1. 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.)

2. Analysis Workflow

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

3. 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 ⁰C

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.

4. 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_ps for all components, and therefore:  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.

5. 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.