List of Tables
Chapter 2 Joining of a tube to a sheet through end curling
2.1 Methodology
2.1.5 Demonstration and validation of the proposed method at lab scale
Chapter 2
Fig. 2.7 Schematic representation of the proposed criteria for joint quality analyses The criteria proposed to characterize a successfully formed joint are:
1. The neck should be formed just above the sheet such that it compresses the sheet to produce a tight and compact joint.
2. The gap between tube and bottom flange of the sheet should be as minimum as possible, about 0.1 to 0.3 mm, for good interlocking. Actually there should not be any gap between the tube bend region and bottom flange of the sheet. But practically it is found that a gap evolves when the tube bends into the sheet bend region because of straightening of bottom flange region. Hence a practical gap of 0.3 mm is allowed in terms of criterion. If the gap is larger than 0.3 mm, it is believed that the joint will be loose and weak.
3. The bottom flange length of the sheet should be optimized for good interlocking. Too long a sheet flange will restrict the movement of tube beyond the groove region and there are chances of the flange region to bend in the opposite direction. Too short a sheet flange will not support the tube against the neck and will finally yield a loose and weak joint.
All the criteria should be satisfied to obtain a successful joint. The joint is considered unsuccessful even if one of the criteria is unsatisfied.
Chapter 2 components of experimental set-up used for the proposed joining method and final joint
fabricated are shown in Fig. 2.8. The load-displacement behaviour from FE simulations and experiments has been validated for all the three cases.
Table 2.4 Cases for which experimental demonstration have been conducted
Cases* L
(mm)
R (mm) r (mm) S (mm) μ h1 (mm) h2 (mm)
1 (Case 2 in Table 2.1) 76 4 0.82 38 0.1 2 0
2 (Case 17 in Table 2.1) 76 3.6 0.82 38 0.1 2 0
3 (Case 4 in Table 2.1) 85 4 0.82 38 0.1 2 0
*refer Table 2.1
Fig. 2.8 (a) Disassembled and assembled view of different components of the experimental set-up (1: Punch with support length of 38 mm, 2: Punch with support length of 30 mm, 3: Tool used for sheet forming, 4: Die with groove radius of 3.6 mm, 5:
Die with groove radius of 4 mm, (b) final joined component 2.1.6 Pull-out test of tube-sheet joint: experimental approach
For each case given in Table 2.4, six joints have been prepared for pull-out test purpose. Dies with three different slopes, i.e., 0°, 10° and 15° with horizontal have been fabricated for testing purpose of these end formed joints. Out of six joints fabricated for each case, two each will be tested with different angles. Totally 18 joints have been fabricated using the proposed method. The material used for dies is cast iron.
In addition to end formed joints, tube-to-sheet welded joints have been fabricated.
Gas welding of tube-sheet has been conducted at a pressure of 0.5 bar. Acetylene and oxygen gas has been used for welding purpose. Galvanized iron has been used as the filler material during welding. Totally 6 welded joints have been fabricated such that 2 each
Chapter 2 can be tested with different angles. Totally 24 joints have been fabricated (18 made using
end forming technique and 6 made using welding). Fabricated joints with different end forming cases and welded tube-sheet joint have been shown in Fig. 2.9. Each experiment has been conducted twice for repeatability purpose. As it has been earlier mentioned that testing has been conducted on three different planes. First plane is flat die, second plane is on a die making an angle of 10° with the horizontal direction, and the third plane is on a die making an angle of 15° with the horizontal direction. The schematic of dies used for testing along with their dimensions and actual dies have been shown in Fig. 2.10.
Fig. 2.9 Joints fabricated with different cases as given in Table 2.4 and tube-sheet welded joint
The schematic of pull-out test has been shown in Fig. 2.11. Fabricated tube-sheet joints have been kept on testing planes (either flat or angular) with the help of two blank holders supporting the sheet. These blank holders are bolted with the die such that the tube-sheet joint is intact. Now a punch is designed such that a part of length of the tube is inside the slot made in the punch and with the help of bolts the tube is tightened with the punch. The punch is connected to the ram of UTM which pulls the tube in vertical direction. Actually a shaft connects the punch and the ram and then pull-out test is conducted through the upward vertical movement of the ram. In case of angular dies, the inclination of shaft is same as that of inclination of die surface with the horizontal and pull-out test is conducted vertically.
Chapter 2
Fig. 2.10 Dies fabricated for pull-out test, (a) die with 0° angle, (b) die with 10° angle, (c) die with 15° angle (all dimensions in mm and not to scale)
Fig. 2.11 Schematic and experimental set-up fabricated for pull-out test 2.1.7 Pull-out test of tube-sheet joint: FE simulations
Instead of fabricating such a set-up for testing purposes, a simpler way for testing evaluation is to rely on computational approach. The FE simulation prediction has been done through FE code ABAQUS/explicit (version 6.17). For this purpose, both two dimensional (2D) and three dimensional (3D) simulation has been done. To propose the joining method, 2D modeling has been done, since 3D modeling proves to be time consuming and number of experiments are quite high. However, for testing purpose
Chapter 2 mainly 3D modeling has been conducted as the numerical experiments are less in number.
Also 3D modeling provides a better visualization of the process.
For pull-out test simulations, punch and die are defined as rigid parts, while tube and sheet are defined as deformable ones. A tube element size of 0.6 mm and sheet element size of 0.4 mm has been used. For joining simulations, tube element size has been chosen as 0.8 mm and sheet element size has been chosen as 0.6 mm which has been standardized using mesh sensitivity analysis. A sheet element size of 0.6 mm makes only one element in thickness direction for sheet. Similarly, a tube element size of 0.8 mm makes only two elements in thickness direction for tube. During pull-out test simulations, when the deformed tube and sheet with these element sizes are pulled upwards, too much mesh distortion in the joint region is witnessed. Hence further refinement of mesh of tube and sheet has been done. For a tube mesh size of 0.6 mm and sheet mesh size of 0.4 mm simulation converges properly for all cases. Hence a tube mesh size of 0.6 mm and a sheet mesh size of 0.4 mm have been chosen for testing purpose. Element types used for 3D analysis are C3D8R and C3D10M. A friction coefficient of 0.01 has been applied between surfaces assuming lesser interaction between them during pull-out tests as compared to joining. Time period used for present analysis is 0.0005 s. Punch has been given downward vertical displacement during simulation till the neck is formed above the sheet. For successful cases (Case 1 and 2, Table 2.4) neck forms above the sheet, while for unsuccessful case, Case 3, neck does not form above the sheet. In this case neck forms slightly above the sheet because of longer length of the tube.
For pull-out tests the deformed part at the last stage of joining simulation is imported to another .cae file. Here after implementing all the modeling conditions the punch is given displacement in upward vertical direction to test the joint in flat die condition. The simulation is stopped when complete unlocking takes place. For pull-out tests on angular dies, after importing all the parts from joining simulation and then implementing all the modeling conditions for pull-out test, the whole model is rotated through the desired angle at which the test is to be conducted.
The predicted outcome is load-displacement behaviour. During the pull-out test, the tube inside the curled region comes out of the bent part of the sheet and unlocking phenomena starts in the joint region. During Pull-out test simulation, it has been observed that the initial distance between diametric opposite faces of the inside surface of the tube
Chapter 2 in the curled region „D‟ decreases with the further vertical upward displacement of the
punch. Actually it is an important phenomenon which describes the local deformation of the tube. The variation in „D‟ with respect to displacement has been further discussed.
The schematic of FE simulation of pull-out tests along with the definition of „D’ during pull-out tests has been described in Fig. 2.12.
Fig. 2.13 shows different stages during pull-out test of tube-sheet joint. The last stage of tube-sheet joint has been shown in Fig. 2.13a. When the punch is pulled in upward direction, an unlocking phenomena starts in joint region (Fig. 2.13b). The bead above the sheet is stretched upwards and the curled region is also stretched in the upward vertical direction. As a result of this „D‟ decreases. With further displacement the curled region of the tube comes out of the bent part of the sheet, and at the same time, the sheet is also bent in the vertical direction upwards (Fig. 2.13c).
Fig. 2.12 Schematic of (a) pull-out test of end formed joints, (b) localized deformation of tube in curled region
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.