Comparisons and Evaluation of Two-dimensional Approach

It is not the purpose to present a detailed evaluation of the two-dimensional generalized plane strain model for the plates being butt welded in two passes, but some results of the thermal as well as the mechanical analysis are presented and

8 In the three-dimensional model, two rows of filler material transverse to the weld are added at a time. The length of these two rows in the direction of the weld is 7.5 mm as well (i.e. the width of each row is 3.75 mm).

CH A P T E R 6 . AN A L Y S I S O F BU T T WE L D

compared with measurements and the three-dimensional model. The industrial application, which is modelled by the two-dimensional methodology in the following chapter, is thoroughly evaluated.

Temperatures

No special attempt has been made to make the calculated weld pool shape agree with experimental obtained micro-samples. The heat source model is applied as it is optimized for the three-dimensional model with the addition of the estimated heat-spot diameter as considered above. In the following Figure 6.25, a comparison is presented. The root pass is calculated too wide especially in the upper part where the numerical model predicts the shape of the weld pool about 40% wider than the experiments shows. The characteristic weld penetration shape of the second pass, the cover pass, is not captured with the model because of the neglected physics of the melt, e.g. the Marangoni and Buoyancy effects, see Figure 5.4, but the overall dimensions of the weld pool shape agree well with the micro-sample. With the extra degree of uncertainty in the two-dimensional heat source model in mind, the general agreement is acceptable for further evaluations.

FIGURE 6.25 Micro-sample of weld penetration profile (etched cross section of weldment) from the application welded in two passes, with overlay of resulting weld pool shape from two-dimensional numerical calculation.

Comparisons of the calculated transient temperatures in the seven selected distances to the weld centre line with thermocouple measurements (similar to Figure 6.13) are shown in Figure 6.26. Very good agreement is obtained with the two-dimensional model, and by comparing the three-dimensional and two-dimensional models, Figure 6.13 and 6.26, it is seen that temperatures are calculated slightly higher with the two-dimensional approach. This is not unexpected since heat conduction is neglected in the direction longitudinal to the weld, i.e. the out-of-plane direction of the two-dimensional model. Anyway, altogether this validates the assumption that

heat transfer mainly occurs as conduction transverse to the weld⁹, and furthermore that there are no concerns using the two-dimensional cross-sectional approach regarding the thermal analysis in respect to welding plates in a butt-weld as described in this chapter.

FIGURE 6.26 Transient temperatures for welding in two passes in seven selected positions. Two-dimensional calculation compared to measurements (the same as in the comparison with the three-dimensional model presented in Figure 6.13).

Strains and Stresses

The stresses in the three orthogonal directions calculated using the generalized plane strain assumption are shown in Figure 6.27, together with the corresponding neutron diffraction measurements and three-dimensional calculated stresses. To some extent, the high tensile stress zone is almost captured reasonably well, though the level, as expected, is lower compared to the full three-dimensional model.

Where the slope is changing radically, approximately 60 mm from the weld centreline, the measurements and three-dimensional model show a much more smooth tendency compared to the two-dimensional model. Further out in the plates, the deviation between the two numerical approaches is significant.

9 This is also the basis in the assumption, the analytical solutions for temperatures are built upon, when the travel speed of the moving heat source is assumed high. This also explains why these solutions actual yield good results for the temperatures from a moving heat source in welded applications, cf. Rosenthal’s solutions, mentioned in chapter 5.

CH A P T E R 6 . AN A L Y S I S O F BU T T WE L D

About halfway out in the plates, the level and slope of the two-dimensional model and the measurements are almost identical. This is merely a matter of coincidence more than an expression of any physical agreement between the two-dimensional approach and the experiments

FIGURE 6.27 Comparisons of calculated and measured residual stresses after welding in two passes. Neutron diffraction measurements, the three-dimensional model and the generalized plane strain model.

The stresses calculated are inconsiderable in the other two perpendicular directions, i.e. the in-plane directions of the generalized plane strain model. There is no external restraints modelled on the structure and no constraints are able to be build-up by the model itself in these directions. In contrast, the residual stresses, which

-200

exist in the direction transverse to the weld in the real structure, are captured with the three-dimensional model apart from the deviation in level as discussed earlier.

This clearly shows that the nature of the welding processes with arcs travelling across the work piece truly is three-dimensional with respect to residual stresses.

Variations of material parameters were tested with the two-dimensional model as well. Different types of hardening did not reveal significant changes in the outcome, nor did the modelling of the thermal expansion for temperatures above the transition temperature.

Plane Strain versus Generalized Plane Strain Assumption

Comparisons of the generalize plane strain and the standard plane strain assumption are presented here as a curiosity. The stresses in the out-of-plane direction longitudinal to the weld are shown in Figure 6.28.

FIGURE 6.28 Two-dimensional stress calculations in the direction longitudinal to the weld. Plane strain model compared with generalized plane strain model in relation to corresponding neutron diffraction measurements.

The correspondence is considerably decreased with the use of the standard plane strain model. No stress response in compression is developed and the tensile stress zone is far too wide. This is not surprising since, in the plane strain case, the cross section is totally constrained against any deformation in the longitudinal direction.

Moreover, taking into consideration, that the stress state is governed entirely by the contraction of the filler metal, the stress state will be tensile throughout. For the generalised plane strain case, however, a stress field in equilibrium with force

-200 -100 0 100 200 300

-240 -200 -160 -120 -80 -40 0 40 80 120 160 200 240

Distance from Weld Centerline [mm]

Stress (longitudinal to weld) [MPa]

ND-measurements σ_Y 2D FEM σ_Y (plane strain) 2D FEM σ_Y

CH A P T E R 6 . AN A L Y S I S O F BU T T WE L D

resultant of zero, when integrated over the cross section, would be expected as confirmed by Figure 6.28.

The stresses in the in-plane directions calculated with the plane strain model, are practically zero for the same reason as for the generalized plane strain model.