List of Tables
Chapter 2 Joining of a tube to a sheet through end curling
2.2 Results and discussion
2.2.1 Validation for standardizing the FE simulation of end forming of tubes
Chapter 2
Fig. 2.13 Different stages as observed during pull-out test simulation of tube-sheet joint 2.1.8 Energy absorbed during pull-out tests
Energy absorbed by the end formed joint and welded joint during pull-out tests can be calculated as the area under the load-displacement curve (Spena et al., 2015) up to the peak load using following equation:
Absorbed energy = ∫ (2.5) where F is the pull-out peak force and x is the displacement at the peak load. Energy absorbed during pull-out tests is an important output which should be monitored as failure occurs neither in the tube nor in the sheet, rather an unlocking phenomenon takes place.
Now the complete unlocking can happen at different displacements for different joint formation and tests cases. Hence energy absorbed could be different under different testing conditions.
Chapter 2
Fig. 2.14 Load-displacement behaviour validation for tube expansion
It is observed that the FE predictions (both 2D and 3D modeling) match well with the available experimental data and FE simulation data. In the case of load-displacement behaviour (Fig. 2.14), slight deviation is seen between the results of the present work and the available data from Almeida et al. (2006), mainly at the end of the process. Moreover, the experimental data from Almeida et al. (2006) for load-displacement behaviour has been characterized by tube failure and hence the load declines at an early stage (about 35- 38 mm of displacement). This is not observed in the FE simulation data as a failure criterion is required for this purpose. In the case of thickness strain prediction (Fig. 2.15), the results match well with the available data, with the 2D model showing slight deviation. Since the FE simulation has been standardized with acceptable accuracy, a similar approach for modeling the proposed joining method will be followed.
Fig. 2.15 Thickness strain evolution validation for tube reduction
Chapter 2 2.2.2 Optimizing mesh size and time period during FE simulations of the proposed
joining
The effect of the initial mesh size of the tube and sheet on the load-displacement behaviour and the total CPU time has been observed through mesh sensitivity analysis of tube (Fig. 2.16) for a particular case –Case 28 (refer Table 2.1). It is observed that the tube mesh size does not affect the load-displacement behaviour much, while sheet mesh size shows little effect on the maximum load. A sheet mesh size of 0.3 mm shows some deviation from other cases (Fig. 2.17). Moreover, it has been observed that lower the tube element size and sheet element size, larger the total CPU time (Table 2.5). Hence an optimum element size is required for FE simulation so that accurate forming behaviour is predicted with lesser CPU time. For the present analysis, tube mesh size of 0.8 mm has been chosen with two elements in thickness direction, while sheet mesh size of 0.6 mm has been chosen as there is not much difference present in the CPU time for mesh sizes of 0.6, 0.9 and 1.2 mm.
Fig. 2.16 Mesh sensitivity analysis of tube
Chapter 2
Fig. 2.17 Mesh sensitivity analysis of sheet
Table 2.5 Effect of tube and sheet element size on the total CPU time and joint quality
Mesh size (mm) Total CPU time (min) Joint quality Tube
0.25 156.6 Successful
0.5 28.91 Successful
0.8 20.98 Successful
1 23.11 Successful
Sheet
0.3 61.02 Successful
0.6 20.93 Successful
0.9 18.45 Successful
1.2 17.02 Successful
The effect of time period which is given as input during FE simulation in ABAQUS has been varied and its effect on total CPU time and joint quality has been studied. It is observed from Table 2.6 that with increase in time period, the CPU time increases considerably. Moreover, the case of 0.1 s delivered an unsuccessful joint, while other cases have delivered a successful joint. The quality of the joint is assessed by the criteria proposed earlier. Finally, a time period of 0.3 s has been chosen for the entire FE analysis as minimum computational time is seen and it produces a successful joint.
Table 2.6 Effect of time period on CPU time and joint quality
Time period during FE simulation (sec) CPU time (min) Joint quality
0.1 6.71 Unsuccessful
0.3 21.51 Successful
0.5 35.16 Successful
0.7 51.14 Successful
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