Page 51 - Biaxial Multiaxial Fatigue and Fracture

36 G. SAVAIDIS ET AL.

Local stress and fatigue life calculation for the submodel of the old design
The displacements taken from the coarser model (used for hot spot stress calculations) have
been applied to the submodel’s boundaries. The stress calculation has been performed for
both load cases separately. Possible contact between free surfaces of the tube and the forged
arm has not been taken into consideration. It is worth noting that consideration of such
geometric nonlinearities would result in the fact that the superposition is no longer valid.
Accordingly, increasing numerical expense would be vast. Neglecting this effect allows the
commercial software [ 131 to manage the handling of the nonproportional superposition of the
load cases in order to calculate local stress-time histories for all stress components. Figure 19
shows a cut through the model with plotted normal stresses 0, at bending. It is shown that the
root of the fillet weld is very highly stressed, too. Because of the notch geometry and the
weakening of the cross section the shear stress at the weld root under pure torsion is higher
than in the new design. The stress O, at bending and the shear stress zyU, at torsion along the
circumference of the circle with radius Imm representing the weld root are plotted in Fig. 20,
thus giving a detailed view of the stress distribution of the weld root region encircled in Fig.
19. The positions of the maximal values of the stress components (absolute values) nearly
coincide. Otherwise, the concept-related and in some way artificial introduction of the lmm
notch would have lead to a partial decoupling of the damaging effect from both load cases.

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form maximum st
7

0 921 1.855 2.783 3 710 4 638 5 566
463 1 391 2 319 3 241 4 174 5 102 6 030
DIST
Fig. 19. Cut through the submodel, Fig. 20. Stresses 0, at bending and zyP, at torsion
0, at bending along the weld root

Predicted lifetime is slightly longer for the old design. Now there are three regions with
nearly identical damage sums. In addition to the failure-critical elements on the welding
undercut on tube and forged arm (Fig. 21), there is another location with high damage at the
weld root. This location is shown in the cut in Fig. 21.
Table 3 contains calculated damage sums and blocks to failure for three multiaxial fatigue
criteria, two load cases, interaction of load cases and load levels 1.0 and 1.4. Locations of
failure have been determined to be the same for each criterion. Speculation that the weld root
of the old geometry is failure-critical, too, is verified.