List of Tables
Chapter 2 Joining of a tube to a sheet through end curling
2.2 Results and discussion
2.2.4 Influence of parameters on the load-displacement behaviour
Chapter 2 2.2.3 Thickness strain evolution, thickness evolution and load-displacement
behaviour of the proposed joining method
The thickness and thickness strain evolution and load-displacement behaviour during the proposed joining method for a typical case (Case 2, Table 2.1) has been described in Fig. 2.18. The joining process can be divided into three regions, region „I‟, region „II‟, region „III‟, as a function of displacement. In region „I‟, in less than 15 mm displacement, the tube moves down and curls along the die groove. In region „II‟, between 15 to 26 mm, the tube moves into the sheet bend; for the rest of the displacement, i.e., above 26 mm, in region „III‟, the unsupported length of the tube above the sheet bends and a neck is formed, completing the interlocking, and forming the joint.
The thickness strain and thickness evolution for Case 2 (Table 2.1) is shown in Fig. 2.18 (a) and 2.18 (b). From Fig. 2.18 (b) it is observed that maximum thinning at the end of the tube is observed at the completion of the tube curling region, region „I‟, after which the thickness of the tube has increased showing tube thickening, although the tube thins down as compared to its initial thickness. Similarly, the maximum load is observed when the tube enters the bend region of the sheet, region „II‟, and the necking starts (Fig.
2.18c). Similar behaviour is observed for all the FE simulation cases of the joining process proposed.
Fig. 2.18 Evolution of (a) thickness strain, (b) thickness, and (c) load, for Case 2 of the proposed joining method
Chapter 2 good representation of the process and it depends on the success and failure of the joint
formed during the proposed process.
The influence of tube length (cases 1-5) on the load-displacement behaviour is shown in Fig. 2.19. It has been found that as the tube length increases, the maximum load decreases, except for Case 2 (Tube length = 76 mm). The case with 70 mm tube length exhibits larger maximum load, while 90 mm tube length needs lesser maximum load. The load requirement is almost same in all the cases, before the maximum load is reached. In case of 70 mm tube length, the tube length is not sufficient to form a full neck in the undeformed part of the tube. In case of tube lengths of 80 mm, 85 mm and 90 mm, the length of the tube is longer than the required tube length and neck is formed above the bent sheet and closer to the bottom surface of the punch and hence the upper surface of the sheet is not compressed. So cases 1, 3, 4 and 5 are the unsuccessful cases depending on the joint formed.
Fig. 2.19 Load-displacement behaviour for different tube lengths (cases 1 to 5, Table 2.1) (US: Unsuccessful, S: Successful)
The load-progression behaviour for different support lengths (cases 6-10) is shown in Fig. 2.20. The case with a tube support length of 34 mm requires minimum load, while that with 36 mm requires maximum. The tube support length of 30 mm delivers an unsuccessful joint. Although tube support length of 40 mm and 42 mm show inconsistent load-progression behaviour, all the four cases (7-10) belong to successful cases of joining and Case 6 is unsuccessful.
Chapter 2
Fig. 2.20 Load-displacement behaviour for different tube support lengths (cases 6 to 10, Table 2.1) (US: Unsuccessful, S: Successful)
From the load-displacement behaviour of different sheet bend radius (cases 11-15, Fig. 2.21), it is observed that with the increase of sheet bend radius, the maximum load decreases, though the variation is small. The reason behind this is with the increase of sheet bend radius the ease with which tube is interlocked inside the bent region increases, so the load decreases, although the decrease in load is insignificant. All these cases belong to the successful cases of joining.
Fig. 2.21 Load-displacement behaviour for different sheet bent radius (cases 11 to 15, Table 2.1) (S: Successful)
It is clear from Fig. 2.22 that with the increase of die groove radius, the maximum load decreases. This is because of the fact that with the increase in die groove radius, the movement of tube across the die groove becomes easier reducing the maximum load. Out of these five cases, Case 17 (die groove radius: 3.6 mm) and Case 18 (die groove radius:
Chapter 2 3.8 mm) are characterized by successful joints, while cases 16, 19 and 20 belong to the
unsuccessful category.
It is observed from Fig. 2.23 that with the increase in Coulomb‟s friction coefficient, maximum load decreases. Here friction is provided between all the interacting surfaces. The decrease in maximum load can be explained with the successfulness and unsuccessfulness of the joint. Here the successful joint is obtained only for friction coefficient of 0.08. For the friction coefficients 0.12 and 0.14, the tube is not locking completely into the bend region of the sheet, so a decrease in maximum load is observed.
For friction coefficient 0.05, the neck in the undeformed length of the tube is not formed just above the sheet; so a good joint has not been obtained. The influence of lower blank holder height and land height are insignificant and arbitrary as seen in Table 2.7.
Fig. 2.22 Load-displacement behaviour for different die groove radius (cases 16 to 20, Table 2.1) (US: Unsuccessful, S: Successful)
Fig. 2.23 Load-displacement behaviour for different Coulomb‟s friction coefficient (cases 21-24, Table 2.1) (S:Successful, US:Unsuccessful)
Chapter 2 Table 2.7 Maximum load observed for different land heights and blank holder heights
Cases Parameter Maximum load (kN)
Land height (mm)
25. 0 95.52
26. 1.5 101.56
27. 2.5 95.49
28. 3 114.033
Lower blank holder height (mm)
29. 0.1 66.12
30. 0.15 65.00
31. 0.20 66.85
32. 0.25 67.78
33. 0.30 65.89