stress ratio fatigue stress amplitude allowable

[albertoruenes]

Hi all,

I know this may sound like a very fundamental question, i just cant find an explanation in the literature.

R is defined as the ratio between the min and max stress, and depending its value has an impact on the fatigue test results by decreasing the stress amplitude as stress ratio decreases for the same number of life cycles.

This R ratio is in direct relation with the mean stress and another graph states that as the mean stress becomes larger the stress amplitude will decrease. This makes total sense as the mean stress will have a greater contribution and actual life of the part will be affected, but i think that mathematically it contradicts the previous R ratio relationship, because as R ratio increases, mean stress also increase.

I know this might be very simple.

I appreciate all the help you can provide.

 

[rb1957]

the maximum stress is less significant than the delta stress of a fatigue cycle.

another day in paradise, or is paradise one day closer ?

 

[albertoruenes]

Thanks for the reply, totally agree the stress range will have the greatest contribution to the fatigue strength, my question is related to the use of fatigue allowables at different r ratios, for example i have a fatigue allowable for a given material of 100 MPa at an R equals -1, for a fully reverse load condition. Another fatigue allowable of 250 MPa for an R ratio equals 0, if i use this R=0 allowable for the goodman diagram and within a straight line connecting this dot, the Su and the stress amplitud(y=axis) i will have bigger allowables for a fully reverse load condition?, i hope i was clear here and you can give me some feedback.

Thanks for all your help

 

[rb1957]

i guess those two allowables are inconsistent with the goodman diagram.

What do you mean by "fatigue allowable" ? The stress for the same life ?
the stress ? which stress ?? (max, alt, cycle, ...)

Looking at AR MMPDS they use Seq = Smax*(1-R)^n, so R = 0 Seq = Smax and R = -1 Seq = Smax*1.4 (approx). Then R = -1 will have a shorter life than R = 0 for the same Smax.

another day in paradise, or is paradise one day closer ?

 

[FastMouse]

The two graphs in the original post are not contradictory.

Restrict the discussion to cases where R < 1.00.

In the first graph, for a given alternating stress, as R increases (and thus the mean stress increases), the fatigue life decreases.

In the second graph, for a given alternating stress, as the mean stress increases (and thus R increases), the fatigue life decreases.

Consistent and logical.

My colleagues are weary of hearing me advise them not to treat R as though it is a physical parameter. It is not. It is a by-product of the measurements (or calculations). For monotonic loading, consider a structural detail in terms of the stress cycle and the fatigue life. The stress cycle can be defined by two physical parameters:
● maximum stress, and
● minimum stress.

An increase in maximum stress while minimum stress is kept constant results in a decrease in fatigue life.
A decrease in minimum stress while maximum stress is kept constant results in a decrease in fatigue life.

All else follows in terms of mean stress effects and R effects.

 

[rb1957]

maximum stress and minimum stress define a stress cycle.

equally, alternating stress and R define a stress cycle.

R has just as much meaning as the three stresses referred to.

the second guide ... "A decrease in minimum stress while maximum stress is kept constant results in a decrease in fatigue life." is valid of +ve R.

-ve R cycles are often truncated to R = 0, conservatively.


another day in paradise, or is paradise one day closer ?

 

[FastMouse]

equally, alternating stress and R define a stress cycle.

Yes. A stress cycle can be defined using any two of:
● maximum stress,
● minimum stress,
● mean stress,
● alternating stress, and
● R
Other parameters could also be imagined. What I meant was that if the focus is on max and min stress, the intuition is easier.

R has just as much meaning as the three stresses referred to.

Mathematically, sure. Physically, less so. R has no units.

the second guide ... "A decrease in minimum stress while maximum stress is kept constant results in a decrease in fatigue life." is valid of +ve R.

Correct. It is also valid for for R<0.

-ve R cycles are often truncated to R = 0, conservatively.

I would hesitate to say that truncation of R<0 stress cycles is conservative. The best I think could be said is that sometimes it does not make the results less conservative.

For instance, when using high load transfer joint data, if the compressive part of an R<0 stress cycle is truncated, the damaging effect of the reversed fastener loading is lost, and the fatigue damage will be under-predicted.

Same kind of thing with open hole data. Truncation means that you loose the effect of the tensile stress at the hole periphery that occurs when the stress is compressive. The location of this tensile stress is not the same as the location of maximum stress when the gross stress is tensile, but still… Depending on the situation being assessed, this can be important.

The lucky thing is that in highly compressive stress fields, da/dn is of course relatively low, so even if the cycles to initiation are under-predicted, the subsequent crack growth is often slow.

 

[albertoruenes]

Thanks for all your answers,

With all your comments i could see now what was the problem. The allowables that i have are actually for Smax at different R ratios(unfortunately the test lab did not specified this at first) , so the Sa will be less for higher r ratios, now when using the goodman diagram it makes sense.

Thanks for sharing all of these key concepts,