# Creep-Fatigue Life Assessment Analysis as per API 579 FFS-I

Some of the equipment’s like tower or reactors are very critical equipment in refineries due to very high temperature and pressure. The temperature is also very high and coke tower works in the creep range for some duration of one full cycle. In such cases, creep along with fatigue plays a very important role in the failure of coke drums.

We will consider the example of coke tower having design temperature as 471 Deg. C and working temperature of 149 Deg. C at the top portion and 441 Deg. C at the bottom portion. Below is the histogram for the thermal loading for the top and the bottom portion of the code tower –

Thermal Histogram –

The skirt to shell junction i.e. Y forging is a critical portion of coke tower because it is highly susceptible to creep and fatigue simultaneously. API 579-1/ASME FFS-1 2007 is used for the creep-fatigue interaction in the present case. A non-linear transient thermal analysis is coupled with the elastic-plastic structural analysis for calculation of stresses and strains. These stresses are further used in deducing a creep damage factor and strains are used for deducing permissible cycles for fatigue as per the approach based on API 579-1. An MPC Omega method code is developed in the Finite Element Analysis Software ANSYS 17.2 for calculation of the creep damage factor and permissible cycles for fatigue. MPC Omega method code validated through manual calculation.

**Now we will see analysis steps to calculate the creep-fatigue life of the equipment for thermal & pressure variation – **

**Transient Thermal Loading Conditions:**

**Loading for Thermal Loading – **

- Temperature Loads for Top/outlet & bottom/inlet section of the tower are applied as mentioned in thermal histogram above, thermal loading profile is as shown in figure 1.
- Effect of Insulation is considered as the effective coefficient of convection and is applied on the outer surface of shell and nozzles as shown below in figure 1, convection calculations are given in table 1
- Effect of fireproofing is considered as the effective coefficient of convection and is applied on outer as well as inside surface of the skirt as shown below in figure 1, convection calculations are given in table 2.

Figure 1 – Thermal loading as per temperature histogram

Table 1 – Convection calculations for shell

Table 2 – Convection calculations for the skirt

**Transient Structural Analysis – **

**Loading & Boundary conditions for Transient Structural Analysis:**

- Imported Thermal result file at all time is coupled with transient Mechanical (structural) loads mentioned below, figure 2 shows imported thermal profile from transient thermal analysis at time 3600Sec. (A schematic of coupled transient thermal and transient structural analysis is shown below in figure 3)
- Self-weight is considered as gravity load in a downward direction as shown in figure 4 below.
- Internal cyclic pressure for top section & bottom section of the tower is applied as shown in figure 4, transient variation of pressure for both sections in graphical format is as shown below in figures 5 & figure 6 for top section & bottom section respectively
- Nozzle Thrusts due to internal pressure are applied to the outer faces of Nozzles as shown in figure 7. Thrust calculations are given in table 3
- Nozzle process loads are applied at the weld edge of the nozzle to shell junction as shown in figure 8. Nozzle loads considered for analysis varies with temperature as shown in figure 11.
- Moment loads are applied at the weld edge of the nozzle to shell junction as shown in figure 9. Moment loads calculations vary with temperature as shown in figure 12.
- Fixed support is applied to the bottom face of the skirt and is shown in figure 13.

Figure 2- Imported Body Temperature

Figure 3- Coupled transient thermal + transient structural analysis layout

Figure 4 – Self-weight & Internal Pressure

Figure 5 – Cyclic pressure for top/outlet section of tower

Figure 6 – Cyclic pressure for bottom/inlet section of tower

** **

Figure 7 – Nozzle Thrusts

Figure 8 – Nozzle Process Loads

Figure 9 – Moment loads on Nozzles

Figure 10 – Nozzle Force & Moment

Figure 11 – Nozzle Force for Nozzle N4 – Detailed view of nozzle load loading

Figure 12 – Moment loads on Nozzles – Detailed view of moment loading

Figure 13 –Boundary Condition-Fixed Support

**Transient Thermal Results**

**Temperature Graph at all time step: –**

**Temperature @ 3600 sec**

**Temperature @ 7200 sec**

**Temperature @ 30600 sec**

**Temperature @ 37800 sec**

**Temperature @ 50400 sec**

**Temperature @ 54900 sec**

**Temperature @ 72000 sec**

**Coupled Transient Structural Results**

**Transient Equivalent von mises Stress plot for cycle**

**Maximum Equivalent Von Mises Stress @ 3600**

**Minimum Equivalent von Mises Stress @ 30600**

**Fatigue Life Calculation for Data Cases according to ASME Section VIII, Division 2, Part 5.**

According to design data, design number of cycles are **400/year** for cyclic temperature & pressure cycle, considering 20 years of design life, the total number of design cycles will be **8000**.

From FEA maximum and minimum stress for the cycle are **305.42** **MPa** & **67.579 MPa** respectively occurred at the skirt to dished end junction as shown in above figure, So the component stress range, ΔS_{P, k }is **237.84 MPa**.

According to point number 5.5.3.2 (ASME Section VIII, Division 2, Part 5, Point 5.5.3.2) the effective alternating stress amplitude for the k^{th }cycle.

Where,

ΔS_{P, k} =237.84 N/mm^{2 }————(The component stress range between two-time point)

K_{f }= Fatigue Strength reduction factor = 1.2 (ASME Section VIII, Div. 2, Table 5.11)

K_{e, k }= Fatigue Penalty Factor = 1.0 (since ΔS_{n,k }< S_{PS })

After solving this we get,

**Salt, k = 142.70 N/mm ^{2}**

To calculate the design no. of cycles following formula is used

Where E_{T} = Young’s modulus for material.

The coefficients C1, C2… are calculated from table 3.F.1 – Coefficient of fatigue curves.

After solving the above equations, we get,

*Et is considered at average cycle temperature.

The fatigue damage factor(D_{f,k}) is **0.13339** which is much less than unity.

As fatigue damage factor is much less than unity, the **design is safe.**

**Creep-Fatigue damage factor calculation as per API 579 Cl 10.5.2.4 (c) For Skirt to dish end junction**

**Cycle Explanation:**

** **The cycle starts with 177 °C & after reaching 441°C in one hour, the cycle will hold at 441°C for next 8000 hours (assuming it as a maximum time of creep range in entire 8000 cycles). Additional 15 min is included at starting the cycle to stabilize temperature from ambient to 177°C. Pressure (0.054917 MPa) is considered throughout the cycle

## Loading & Boundary Condition –

**Transient Thermal load – Temperature**

**Transient Thermal load – Convection**

**Transient Structural Load – Internal Pressure**

**Transient Structural boundary condition**

**Note:** In displacement boundary condition, X-directional displacement is constrained and Y-directional displacement is Free.

## Results –

**Transient Thermal plot for the cycle**

**Temperature counter plot at the end of the cycle**

**Transient Equivalent Von Mises Stress plot for cycle**

**Maximum Equivalent Von Mises Stress****plot at the end of the cycle**

**Accumulated inelastic (creep) strain plot at the end of the cycle**

**Accumulated inelastic (creep) strain plot at the end of the cycle (zoom view)**

Creep damage factor calculation as per API 579 Cl 10.5.2.4 (C)

Creep damage factor calculation as per API 579 Cl 10.5.2.4 (C)

**Solver Output Result (MPC Omega Method Output from Finite Element Analysis Software):**

Creep damage factor(Dc) is 3.058E-05 at the end of the cycle and total accumulated inelastic (creep) strain is 7.88E-06. So, **as per API 579 CL 10.5.2.4 (g)** for total creep damage(3.058E-05) & total accumulated inelastic strain(7.88E-06) are satisfied the limit D_{c}^{Allow}=1 & the equivalent total accumulated inelastic strain (0.005) respectively. As the design is acceptable for this loading conditions.

**As per 10.5.3 Creep-Fatigue Interaction**, Creep damage factor (3.058E-05) and fatigue damage factor (0.13339) are lying down in the chart of figure 10.29 (creep-fatigue damage criteria) for carbon steel. Thus, the design is acceptable for this loading conditions.

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