Dec92 - Evaluation of fatigue stress for life extension

Hello,

I'm reading Mechanical Engineering News Dec92 about life extension estimation of piping system (page 12 to 17). I summary as below. Hoping someone already read thi article to explain more.

In section 3 "System Modification for Life Extension" mention about piping system in Figure 3. The system has 14000 design equivalent cycles for 20 design years. After 18 years, the system undergone 12600 cycles (rate = constant = 12600 cycles/18 years = 700 cycles/year). The goal is to use the system more 20 years beyond original 20 design years.

Maximum stress range 30902 psi in first 18 years gives actual equivalent cycles 15959 cycles which permit 15959-14000 = 1959 additional cycles. It means the system can only be extended life for 1959 cycles/700 cycles per year = 2 years 9 months

Solution is reducing stress range to reduce number of cycles. After modification, reduced stress range is 19582 psi (with expect 22 years x 700 cycles per year = 15400 cycles), the new equivalent cycles is calculated base on below conditions:

a. 12600 cycles @ 30902 psi (undergone first 18 years)
b. 15400 cycles @ 19582 psi (will be undergo next 22 years)
--> N = 12600 + (19582/30902)^5*15400 = 14173 cyles

The paper concludes "this value is less than the calculated allowable number of cycles for maximum stress range, which was 15959. Therefore, with this modification, this system should be adequate for 20 years life beyond its original design life of 20 years."

My question: I don't understand why 14173 cycles smaller than 15959 cycles will help the system to extend more 20 years life?

The author converted the "b cycles" into "equivalent a cycles" and is comparing 14,173 vs the original 14,000.

My approach as below steps:

1. Remaining expect cycles for next 22 years = 22 x 700 = 15400 cycles
2. f shall be 0.8 base on 15400 cylces
3. Calculate SA = 0.8 x [1.25 x (Sc + Sh) - SL]
4. Check SE = 19582 psi < SA
5. Calculate allowable number of equivalent cycles under 19582 psi stress range
---> N = ( 6 x SA / 0.8 / 19582)^5
6. Calculate allowable year "AY" under 19582 psi stress range
---> AY = N cycles / 700 cycles per year
7. If AY > 22 years, then modification is OK

Any comment?

Your calculation has no provision for existing cycle damage. Your original post shows how the new cycles lay on top of the existing (damaged) state of the system. Apply this concept to your calculation.

Using your SA equation as your "fatigue curve" (I find (1a) easier to work with than (1b)), you can calculate how many cycles you are allowed. Call that Na1. Divide the current number of cycles used (N1) by this Na1 - this ratio is the amount of total life used (N1/Na1). Now go to your fatigue curve with your new calculated expansion stress range and see how many cycles you are allowed for this reduced stress range (Na2).
Total, accumulated damage is (N1/Na1)+(N2/Na2). Since you can only consume one "life", you can say (N1/Na1)+(N2/Na2)=1. Now solve for N2.

Hi Dave,

With your N2, if N2/700 > 22 years, then modification is OK. Right?

Regarding my calculation, I will add step 0 and step 5a as folows:

0. Caculate Na1
5a. Check N1/Na1 + "my N2"/Na2 < 1

with:
N1 = 12600
"my N2" = 15400
Na2 from step 5

When "FAT" type load cases are used to determine cumulative usage, does a 100% usage indicate imminent failure ? What order of maginitude of safety factor is built in,in case the actual failure is to be predicted?

Usage factor over 1.00 indicates a fatigue failure. There is no design factor applied in CAESAR II.
Your "typical" fatigue curve used for piping works off a design factor of 2 on stress and 20 on cycles. So there is some room here.

Hi Dave,

Do you have any comment about my question in my 2nd post?

What you state seems reasonable. Since your approach is a little different than mine, I cannot assume that we are saying the same thing in this short exchange. For that reason, I shy away from simply agreeing with what you wrote.