PSI - Issue 5

Etienne Bonnaud et al. / Procedia Structural Integrity 5 (2017) 310–317

315

Author name / Structural Integrity Procedia 00 (2017) 000 – 000

6

Fig. 7. Sketch of the weld cross-section. Numbers 1 to 8 refer to the positions of each pass. The symmetry plane is shown in red.

During welding, the weld region moves inwards and outwards. The mean value of the horizontal displacement immediately below and above the weld is monitored and used as the optimization criterion. Here again the root pass is not part of the optimization process. The horizontal plane is identified as a plane of symmetry and without any loss of generality, it is possible to impose that the first weld pass be located at either position 1 or 3. The rules to fill the pair matrix in that particular case are: a pass cannot be followed by itself; passes at position 5 and 6 cannot be laid unless both passes at position 1 and 2 are already laid; passes at position 7 and 8 cannot be laid unless both passes at position 3 and 4 are already laid. These rules give rise to 0's in the pair matrix. With symmetry taken into account, the total number of possible weld sequences is reduced to 560. Here the number of selected runs which fills the non-zero entries in the pair matrix can be taken down to 10 (which compared to 560 is a substantial improvement). Table 5 shows the selected runs which by construction all start with a pass at position 1 or 3. Table 6 shows the pair matrix where the vertical index corresponds to the previous pass and the horizontal index to the current pass. The number in the matrix indicates how many times this particular pass combination appears in the selected runs. Results of actual simulations for the 10 selected runs are shown in Fig. 8. All these runs feature a small final displacement inwards.

Table 5: Selected runs for pipes (original).

Table 6: Pair matrix for pipes (original).

3 1 1 3 1 1 3 3 1 3

1 3 4 4 2 2 4 4 2 4

2 2 2 1 6 5 7 2 6 8

4 5 3 8 4 4 2 1 4 2

7 4 6 2 5 6 8 7 3 7

6 8 8 7 3 3 1 8 5 1

5 6 5 5 7 8 6 6 8 5

8 7 7 6 8 7 5 5 7 6

1 0 1 1 1 0 0 1 1

2 4 0 1 2 0 0 1 2

3 1 1 0 1 1 1 0 0

4 1 1 4 0 2 2 0 0

5 1 2 1 1 0 3 1 1

6 1 2 1 1 2 0 1 2

7 1 2 1 2 1 1 0 2

8 1 1 1 2 2 1 2 0

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9

1 2 3 4 5 6 7 8

Run 10

Fig. 8. Simulations results for the 10 selected runs.