Surface stress close to the weld bead of plates in cross joints



I initiated this research with Prof. Bruno Atzori, director of the Fatigue Team at the University of Padua. The results have been successively refined and expanded by the Fatigue Team.
This work aims to separate the overall stress of structural components into a structural contribution (due to the overall shape) and a local contribution (due to the geometric details of the welding). Two models are proposed by using as a study case the symmetrical cross joint whose geometry is specified in Fig. 1.

cross joint butt weld joint
Figure 1: Geometry of one fourth of the cross
joint (FW geometry).		 Figure 2: FEM mesh of the cross joint close to
the weld bead.

In the first model the local stress field corresponds to that of a butt-weld joint, whereas in the second model it is that of a sharply notched joint. The geometries of these components are defined from that of the actual cross joint. The first model is more suitable for practical applications, since it is derived from the common definition of "hot-spot" stress, whereas the second model is more useful from a methodological point of view.
The two-dimensional structural geometries of this study have been analyzed with an ANSYS finite element method (FEM) code by using plain strain elements with three-degree-of-freedom nodes. Figure 2 highlights the FEM mesh of the cross joint close to the weld bead. Analogous meshes were obtained for the other geometries. Since each geometry and its loads are symmetric, only one fourth of the geometry has been analyzed by applying suitable symmetry constraints. Furthermore the following simplifying hypotheses have been adopted.

  • deformations are purely elastic
  • the physical properties of the metal of the plates and of the weld are identical
  • there is perfect penetration between the plates and the weld bead
  • residual thermal stresses caused by welding are neglected
  • errors in the relative position (angles) of the plates are negligible (i.e. secondary bending moments are insignificant)

In model 1 the surface stress is considered to be the combination of the structural stress of a cross joint with fillet bounded by the weld bead, Fig. 3, and the local stress of a butt-weld joint, Fig. 4.

cross joint with R=5 mm butt-weld joint
Figure 3: Geometry of one fourth of the cross joint
with fillet bounded by the weld bead (C1 geometry).		 Figure 4: Geometry of one fourth of the butt-weld
joint (BW geometry).

Figure 5 shows the normalized (by the nominal value) surface stress distribution for the actual cross joint FW, the joint with fillet (C1), the butt-weld joint (BW), and the combination of the last two (C1*BW).

model 1 stresses
Figure 5: Normalized surface stress distribution for the actual cross
joint (FW) and the geometries of model 1 (C1 and BW).

The results support the hypotheses of model 1 since the combined structural and local stress fields from the model closely match that of the actual cross joint.

In model 2 the surface stress is considered to be the combination of the structural stress of a cross joint with fillet bounding the weld bead, Fig. 6, and the local stress of a sharply notched joint, Fig. 7.

cross joint with R=8.536 mm notched butt weld joint
Figure 6: Geometry of one fourth of the cross joint
with radius bounding the weld bead (C2 geometry).		 Figure 7: Geometry of one fourth of the sharply
notched joint (SN geometry).

Figure 8 compares the normalized surface stress distributions of the geometries of model 2 with that of the original cross joint. Again the results validate the model since the combined structural and local stress fields from the model closely match that of the actual cross joint.

model 2 stresses
Figure 8: Normalized surface stress distribution for the actual cross
joint (FW) and the geometries of model 2 (C2 and SN).



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Last modified on: 20 April 2020