Power point presentation on wrinkling behavior of sheet metals

1. Wrinkling behaviour of pure aluminium ,
copper and IF steel sheets
Dr.R.Narayanasamy, Professor
Department of Production Engineering
National Institute of Technology
Tiruchirappalli 620015
Tamil Nadu
India
By

2. oStudy on wrinkling limit of commercially pure aluminium
sheet metals of different grades when drawn through conical
and tractrix dies:
Chemical composition of commercially pure aluminium grades:

3. oMechanical properties of commercially pure aluminium grades annealed
at different temperatures:

4. oMechanical properties :

5. oTool set-up for the drawing operation (dimensions: mm):

6. After Stretching
(Tension -Tension)
Plane strain
(Tension)
Deep Drawing
(Tension-Compression)
Majorstrain
Minor strain (+)Minor strain (-)
Forming Limit Diagram : Deformation of grid circles
Wrinkling or Buckling

7. oFig (a–d) Variation of the radial strain with respect to the hoop strain :
The ratio of strain increments (dεr/dεѲ) at the onset of wrinkling can be obtained from the
strain values, namely εr and εѲ measured for the drawing operation.
Fig : b
Fig : a

8. oFig (c) and (d) Variation of the radial strain with respect to the hoop strain :
Fig :c Fig :d

9. 3 (b) Wrinkling tendencies shown in stress and strain
space
Fig. 3. (a) Stress state in the cup wall.
Continue……..

13. Fig. 4. Wrinkling limit diagram in terms of strain
increments ratio for Al 19000 for conical die.
oFigs. 4–6 have been plotted between the strain increments ratio (dεr/dεѲ) and the
effective strain increment for the case of drawing through the conical die for different
aluminium grades, namely ISS 19000, ISS 19600 and ISS 19660 :
Fig. 5. Wrinkling limit diagram in terms of
strain increments ratio for Al 19600 conical die.

14. Fig. 6. Wrinkling limit diagram in terms of strain increments ratio for Al 19660 conical die
It is observed that the area of safe region is found to be greater for ISS 19660 and lower
for ISS 19000. The behaviour of ISS 19600 is in between ISS 19000 and ISS 19660.
It is observed that the strain increments ratio obtained at the onset of wrinkling is found
to be low or less value for the grade namely ISS 19000 comparing with other grades ISS
19600 and 19660.

15. Fig. 7. Wrinkling limit diagram in terms of stress
ratio for Al 19000 conical die
oFigs. 7–9 have been plotted between the stress ratio (σr/σeff) and the stress ratio (σѲ
/σeff),
for the onset of wrinkling when drawing through the conical die for different aluminium
grades, namely ISS 19000, ISS 19600 and ISS 19660:
Fig. 8. Wrinkling limit diagram in terms of
stress ratio for Al 19600 conical die
For the case of ISS 19000, the line is like more or less straight line and for the case of
ISS 19660 the line is more like a curve leaning towards Y-axis (σr/ σeff axis).

16. Fig. 9. Wrinkling limit diagram in terms of stress ratio for Al 19660 conical die:
Further, it is noted that there is a clear demarcation line between the safe region and the
wrinkling region when the graph is plotted between the ratio of (σr/σeff) and the ratio of
(σѲ /σeff) , for the onset of wrinkling.
The behaviour of the grade ISS 19600 is in between the grades, namely ISS 19000 and ISS
19660.

17. Fig. 11. Wrinkling limit diagram in terms of strain
increments ratio for Al 19600 for tractrix die.
Fig. 10. Wrinkling limit diagram in terms of strain
increments ratio for Al 19000 for tractrix die.
oFigs. 10 and 11 have been plotted between the strain increments ratio (dεr/dεθ) and
the effective strain increment (dεeff) for the case of drawing through the tractrix die
for aluminium grades, namely ISS 19000 and ISS 19600:
It is observed that the aluminium grade ISS 19600 shows better resistance in suppressing
the wrinkles comparing with the aluminium grade of ISS 19000.
It is observed that the area of safe region is found to be greater for ISS 19600
and lower for ISS 19000.

18. Fig. 13. Wrinkling limit diagram in terms of stress
ratio for Al 19600 for tractrix die.
Fig. 12. Wrinkling limit diagram in terms of stress
ratio for Al 19000 for tractrix die.
oFigs. 12 and 13 have been plotted between the stress ratio (σr/σeff) and the stress ratio
(σѲ /σeff), for the onset of wrinkling when drawing through the tractrix die for aluminium
grades , namely ISS 19000 and ISS 19600 :
When drawing through the conical die the aluminium grade ISS 19660 having high
normal anisotropy value (R), high maximum uniform strain or high work hardening
exponent has shown the best resistance against wrinkling when compared with other
aluminium grades tested.

19. o Wrinkling behaviour of commercially pure aluminium sheet
metals of different grades when drawn through conical and
tractrix dies:
Chemical composition of commercially pure aluminium grades:

20. oPlot between σr/σeff and σѲ /σeff for all grades of aluminium in the case of
conical die draw:
 It is observed that there is a clear
curve, which is in the shape of part of an
ellipse when plotted between the stress
ratio, σr/σeffand the stress ratio, σѲ /σeff.
 Further, it is observed that there is a
clear demarcation line between two
regions namely, safe and wrinkled for
the drawing operations.
From the figures, it is understood that
there is a separate segment of curve for
each different aluminium grades namely
19000, 19600 and 19660.
Figure. 1

21. oPlot between σr/σeff and σѲ /σeff for all grades of aluminium in the case of
tractrix die draw:
The radius of the curvature of the curve
is different for different aluminium grades
due to the reason that these grades have
different chemical composition (even
though thickness of sheets and heat
treatment procedure are same).
 This clearly shows that the wrinkling
behaviour of the above three grades of
aluminium, which have different chemical
composition and second phase inclusions
ratings, can be distinguished using stress
diagram when using either conical die or
tractrix die.
Figure. 2

22. Continue…..
• From tangents drawn from two sides of the curve as shown in
Figs. 1 and 2, one can determine the ratio of stress (σr/ σѳ)
value at the onset of wrinkling.
• The values are 0.8995 and 0.875 for the conical and tractrix
dies, respectively.
• This clearly indicates that the tractrix die can accommodate
more hoop stress before the onset of wrinkling compared to
the conical die.
• This proves that the tractrix die is superior compared to the
conical die in suppressing of wrinkles.

23. Figs. 3a and b for the drawing operation of commercially pure aluminium
19000 grade using different blank diameters under no lubrication condition.
These figures clearly indicate the starting point of drawing operation, which is
nothing but first stage bending operation and other stages, namely, later part
of bending stage and tube sinking stage.
oVariation of plastic strain increments ratio w.r.t. effective strain increment
for Al 19000 drawn through tractrix die:
Figure. 3a Figure. 3b

24.  The end points represent the onset of wrinkling which takes place during
drawing operation. In these figures, the end point terminates at larger
effective strain increment value (dεeff )
 The strain increment ratio (dεr/dεθ) at the onset of wrinkling is different
for different blank diameter.
 The maximum ratio of (dεr/dεθ) by (dεeff ) value at the onset of wrinkling is
found to be in the order of 3.1–3.7. This value determines about the
criticality of wrinkling behaviour of sheet metals.
Continue………

25. oVariation of plastic strain increments ratio w.r.t effective strain increment
for
Al 19600 drawn through conical die :
(a) Initial blank diameter 114.33 (b) initial blank diameter 119.06
It is observed that the strain increments ratio (dεr/dεθ) at the onset of
wrinkling is different for different blank diameters.
In these figures, the end terminates at lower effective strain increment value
(dεeff ) compared to the grade of Aluminium 19000.

26. Continue….
 It is observed that the strain increments value (dεr/dεθ) at the onset of
wrinkling which is nothing but end point terminates at higher (dεr/dεθ)
value compared to Aluminium grade 19000.
 The maximum ratio of (dεr/dεθ) by (dεeff ) at the onset of wrinkling is found
to be very high, which is in the order of 22.00.
 Therefore, this grade shows better performance in resisting wrinkles
formation.

27. oVariation of plastic strain increments ratio w.r.t effective strain
increment for Al 19660 drawn through conical die:
(a) Initial blank diameter 99.73 (b) Initial blank diameter 114.83
It is observed that the strain increments ratio (dεr/dεθ) at the onset of wrinkling also
varies with different Aluminium grades tested.
The strain increments ratio at the onset of wrinkling depends on the blank diameter or
geometry and the chemical composition of Aluminium grade tested for any given heat
treatment.
The grade 19660 shows better performance in suppressing the wrinkles because, the
above ratio is very high compared to other two grades.

28. oVariation of plastic strain increments ratio w.r.t. effective strain increment
for
Al 19600 drawn through tractrix die:
(a) Initial blank diameter 99.38 (b) Initial blank diameter 107.06
The behaviour of strain increments (dεr/dεθ) plot with respect to the effective strain
increment is different for tractrix die and the same is somewhat linear in the direction of
effective strain increment compared to the conical die.
The onset of wrinkling point terminates at higher effective strain increment value
compared to the conical die.

29. (c) Initial blank diameter 120.06 (d) Initial blank diameter 124.84
Continue….
This further proves that the onset of wrinkling takes place at higher strain increments ratio
(dεr/dεθ) compared to conical die.
The drawing of sheets through tractrix die resists wrinkling to a greater extent compared
to
conical die, because the draw-sizing operation is very gradual and smooth compared to
conical die.

30. oVariation of plastic strain increments ratio w.r.t. effective strain increment for
Al 19600 drawn through tractrix die:
(a) Initial blank diameter 97.37 (b) initial blank diameter 104.76
The behaviour of two different Aluminium grades namely 19000 and 19600 are almost
same when drawing through tractrix die.
At onset of wrinkling the strain increments ratio shows almost same behaviour with
respect to the effective stain increment irrespective of the type of aluminium grade
tested.

31. (c) initial blank diameter 112.46 (d) initial blank diameter 124.84
Continue…
Aluminium grade 19660 having high strain hardening index value, low ratio of tensile to
yield and fairly good value of normalized hardening rate shows better resistance against
wrinkling.

32. oEffect of annealing on the wrinkling behaviour of the commercial
pure aluminium grades when drawn through a conical die:
Results of wrinkling test for: (a) 150 C annealed aluminium
grades
As the annealing temperature increases Aluminium grades shows better resistance
against wrinkling.

33. o Relationship between wrinkling factor and strength factor for 150 C
annealed aluminium grades:
For annealed at 150 C, the ratio of strain increments (dεr/dεθ) is found to be high for Al
19600 grade among different Aluminium grades tested when drawing through a conical
die.
This Aluminium grade 19600 having low Youngs modulus value, high normalized
hardening rate and low yield stress shows better resistance against wrinkling when
compared with other Aluminium grades tested.

34. o(b) 200 C annealed aluminium grades :
As the annealing temperature increases, the strain increments ratio (dεr/dεθ) also
increases. This shows that good annealed Aluminium grades shows better resistance against
wrinkling.
Among annealing-heat treated blanks, annealed at 200 C, furnace cooled blanks shows
the higher value of strain increments ratio (dεr/dεθ) when comparing with air cooled blanks.

35. o Relationship between wrinkling factor and strength factor for
200 C annealed aluminium grades:
Aluminium grades having high strain hardening index value, low yield stress and high
normalized hardening rate shows better resistance against Wrinkling.
For annealed at 200 C, the ratio of strain increments (dεr/dεθ) is found to be high for Al
19000 grade when compared with other grades.

36. o (c) 250 C annealed aluminium grades:

37. oRelationship between wrinkling factor and strength factor for 250 C annealed
aluminium grades:
For annealed at 250 C, the ratio of strain increments (dεr/dεθ) is found to be high for Al
19600 grade when compared with other two grades.
The Al 19600 grade having high strain hardening index value, high normal anisotropy
value, high tangent modulus value and low yield stress shows the best resistance against
wrinkling when compared with other two grades.

38. o(d) 200 C (furnace cooled) aluminium grades:

39. o Relationship between wrinkling factor and strength factor for
200 C annealed (furnace cooled) aluminium grades:
For annealed at 200 C furnace cooled, the ratio of strain increments (dεr/dεθ) is found
to be high for Al 19600 grade when compared with other two grades.
Furnace cooled Aluminium grades shows better resistance against wrinkling when
compared with air cooled Aluminium grades.

40. oWrinkling of commercially pure aluminium sheet metals of
different grades when drawn through conical and tractrix dies:

41. oFig. 5. (a–d) Wrinkling tendency in strain increment space for different grades of
aluminium sheets for conical die:
Fig. (a) Fig. (b)
Fig. 5a, for annealed at 150 C, the ratio of strain increments (d◦ εr/dεθ) is found to
be high for aluminium 19660 grade among three different aluminium grades
tested when drawing through the conical die.
Fig. 5b, for annealed at 200 C, the ratio of strain increments (d◦ εr/dεθ) is found
to be high for aluminium 19660 grade when compared with other grades.

42. Continue…..
Fig. (c) Fig. (d)
Fig. 5c, for annealed at 250 C, the ratio of strain increments (d◦ εr/dεθ) is found to be high
for aluminium 19600 grades when compared with other two grades.
Fig. 5d, for annealed at 200 C, furnace cooled, the ratio of strain increments (d◦ εr/dεθ) is
found to be high for aluminium 19600 grade when compared with other two grades.
As shown in Fig. 5a–d, as the annealing temperature increases, the strain increments ratio
(dεr/dεθ) also increases.
This shows that annealed at higher temperature of aluminium grades shows better
resistance against wrinkling.

43. oFig. 6. (a–d) Wrinkling tendency in strain increment space for different grades of
aluminium sheets for tractrix die :
Fig. (a) Fig. (b)
Fig. 6a–d have been plotted between the radial strain increment and the hoop strain
increment developed at the onset of wrinkling for two different grades of aluminium
sheets which were heat-treated at different temperatures for the case of tractrix die.
It is observed that aluminium 19600 grade shows the high ratio of strain increments
(dεr/dεθ) compared with aluminium 19000.
As the annealing temperature increases the strain increments ratio (dεr/dεθ) also
increases. This also shows the good annealed grades shows better resistance against
wrinkling.

44. Fig. (d)Fig. (c)
Continue…..
Among annealing–heat-treated blanks, annealed at 200 C furnace cooled blanks shows◦
the higher value of strain increments ratio (dεr/dεθ) when compared with air cooled blanks.
For higher annealing temperature namely 250 C air cooled or 200 C furnace cooled,◦ ◦
aluminium 19000 grade shows better resistance against wrinkling compared with the
aluminium grade 19600, when drawn through the tractrix die.

45. oFig. 7. (a–d) Wrinkling tendency in stress space for different grades of aluminium
sheets for conical die :
Fig. (a) Fig. (b)
Fig. 7a–d have been plotted between the radial stress and the hoop stress at the onset
of wrinkling for different grades of aluminium sheets which were heat-treated at different
temperatures for the case of conical die.
It is observed that the ratio (σr/σѲ) at which the wrinkling takes place is tends to almost
same value irrespective of the temperature of annealing selected for all three grades of
aluminium when drawn through the conical die.

46. Continue…..
Fig. (c) Fig. (d)
At temperatures namely 150 C and 200 C aluminium 19660 grade shows better◦ ◦
performance when suppressing the wrinkles when compared with other two grades.
This means that the ratio (σr/σѲ) should be very high for suppressing the wrinkles. The
reason is due to the fact that the ratio of (σr/σѲ) is found to be very high at the onset of
wrinkling to suppress the formation of wrinkles.

47. oFig. 8. (a–d) Wrinkling tendency in stress space for different grades of aluminium
sheets for tractrix die:
Fig. (a) Fig. (b)
Fig. 8a–d have been plotted between the radial stress and the hoop stress at the onset
of wrinkling for two different grades of aluminium sheets namely aluminium 19000 and
aluminium 19600, which were heat-treated at different temperatures for the case of
tractrix die.

48. Continue…..
Fig. (c)
Fig. (d)
As shown in the figures, aluminium 19600 grade shows better resistance against
wrinkling at lower annealing temperatures. For higher annealing temperature and
furnace cooled blanks aluminium 19000 grade shows better resistance against
wrinkling when the blanks are drawn through the tractrix die.

49. oFig. 9. (a-b) The effect of annealing temperature and cooling rate on suppressing the
wrinkling for the conical die :
(a) The effect of annealing temperature on
suppressing the wrinkling for the conical die
Fig. 9a shows the effect of annealing temperature on the ratio of strain increments
(dεr/dεθ) at the onset of wrinkling when drawn through the conical die.
As the annealing temperature increases the ratio of strain increments (dεr/dεθ) also
increases for the case of aluminium 19600 grade.

50. Fig. 9b shows the effect of cooling rate on the ratio of strain increments ratio (dεr/dεθ) at
the onset of wrinkling when drawn through conical die. It is noted that the furnace cooling
is better than air cooling in suppressing the wrinkles.
(b) The effect of cooling rate on suppressing
the wrinkling for the conical die.

51. oFig. 10. (a-b) The effect of annealing temperature and cooling rate on suppressing the
wrinkling for the tractrix die :
(a) The effect of annealing temperature on
suppressing the wrinkling for the tractrix die
Fig. 10a shows the effect of annealing temperature on the ratio of strain increments
(dεr/dεθ) at the onset of wrinkling when drawn through the tractrix die for two different
aluminium grades namely ISS 19000 and ISS 19600.
The increase in annealing temperature shows better resistance against wrinkling in the
case of aluminium 19000 grade.

52. (b) The effect of cooling rate on
suppressing
the wrinkling for the tractrix die
Fig. 10b shows the effect of cooling rate on suppressing the wrinkling when drawn
through tractrix die, for the case of aluminium grades, namely 19000 and 19600.
 In the case of aluminium 19600, the air cooling shows better performance compared
with the furnace cooling.

53. The deep drawing of circular blanks of three different grades
of annealed, commercially pure aluminum sheets of different
grades, namely ISS 19000, ISS 19600 and ISS 19660, having a
thickness of 2.00 mm, into cylindrical cups through Conical die
using a flat bottomed punch
o Wrinkling behavior of different grades of annealed
commercially pure aluminum sheets when drawing
through a conical die

54. o Mechanical properties of aluminum grades annealed at various
temperatures:
 Chemical composition of various
Aluminum sheet metal Grades:

55. o Micro structures of various Al grades:

56.  The ratio of initial blank diameter to initial
thickness increases, the draw deformation
percentage at the onset of wrinkling
decreases in general for all types of
annealing.
 By increasing annealing temperature, a
deeper cup can be obtained in a single draw.
 When comparing the air cooled blanks
with furnace-cooled blanks of the same
temperature (2000
C), the obtainable draw
deformation is high for furnace-cooled
blanks at the higher values of (D0/t0).
o The variation of % draw deformation before wrinkling to the
ratio of initial blank diameter to initial thickness for Al 19000:

57.  Among the different types of annealing,
the Al-19600 furnace cooled sheets show
better resistance against wrinkling when
the ratio of (D0/t0) is low
 In Al-19600 The furnace-cooled sheets
show almost the same amount of
percentage draw deformation similar to
that of the air-cooled one when the ratio of
(D0/t0) is high
The behaviour of Al 19600 is different
when compared with Al 19000 grade
because of change in chemical
composition.
o The variation of % draw deformation before wrinkling to the
ratio of initial blank diameter to initial thickness for Al 19600:

58.  The effect of annealing does not have
a significant effect on the obtainable
draw deformation in Al 19660
 The lower temperature of annealing
shows better performance in inhibiting
wrinkles compared with higher
temperature of annealing in the case of
Al 19660.
 The behaviour of Al 19660 is entirely
different when comparing with Al 19000
and Al 19600
the reason is that Al 19660 is very pure.
o The variation of % draw deformation before wrinkling to the
ratio of initial blank diameter to initial thickness for Al 19660:

59.  The (D0/t0) ratio increases, the percentage
change in thickness at the onset of wrinkling
decreases in general for all the annealing
temperatures tested in the case of Al 19000.
 For 1500
C and 2000
C air cooled blanks, the
rate of change of percentage change in
thickness at the onset of wrinkling is very high
when compared to temperatures 2000
C
furnace cooled and 2500
C air cooled.
 For temperatures 2000
C furnace cooled and
2500
C air cooled, the percentage change in
thickness at the onset of wrinkling is almost
constant irrespective of blank diameters.
this is due to softening of aluminum at higher
annealing temperature or due to furnace
cooling.
o The variation of % change in thickness at wrinkling to the ratio
of initial blank diameter to initial thickness for Al 19000:

60. o The variation of % change in thickness at wrinkling to the ratio
of initial blank diameter to initial thickness for Al 19600:
 For smaller blank diameters, the rate of
change of percentage change in thickness
at the onset of wrinkling is high and at the
same time it is less for larger blank
diameters for 2000
C furnace cooled blanks
 At the 2500
C air cooled blanks the
lowest percentage change in thickness at
the onset of wrinkling among all the
annealing temperatures
because the metal is soft at this
particular temperature in the case of Al
19600.

61. o The variation of % change in thickness at wrinkling to the ratio
of initial blank diameter to initial thickness for Al 19660:
 For annealing at 2500
C air cooled
blanks, the percentage change in
thickness at the onset of wrinkling
is lowest among the annealing
temperatures because, the metal is
soft at this particular temperature

62. o Some important points….
 As the annealing temperature increases, aluminum grades show
better resistance against wrinkling. This is very common in Al
19000.
 Furnace cooled aluminum grades show better resistance against
wrinkling when compared with air cooled aluminum grades,
namely 19600
 For higher temperatures of annealing, the percentage change in
thickness at the onset of wrinkling is almost constant irrespective
of blank diameters.
this is due to softening of aluminum at higher annealing
temperature or due to furnace cooling and this is very common
in Al 19000.

63. o Wrinkling behavior of cold-rolled sheet metals
aluminium and copper when drawing through a tractrix
die
 Mechanical and anisotropy properties of cold-rolled
commercially-pure aluminum and copper:
 (a) Tensile strength properties

64.  (b) % Elongation
 (c) Anisotropy parameters

65. o Drawing behavior of cold-rolled commercially-pure
aluminum sheet (flat-bottomed punch):

66. o Drawing behavior of cold-rolled commercially-pure
aluminum sheet (Hemi spherically-ended punch):

67. o Drawing behavior of cold-rolled commercially-pure copper
sheet (Flat-bottomed punch):

68. o The percentage draw-deformation against the initial
diameter of the blank for the cold-rolled commercially-pure
aluminum and copper sheets:
(a) Cold rolled Aluminum sheet (b) Cold rolled Copper sheet

69.  The percentage draw-deformation at the onset of
wrinkling decreases with increasing initial blank
diameter.
 For any given thickness, the critical compressive hoop
stress that causes wrinkling to occur can develop even at
the early stages of the drawing operation as the initial
blank diameter increases
 For this reason, the draw depth and the equivalent
draw-ratio obtainable before wrinkling decreasing with
increasing diameter of the initial blank.

70. o Variation of percentage thickness-strain from the centre of the
cup, for a copper blank of 100 mm diameter using a fiat-bottomed
punch: 90 ° orientation:

71.  In the case of aluminum sheets, the critical percentage
thickness- strain determined at the onset of wrinkling is found
to be 12%
 The number of wrinkles developed on the copper sheets
varies from one to three
 The 90 degree orientation corresponds to the direction of
lowest R-value and yield stress.
 These copper sheets develop wrinkles more readily when the
sheet blank is not flat or when it has any weak spots due to
material defects, in such cases, the sheet wrinkling at the very
early stage of the drawing process.

72. o Variation of percentage change in thickness with position from the centre of
the cup for wrinkled samples Initial diameters of 94.91, 84.92 and 84.90 mm,
45° orientation for Commercially-pure aluminium (flat bottomed punch):

73. o Variation of percentage change in thickness with position from the centre of
the cup for partially drawn and wrinkled at 45° for Commercially-pure
aluminium (flat bottomed punch)
(b) Initial diameters of 114.90 mm :

74. o Variation of percentage change in thickness with position from the centre of
the cup for partially drawn and wrinkled at 45° for Commercially-pure
aluminium (flat bottomed punch)
(c) Initial diameters of 84.92 mm:

75. o Variation of percentage change in thickness with position from the centre of
the cup for partially drawn and wrinkled at 45° for Commercially-pure
aluminium (flat bottomed punch)
(d) Initial diameters of 84.90mm:

76. o Variation of percentage change in thickness along the cup wall, all cups
being partially drawn and wrinkled at 45° for Commercially-pure aluminum
(hemi spherically–ended punch)
(a) Initial diameter 100 mm:

77. o Variation of percentage change in thickness along the cup wall, all cups
being partially drawn and wrinkled at 45° for Commercially-pure aluminum
(hemi spherically–ended punch)
(b) Initial diameter 95 mm:

78. o Variation of percentage change in thickness along the cup wall, all cups
being partially drawn and wrinkled at 45° for Commercially-pure aluminum
(hemi spherically–ended punch)
(c) Initial diameter 90 mm:

79. o Variation of percentage change in thickness along the cup wall, all cups
being partially drawn and wrinkled at 45° for Commercially-pure aluminum
(hemi spherically–ended punch)
(d) Initial diameter 80 mm:

80.  The percentage draw-deformation obtainable at the onset of wrinkling
decreases with increasing initial blank diameter.
 The percentage draw-deformation obtainable in drawing with a fiat bottomed
punch is always greater than that obtained with a hemi spherically ended
punch.
 The critical percentage thickness-strain obtained in the drawing process at the
onset of wrinkling is 12 to 15, irrespective of the punch and material used in
the drawing operation.
 The orientation of forming wrinkles corresponds to the direction of greatest R-
value and yield stress in the case of aluminium sheets. And this is the converse
in the case of copper sheets.

81. Conical die Tractrix die
o Wrinkling behavior of interstitial free steel sheets
when drawn through tapered dies
 Dies used for the drawing operation:

82.  The normal anisotropy (R) and the planer anisotropy (∆R)
were calculated from the ‘R’ values determined along 00
, 450
,
900
orientation to the rolling directions using the expression
given below
R =¼(R0+R45+R90)
 The normal anisotropy and strain hardening exponent
values of the steel sheets are shown below:

83. o The limiting draw ratio and limiting diameter when the
sheets are drawn in conical die are shown below:

84. o Variation of limiting draw ratio with sheet thickness in conical &
tractrix die:
 In both cases as the limiting draw ratio increases with the
thickness of the sheet

85. o Variation of limiting draw ratio with (dp/t0
) sheet thickness in
conical & tractrix die:
 In both cases as the limiting draw ratio decreases with (dp/t0
)

86. o Variation of limiting draw ratio with normal anisotropy in
conical & tractrix die:
 As the limiting draw ratio increases with normal anisotropy for
conical die and decreases for tractrix die

87. o Variation of limiting draw ratio with non dimensional parameter
sheet thickness in conical & tractrix die:
 In both cases as the limiting draw ratio decreases with increasing value of non
dimensional parameter
 Comparing the conical die and tractrix die, the limiting draw ratio is higher when
the sheets are drawn in tractrix die.

88. o Variation of plastic strain increment ratio with (dp/t0) in
conical & tractrix die:
 The plastic strain ratio increases gradually with (dp/t0) but
the plastic strain value increases along with (dp/t0) up to the
ratio 150 and then plastic strain ratio decreases.

89.  Chemical composition of steels:
o Wrinkling limit of interstitial free steel sheets of
different thickness when drawn through Conical and
Tractrix dies

90.  Tensile properties of various steel
sheets:
 Normal anisotropy of various
steels:

91. o Wrinkling limit diagram in terms of strain increments ratio for
IF Steel of thickness 0.6mm and 0.85mm:
 The wrinkling takes place over the effective strain increment range from 0.01 to 0.1, for
the case of IF Steel sheet 0.6mm.
 The effective strain increment range over which the wrinkling takes place is reduced for
the case of 0.85 mm
 IF Steel sheet namely coated and non coated supplied by Ford motors,
for this particular IF Steel sheet the normal anisotropy (R) value and strain hardening
index (n) value are found to be very high

92. o Wrinkling limit diagram in terms of strain increments ratio for IF
Steel of thickness 0.9mm and 1.2mm:
 The wrinkling region gets reduced for 0.9mm and 1.2mm because of higher thickness.
 As the thickness of IF sheet Steel increases the wrinkling region gets reduced and the safe
region increases.

93.  There is a clear demarcation line between the safe region and the
wrinkling region when the plot is made between the ratio of (σθ /σeff), and
the ratio of (σr /σeff) for the onset of wrinkling.
o Wrinkling limit diagram in terms of stress ratio for IF Steel of
drawn through conical die:

94. o Wrinkling limit diagram in terms of stress ratio for IF Steel of
drawn through conical die:
 There is a clear demarcation line between the safe region and the wrinkling
region and the curve is more leaning towards y-axis in the case of Conical die.
This means that the wrinkling region is more in the case of Conical die and less in
the case of Tractrix die.
 This directly shows that the wrinkling is postponed when the sheets are drawn
through Tractrix die.

95. o Wrinkling limit diagram in terms of strain increments ratio for
IF Steel of thickness 0.6 mm, 0.85mm:

96.  The area of safe region is found to be greater for the Tractrix die comparing
with the Conical die, for any given sheet thickness.
 When the IF Steel sheet grades are drawn through the Tractrix die the
wrinkling takes place over the effective strain increment of the shorter range.
This means that the safe region is found to be high compared with wrinkling
region.
o Wrinkling limit diagram in terms of strain increments ratio for
IF Steel of thickness 1.6mm:

97. o Variation of strain increments ratio w.r.t. (D0/t0) for
prestrained condition sheet in Conical die and Tractrix die:
 The plastic strain increments ratio is to be increasing with increasing ratio of
initial blank diameter to sheet thickness.
 the safe region is found to be higher for the case of drawing through Tractrix
die when comparing with Conical die.
This proves that the wrinkling is postponed when drawing through the Tractrix
die comparing with Conical die.

98. References:
 C. Loganathan , R. Narayanasamy - Wrinkling behaviour of
different grades of annealed commercially pure aluminium sheets
when drawing through a conical die.
 R. Narayanasamy , C. Loganathan , J. Satheesh- Some study on
wrinkling behaviour of commercially pure aluminium sheet metals
of different grades when drawn through conical and tractrix dies.
 R. Narayanasamy , R. Sowerby - Wrinkling behaviour of cold-rolled
sheet metals when drawing through a tractrix die.
 C. Loganathan , R. Narayanasamy -Wrinkling of commercially pure
aluminium sheet metals of different grades when drawn through
conical and tractrix dies.

99.  R. Narayanasamy , C. Loganathan - Study on wrinkling limit of
interstitial free steel sheets of different thickness when drawn
through Conical and Tractrix dies.
 C. Loganathan , R. Narayanasamy , S. Sathiyanarayanan - Effect of
annealing on the wrinkling behaviour of the commercial pure
aluminium grades when drawn through a conical die .
 R. Narayanasamy , C. Sathiya Narayanan -Wrinkling behaviour of
interstitial free steel sheets when drawn through tapered dies.
 R. Narayanasamy , C. Loganathan- Study on wrinkling limit of
commercially pure aluminium sheet metals of different grades
when drawn through conical and tractrix dies.

100. THANK YOU