Dr.R.Narayanasamy - FLD on HSLA, IF steels and Al alloys.

Forming limit diagram for Interstitial free steels,
HSLA steel sheets,
pure aluminium and AL 5052 alloy sheets
Dr.R.Narayanasamy, Professor
Department of Production Engineering
National Institute of Technology
Tiruchirappalli 620015
Tamil Nadu
India
By

o Forming, fracture and wrinkling limit diagram for
IF steel sheets of different thickness :
 Definition:
“Forming limit diagram is graphical representation
which shows the forming limit for various conditions
of strain ratios corresponding to different sheet metal
forming of operations”

Fig: A schematic diagram of a typical tool set up for FLD

 Chemical composition of steels (in weight %)


a) IF steel sheet of 0.6 mm thickness – 250 X – Nital etched;
b) IF steel sheet of 0.9 mm thickness – 250 X – Nital etched;
c) IF steel sheet of 1.2 mm thickness – 250 X – Nital etched;
d) IF steel sheet of 1.6 mm thickness – 250 X – Nital etched;
e) IF steel sheet of 0.85 mm thickness coated (Ford) – 250 X – Nital etched;
f) IF steel sheet of 0.9 mm thickness non coated (Ford) – 250 X – Nital etched.
 Microstructure of IF steel sheets

 The normal anisotropy (r) calculated by using the expression
 The average strain hardening exponent (n) and the average strength
coefficient (K) were calculated using the following expressions
 The strain hardening exponent (n) value indicates stretchability and formability
 The average n-value of all the IF steel sheets are high and they show high
stretchability

 Tensile properties of steel sheets:

 Formability parameters of steels sheets:
The metal which shows high normal anisotropy value has high drawability
because it shows good resistance to thinning in the thickness direction during
deep drawing
The planer anisotropy for all IF steel sheets is very less and indicates
resistance to earing.

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

 Forming, fracture and wrinkling limit diagram
for IF steel sheet of thickness 0.6 mm:

for IF steel sheet of thickness 0.85 mm coated:

 Details of forming limit major strains for a fixed minor strain:
 Details of fracture limit major strains for a fixed minor strain:

 Forming, fracture and wrinkling limit diagram for
IF steel sheet of thickness 0.85 mm non coated:

 Some important points….
 The strain combinations above the FLD line will lead to fracture and those
below the WLD line will produce wrinkles during deep drawing.
 Therefore, higher gap between the FLD line and WLD line for a fixed minor
strain indicates higher suitability for forming in the tension– compression
region (deep drawing condition)
 The IF steel sheet of thickness 1.6 mm is more suitable for deep drawing
because it has higher thickness and it shows higher gap between the FLD
line and WLD line for a fixed minor strain, i.e. 0.1.
 The gap between the FLD line and WLD line for a fixed minor strain
reduces as the sheet thickness decreases.
 This shows that the sheets with lesser thickness shows lower suitability
for forming in the deep drawing conditions when compared to the sheets
with higher thickness

 As the minor strain increases the gap between the FLD line
and WLD line decreases. This shows at lower minor strain
level the sheet is more safe.
 The slope of the WLD line decreases as the thickness of the
sheet increases. Therefore the safe area increases as the
thickness of the sheet increases.
 the sheet with lower thickness shows higher gap between FLD
line and WLD line due to its higher normal anisotropy value.
 The forming limit major strain at a fixed minor strain value for
the tension–compression strain condition increases as the
thickness and normal anisotropy value increase.

• Some analysis on stress and strain limit for necking
and fracture during forming of some HSLA steel sheets
 Chemical composition of steels (in weight %)

 Microstructure of different steel sheets:
Fig: (a) microstructure of HSLA steel at magnification 400× nital etched
(b) microstructure of carbon–manganese steel at magnification 500× nital
etched (c) microstructure of carbon–manganese steel at magnification
200× nital etched,

Fig: (d) microstructure of micro alloyed steel at magnification 500× nital etche and
(e) microstructure of micro alloyed steel at magnification 200× nital etched.
Continue….

 Tensile properties of different steel sheets:
The strain hardening index value(n) of the HSLA steel is maximum along the
rolling direction and minimum along 45◦ orientation to rolling direction
The strength coefficient (K) of the HSLA steel is minimum for 90◦ orientation
to the rolling direction and maximum for 45◦ direction to the rolling direction

 The strain hardening exponent (n) value indicates stretchability and
formability. As the strain hardening index value (n) increases, the
stretchability also increases
 Since the HSLA steel consists of larger grains compared to both carbon–
manganese and microalloyed steels, it possess comparatively less strength
coefficient value (K)
 whereas the grain size of carbon–manganese and microalloyed steels is
fine and pancake type and they also possess higher strength coefficient
value
Continue….

Formabilility parameters of different steel sheets:

Forming limit strains:
 Carbon–manganese steel with 1.4mm thickness shows better
formability in tension–tension region and plane strain region.
The microstructure of the C–Mn steel showing pancake type grain
structure, exhibits higher plasticity range higher (UTS/σy) ratio apart from
low yield stress compared to other two steels
C-Mn steel shows better formability in all regions
The HSLA steel shows poor formability because it contains more
amounts of coarse carbides apart from coarse-grained and equiaxed
microstructure

Fig: Comparison of FLDS for HSLA, microalloyed and carbon–manganese steels
(—) FLD of C–Mn steel ,( ) FLD of microalloyed steel, ( )FLD of HSLA steel,
And (– – –) fracture of C–Mn steel, ( ) fracture of microalloyed steel
and ( ) fracture of HSLA steel
Forming Fracture limit Diagram:

 The plastic major strain obtained is very high in the case of tension–
compression region compared with tension–tension region because the
maximum shear strain developed is very high in tension–compression
region compared with tension–tension region
 The microalloyed steel exhibits fine-grained microstructure with slightly
pancake type .So steel exhibits higher normal anisotropy value and the
ratio of (UTS/σy) value compared to the HSLA steel
 This implies that the microalloyed steel exhibits greater or higher
formability than the HSLA steel

Forming and fracture limit stress diagram:
Fig: (♦) 1.6mm HSLA steel neckingstress, (♦)1.2mm microalloyed steel necking
stress,( ♦) 1.4mm C–Mn steel neckingstress, (◊) 1.6mmHSLA steel fracture stress,
(◊) 1.2mmmicroalloyedsteel fracture stress, ( Δ) 1.4mm C–Mn steel fracture stress,
( ) poly.(1.2mm microalloyed steel necking stress), ( ) poly. (1.6mm HSLA steel
necking stress),( ) poly. (1.2mm microalloyed steel fracture stress), (----) poly.
(1.4mm C–Mn steel fracture stress) and ( )poly. (1.6mm HSLA steel fracture
stress).

 The forming and fracture limit stress values obtained for the HSLA steel are
very much lower compared to other two steels, namely microalloyed andn C–
Mn.
It is due to the presence of coarse and equiaxed microstructure with more
carbides, which are responsible for poor formability at room temperature
 During the tensile test that the HSLA steel exhibited poor percentage elongation
compared to other two steels. Whereas the forming and fracture limit stress
values obtained for microalloyed and C–Mn steels are higher compared to the
HSLA steel
 Among the steels tested, the C–Mn steel exhibits higher forming and fracture
stress values and the gap between forming stress limit curve and fracture
stress limit curve is found to be higher for the C–Mn steel.
Due to the reasons that the C–Mn steel has pancake type of microstructure

 σ1/σy vs. σ2/σy based forming and fracture limit diagram for HSLA
and microalloyed steel and carbon–manganese steel:
The gap between the forming curve and fracture curve in these plots is
higher for the C–Mn steel and lower for the HSLA steel because the
normal anisotropy value is higher for the C–Mn steel and lower for the
HSLA steel.

The normal anisotropy value of microalloyed steel is in between that of
the C–Mn steel and the HSLA steel.
Therefore, the gap between the forming curve and fracture curve for the
microalloyed is in between that of the C–Mn steel and the HSLA steel
Continue….

 Void size:
 The measured void size for each sheets used in forming and fracture is
reported in Table given below and the corresponding SEM photomicrographs
are provide as described in figures(1),(2),(3).

 SEM images for the fracture surfaces of microalloyed steel:
Fig.1: (a) Fracture surface for tension–compression conditions at magnification 5000×,
(b)fracture surface for tension–compression conditions at magnification 7000×,(c)
fracture surface for plane strain condition at magnification 3000×,(d) fracture surface
for plane strain condition at magnification 15,000×,(e) fracture surface for tension–
tension conditions at magnification 5000× and (f) fracture surface for tension–tension
conditions at magnification 10,000×.

 SEM images for the fracture surfaces of HSLA steel:
Fig.2: (a and b) Fracture surface for tension–compression conditions at
magnification 1500×, (c) fracture surface for plane strain condition at magnification
1500× and(d–f) fracture surface for tension–tension conditions at magnification
1500×

 SEM images for the fracture surfaces of carbon–manganese steel:
Fig.3: (a) Fracture surface for tension–compression conditions at magnification
3000×,(b) fracture surface for tension–compression conditions at magnification
5000×, (c) fracture surface for plane strain condition at magnification 2000×, (d)
fracture surface for plane strain condition at magnification 10,000×, (e) fracture
surface for tension–tension conditions at magnification 5000× and (f) fracture surface
fortension–tension conditions at magnification 10,000×.

 Mohr’s circle for shear stresses:
 To determine shear stresses the expressions used,

 Void size vs. (γ12/εm) for HSLA, microalloyed and C-Mn steel sheets

 The ratio of shear strain (γ12/εm) increases the void size increases.
 Also the rate of increase in void size with respect to is (γ12/εm) higher for C–Mn
steel due to the reason that it exhibits higher formability and higher normal
anisotropy value apart from higher thickness compared to other steels.
 In the case of HSLA, the rate of increase in void size with respect to (γ12/εm) is
lower.
Continue….

 The C–Mn steel compared with other steels for which t (γ23/εm) range value varies
from(−25 to 5) in case microalloyed steel and (−20 to 10) in the case of HSLA steel
compared to other steels
 The pancake type of grain structure is responsible for higher normal anisotropy
which resists thinning in the thickness direction during forming
Since the thickness of the C–Mn steel is high, the void sizes observed are also
bigger in size compared with other two steels.
Continue….

o A study on fracture behaviour of three different high
strength low alloy steel sheets during formation with
different strain ratios

• (a) Microstructure of HSLA steel at magnification 400x– nital etched.
(b) Microstructure of Carbon–Manganese steel at magnification 500x –
nital etched.
 The microstructures of HSLA, Micro alloyed and C–Mn steels:

(c) Microstructure of of C–Mnsteel magnification 200x–nital etched.
(d) Microstructure of microalloyed steel at magnification 500x – nital etched.
(e) Microstructure of microalloyed steel at magnification 200x–nital etched.

 L/W ratio of voids versus (єm/єeff ) for different steel sheets:

The effective strain and mean strain are important in determining this
mechanism and formability.
As the strain ratio (єm/єeff ) increases, the L/W ratio decreases.
The rate of decrease in the L/W ratio is higher for HSLA because of
the presence of more coarse carbide particles compared with the other
two steels.
Continue….

 Difference between necking and fracture stress ratios versus n-value:
Fig: (a) Difference between necking and fracture stress ratios versus n-values
for 100 mm blank width (tension–compression region)
(b) Difference between necking and fracture stress ratios versus n-values
for 140 mm blank width (plane strain region)

Continue….
Fig: (c) Difference between necking and fracture stress ratios versus n-value for
200 mm blank width (tension–tension region).
 As the n-value increases, the tension-compression range increases and this
slope is found to be maximum for tension–compression region of forming for all
steels and this slope is found to be minimum for tension–tension region for all
steels

 Difference between necking and fracture stress ratios versus r-value:
Fig: (a) Difference between necking and fracture stress ratios versus r-values
for 100 mm blank width (tension–compression region)
(b) Difference between necking and fracture stress ratios versus r-values for
140 mm blank width (plane strain region)

Continue….
Fig: (c) Difference between necking and fracture stress ratios versus r-values for
200 mm blank width (tension–tension region).
 The variation of localized necking with respect to r-value of the sheets is
similar to that with respect to n-value of the sheets.
This range is found to be maximum for the C–Mn steel and minimum for the
HSLA steel
 The behaviour of Micro alloyed steel is in between the C–Mn and the HSLA
steels.

oStrain Limit of Extra Galvannealed Interstitial-Free and Bake
Hardened Steel Sheets Under Different Stress Conditions:
 Chemical composition of bake hardened steel: (mass percent, %)
 Chemical composition of extra galvannealed IF steel: (mass percent, %)

Chemical composition :
• Both the steels have lower amounts of carbon.
• The BH steel contains lower amount of manganese and silicon compared
to extra galvannealed IF steel.
• The presence of manganese and silicon in extra galvannealed IF steel
increases the strength.
• The presence of sulphur is detrimental to hot forming process. It
enhances machinability.
• Aluminum is an active deoxidizer; it controls the inherent grain size in the
BH steel rather than extra galvannealed IF steel.
• Titanium is added in extra galvannealed IF steel to give porcelain enamel
finishing.

Microstructure of bake hardened steel [(c) and (d) ] :
Microstructure of extra galvannealed IF steel [(a) and (b)] :
(All the samples were etched with Nital)

o Microstructure:
• The microstructure of the extra galvannealed IF steel shows the pancake
type of grain structure and BH steel possesses necklace type of grain
structure.
• It is again a well-known phenomenon, that the former enhances the
formability than the later.
• It is well seen from the microstructure, that the grains are fully
recrystallized in the case of extra galvannealed IF steel.

oGalvanized steel coating cross section showing a typical coating
microstructure consisting of three alloy layers and a layer of pure metallic zinc :
The steel industry uses a "galvannealing process" to produce the corrosion-
resistant sheet metal now used in virtually all the world's automobiles.
The process combines zinc atoms with iron atoms in a steel surface at high
temperatures.
The protective layer of zinc-iron alloy formed prevents the steel from rusting
through, as shown in Figure.

Tensile properties of bake hardened steel
From the tensile test, n-value, K-value, and r value of extra galvannealed
IF steel are greater than those of BH steel, which are attributed to the
superior formability of the steel sheet.
oTensile properties :
Tensile properties of extra galvannealed
IF steel

FLD of extra galvannealed steel FLD of bake hardened steel
o Forming limit diagram:

Continue…….
 The formability of extra galvannealed IF steel is superior to the steel. In
plane strain region, the extra galvannealed IF steel accommodates 23. 5%
of major strain and for BH steel, the strain accommodation is only 17. 5 %.
 In the tension-tension region, the extra galvannealed IF steel
accommodates 35% of major strain corresponding to 10% minor strain.
 The BH steel accommodates only 30% of the major strain corresponding
to 10% of the minor strain.
 This further proves that extra galvannealed IF steel possesses superior
formability characteristics compared to BH steel.

oForming limit diagram for Indian interstitial free steels:
Chemical composition of the two IF steels (in weight %) :
Since IF steels are free from interstitial elements namely carbon and nitrogen, these
steels possess excellent ductility and formability.
The interstitial free (IF) steels are made by adding titanium and/or niobium to the
molten steel after degassing and this usually offers excellent drawability.

(a) IF steel of thickness 0.6 mm, (b) IF steel of thickness 1.6 mm.
oMicrostructure of IF steels – magnification 250x – Nital etched :
IF steels are the materials with good formability and also with stiffness which is
required for vehicle safety. So, IF steels are now used for automobile body applications.

Tensile properties of IF steel of
thickness 0.6 mm
Tensile properties of IF steel of thickness
1.6 mm
oTensile properties :
The IF steel of 0.6 mm thickness possesses maximum n-value along rolling direction and
minimum n-value along 45 orientation to rolling direction.
For the same sheet, K-value is maximum along rolling direction and minimum at 90
orientation to the rolling direction.
 The IF steel sheet of thickness 1.6 mm also shows maximum n-value along rolling direction
and minimum n-value along 90 orientation to rolling direction.
The K-value is maximum along the rolling direction and minimum along 90 orientation to
the rolling direction.

Formability Parameters of IF steel of thickness 0.6 and 1.6 mm :
The IF steel sheet of thickness 0.6 mm exhibits maximum r value along 45 orientation to
the rolling direction and minimum r value along rolling direction.
The IF steel sheet of thickness 1.6 mm exhibits maximum r value along 90 orientation to
the rolling direction and minimum r value along the rolling direction.
The average nr value represents stretchability and as the nr value increases, stretchability
also increases.
The average n-value is maximum for the IF steel of thickness 1.6 mm which shows high
stretchability when comparing with the IF steel of thickness 0.6 mm.

oForming limit diagram :
FLD for IF steel sheet with 0.6 mm thickness. FLD for IF steel sheet with 1.6 mm thickness.

Continue…..
 When comparing both sheets, it is clear that IF steel sheet of thickness 1.6 mm
exhibits better stretchability and drawability than that of other one.
 In particular, in tension–tension region, IF steel sheet of thickness 1.6 mm
possesses a maximum minor strain of 22 percent where as the other one
possesses only 16.5 percent.
 In tension–compression strain condition also the IF steel sheet of thickness 1.6
mm exhibits better formability than the other one.
 For both sheets, in the tension–compression region the formability is good
because sheet metals accommodate more amount of plastic deformation
when comparing with the tension–tension region.

oLongitudinal strain distribution profiles for IF steel :
IF steel of thickness 1.6 mmIF steel of thickness 0.6 mm

 The strain distribution profiles for both sheets are similar and they are
almost symmetrical about the pole.
 The IF steel sheet of thickness 0.6 mm is subjected to a major strain of 4–
11 percent at the pole region (where there is no fracture found) for
various blanks.
 The major strain value increases as the distance from the pole increases
on both sides.
Continue…

oThickness strain distribution profiles for IF steel of thickness 0.6 mm in
different directions :
Longitudinal direction (i.e., parallel to
rolling direction)
Transverse direction (i.e., perpendicular
to rolling direction)

Diagonal direction (i.e., 45 to rolling
direction)
 The thickness strain distribution
profiles for various blanks of both
sheets are shown in Figs.
 Both the sheet metals show that
there is a minimum thickness
strain at the pole in the case of all
the blanks formed.
 The thickness strain increases as
the distance from the pole
increases, reaches the peak value
and then decreases.
Continue…

oThickness strain distribution profiles for IF steel of thickness 1.6 mm in
different direction :
longitudinal direction (i.e., parallel
to rolling direction)
Transverse direction (i.e.,
perpendicular to rolling direction)

Diagonal direction (i.e., 45 to rolling
direction)
The thickness strain of various blanks of
IF steel sheet of thickness 0.6 and 1.6 mm
at the pole is about 4–9 percent and 6–12
percent , respectively.
This proves that the sheet metal which
has high thickness accommodates more
amount of plastic strain or deformation.
In the case of longitudinal and diagonal
directions, the peak value represents the
fracture. Where as along the transverse
direction, no fracture region has been
encountered.
Continue…

oLimiting minor strain (Є2 )at
fracture versus blank width :
oVariation of strain ratio (Є2/ Є1) with
respect to blank width:
The limiting minor strain values obtained are higher for the IF steel having 1.6 mm
thickness compared with the IF steel of 0.6 mm thickness.
 This shows that the higher thickness sheet shows greater formability.
For both sheets, the limiting minor strain at fracture increases as the blank width
increases. This shows the variation from the tension–compression to tension–tension
conditions.

oVariation of depth of cup with respect to
shear strain :
oVariation of depth of cup with respect
to blank width :
It is known that as the shear strain increases, the depth of the cup increases because
the high shear strain represents more plastic deformation.
It is also observed that as the blank width decreases, the depth of the cup increases for
both the sheets as shown in the Fig.

oSEM images of various blanks of IF steel of thickness 0.6 mm and 1.6 mm (a–c) Fracture
surface for tension–compression conditions at 750x magnification. (d) Fracture surface
for plane strain condition at 750· magnification. (e and f) Fracture surface for tension–
tension conditions at 750 x magnification.
1. Thickness 0.6 mm 2. Thickness 1.6 mm

 For the blanks subjected to tension–compression strain condition, the SEM images
show many number of bigger size micro voids and dimples and its surface seems
rough and irregular as shown in the Figs.
 For the blanks subjected to plane strain condition, the surface is smooth compared
with the tension–compression condition and number of voids are less, dimples are
shallow and some are of feature less areas.
 For the blanks subjected to the tension–tension strain condition, the number of
voids is less and it appears to be partly ductile and partly brittle.
 The SEM images of IF steel sheet of thickness 1.6 mm show very big and deep
voids which means that the higher thickness sheet can accommodate more
amount of plastic deformation.
Continue…

oShear strain obtained from Mohr circle radius vs. average diameter of the voids :
oAverage void sizes for various blanks :
 The plot is a linear line and as the shear strain developed on the material increases,
the average void size also increases.

oAn analysis of void coalescence in AL 5052 alloy sheets annealed
at different temperatures formed under different stress conditions:
 Chemical composition of aluminium 5052 alloy (in wt%):
Al 5052 is one of the higher strength non-heat-treatable alloys.
It has high fatigue strength and is a good choice for structures subjected to excessive
vibration.
The alloy has excellent corrosion resistance, particularly in marine atmospheres.
The magnesium in the Al 5052 is 2.8%, the presence of magnesium in larger quantity
retards formability but enhances castability and strength.
The percentage of iron in the material is 0.40%, its presence in the alloy increase the
recrystallization temperature.
The presence of silicon is about 0.25% and it improves the fluidity of the alloy

o Microstructure of Al 5052 sheets annealed at different temperatures :
The microstructure of the sheets annealed at 200 ◦
C shows cold worked and elongated
microstructure. No recrystallization has taken place in this case .
The sheets annealed at 250 ◦
C shows partial recovery and no recrystallization.
The microstructure of sheets annealed at 300 ◦
C shows fully recovered and partial
recrystallized grain structure.

Tensile properties of Al 5052 alloy annealed at 200 ◦
C :
C :

C :
C :

• The average strain hardening exponent ( ¯n) value indicates stretchability
and formability. As the n value increases, the stretchability also increases.
• The sheets annealed at 350 C temperature possess a higher value of◦
UTS, compared to other lower annealing temperatures but it possesses a
low yield stress, compared to the rest.
Continue…….

The sheet annealed at 200 C shows poor formability due to the◦
presence of cold rolled grains microstructure.
The microstructure of the sheet annealed at 350 C shows a refined◦
and recrystallized grains show better formability in all regions.
o FLDS for Al 5052 sheets annealed at different temperatures :

o FLDS for Al 5052 sheets annealed at different temperatures :
The sheet annealed at 350 C exhibits higher (UTS/◦ σy) ratio with low
yield stress, higher (¯r) value and favorable microstructure for the
formability, when compared to the rest of the annealing temperatures.
 The sheets annealed at 350 C have higher (UTS/◦ σy), which in turn
increases the formability.

o SEM images taken for the fracture surfaces for Al 5052 sheets annealed at
different temperatures:
b. 250 ◦
C.
a. 200 ◦
C.
The sheets annealed at 350 C shows large number of voids◦ in the SEM images taken
at its fracture surface compared to rest of the other three annealing temperatures, viz.
200 , 250 and300◦
C.

o SEM images taken for the fracture surfaces for Al 5052 sheets annealed at
d. 350 ◦
C.c. 300 ◦
C.
This large number of voids is because of the accommodation of high plastic strain by
the presence of fully or partially recrystallized grains in the annealed microstructure of Al
5052.

o d-factor versus mean strain (εm) for Al 5052 sheets annealed at
different temperatures :
The d-factor linearly increases as the hydrostatic strain increases for all the four annealed
temperatures.
The rate of increase in d-factor with respect to mean strain is naturally high in the case of
lower annealing temperature, viz. 200 C because the cold worked microstructure is not◦
completely eliminated and hence there is no instance of recrystallization.

o d-factor versus strain triaxiality factor for Al 5052 sheets
annealed at different temperatures:
As the strain triaxiality factor increases the d-factor also increases. Form the figure, the
sheets annealed at 350 C show lower slope value and therefore this sheet exhibits better◦
formability.

o d-factor versus mean strain (εm) for Al 5052
sheets annealed at different temperatures:
o d-factor versus strain triaxiality factor for Al
5052 sheets annealed at different temperatures:
The rate of change of both d-factor and d-factor with respect to hydrostatic strain and
strain triaxiality factor are different because of the different void radius observed for in
different sheets annealed at different temperatures.

o Void area fraction versus mean strain (εm)
for Al 5052 sheets annealed at different
temperatures :
From Figs. 1 and 2, it is observed that the void area fraction is highest for the sheets
annealed at 350 C temperature in tension–tension strain condition, because for this◦
condition the SEM images shows more void surface area per a constant representative
material area compared to the tension compression condition.
o Void area fraction versus strain triaxiality
factor Al 5052 sheets annealed at different
temperatures :

o Lode factor versus stress triaxiality factor
temperatures:
It is observed that the Lode’s factor is lesser with respect to stress triaxiality factor, for
sheets annealed at 350◦
C and the same increases with decreasing annealing
temperatures.
It implies that lesser Lode’s factor promotes higher formability in sheets annealed at
350 ◦
C.
o Lode factor versus strain triaxiality factor
temperatures:

o Strain triaxiality factor versus stress triaxiality
factor Al 5052 sheets annealed at different
temperatures:
It is also understood that stress triaxiality factor also has very good correlation with the
strain triaxiality factor.
It is evident that as the annealing temperature increases the L/W ratio gradually
decreases.
The L/W ratio is lesser value in for tension–compression condition to a higher value for
tension–tension condition. As the L/W ratio increases the proneness to fracture also
increases.
o (L/W) ratio of voids versus minor strain
at fracture for Al 5052 sheets annealed at

o Mohr’s circle shear strain :
Strain triaxiality factor (To) is calculated by
To = εm/εe

A plot drawn between the ratio (L/W) voids and Mohr’s circle shear strain , shows straight
line with negative slope.
Since , one of the strains is tensile in nature and the other is compressive, the tension–
compression condition exhibits a larger Mohr’s circle shear strain .
It is also evident that with decrease in the L/W ratio of the void the increase in Mohr’s
circle shear strain is greater for sheets annealed at 300 ◦
C
.
o (L/W) ratio of voids versus γ23 for Al 5052 sheets annealed at different
temperatures:

temperatures:
In a plot drawn between the ratio (L/W) of voids and the shear strain , the shear strain
measured is the lowest in tension–tension region and the (L/W) ratio of voids is larger
for the sheet annealed at 200 ◦
C compared with rest of the annealed temperatures.

temperatures:
 All the sheets annealed show negative slope value, and the range of γ13 is higher for sheets
annealed at 350 ◦
C, which represents higher formability, compared to rest of the annealing
temperatures.

o (L/W) ratio of voids versus (γ12 /εm) for Al 5052 sheets annealed at
The plot made between (L/W) ratio and (γ12 /εm), shows that the (L/W) ratio decreases
with the increasing ratio of (γ12 /εm).

o (L/W) ratio of voids versus strain triaxiality factor for Al 5052 sheets
annealed at different temperatures.
 As the strain triaxiality factor (εm/εe) increases the (L/W) ratio also decreases .
The rate of decrease in (L/W) ratio is higher for sheets annealed at 200 ◦
C due to its cold
worked microstructure.

oStudies on void coalescence analysis of nanocrystalline cryorolled
commercially pure aluminium formed under different stress conditions:
 Fractographs of cryorolled commercially pure aluminium of 0.25 mm thickness:
(a) notch radius of 1.0 mm;
(b) notch radius of 1.5 mm;
(c) notch radius of 2.0 mm;
(d)notch radius of 2.5 mm
.

(e) notch radius of 3.0 mm; (f) notch radius of 3.5 mm;
(g) notch radius of 4.0 mm; (h) notch radius of 5.0 mm.
Continue…..

o TEM micrograph in cryorolled condition :
o TEM micrograph in cryorolled condition exhibiting severe dislocation cell structure;
inset exhibits ring pattern with streaks:

o Variation of major strain with respect to minor strain for both forming and
fracture:
 The strain obtained for fracture limit diagram is higher than that of forming limit
diagram.
 The reason is that the fracture limit diagram includes the deformation due to
necking and fracture. Necking and fracture takes place after forming only.

o Variation in d-factor with strain triaxiality ratio (T0):
o Variation in void area fraction with strain triaxiality ratio (T0):

o Variation in L/W ratio of voids with minor strain (e2):
The length to the width (L/W) ratio of voids varies from 1.6 to 2.4 in the case of
conventionally rolled sheet. In contrast, L/W ratio is very close to 1.0 in the case of
cryorolled sheet.
Thus no oblate or prolate voids were observed during cryorolling and the formation of
equiaxed nanostructured grains was also observed.

o Variation in L/W ratio of voids with c12:

In the case of cryorolled sheets, minimal variation in L/W ratio was observed with
the variation in the shear strains, due to the presence of nanostructured grains .
In the case of conventionally rolled material, wide variation in the L/W ratio with the
variations in the shear strains was observed.

o Variation in L/W ratio of voids with strain triaxiality ratio (T0):
Figure has been plotted between L/W ratio of voids observed in the SEM
images and the strain triaxiality ratio (T0) and it is observed that the L/W ratio
variation and void area fraction is similar with respect to T0.

o Effect of microstructure on void nucleation and
coalescence during forming of three different HSLA
steel sheets under different stress conditions
 Geometrical details of microstructural constituents:
 Void nucleation and growth inducing factor:

 d-Factor versus mean strain (εm) for three different steel sheets:
 The d-factor for any given mean strain in the case of C–Mn steel is found to be
the least of all sheets tested
Due to the reason that it has developed very bigger size of voids compared to the
ligament thickness of metal section in between two voids
 D-factor is highest for HSLA steel due to the presence of coarse carbide
microstructure
And the behaviour of microalloyed steel is in between HSLA and C–Mn steel.

δd-Factor versus mean strain (εm) for three different steel sheets
HSLA steels:
 δd-factor which is nothing but the ligament thickness in between two voids
In the case of C–Mn steel the carbide sizes are lengthy with largest aspect ratio
compared to microalloyed steel.
The rate of change of δd-factor with respect to the mean strain is found to be the
highest for microalloyed steel compared to other two steels

 Void area fraction (Va) versus mean strain (εm) for three different
steel sheets:
 The lowest void area fraction in the case of microalloyed steel is due to its
microstructure containing fine carbides with lowest aspect ratio
 The C–Mn steel exhibited carbides with largest aspect ratio has shown the
highest void area fraction for all stress state conditions.
The void area fraction measured in the case of HSLA steel is as same as C–Mn
steel

 d-Factor versus strain triaxiality ratio (T0) for three different steel sheets:
As the strain triaxiality ratio increases, the d-factor also increases. The rate of
change of d-factor with respect to strain triaxiality ratio is found to be the
lowest for C–Mn steel and highest for HSLA steel.
This means that HSLA steel is very sensitive to stress and strain triaxiality ratios
compared to other two steels.

 δd-Factor versus strain triaxiality ratio (T0) for three different steel sheets.
The highest δd-factor has been observed for C–Mn steel and nd microalloyed
steel, δd-factor is found to be the lowest

 Lode’s factor versus stress triaxiality ratio (T) for three different steel
sheets:
Stress triaxiality ratio is found to be highest for HSLA steel and lowest for C–
Mn steel.
The behaviour of microalloyed steel is in between these two steels.
The rate of change of Lode’s factor with respect to stress triaxiality is found
to be the lowest for microalloyed and C–Mn steels and highest for HSLA steels

 Strain triaxiality ratio (T0) versus stress triaxiality ratio (T) for three
different steel sheets:
 The rate of change of strain triaxiality ratio with respect to stress triaxiality
ratio is found to be lowest for microalloyed steel compared to other two
steels.
 The reason may be associated with fine carbides with low aspect ratio.

 (L/W) ratio of voids versus minor strain at fracture for three different
steel sheets:
The HSLA steel shows the highest (L/W) ratio of voids compared to other
steels for any given minor strain value,
 Whereas the C–Mn steel shows the lowest (L/W) ratio of voids and exhibits
better formability

 (L/W) ratio of voids versus shearstrain12, 23 &13 for three different steel sheets:

 (L/W) ratio of voids versus strain triaxiality ratio (T) for three different
steel sheets:
 The plot made between (L/W) ratio and strain triaxiality ratio shows
that the (L/W) ratio increases with the increasing strain triaxiality ratio.
 As the stress triaxiality ratio increases, the (L/W) ratio also increases
and the rate of increase in (L/W) ratio is higher for HSLA steel due to its
microstructure, compared to other two steels

Fig: Microstructure of 19000 Al annealed (a).at 3000
C at 100x and (b).at 3000
C at
400x
 Chemical composition of Al 19000
o Effect of annealing on formability of Aluminium 19000

 Tensile properties of Al 19000 & Formability parameters of Al 19000:

 Forming limit diagram for Al 19000 annealed (a) at 1600
C (b) at
2000
C and (c) at 3000
C:

 Continue…
 The maximum major strain values for sheets annealed at 3000
C is 48%
and the corresponding minor strain value is 12% in tension–compression
region, which is high when compared to other two temperatures
This is due to the fact that the sheet annealed at 3000
C shows high plastic
strain ratio value compared to other two annealed sheets

 Major and minor strain distribution profiles (Longitudinal) 3000
C & 2000
C
annealed. (a) Tension–compression condition, (b) plane strain condition and (c)
tension–tension condition:
◄For 3000
C
►For 2000
C

 Major and minor strain distribution profiles (Transverse) 3000
C & 2000
C
◄For 3000
C
►For 2000
C

 Major and minor strain distribution profiles (Diagonal) 3000
C & 2000
C
◄For 3000
C
►For 2000
C

 Major and minor strain distribution profiles at 1600
C annealed. (a) Tension–
compression condition, (b) plane strain condition and (c) tension–tension
condition:
◄For Longitudinal
►For Transverse

►For Diagonal
 For the blanks subjected to the tension–tension strain condition, the
minor strain (which is tensile in nature) increases to maximum value and
then it decreases
 For the tension–compression condition, the difference between the
magnitude of major strain peak and the minor strain peak is high
 when comparing with the tension–tension condition it because the sheet
accommodates more amount of plastic deformation in the tension–
compression region

 Thickness strain distribution profiles (Longitudinal) 3000
C & 2000
C
annealed. (a) Tension–compression condition, (b) plane strain condition and
(c) tension–tension condition:
◄For 3000
C
►For 2000
C

 Thickness strain distribution profiles (Transverse) 3000
C &
2000
C annealed. (a) Tension–compression condition, (b) plane
strain condition and (c) tension–tension condition:
◄For 3000
C
►For 2000
C

 Thickness strain distribution profiles (Diagonal) 3000
C & 2000
C
annealed. (a) Tension–compression condition, (b) plane strain
condition and (c) tension–tension condition:
◄For 3000
C
►For 2000
C

 Thickness strain distribution profiles at 1600
C annealed. (a)
Tension–compression condition, (b) plane strain condition and (c)
◄For Longitudinal
►For Transverse

►For Diagonal
Continue....
 The strain increases as the distance from the pole increases, reaches the peak value
and then decreases
 Thickness strain distribution profiles are also symmetrical about the pole and the
nature of the variation is similar for all blank
 In the case of longitudinal and diagonal directions, the peak value represents the
fracture whereas, in transverse direction, no fracture region has been encountered.

 Variation of limiting minor strain with respect to blank width. (a) 1600
C
annealed, (b) 2000
C annealed and (c) 3000
C annealed:
 The limiting strain value depends on the temperature of annealing and this
value is found to be maximum for sheets annealed at 3000
C.
 This limiting strain varies from negative values to positive values and this
indicates variation from the tension–compression to tension–tension
condition.

 Variation of depth of cup with respect to blank width. (a) 1600
C
annealed, (b) 2000
C annealed:
 As the blank width decreases the depth of cup increases

 Variation of depth of cup with respect to shear strain obtained from Mohr’s
circle radius. (a) 1600
C annealed, (b) 2000
C annealed:
 The shear strain increases, the depth of cup also increases. The sheet which is
annealed at 3000
C, possessing higher r-value, exhibits higher depth of cup
compared to the other two annealing temperatures.

 Fractography of Al-19000 annealed at 3000
C at 3000x:
Fig: (a) Blank width 220 m (Tension–Tension), (b) blank width 200 m (Tension–Tension),
(c)blank width 180 m (Tension–Tension), (d) blank width 160 m (Tension–Tension), (e) blank
width 140 m (Plane strain) and (f) blank width 120 m (Tension–Compression).

C at 3000x:
Fig: (a) Blank width 220 m (Tension–Tension), (b) blank width 200 m (Tension–Tension), (c)blank width
180 m (Tension–Tension), (d) blank width 160 m (Tension–Tension), (e) blank width 140 m (Plane strain)
and (f) blank width 120 m(Tension–Compression), and (g) blank width 100 m (Tension–Compression).

 For the blanks subjected to tension–compression strain condition (blank
width less than 140 mm) the SEM images show many number of bigger size
micro voids and dimples and its surface is rough and irregular.
It shows the shear type of fracture with deep dimples
 For the blanks subjected to plane strain condition, the surface is smooth
compared with the tension–compression condition and number of voids is less,
dimples are shallow and some are of featureless areas.
 For the blanks subjected to the tension–tension strain condition, number of
void is less and it appears as partly ductile and partly brittle.

 Average Void size:
The average void size decreases as the blank width increases
The sheet which is annealed at 3000
C shows large voids compared to the
other temperatures because these sheets accommodate more amount of
plastic deformation.
The sheet annealed at 1600
C shows smaller void size because this
accommodates lesser amount of plastic deformation

 Variation of average void size with respect to shear strains ε12 (a) 1600
C
annealed, (b) 2000
C annealed:

C
annealed, (b) 2000
C annealed:

C
annealed, (b) 2000
C annealed:
 Fracture occurs when this strain ratio reaches a particular value
 As this strain ratio increases, the average void size also increases because
sheet metals accommodate more plastic deformation

 Variation of Average void size with respect to εm (a) 1600
C annealed, (b)
2000
C annealed:
 For tension compression region the average void size is bigger, because in the
tension–compression condition the metal accommodates more amount of
plastic deformation, bigger void size refers ductile fracture
 In tension–tension condition, the average void sizes are small because of
lesser strain accommodation

oReferences:
 R. Narayanasamy , C. Sathiya Narayanan- Forming, fracture and wrinkling
limit diagram for if steel sheets of different thickness.
 R. Narayanasamy , C. Sathiya Narayanan, N.L. Parthasarathi - Some
analysis on stress and strain limit for necking and fracture during
forming of some HSLA steel sheets.
 R. Narayanasamy , M. Ravi chandran, N.L. Parthasarathi –Effect of
annealing on formability of aluminium grade 19000.
 R. Narayanasamy , N.L. Parthasarathi , C. Sathiya Narayanan ,T. Venugopal
, H.T. Pradhan - A study on fracture behaviour of three different high
strength low alloy steel sheets during formation with different strain
ratios.
 R Narayanasamy, N L Parthasarathi, R Ravindran, C Sathiya Narayanan-
Strain Limit of Extra Galvannealed Interstitial-Free and Bake Hardened
Steel Sheets Under Different Stress Conditions

 R. Narayanasamy , C. Sathiya Narayanan -Some aspects on fracture limit
diagram developed for different steel sheets.
 R. Ravindrana, K. Manonmanib, R. Narayanasamy - An analysis of void
coalescence in AL 5052 alloy sheets annealed at different temperatures
formed under different stress conditions.
 R. Narayanasamy , N.L. Parthasarathi, C. Sathiya Narayanan - Effect of
microstructure on void nucleation and coalescence during forming of three
different HSLA steel sheets under different stress conditions.
 N. Naga Krishna , A.K. Akash , K. Sivaprasad , R. Narayanasamy - Studies on
void coalescence analysis of nanocrystalline cryorolled commercially pure
aluminium formed under different stress conditions.

Dr.R.Narayanasamy - FLD on HSLA, IF steels and Al alloys.

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