Failure Assessment Diagrams
Failure Assessment Diagrams
Construction of failure assessment diagrams
A failure assessment diagram (FAD) gives a 2-parameter approach to assessing a defect. It accounts for the possibility of fracture and plastic collapse separately. These possibilities are plotted on the axes of the FAD as Kr against Lr. The concept of the FAD requires the use of fracture parameters that cater for large scale plasticity. The j-integral is widely used for this purpose. Once the diagram is generated, an assessment point is considered which may lie in the "acceptable" or "unacceptable" region of the diagram.
FAD generated from Zencrack analyses
Several codes of practice provide guidelines for use of the finite element method in creating and using a failure assessment diagram, e.g. R6, API 579, BS7910. The approach is similar in all of these codes. For example to create a FAD:
- undertake a linear elastic FEA and determine the J-Integral values: Jelas
- undertake a plastic FEA and determine the J-Integral values as a function of load, P, or stress, Sigma: Jtotal=Jelas+Jplas
- determine the reference load or stress of plastic collapse (Pref or Sigmaref)
- draw the failure assessment diagram using points (Kr,Lr) where:
Kr = (Jelas/Jtotal)½
Lr = P/Pref or Sigmaref/Sigmays
- draw the vertical cut-off on the Lr axis; this depends on the material properties; for some materials:
Lr(max) = flow stress / yield stress
How can Zencrack help?
Zencrack has been successfully used to carry out Engineering Criticality Analysis (ECA) as per BS7910 and Fitness-for-Service (FFS) investigations and Remaining Life Evaluations as per API 579-RP (2000) and later editions. Plotting of the FAD and Level 2 (stationary crack) or Level 3 (growing crack) investigations can require a number crack sizes and shapes to be considered.
Zencrack provides the capability to speed up the creation of these meshes and the processing of their results. Zencrack can help in generation of a FAD and assessment of an operating condition.
Creation of a FAD
A typical procedure for creating a FAD requires two Zencrack analyses - one elastic and one plastic. The analyses are post-processed using Zencrack's Process utility program to extract the results for particular crack front nodes into csv files for import to Excel. The data can then be manipulated by the user in a spreadsheet to generate the FAD according to the requirements of the particular code they are using. Here we use notation in terms of j-integrals rather than stress intensity factors:
- Elastic analysis: An uncracked mesh is set up for a linear elastic analysis. A single load level is analysed. A Zencrack input file is created to analyse a chosen crack position and size. After the Zencrack analysis is completed, the results are processed and generate a single set of j-integral values at the applied load level in a csv file. In general, each crack front node has a different Jelas value. The Jelas elastic data is then ready for use with the results from a subsequent plastic analysis.
- Plastic analysis: The uncracked mesh is now reconfigured for a plastic analysis of the same defect size by changing the material definition and adding an appropriate specification to increment the load from zero to a maximum value up to a collapse condition. Each load level analysed in the f.e. analysis produces a set of j-integral values. These Jtotal values are extracted into a csv file.
By combining the results in the two .csv files from the two analyses, the FAD can be generated:
- The elastic j-integral values must be scaled to give Jelas at each load level in the plastic analysis. Jelas/Jtotal can then be calculated for each load level and the Kr values are calculated as Kr=(Jelas/Jtotal)½.
- Pref or Sigmaref must be entered into the data (depending upon the code requirement). The calculation of Pref or Sigmaref requires use of the cracked mesh plastic analysis. For example, API 579 (RP-2000) has an equation based approach for Pref, replaced in later editions by use of Sigmaref. An alternative condition could be the use of 5% plastic strain or principal stress criteria. The ratio P/Pref or Sigmaref/Sigmays then gives the Lr values.
The FAD can be plotted using the (Kr,Lr) points.
Assessment using a FAD
When a point is assessed after creating the FAD, an elastic J-integral value is required for the operating load condition and crack size of interest. The Kr value is then calculated as Kr=Koperating/Kmat, where Kmat is an appropriate value of material toughness.
Lr must also be calculated for the operating load. Further input from Zencrack may be required for this purpose.
The assessment point can then be plotted on the FAD.
Note on the Example below
This example was originally generated when code API 579 - RP2000 was current. The example was updated in 2010. The API code has subsequently been revised:
- API 579-RP (January 2000) - American Petroleum Institute’s Recommended Practice 579, Fitness-For-Service, in January 2000.
- API 579-1/ASME FFS-1-2007 - the API and ASME Fitness-For-Service Joint Committee published the first edition of API 579-1/ASME FFS-1 Fitness-For-Service in June 2007.
- API 579-1/ASME FFS-1-2016 (June 2016).
- ASME API 579-1/ASME FFS-1-2021 (December 2021).
Example - Producing a FAD for a nozzle (using API 579 - RP2000)
This example shows the creation of a failure assessment diagram for a nozzle on a pressure vessel. The nozzle is subjected to an internal pressure and a single crack configuration is considered. The crack configuration has two crack fronts - the FAD is generated using results from one crack front node from one of the crack fronts.
The FAD has been produced according to API 579 (RP-2000) (i.e. Pref was calculated using equation B.111).
For this analysis the plastic Zencrack run was configured to contain user specified multiple load increments (rather than using automatic load incrementation). The elastic Zencrack analysis was configured to use the same series of load increments. So in this case, the outputs of the elastic and plastic analyses both contains J values at equivalent load levels. For the elastic analysis this isn't necessary as the J values can be scaled based on results for a single load level. However, for a small model the overhead of running multiple increments is negligible.
Sections of the .csv files from the two analyses with the j-integral values highlighted are shown in Figures 5 and 6.
Figure 7 shows how these results are used directly in a separate worksheet to calculate Kr and Lr. In this example some additional processing of the Zencrack analysis has been carried out to determine Pref using API 579 (RP-2000) equation B.111. The curve of Jtotal/Jelas is used to help determine Pref as shown in Figure 8.
The final FAD from all the data points is shown in Figure 9 with a cut-off for Lr applied in Figure 10.
Figure 1 - Geometry (all dimensions in mm)
Figure 2 - Defect sizes and positions for ten crack configurations. The FAD is generated for run ID #1 containing a crack at position A. (All dimensions in mm)
Figure 3 - Uncracked mesh suitable for all ten defect combinations
Figure 4 - Model with one defect for run id #1. (Plot of maximum principal stress)
Figure 5 - Extract from .csv file from Zencrack elastic analysis (j-integral values highlighted)
Figure 6 - Extract from .csv file from Zencrack plastic analysis (j-integral values highlighted)
Figure 7 - Processing of the Zencrack analyses to calculate Kr and Lr
Figure 8 - Using API579 (RP-2000) equation B.111 to calculate Pref
Figure 9 - The FAD without a cut-off for Lr
Figure 10 - The finalised FAD with a cut-off for Lr
API 579-2/ASME FFS-2 2009 Fitness-For-Service Example Problem Manual, August 2009 (section 9.10).
Comparison of fracture methodologies for flaw stability analysis for high level waste storage tanks (u), P.S. Lam, WSRC-TR-2000-00478, November 2000.