Mean Stress Correction - Alternative Criteria

[wnmascare]

Hi everyone!

These days, I was reading a paper written by Prof. Norman Dowling on mean stress effect on fatigue life, whose title is “Mean Stress Effect in Stress-Life and Strain-Life Fatigue”. This paper and his book on mechanics of materials demonstrate that Goodman, Gerber and Soderberg mean stress correction approaches are not that good because they were proposed, based on a basic error: for Goodman and Gerber criteria, for example, as the alternating stress approaches zero, the mean stress approaches the ultimate stress. Thus, if the alternating stress is zero, how can there be fatigue, since these diagrams were proposed to represent fatigue?

Fatigue and tensile failures are different failure modes and they can’t be treated as if one was a limiting case of the other. As an alternative criterion, Prof. Dowling proposes the use of the Smith-Watson and Topper (SWT) or the Walker criteria, because they don’t depend on tensile properties.

Do you guys agree with that?

I would like to hear the opinion of someone else; because all of this goes against what we have learnt in our machine design classes.

Thank you very much.

 

[metengr]

There is much more to this than you have summarized;

https://www.google.com/url?sa=t&rct...QfcRwMyqw52ODFhlA&sig2=GMCQ-88oAvx_DNLAlNrPFw

 

[mp87]

Hi wnmascare,

I have dealt a bit with the topic in the past and have read both the article you mention and that linked by metengr (plus others).

It makes sense to say that there where no alternating stress is applied, fatigue does not occur. But to a first approximation a tensile load can be considered as a fatigue load which brings to failure in only one cycle (to be precise, the first half cycle where load is increased): this does not sound odd to me and it has actually proven to account reasonably well for the mean stress effect on fatigue strength, provided that the true fracture strength is used instead of the tensile strength (Morrow criterion). If you can provide a reference that challenges this approach, either from Dowling or others, I will be glad to have a look at it.

Both the SWT and the Walker criterion work well provided that the mean stress is non-negative. The latter uses an adjustable fitting exponent which is fixed at 0.5 in the former. Mean stress sensitivity does depend on tensile properties and in fact Dowling proposed a linear dependence of this exponent on the tensile strength for steels (cf. Dowling, Mechanical Behaviour of Materials, 4th ed., p. 456).

 

[TVP]

Lots of information on fatigue at this website:

https://www.efatigue.com/fatiguecalc.html

 

[mrfailure]

I hope this is not off topic, but I always had the impression that any criterion would be based on yield strength, not ultimate tensile strength as is used in both the paper Dowling paper and the site TVP connected to. I guess part of this rationale in my world is the material would be considered to have failed once it has yielded during service. For example, I had used Goodman diagrams using yield strength to define limits and I considered fatigue strength as a constant proportion to yield, not tensile strength. Am I incorrect in this thinking?

 

[metengr]

Not for high cycle fatigue crack propagation. In this case, there is excellent correlation with UTS. Low cycle fatigue crack propagation is a different story.

 

[mp87]

Indeed there exists a modified Goodman diagram which includes yielding as a possible failure mechanism, but the change in slope occurs at quite high mean stresses and is therefore of limited practical usefulness. An exception that is worth mentioning are gas turbine blades, which operate at high (static) mean stress and low (vibratory) alternating stress, but due to the criticality of the application some dedicated methods have been developed which frequently involve the use of fracture mechanics. It is also worth noticing that the threshold stress intensity factor (a quite common material property in fracture mechanics calculations) tends to converge to a a small but finite value at high stress ratios, unlike the admissible stresses approaching zero forecast by stress-based criteria.

 

[mrfailure]

Thanks, mp87. That accounts for my viewpoint: at the time I was working with Goodman diagrams I was also working in the gas turbine industry.

 

[wnmascare]

Hi everyone!

Thank you very much for your replies. I'm sorry for taking too long to thank all of you for your comments, but I had lost my password.

mp87, you said that a tensile load can be considered as a fatigue load which brings to failure in only one cycle. So, based on your statement, do you think the popular criterion we know (Gerber, Sodeberg, Goodman, etc.) will still be in use? or do you think there will be some space for new ones (SWT and Walker criteria) which do not account for material properties like yield and ultimate strenghts?

Thank you very much in advance.

 

[mp87]

IMHO the classical criteria will still be in use for quite a long time, since:
- they provide a simple, phenomenological way to approach the problem;
- as a natural consequence, they are the first mentioned as soon as the mean stress effect is introduced in engineering courses, becoming thus part of the DNA of every engineer dealing with mechanical design;
- they do their work well in many cases (*) and can be employed with success without introducing more sophisticated theories.

For this reason, the "new" criteria are more likely to find room in advanced analyses, which can be both at a stage of basic research as at that of a mature industrial application. I have seen the SWT criterion applied in studies as different as fretting fatigue, notch fatigue, multiaxial fatigue, and contact fatigue. The Walker criterion is less popular, probably because of the imbalance between the higher efforts needed to determine the additional fitting coefficient (which varies from one material to the other) and the somewhat limited increased accuracy with respect to the SWT criterion.

(*) Even the often vituperated Gerber parabola provides an excellent fit for some aluminum and magnesium alloys. Some nice illustrative graphs are reported in Milella, Fatigue and Corrosion in Metals, p. 286.

 

[wnmascare]

mp87

Thank you very much for your clear answer. This was the kind of question I wanted to discuss with someone more experienced.