**Introduction**

This short example has been prepared to demonstrate usage of FEA tool for pressure vessel lifecycle prediction in regard to ASME regulations.

FEA software when properly tempered by comparisons with test data can be highly helpful to provide better answers for many cases.

The purpose of this analysis is to show that this pressure equipment is capable of withstanding

the operation for its intended life cycles. Pressure and temperature is changed for operating condition. Due to the stress range induced by pressure and temperature variation, fatigue crack can be initiated at the discontinuity where fatigue strength is very weak.

The base code for the demonstration is ASME Sec.VIII, Div.2,Appendix.5 (‘10 ED.& ’11 ADD.)

**Analysis Workflow**

Complete analysis process has been presented below. Related video example starts from the point where FEM discretization has been already made.

**Modeling in midas NFX**

**3.1. Analyzed Model**

For the demonstration purposes, only one nozzle has been selected for detailed investigation.

Figure 3: Model Mesh – Nozzle Details

**3.2. Material Data**

Assumed Material data:

Limit Properties at 150 ^{0}C

**3.3. Loads for fatigue calculation **

- One cycle condition has been defined as below:
- Operating Case 1 : 0.5 MPa at 150°C (Unload Phase)
- Operating Case 2 : 0.3 MPa at 150°C (Load Phase) – not presented
- Design Life Cycle, n = 180 000 cycles
- Nozzle Load (Case 2 is not presented):

**3.4. Boundary Conditions**

Constraints have been applied to support lugs. All necessary Degrees of Freedom have been checked for corresponding surfaces and planes.

**Result Post-processing**

**4.1. Results for Case 1 – Unload Phase**

The results below are presented only for display purpose:

In a fatigue analysis, the item of interest is the Von Mises of the Stress Range.

**4.2. Fatigue Analysis**

**4.2.1 Evaluation Point – SCLs
– **Selection of Stress Classification Lines (ASME Section VIII Division 2. ANNEX 5.A.3) :

Pressure vessels usually contain structural discontinuity regions where abrupt changes in geometry, material or loading occur. These regions are typically the locations of highest stress in a component.

For the evaluation of failure modes of plastic collapse and ratcheting, Stress Classification Lines (SCLs) are typically located at gross structural discontinuities. For the evaluation of local failure and fatigue, SCLs are typically located at local structural discontinuities.

For this paper evaluation will be performed for one nozzle only for demonstration purposes. To determine the fatigue lifecycle for pressure vessel it is mandatory to study all critical areas. For SCL other locations should be checked, like: nozzle-to-repad intersection, repad-to-nozzle intersection and varying locations around circumference of the nozzle.

Figure 11: Stress classification line for the nozzle

**4.2.2 Fatigue Assessment Procedure (ASME Section VIII Division 2. 5.5.3)**

**STEP 1** – Determine a load history for vessel.

– Case 01 (Operating Case 1) : 0.5 MPa at 150°C (Unload Phase)

– Case 02 (Operating Case 2) : 0.3 MPa at 150°C (Load Phase)

**STEP 2** – Determine the individual stress-strain cycles and cyclic stress ranges.

– Cycle 1(Normal Operating Case) : Case01(Unload Phase) ~ Case02 (Load Phase)

**STEP 3** – Determine the equivalent stress range for the cycle determined in STEP 2

**Calculated Values for**** (Range of Primary plus Secondary plus Peak Equivalent Stress) for the kth cycle**

**STEP 4** – Determine the effective alternating equivalent stress amplitude (S_{alt,k}) for the cycle

using the stresses calculated in STEP 3.

– As the local notch and effect of the weld is not accounted for in the numerical model,

K_{f} = 4.0

– for fatigue penalty factor, K_{e,k}

Comparing to **S _{ps}** shows that ≤

**S**for all components, and therefore:

_{ps}**1.0**

As the temperature distribution is uniform to all component in each case, there are no thermal effects (ΔS_{LT,k }=0). Therefore, the alternating stress is calculated as follows:

**STEP 5 **– Determine the permissible number of cycles, N_{k} , for the alternating equivalent stress computed in STEP 4, using the fatigue curves provided in Annex 3.F.

For the vessel materials of construction, the smooth bar fatigue curve for carbon steel with cycle temperature below 371ºC and σ_{uts }≤ 552MPa are listed in Table 3.F.10 (ASME Section VIII Div.2 Annex 3.F). Fatigue Curve for 3.F.1 is as follows.

The calculated allowable number of cycles for selected SCL.

**Conclusion**

Considering the result above, current design is not acceptable to resist cyclic condition. The allowable number of cycle for selected component is lower then design cycle of 180 000 .This does not meet code requirement for fatigue.

A couple of comments:

You have assigned a value to Kf of 1, indicating that the local notch and effect of the weld is accounted for in the numerical model. Based on the FEA model that you have shown, you most certainly have not accounted for the effects. And I would suggest that it is not possible to appropriately account for these effects in an FEA – and therefore the use of an appropriate FSRF is always required. At the toe of the fillet weld, your FSRF will depend on the quality level (per Table 5.11/5.12), but it will be no less than 1.5. The root of the fillet, on account of it being uninspectable, will have a FSRF of 4.0. It is often not possible to know, a priori, which weld location will give to you the worst case fatigue stress amplitude, because the FSRF will vary.

S-N curves should always be presented in log-log graphs.

You have made a mistake in units that I have made several times in the past. You went into the fatigue curves assuming that your stress amplitude was in units of ksi, not MPa. At the stress amplitude you report (~10 MPa), you are below the endurance limit. Of course, once you multiply your calculated stress amplitude by the appropriate FSRF, you may end up being above the endurance limit.

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