7. Limiting strains

The forming and fracture limit diagrams of various grades of aluminium alloys chosen have been presented in Figure 7 along with the limiting strains of various grades of aluminium at different annealing temperatures. A minor strain of 19% and major strain of 21% have been recorded at the lowest temperature of 200°C. The major strain of the same sheet at PS condition was 31%. In TC region major and minor strains were found to be 33% and 3% respectively. Due to the presence of cold rolled refined grains in microstructure, poor formability was shown by the

sheet annealed at 200°C. The proportionate increase in formability with the annealing temperature has been confirmed through these experiments.

In tension-tension region, the sheet annealed at 250°C possessed a maximum minor strain of 17% and maximum major strain of 37%. In plane strain condition, the limiting major strain was about 39%. In tension-compression strain condition, the maximum minor and major strains were �7 and 38%, respectively. In tensiontension region, the sheet annealed at 300°C possessed a maximum minor strain of 15% and maximum major strain of 41%. In plane strain condition, the limiting major strain was about 41%. In tension-compression strain condition, the strain values increased as the annealing temperature increased. At an annealing temperature of 350°C TT region, the minor strain was 13% and major strain 51%. The fracture limit minor strain was found to be—17% and limit major strain was 53% in the TC region.

The sheet annealed at 350°C exhibited lower yield stress, higher n-value, higher r-value and favourable microstructure for its better formability, when compared to the other sheets. These results were in good agreement with the findings of Narayanasamy et al. [1]. The increased value of n and r for sheet annealed at 350°C showed good stretchability, and it was in agreement with the evaluation carried out using FLD. The tendency for earing was very less during drawing operations due to its very high r-value. This was in good agreement with the findings of Ravindran et al. [26].

### 8. Fractography

The fractured surfaces were studied using scanning electron microscopy (SEM) which revealed the nature of fracture and correlated with formability and its parameters. The fracture zone of formed samples in 10 mm � 10 mm size portion was removed from the fractured specimen, and SEM images were captured from perpendicular face having dimples and voids as a result of fracture. The fractured surfaces were observed using a SEM model LEO 420. The void parameters were recorded from the SEM images through void coalescence studies using CAD 2010 modelling software. Magnifications at 3000, 2000 and 800 X were done using an accelerating voltage of 3 � <sup>10</sup><sup>4</sup> V and an emission current of 9.1 � <sup>10</sup><sup>5</sup> nA.

#### 8.1 Void coalescence study

The voids were analysed with respect to perimeter (πd), relative spacing of the ligaments present between the two consecutive voids (δd), length of void (L) and width of void (W) by using the mouse of the computer. From the perimeter (Tables 6 and 7), the diameter of the voids was determined. In the void parameter, d-factor was determined by using the empirical relation arrived by dividing (δd) by the average radii of the voids present in void perimeters. To find the void area fraction, the total area of voids in that particular area (called representative material area) was calculated:

d � factor ¼ ligament thickness=average radii of the voids (1)

8.2 Void shape

forming) [30, 32–35].

Figure 6.

Table 6.

Table 7.

8.3 Void size

41

plane of the sheet [29].

The shape of the voids and L/W ratio was found to vary with stress/strain ratios. The L/W ratio was high in TT conditions and less in the TC condition. The prolate voids showed elongation along the thickness region whereas the oblate along the

Cupping test specimens of aluminium alloy of three thicknesses, annealed at different temperatures (after

Annealing temperature (°C) Average void size in μm for various metal specimens Deep drawing (tension-compression)

Aluminium and Its Interlinking Properties DOI: http://dx.doi.org/10.5772/intechopen.86553

 7.3 6.19 6.08 5.09 4.51 4.11 3.9 3.7 7.8 7.5 6.55 6.1 5.5 5.2 4.8 4.2 8.5 8.3 7.9 7.5 7.2 6.751 6.24 5.76 10.22 9.92 9.89 9.01 8.5 8.21 8.1 7.99

Average void size found on formed and annealed Al 1350 alloy sheets with different specimen width.

200–250°C zone 1 TC 15.96 7.73 41.90 40.41 42.67

250–300°C zone 2 TC 10.22 8.97 30.99 20.25 25.51

300–350°C zone 3 TC 18.85 19.51 51.70 24.15 29.10

Annealing temperature range Percentage change in void parameters

Percentage change in void parameters for different annealing temperature ranges.

Plane strain Biaxial stretching

60 mm 80 mm 100 mm 120 mm 140 mm 160 mm 180 mm 200 mm

Region δd Void size d-factor (L/W) ratio Va

PS 13.34 19.84 32.39 31.13 19.52 TT 12.07 23.07 31.42 25.05 7.35

PS 10.12 22.95 24.37 18.32 18.07 TT 5.54 29.92 16.65 14.56 11.38

PS 30.48 21.61 52.46 23.27 24.76 TT 33.02 38.71 51.88 28.49 20.11

(tension-tension)

For the blanks subjected to tension-compression strain condition, the SEM images showed many bigger micro-voids and dimples, and their surface was rough

Void area fraction ¼ total area of the voids=representative material area (2)

SEM images were used to measure the relationship between fracture and fomability parameters from the blank shown in Figures 6 and 7.

## Aluminium and Its Interlinking Properties DOI: http://dx.doi.org/10.5772/intechopen.86553


#### Table 6.

sheet annealed at 200°C. The proportionate increase in formability with the annealing temperature has been confirmed through these experiments.

the TC region.

Aluminium Alloys and Composites

et al. [26].

8. Fractography

8.1 Void coalescence study

area) was calculated:

40

In tension-tension region, the sheet annealed at 250°C possessed a maximum minor strain of 17% and maximum major strain of 37%. In plane strain condition, the limiting major strain was about 39%. In tension-compression strain condition, the maximum minor and major strains were �7 and 38%, respectively. In tensiontension region, the sheet annealed at 300°C possessed a maximum minor strain of 15% and maximum major strain of 41%. In plane strain condition, the limiting major strain was about 41%. In tension-compression strain condition, the strain values increased as the annealing temperature increased. At an annealing temperature of 350°C TT region, the minor strain was 13% and major strain 51%. The fracture limit minor strain was found to be—17% and limit major strain was 53% in

The sheet annealed at 350°C exhibited lower yield stress, higher n-value, higher r-value and favourable microstructure for its better formability, when compared to

Narayanasamy et al. [1]. The increased value of n and r for sheet annealed at 350°C showed good stretchability, and it was in agreement with the evaluation carried out using FLD. The tendency for earing was very less during drawing operations due to its very high r-value. This was in good agreement with the findings of Ravindran

The fractured surfaces were studied using scanning electron microscopy (SEM)

The voids were analysed with respect to perimeter (πd), relative spacing of the ligaments present between the two consecutive voids (δd), length of void (L) and width of void (W) by using the mouse of the computer. From the perimeter (Tables 6 and 7), the diameter of the voids was determined. In the void parameter, d-factor was determined by using the empirical relation arrived by dividing (δd) by the average radii of the voids present in void perimeters. To find the void area fraction, the total area of voids in that particular area (called representative material

d � factor ¼ ligament thickness=average radii of the voids (1)

Void area fraction ¼ total area of the voids=representative material area (2)

SEM images were used to measure the relationship between fracture and

fomability parameters from the blank shown in Figures 6 and 7.

which revealed the nature of fracture and correlated with formability and its parameters. The fracture zone of formed samples in 10 mm � 10 mm size portion was removed from the fractured specimen, and SEM images were captured from perpendicular face having dimples and voids as a result of fracture. The fractured surfaces were observed using a SEM model LEO 420. The void parameters were recorded from the SEM images through void coalescence studies using CAD 2010 modelling software. Magnifications at 3000, 2000 and 800 X were done using an accelerating voltage of 3 � <sup>10</sup><sup>4</sup> V and an emission current of 9.1 � <sup>10</sup><sup>5</sup> nA.

the other sheets. These results were in good agreement with the findings of

Average void size found on formed and annealed Al 1350 alloy sheets with different specimen width.


#### Table 7.

Percentage change in void parameters for different annealing temperature ranges.

#### Figure 6.

Cupping test specimens of aluminium alloy of three thicknesses, annealed at different temperatures (after forming) [30, 32–35].

## 8.2 Void shape

The shape of the voids and L/W ratio was found to vary with stress/strain ratios. The L/W ratio was high in TT conditions and less in the TC condition. The prolate voids showed elongation along the thickness region whereas the oblate along the plane of the sheet [29].
