of anisotropy

• Average normal

anisotropy:

• Planar anisotropy:

r m

∆r

=

r

0

+

r

4

+

r

2 45 90

The value r m determines the limiting drawing ratio,

and ∆r is in correlation with the extent of earing.

A combination of high r m and low ∆r provides

optimal drawability.

=

r

45

r

0

+

2

r

90

28

Average normal anisotropy and

hardening exponent of metals

Mild steel

Drawing steel

Austenitic steel

Copper

Aluminium

Titanium

n

0,2-0,5

0,22-0,26

0,4-0,55

0,35-0,5

0,2-0,3

0,05

r

1,0-1,4

1,4-1,8

0,9-1,2

0,6-0,9

0,6-0,8

3,0-5,0

30

Forming Limit Diagram (1)

Safe

Major engineering strain, %

Failure

Safe

Minor engineering strain, %

31

Forming Limit Diagram (2)

32

Forming Limit Diagram (3)

• Sheet metal can be deformed only to a

certain level – before local thinning

(necking) and failure occur

• FLD shows the limit of necking (or

failure) as function of minor and major

strain

• Strains can be evaluated from the

deformation of circle grids plotted on

the surface of sheet metal

33

Other formability tests

• Ball punch test (Erichsen test)

• Hydraulic bulge test

• Hemispherical dome test

• Cup drawing test (drawing test)

34

Well known

as Olsen or

Erichsen test

The cup

height at

fracture is

used as the

measure of

strechability

Ball punch test

Die

Specimen

Punch

Blankholder

ring

35

Ball punch test

Examples

37

Hydraulic bulge test

Material

characterisation

in biaxial

streching

Testing to much

higher strain

levels than those

achievable in

tensile testing

Research in

plasticity theory

Hydraulic fluid

Die ring

Base plate

38

Hemispherical dome test

Lubricated

punch is used

for deformation

of sheet metal

The dome

height at

fracture is

measured

The test yields

reproducible

results

Die ring

Blankholder

ring

Punch

40

Circular blanks of

various diameters

are used

Tooling is

standardised

Limiting drawing

ratio (LDR) is the

ratio of the

diameter of the

largest blank that

can be successfully

drawntothe

diameter of the

punch

Cup drawing test

41

Cup drawing test

Examples

43