PSI - Issue 5

Etienne Bonnaud et al. / Procedia Structural Integrity 5 (2017) 310–317 Bonnaud / Structural Integrity Procedia 00 (2017) 000 – 000

312

3

by an equivalent heat conduction model. As the actual 3D welding process is modelled by 2D analyses, a central issue is to evaluate the amount of heat transferred to the model for every added bead. Heat source calibration is conducted using the travelling heat source method based on actual Welding Procedure Specifications for Shielded Metal Arc Welding. In practice, temperature is ramped between 20°C to 1500°C under 3s; the bead is then deposited and subsequently hold at 1500°C during 2s. The inter-pass temperature is set to room temperature. The parent and the filler materials are stainless steel AISI 316L. The material behavior is modelled by nonlinear mixed isotropic and kinematic hardening. Strain-stress data for temperatures ranging from 20°C to 1100°C are extracted from Lindgren et al. (2008). Annealing is furthermore assumed to take place above 1000°C. Note that the plate and the pipe simulations share the same geometry and mesh, see Fig. 2; only boundary conditions differ. The model consists of 1468 four nodes elements and 1485 nodes. All simulations are run on the commercial software Abaqus (2014).

(a)

(b)

Fig. 2. Geometry (a) and mesh (b) in the weld region.

4. Plate welding The geometry studied here consists of two 10mm thick plates. The in-plane length is sufficiently large (400mm) to neglect boundary effects and the out-of-plane dimension is supposed to be large enough for plane strain conditions to prevail. The X-weld consists of eight 2mm thick beads, four on each side, see Fig. 3. Boundary conditions are as follows: the left plate is constrained at its outer edge in all three directions whereas the right plate is totally unconstrained. During welding, the right plate moves therefore upwards and downwards and vertical displacement at its right edge is monitored and used as the optimization criterion. Note that the root pass, which obviously does not affect vertical displacement, is not part of the optimization process. In order to take full advantage of this particular geometry, the vertical plane is identified as a plane of symmetry and the horizontal plane as a plane of antisymmetry.

Fig. 3. Sketch of the weld cross-section. Numbers 1 to 8 refer to the positions. Symmetry and antisymmetry planes are shown in blue and red respectively.

Without any loss of generality, it is therefore possible to impose that the first weld pass always be located at position 1. In previous works such as those presented in Section 2, the only rule before starting to fill the pair matrix was to ensure that a pass only could be laid once, in other words that a pass could not be followed by itself. When dealing with a X-weld, it is however compulsory to define additional rules to ensure that the passes are laid in a realistic order: no pass can be followed by the pass at position 1; a pass at position 1 cannot be followed by a pass at position 5, 6, 7 or 8; 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 additional 0's in the pair matrix. With symmetry and antisymmetry taken into account, the total number of possible weld combinations is reduced to 280. As previously mentioned, the first step is to generate the smallest possible set of selected runs which fills the non-zero entries in the pair matrix. Ideally, the pair matrix would only contain 0's and 1's but it generally contains some 2's and sometimes even higher numbers. Here the number of selected runs can be taken down to 6 (which compared to 280 is a substantial improvement) and only three 2's enter the pair matrix. Table 1 shows the selected runs which by construction all start with the pass at position 1. Table 2 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 6 selected runs are shown in Fig. 4. All these runs feature a substantial final displacement, either upwards and downwards.