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, ProfessorDepartment of Production Engineering

National Institute of TechnologyTiruchirappalli 620015

Tamil NaduIndia

By

o Forming, fracture and wrinkling limit diagram for IF steel sheets of different thickness :

Definition:

“Forming limit diagram is graphical representationwhich shows the forming limit for various conditionsof 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)M

ajor

stra

in

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:




Forming, fracture and wrinkling limit diagram 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

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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.

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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.

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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)

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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)

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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 BakeHardened 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.

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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.

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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.

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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.

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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 annealedat 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.

The sheets annealed at 350 ◦ C shows very fine recrystallized grains.

Tensile properties of Al 5052 alloy annealed at 200 ◦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 different temperatures:

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 for Al 5052 sheets annealed at different 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 for Al 5052 sheets annealed at different 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 different temperatures:

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:


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.


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 different temperatures:

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.

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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 voidsIn 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 3000C at 100x and (b).at 3000C 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 3000C 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 3000C shows high plastic strain ratio value compared to other two annealed sheets

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

◄For 3000C

►For 2000C

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

◄For 3000C

►For 2000C

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

◄For 3000C

►For 2000C

Major and minor strain distribution profiles at 1600C 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) 3000C & 2000C annealed. (a) Tension–compression condition, (b) plane strain condition and (c) tension–tension condition:

◄For 3000C

►For 2000C

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

◄For 3000C

►For 2000C

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

◄For 3000C

►For 2000C

Thickness strain distribution profiles at 1600C annealed. (a) Tension–compression condition, (b) plane strain condition and (c) tension–tension condition:

◄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) 1600C annealed, (b) 2000C annealed and (c) 3000C annealed:

The limiting strain value depends on the temperature of annealing and this value is found to be maximum for sheets annealed at 3000C.

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) 1600C annealed, (b) 2000C annealed and (c) 3000C 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) 1600C annealed, (b) 2000C annealed and (c) 3000C annealed:

The shear strain increases, the depth of cup also increases. The sheet which is annealed at 3000C, possessing higher r-value, exhibits higher depth of cup compared to the other two annealing temperatures.

Fractography of Al-19000 annealed at 3000C 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).


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).


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 3000C shows large voids compared to the other temperatures because these sheets accommodate more amount of plastic deformation.

The sheet annealed at 1600C shows smaller void size because this accommodates lesser amount of plastic deformation

Variation of average void size with respect to shear strains ε12 (a) 1600C annealed, (b) 2000C annealed and (c) 3000C 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) 1600C annealed, (b) 2000C annealed and (c) 3000C 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.

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