The Fracture Mechanics approach uses both the API 579-1/ASME FFS-1, Part 9 [1] and ASME BPVC Section VIII Division 3 [2] Fracture Mechanics Approaches.

The software estimates the crack stability and crack growth rate for pressure vessels, piping systems and storage tanks in service.  The geometries simulated in the workbook are shown in Table 1.  The software can manage multiple load cases (no practical limit on number of load cases) where the number of cycles per year is input as part of the load cases definitions inputs.  These load cycles are described relative to two stress loading conditions, which are referred to as ‘Analysis Cases’. This provides the user with a great deal of flexibility in defining the load cases and allows consideration of multiple simultaneous loads in crack growth modeling.

The software also contains a separate column for the user to enter the through-thickness maximum primary stresses. If this column is not populated, the software uses the Analysis Case 1 stresses to determine the primary stresses for the failure assessment diagram (FAD) stability calculation.

The software has separate input columns for secondary (thermal) stresses and weld residual stresses, which are optional and used as needed to fully describe the state of stress in the component.

An ‘Analysis Case’ (up to two) refers to a single set of stress loading conditions, determined via finite element analysis (FEA) or other calculation approach. Because of the key assumption that after autofrettage or pressure test, the stress range is linear, only two stress solutions and a scale factor are required to fully describe each of the Analysis Case load conditions. The necessary stress profiles are the maximum stress condition (maximum) and the minimum stress condition (minimum). The scale factor describes the relative variation of amplitude among load cases.  The maximum stress FEA loading condition should be based on the maximum total loading experienced.  This is the loading that produces the highest tensile stresses in the fatigue sensitive location and it represents the “100% loading case (i.e. the scale factor =100%). The critical crack size calculations are based on this condition.  If there is a compressive residual stress at this location, the software permits the option of using the total range of crack tip stress intensity to calculate the critical crack size rather than the maximum stress considering the favorable compressive residual stress field.  This produces a conservative result even if the residual stress is not maintained for the life of the vessel.  In addition, this is consistent with the provisions of ASME Section VIII, Division 3, paragraph KD-311.1 (c), which does not permit credit for favorable residual compressive stresses in the weld metal or heat affected zone.  However, this requirement applies only to the traditional fatigue analysis approach described in Article KD-3.  For applications using the fracture mechanics approach in article KD-4, it is possible to determine the weld residual stresses using the approach in Reference [1] Annex E.  The residual stress distribution after autofrettage can then be determined and used in the analysis.

As previously mentioned, each Analysis Case requires its own stress distribution (use of both Analysis Cases is not required) and the crack growth calculation is essentially the same for each Analysis Case. Crack growth loading due to pressurization cycles requires its own pair of stress solutions to define the load conditions and can be addressed as one of the load cases on the cycle definitions worksheet.  These solutions are the maximum pressure condition and the minimum pressure condition.  Scaling is permitted for all load conditions. A minimum and maximum crack opening pressure and the range and maximum (in percent) of the FEA stresses are defined for each load case on the Cycle Definitions worksheet.

The method for fracture mechanics evaluation outlined in API 579-1/ASME FFS-1 and ASME BPVC 2007 Section VIII – Div 3 [2], Article KD-4 and Appendix D are both options for the general calculation approach.  The stress intensity factor solutions provided by API 579-1/ASME FFS-1 [1], Part 9B are used. Part 9B outlines crack front stress intensity solutions for many types of cracks.  The solutions provided are based on a piecewise 3rd order polynomial through-wall stress distribution in the case of a nozzle corner crack. Other components are analyzed using a weight function approach for an arbitrary stress distribution in the uncracked component.  If closed form stress solutions are not available, (as is the usual case), the stress distribution is obtained by curve fitting – typically to a 4th order polynomial – the entered stress solutions. 

In summary, the spreadsheets provide for the calculation of the stress intensity using one of three methods:

1. For nozzle corner cracks, use the solutions in Reference [1] Annex 9B for third order polynomial curve fits and adjust for the discontinuity in the calculated value of KI when switching from one curve fit to the next as described in [2] Div. 3.
2. Closed form solutions as provided in Annex C [1].
3. For other components, use the general weight function solution in Annex C [1].  In this case, KI is determined by integration over the crack depth.   The spreadsheet performs a numerical piecewise integration using the stress at each of the nodes in the FEA solution. The number of steps in the integration is therefore equal to the number of stress nodes minus one.  This results in about 50 to 80 steps for a typical analysis, since a fine FEA mesh is necessary in areas of steep stress gradients.  The specific method is described in [3]