I have taken up this topic to explain the fatigue analysis (Click here to read the basic article on Fatigue Analysis) methodology using caesar II with an example problem of a typical piping system. To perform fatigue analysis we need to calculate the thermal and pressure fluctuations the piping system will undergo in its design life. We have to calculate the worst possible cycles from preliminary data provided by the process/operation department. Let’s assume we received the following data from the process for a typical piping system.
- Operating cycle from ambient (40°C) to 425°C (400,000 cycles anticipated)
- Shutdown external temperature variation from ambient (40°C) to -20°C (300,000 cycles anticipated)
- Pressurization to 5.5 Bars (400,000 cycles anticipated)
- Pressure fluctuations of plus/minus 1.5 Bars from the 5.5 Bars (1,000,000 cycles anticipated)
Now, in order to do a proper fatigue analysis, these should be grouped in sets of load pairs which represent the worst-case combination of stress ranges between extreme states which we can do in the following way (Refer Attached Figure, Fig.1 for proper understanding):
The above figure (Fig. 1) explains calculation of the worst case cycle combination for fatigue analysis
- From -20°C, 0 Bars to 425°C, 7 Bars. 300,000 Cycles
- From 40°C, 0 Bars to 425°C, 7 Bars.: 100,000 Cycles
- From 425°C, 4 Bars to 425°C, 7 Bars: 600,000 Cycles
- From 425°C, 4 Bars to 425°C, 5.5 Bars: 400,000 Cycles
So in Caesar II we can define the above data as follows (Refer Fig. 2): T1= 425°C; T2= -20°CP1= 5.5 Bar; P2= 4 Bar and P3= 7 Bar
Fig.2 above shows the Caesar II spreadsheet explaining the input requirement Now go to the load case editor and define load cases as shown in Fig.3 for fatigue analysis. Click on the load cycles button to input the number of cycles calculated above.
Fig.3 above shows the fatigue analysis Load cases that have to be created for Fatigue Analysis Don’t forget that all load cases with stress type FAT (for fatigue) must have their expected number of Load Cycles specified. After the load cases are prepared, run the analysis to find out the results from the output processor. Part of the output results are provided in the below-attached figures for your reference (Fig. 4 and Fig. 5) The fatigue stress range (Maximum Stress Intensity as calculated in Expansion stress case) may be checked against the fatigue curve allowable for each fatigue load case as shown in Fig 4.
However, this is not a true evaluation of the situation, because it is not a case of “either-or.” The piping system is subjected to all of these load cases throughout its expected design life, not just one of them. Therefore, we must review the Cumulative Usage report, which shows the total effect of all fatigue load cases (or any combination selected by the user) on the design life of the system. Refer to Fig 5 for example.
This report lists for each load case the expected number of cycles, the allowable number of cycles (based upon the calculated stress), and the Usage Ratio (actual cycles divided by allowable cycles). The Usage Ratios are then summed for all selected load cases; if this sum exceeds 1.0, the system has exceeded its fatigue capabilities.