PSI - Issue 2_A

Petteri Kauppila et al. / Procedia Structural Integrity 2 (2016) 887–894 7 under a static internal pressure of 14.0 MPa(g), the static axial stress components caused by the internal pressure, time-varying creep temperature and a time-varying displacement at the end of the tube nozzle Ø44.5x6.3 mm. The displacement is considered to be a result of thermal expansion caused by variable operating temperature and local temperature differences in a large superheater structure. The analyzed lifetime of the header is 150 creep fatigue cycles in which the duration of load changes is one hour and the duration of hold periods at constant load is 200 hours. 893 P. Kauppila et al. / Structural Integrity Procedia 00 (2016) 000–000

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Fig. 2. The FEM-model mesh in ANSYS (a) and the time-varying displacement at the end of the tube nozzle (b). The displacement at the end of the tube nozzle and the creep temperature changes periodically and the periods consist of ramp and hold times (c). Fig. 2. The FE mesh, mainly 20 node hexahedral ANSYS SOLID186 elements & some 10 node tetrahedal SOLID187 elements, and the prescribed displacement history at the end of the tube nozzle. The displacement at the header end and the creep temperature changes periodically and the per ods consist of ramp and hold times. P. Kaup ila et l. / Structural Integrity Procedi 00 (2016) 000–000

0,003 0,004 0,005 0,006 0,007 0,008 0,009 0,010

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Model 1 Model 2

Model 1 Model 2

The main results of the analyses, the values of the damage parameter and the equivalent creep strains at the most critical location are shown in Fig. 3. The most critical location in these analysis was on the surface of the weld between the header pipe and the tube nozzle in all situations, although it shall be noted that these models do not take the special characteristics of a welded joint into account. According to the results, the values of the damage parameter calculated using the model 1 are slightly higher than the values calculated using the model 2. In any case, the values of the damage parameter calculated using the model 1 are only 3–7 pp greater than the values calculated using the model 2, and thus the results of the both models are relatively precise for practical applications. In practical applications the analyzed material can be considered to be damaged, when the value of the damage parameter is over 0.3 and the onset of the tertiary creep phase has occurred. Despite the slight difference in the values of the damage parameter between the models, the equivalent creep strains at the most damaged location are almost equal between the models 1 and 2. 0 0,2 0,4 0,6 0,8 Damage (-) Displacement (mm) Eq. creep strain (-) Fig. 3. Damage distribution near the most critical location of he header. The accumulated damage and the equivalent creep strain at the most critical location as functions of the prescribed displacement. (a) (b) (c) Fig. 3. The accumulated damage of the header at the most critical location (a). The accumulated damage at the most critical locati the accumulated equivalent creep strain at the most damaged location (c) as functions of the length of the displacement in the analys From a practical point of view, the both developed models yield relatively equal results within the tem range 500–600 °C. However, the model 2 is accurate only in relatively high creep temperatures and it b slightly inaccurate as the temperature lowers, which is a result of the assumed Monkman-Grant relations model 1 is more accurate also in low creep temperatures mainly because of its greater flexibility due t number of calibration parameters. Acknowledgements. This work was carried out in the research program Flexible Energy Systems (FLE supported by Tekes and the Finnish Funding Agency for Innovation. The aim of FLEXe is to creat technological and business concepts enhancing the radical transition from the current energy systems sustainable systems. FLEXe consortium consists of 17 industrial partners and 10 research organisatio programme is coordinated by CLIC Innovation Ltd. www.clicinnovation.fi The described model has been implemented in a structural FE-code ANSYS as a user-defined material subroutine USERMAT. Integration of the rate dependent model is performed by using the implicit backward Euler method, which has proven to be accurate especially for large practically usable time step sizes in solving rate-dependent problems (Kouhia et al., 2005), although it does not completely inherit such a nice property when combined with damage, see e.g. Wallin and Ristinmaa (2001). A part of a typical steam boil r superheater header (ø 355.6 mm × 36 m with two symmetry planes) made of T24 steel and operating wi hin a tempera ure range from 500 to 600 ◦ C has been analysed under creep-fatigue loading. The loading consist of a static internal pressure of 14.0 MPa(g), time-varying temperature and displacement at the end of the tube nozzle ø 44.5 mm × 6.3 mm. The displacement is considered to be a result of thermal expansion caused by variable operating temperature and local temperature di ff erences in a large superheater structure. The Young’s modulus has values 175 MPa at 500 ◦ C, 168 MPa at 550 ◦ C and 163 MPa at 600 ◦ C, and it is linearly interpolated betwee these values (Arndt et al., 2000). The Poisson’s ratio is assumed to be independent of temparature and the val e ν = 0 . 3 is used. The analys d lifetime of the header is 150 creep-fatigue cycles in which the duration of load changes is one hour and the duration of hold periods at constant load is 200 hours. The main results of the analyses, damage field ( D = 1 − ω ) and the values of the damage and the equivalent creep strains at the most critical location are shown in Fig. 3. The most critical location in these analysis is on the 0 0,2 0,4 0,6 0, isplacement (mm) 6. Implementation

References

Altenbach, H., Gorash, Y., Naumenko, K., 2009. Steady-state creep of a pressurized thick cylinder in both the linear and the power law Acta Mechanica 195, 263–274. Arndt, J., Haarmann, K., Kottmann, G., Vaillant, J., Bendick, W., Kubla, G., Arbab, A., Deshayes, F., 2000. The T23/T24 Book. 2nd ed., Va