PSI - Issue 35

Domen Šeruga et al. / Procedia Structural Integrity 35 (2022) 150–158 Sˇ eruga et al. / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 6. a) Strain tensor components at control point 1 and b) stress-strain response at control point 1. Green line represents the response due to inner pressure, blue line represents the response at 20 ◦ C and red line represents the response at 300 ◦ C. The dashed line represents the simulation using the reference model.

components σ 22 and σ 33 are the highest at control point 1 despite the elastic stress-strain response throughout the load history. The temperature change can be noticed in all the stress and strain-tensor components by the change of the slope of the stress-strain response (blue and red lines in Fig. 6). Due to the position of the control point 2, the stress-strain response is more pronounced as compared to the response at control point 1. As none of the global coordinate system axes coincide with the radial direction to the surface, considerable values of stresses occur in all stress-tensor components. The highest value of stress occurs in the stress-tensor component σ 33 , although the widest hysteresis loop occurs in the direction 11. This result is a direct consequence of the rigidity di ff erence of the pipe bend in the two directions at control point 2. Moreover, the kinematic hardening of the material is especially apparent in this direction as symmetrical hysteresis branches appear between 20 and 40 s. The temperature influence can be seen for all the stress and strain-tensor components at control point 2 (blue and red lines in Fig. 7). It is most expressed for the component σ 11 − ε 11 where the hysteresis loop shifts between the reversal points at 50 and 70 s. Additionally, it increases in size due to the decrease of the elastic modulus and the hardening behaviour of the material at 300 ◦ C. This e ff ect consequently increases the dissipated strain energy density and leads to accelerated durability decrease of the pipe bend. A comparable stress-strain response at control points 1 and 2 can be obtained using the reference model (dashed lines in Figs. 6 and 7). Discrepancies occur most probably due to the di ff erent interpolation of the material properties between the test temperatures of 20 ◦ C and 300 ◦ C. Displacements of the pipe bend in steps 1, 2 and 3 are depicted in Fig. 9. It can be concluded from the displacements in x and z-directions (Figs. 9a and 9g) that the pipe bends upwards due to the internal pressure in the first step whilst the arch moves inwards which is evident from the displacements in y-direction in step 1 (Fig. 9d). During the application of the mechanical load in step 2, the horizontal part of the pipe bend moves downwards (displacement in z-direction (Fig. 9h) and the vertical part moves backwards (Fig. 9b) whereas the arch moves outwards (displacement in y direction (Fig. 9e). The displacement of the pipe bend in step 3 is the opposite to the displacement in step 2 (Figs. 9c, 9f and 9i). The fatigue lifetime analysis shows that negligible fatigue damage is accumulated at control point 1 whereas considerable fatigue damage accumulation is expected at control point 2. Using the Prandtl operator approach for the simulation of the stress-strain response, 675 repetitions of the load history would be expected to cause the crack initiation at control point 2. The majority of the fatigue damage accumulation occurs during the mechanical loading at 300 ◦ C (Fig. 8). Similarly, the fatigue lifetime prediction considering the stress-strain simulation with the reference model results in 648 repetitions of the load history. The fatigue lifetime predictions hence di ff er for about 4 %. The