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.

Figure 1: Cyclic pressure test and fatigue failure

Figure 2: Analysis Process

1. Introduction

Lock Hopper – example

Page 1

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,Part 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.

Lock Hopper– example

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

Figure 3: Model Mesh - Nozzle Detail

3. Modeling in midas NFX

Assumed Material data:

3.1. Analyzed Model

3.2. Material Data

Page 2

Temperature

(°C)

Elastic Modulus

(MPa)

Thermal

expansion

coefficient

Poisson’s ratioDensity

(kg/m3)

20 203300 1.15e-005

0.3 785090 198000 1.2e-005

200 190000 1.28e-005

MaterialMinimum

Yield Strength (MPa)

Minimum Tensile

Strength (MPa)

MaximumAllowable Stress

(MPa)

Carbon Steel 230 420 120

Limit Properties at 150 0C:

Lock Hopper– example

One cycle condition has been defined as below:

3. Modeling in midas NFX

3.3. Loads for fatigue calculation

3.4. Boundary Conditions

Page 3

- 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:

0

0,1

0,2

0,3

0,4

0,5

0,6

1 2

Pre

ssu

re [M

Pa

]

Internal Pressure load cycle

0

20

40

60

80

100

120

140

160

1 2

Te

mp

era

ture

[0C

]

Temperature load cycle

Case 1 Force (N) Moment (N-m)

Nozzle No. Fx Fy Fz Mx My Mz

I1 -120 -710 120 14,5 0 14,5 Figure 4: Loads on Nozzle

Constraints has been applied to support lugs. All necessary Degrees of Freedom has been

checked for corresponding surfaces and planes.

Figure 5: Constrained Y translation Figure 6: Constrained X and Z translations

* Case 2 – not presented

Lock Hopper– example

Solid Von Mises stress contour plot has been presented

below:

4. Result Post-processing

4.1. Results for Case 1 – Unload Phase

Page 4

Figure 9: Stress result at Ring Figure 10: Stress result at MANWAY

251.152

44.11

80.8247

34.2517 35.3551

79.4201

Figure 7: Stress result at top area Figure 8: Global Stress result contour map

Results for Case 2 are not published in this paper.

Lock Hopper– example

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.

4. Result Post-processing

4.2. Fatigue Analysis

Page 5

Figure 11: Stress classification line for the

nozzle

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 appropriate areas.

SCL

Figure 12: Stress linearization results

Lock Hopper– example

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

4. Result Post-processing

4.2. Fatigue Analysis

Page 6

Sxx

Figure 12: Stress distribution – nozzle area (Unload Phase),

Stress Distribution Result for Stress Classification Lines

Syy Szz

Sxy Syz Szx

Lock Hopper– example

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

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

(Stress Linearization and Stress calculations in Appendix A.) - continued

4. Result Post-processing

4.2. Fatigue Analysis

Page 7

Cycle ∆𝑺𝒏,𝒌(MPa) ∆𝑺𝒑,𝒌(MPa)

Cycle 1

(Case01~Case02)21.15 21.94

Calculated Values for ∆𝑺𝒏,𝒌 (Primary plus Secondary Equivalent Stress Range)

and ∆𝑺𝒑,𝒌 (Range of Primary plus Secondary plus Peak Equivalent Stress) for

the kth cycle

STEP 4 - Determine the effective alternating equivalent stress amplitude (𝑆𝑎𝑙𝑡,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,

Kf = 4.0

- for fatigue penalty factor, Ke,k Material

S at 150°C= Allowable Stress

(MPa)

Sy at 150°C= Yield Strength

(MPa)

Sps

= Max[3S, 2Sy]

(MPa)

Carbon Steel 120 230 460

Comparing ∆𝑺𝒏,𝒌 to Sps shows that ∆𝑺𝒏,𝒌 ≤ Sps for all components, and therefore: 𝐊𝐞,𝐤 = 1.0

Lock Hopper– example

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

STEP 4 - Determine the effective alternating equivalent stress amplitude (𝑆𝑎𝑙𝑡,𝑘) for the cycle

using the stresses calculated in STEP 3. - continued

4. Result Post-processing

4.2. Fatigue Analysis

Page 8

As the temperature distribution is uniform to all component in each case, there are no

thermal effects (∆𝑺𝑳𝑻,𝒌 = 𝟎). Therefore, the alternating stress is calculated as follows :

Cycle 𝑲𝒇 𝑲𝒆,𝒌 𝑺𝒂𝒍𝒕,𝒌 (𝑴𝑷𝒂)

Cycle 1 (Case01~Case02) 4.0 1.0 43.88

STEP 5 - Determine the permissible number of cycles, Nk , 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 σuts ≤ 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.

Number of Cycles

Stress

(MPa)

Figure 13: Fatigue curve for Carbon Steel

Lock Hopper– example

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

STEP 5 - Determine the permissible number of cycles, Nk , for the alternating equivalent stress

computed in STEP 4, using the fatigue curves provided in Annex 3.F. - continued

4. Result Post-processing

4.2. Fatigue Analysis

Page 9

Cycle 𝑺𝒂𝒍𝒕,𝒌 (𝑴𝑷𝒂) 𝑵𝒌 (𝑪𝒚𝒄𝒍𝒆𝒔)

Cycle 1 (Case01~Case02) 43.88 ≈ 8 * 103

The calculated allowable number of cycles for selected SCL

Cycle𝑵𝒌

(Cycles)𝒏𝒌

(Design Life Cycles)Remark

Cycle 1 (Case01~Case02) 8*103 180 000 Condition is not satisfied

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.