dr.r.narayanasamy - wrinkling behaviour of sheet metals

Wrinkling behaviour of pure aluminium , copper and IF steel sheets

Dr.R.Narayanasamy, ProfessorDepartment of Production Engineering

National Institute of TechnologyTiruchirappalli 620015

Tamil NaduIndia

By

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:

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

oMechanical properties :

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

After Stretching(Tension -Tension)

Plane strain(Tension)

Deep Drawing(Tension-Compression)

Maj

or st

rain

Minor strain (+)Minor strain (-)

Forming Limit Diagram : Deformation of grid circles

Wrinkling or Buckling

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 : bFig : a

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

Fig :c Fig :d

3 (b) Wrinkling tendencies shown in stress and strain space

Fig. 3. (a) Stress state in the cup wall.

Continue……..

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.

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.

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 (σ Ѳ /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).

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 (σ Ѳ /σeff) , for the onset of wrinkling.

The behaviour of the grade ISS 19600 is in between the grades, namely ISS 19000 and ISS 19660.

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.

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 (σ Ѳ /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.

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:

oPlot between σr/σeff and σ Ѳ /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, σ Ѳ /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

oPlot between σr/σeff and σ Ѳ /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 chemicalcomposition and second phase inclusions ratings, can be distinguished using stress diagram when using either conical die or tractrix die.

Figure. 2

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.

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

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………

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.

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.

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 114.83It 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.


(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.

(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.


(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.

(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.

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.

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.

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.

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.


19000 grade when compared with other grades.

o (c) 250 C annealed aluminium grades:

oRelationship between wrinkling factor and strength factor for 250 C annealed aluminium grades:


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.

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

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.

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

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 (dεr/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 (dεr/dεθ) is found

to be high for aluminium 19660 grade when compared with other grades.

Continue…..

Fig. (c) Fig. (d)Fig. 5c, for annealed at 250 ◦C, the ratio of strain increments (dεr/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 (dεr/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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

(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.

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

o Mechanical properties of aluminum grades annealed at various temperatures:

Chemical composition of various Aluminum sheet metal Grades:

o Micro structures of various Al grades:

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 (2000C), 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:

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.


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.


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 1500C and 2000C air cooled blanks, the rate of change of percentage change in thickness at the onset of wrinkling is very high when compared to temperatures 2000C furnace cooled and 2500C air cooled. For temperatures 2000C furnace cooled and 2500C 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:


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 2000C furnace cooled blanks

At the 2500C 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.


For annealing at 2500C 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

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.

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

(b) % Elongation

(c) Anisotropy parameters

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

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

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

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

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.

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:

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.

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):

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 :


(c) Initial diameters of 84.92 mm:


(d) Initial diameters of 84.90mm:

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:


(b) Initial diameter 95 mm:


(c) Initial diameter 90 mm:


(d) Initial diameter 80 mm:

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.

Conical die Tractrix die

o Wrinkling behavior of interstitial free steel sheets when drawn through tapered dies

Dies used for the drawing operation:

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:

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

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

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)

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

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.

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.

Chemical composition of steels:

o Wrinkling limit of interstitial free steel sheets of different thickness when drawn through Conical and Tractrix dies

Tensile properties of various steel sheets:

Normal anisotropy of various steels:

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

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.

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), andthe 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:

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 drawnthrough Tractrix die.

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

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:

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.

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.

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.

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