In my last article on Fatigue Analysis, I had explained the basics required for performing fatigue analysis of piping systems. Click here to refresh yourself once again before proceeding further. This article will explain the step by step methodology of actual analysis steps which need to be followed during fatigue analysis using Caesar II. Before I start the analysis steps, a short description of typical fatigue curves is required from where we have to take the allowable limit for fatigue analysis.
The plot of the Cyclic Stress capacity of a material is called the fatigue curve, also known as the S-N curve. ASME Section VIII Div 2 Provide a fatigue curve for various materials.
Fatigue design curves are generated from test data by applying large safety margins to the average property curve. While considering material fatigue in design, an additional safety margin is often applied against the cycles-to-failure at a given stress amplitude. As an example, if a component is cycled continuously over the same stress range (Any constant stress range), a design limit on allowable (permitted) cycles may correspond to the cycle life multiplied by a factor (safety margin) such as 0.8. This is the common safety margin employed in a vessel and piping design. For every material, a fatigue curve is normally generated by an experimental analysis that correlates peak stress range with the number of cycles to failure.
The alternating stress Sa is defined as one-half of the calculated peak stress.
As already mentioned in my last article that fatigue failure may be prevented by ensuring that the number of load cycles N that the system experiences are fewer (lower) than the number permitted for the alternating stress developed. The cumulative effect shall be evaluated in case if there are two or more types of stress cycles that produce significant stresses. The material fatigue resistance at a given applied stress or strain range is a function of a number of factors, including material strength and ductility.
When to perform Fatigue Analysis
Normally the fatigue analysis is performed for existing plants to evaluate the actual cause for any failure. For new plants, the analysis can be performed only if the project specification permits to do so. Refer to project guidelines on the application requirement for fatigue analysis.
Input for fatigue Analysis
Before starting the analysis be ready with the following data which will be required during analysis:
- Fatigue Curve of the piping material
- Enough process data for finding the total number of cycles throughout the design life of the piping system.
Steps for Fatigue Analysis using Caesar II
Assigning the fatigue curve data to the Piping Material in use:
This is done on the Allowable auxiliary screen. Fatigue data may be entered directly or can be read from a text file by clicking the Fatigue Curves Button. Seven commonly used curves are available in \Caesar\System\*.Fat. (For Caesar version 2012, 2013 &2014 you may not find it in few computers, But these are available in earlier versions) Fatigue curves provide a series of S-N data that define the allowable stress with given anticipated cycle and vise versa.
Defining the fatigue load cases:
For this purpose, a new stress type, FAT, has been already defined in the Caesar II database. For every fatigue case, the number of cycles anticipated must also be entered in appropriate space.
Calculation of the fatigue stresses:
Caesar II automatically does this calculation for us. The fatigue stresses, unless explicitly defined by the applicable code are the same as Caesar II calculated stress intensity (Max Stress Intensity), in order to conform to the requirement of ASME Section VIII, Division 2 Appendix 5.
Determination of the Fatigue stress allowable:
The allowable stresses for fatigue analysis are required to be interpolated logarithmically from the fatigue curve based upon the number of cycles (throughout its life) designated in the fatigue load cases. The calculated stress is assumed to be a peak-to-peak cycle value (i.e., thermal expansion, settlement, pressure, etc) for static load cases, so the allowable stress can be extracted directly from the fatigue curve. On the other hand for harmonic and dynamic load cases, the calculated stress is assumed to be a zero–to-peak cycle value (i.e., vibration, earthquake, etc), so the extracted allowable need to be divided by 2 prior to use in the comparison.
Determination of the allowable number of cycles:
The flip side of calculating the allowable fatigue stress for the designated number of cycles is the calculation of the allowable number of cycles for the calculated stress level. This is done be logarithmically interpolating the “Cycles” axis of the fatigue curve based upon the calculated stress value. Since static stresses are assumed to be peak-to-peak cycle values, the allowable number of cycles is interpolated directly from the fatigue curve. Since harmonic and dynamic stresses are assumed to be zero-to-peak cyclic values, the allowable number of cycles is interpolated using twice the calculated stress value.
Reporting the analysis results:
Caesar II provides two reports for viewing the results of load cases of stress type FAT; standard stress report and cumulative usage report. The first of these is the standard stress report for displaying the calculated fatigue stress and the fatigue allowable at each node. Stress reports could be generated individually for each load case and show whether any of the individual load cases in isolation would fail the system or not.
However, in situations where there is more than one cyclic load case potentially contributing to fatigue failure, the cumulative usage report is more appropriate. In order to generate this report, the user should select all of the FAT load cases which contributes to the overall system degradation (possible failure). The cumulative usage report lists for each node point the usage ratio (actual cycles divided by allowable cycles), and then sums (combines) these up for total cumulative Usage. A total value greater than 1.0 indicates a potential fatigue failure.