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# Thermal stress for fatigue

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## Thermal stress for fatigue

(OP)
Dear All

This is the first time I want to perform fatigue calculations based on Sec.VIII div.2 and have got some problems. I am using Ed.2015 of the code.
In the assessment procedure mentioned in 5.5.3.2 it is necessary to calculate the stresses σLTij . The procedure for calculating these stresses is explained in annex. 5-C. My problem is that in part 5-C.3.2 the formula 5-C.5 for Tp does not look correct. This formula can be correct in the following form:
Tp=T-(Tavg+Tb) if Tp is required at the surface. Or in the more general form as:
Tp=T-(Tavg+(1-2x/t)Tb) if Tp is required through arbitrary points on the thickness.
After all, the expression for Tp in Eq. 5-C.5 is not true at all because of the dimensional difference between Tavg and 2Tb/t.
Can anybody help me understand if I am missing something here or if I am right.
Warm Regards.

### RE: Thermal stress for fatigue

You have rightly pointed out a dimensional concern regarding equation 5-C.5. I will check into it further.

Here's my two cents regarding the separation of thermal stresses...

The purpose of separating the thermal stresses from the non-thermal stresses in solely in respect to the calculation of the plasticity correction factor. This factor is imposed because the fatigue curves assume that there is no ratcheting and no stabilized cyclic plasticity. Before the advent of elastic-plastic fatigue methods, it was necessary to invent fudge-factors to bridge the gap between a proper elastic-plastic fatigue analysis and an elastic fatigue analysis. If your cycle does not generate cyclic structural plasticity (Sps<3S or 2Sy), then there is no need for this fudge-factor (the Ke factor). Nevertheless, it may be overly-conservative to apply the full fudge-factor to the total stress range, when it is typically only the thermal stresses which will cause the cyclic plasticity. Hence separating the thermal from the non-thermal.

In my engineering practice, I generally fall into two categories: no cyclic structural plasticity, in which case I use elastic fatigue without any Ke or Kv (that's actually nu, the Greek letter); or I have cyclic structural plasticity, in which case I prefer to use the elastic-plastic fatigue analysis (which also doesn't require any fudge-factors).

Annex 5-C was developed by and for the nuclear folks, who for archaic reasons relating to nuclear plant licensing in the US have been forced to develop these convoluted approaches. My plain and simple advice: stay away from Annex 5-C. Stay away from 5.5.3.2, Step 3 (a) and equation 5.30, but rather use equation 5.36. If that doesn't give you the fatigue life that you need, because of the Ke factor, then skip equation 5.30 and go straight to 5.5.4. You can quickly get mired down in that bog, even for engineers with tonnes of experience.

### RE: Thermal stress for fatigue

(OP)
@TGS4
Thank you so much for your reply. I have some doubts about fatigue calcs. in ASME Sec. VIII Div.2. As far as I know from university days and from other industries, like automotive engineering, when we want to deal with SN curves of fatigue life we must keep in mind that those curves were generally developed for fully reversed condition of loading. Then, if in actual service there is some sort of mean stress we have a problem because the loading is not fully reversed anymore. Therefore, we must use some methods and criteria like Goodman criterion to deal with such problems. In ASME Sec. VIII Div.2 part 5.5 however, there is no mention of mean stresses and in ANNEX 3-F there is no mention of the mean stress also. I mean there is no reference to the spec. based on which these SN curves are developed although the name of smooth bar somehow indicates that the loading condition has been fully reversed.
Now here comes some questions:
- How does part 5.5 include mean stress effects? Mean stress can have significant effect on the fatigue life of a component subject to cyclic loading.
You have mentioned above:
“This factor is imposed because the fatigue curves assume that there is no ratcheting and no stabilized cyclic plasticity.”
Does this mean that with no ratcheting and stabilized cyclic plasticity, the SN curves are developed under the condition of elastic shakedown? Because it seems to be the only remaining case.
Warm Regards

### RE: Thermal stress for fatigue

To answer your last question, yes, elastic shakedown.

Regarding mean stress, the curves assume mean stresses approximately equal to the allowable stress. There is no need to do a mean stress correction. Except for the structural stress method for fatigue of weldments. That has an explicit mean stress correction.

There's a Fatigue of Weldments tutorial being given at the ASME PVP Conference coming up in a few weeks, being given by the creator of the Structural Stress Method.

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