Palmgren - Miner's Rule exponent P query

[morris9791]

Dear Experts,

I wish to know is it possible use Palmgren's - Miner's rule to calculate the equivalent torque for a given group of torques / cycles.

We have sufficient data in terms of these torque load cases but I am not sure how I may obtain the exponent p. I understand that I am using the Marco and Starkey Method which augments Miner's rule via the exponent p.

Does anyone know how I may obtain this parameter? Is this a specific material constant? Is there an approximate value we can use for ADI (Austempered Ductile Iron) and Aluminium materials for this exponent?

Any information will be greatly appreciated.
Kind Regards

Eddie

 

[unclesyd]

Here is a little information about the exp "p". It looks as the value using the Marco-Starkey method will be from 0.0 to 1.0. The module from Engineering Tool Box looks interesting and you may be able to download a trial version.
There are several papers from NASA that cover the subject covering metals.

http://www.engrasp.com/doc/etb/mod/fm1/miner/miner_help.html

http://ntrs.nasa.gov/search.jsp?N=4294830851&Ns=PublicationYear|0

 

[morris9791]

Thank you unclesyd

I see that the value for p varies between 0 and 1, however, I have seen values of 3 and above been used....
Perhaps there is a different version of Miners rule used to calculate the equivalent torque from the cumulative torques / cycles.

Regards
Eddie

 

[unclesyd]

I don't believe that you will see any value > 1.0 using the Marco-Starkey method. It states that with an exp value of 1.0 your are reverting to Miner's rule which I take to mean that there is no exp value > 1.0 using the Marco-Starkey method.
We made an attempt to use this approach on some H11 fasteners that we use by thousands in our process and as I recall there was a lot of work to set the value of "p". It ended up that we had made some assumptions concerning our input data on loading the fasteners that created too much scatter. The problems weren't resolved until our mathematician got involved to work on the input data.

 

[morris9791]

Dear Unclesyd,

Thank you for your response. I guess I could be opening up a can of worms trying to get a value for P. This is not necessarily a material constant is it?
Here is the equation that I have seen....
Torque equivalent = (((No Cycles(1)*Applied Torque)^P + (No Cycles(2)*Applied Torque)^P +...... (No Cycles*Applied Torque)^P)^1/p)/total number of cycles

I cant imagine that P for this equation would be a material constant?...
Determining this equivalent torque appears to be more difficult than I thought! Any suggestions will be appreciated.

Kind Regards
Eddie

 

[TVP]

This is most definitely not a material constant.

 

[unclesyd]

From the ETBX page:
The value of P is considered to be greater than 0.0 and less than or equal to 1.0, with the value increasing with stress level. Note that with P = 1.0, this method is equivalent to Miner's Rule.


I would contact the Linda Hall Libary or the ASME to see if you can get a copy of this paper.

Marco, S.M. and Starkey, W.L. (1954) "A Concept of Fatigue Damage," Trans. ASME, Vol. 76, No. 4, pp. 627-632.

http://www.lindahall.org/

 

[prost]

If 'p' is not a material constant, then what is its purpose? To 'adjust' the model to match the results? In which case, it would not be hard to imagine having to empirically determine a 'p' as a function of material, structural geometry, and load spectrum. I assume you have more experience than I do with fatigue, 10 years or more? In my own 10 yrs. experience with this stuff, fatigue analysis still is more art than science, and it is rare to find a 'model' of one sort or another that has some kind of constant that is NOT material, specimen type, and/or load spectrum dependent.

I can't vouch for the veracity of the statements, however you might note at website

http://www.engrasp.com/doc/etb/mod/fm1/miner/miner_help.html

that the author(s) state that "The nonlinear method described has good correlation to observed material behavior and can be used to sum damage in high temperature applications where there is interaction between creep and fatigue. However, like all nonlinear theories, it requires a material constant that requires a considerable amount of testing to determine and may not be available for a given material or application." So 'p' appears to me to be material dependent at least.

 

[metengr]

From the literature I have seen on this to put it simply and to paraphrase, Miner's rule looks at cumulative fatigue damage from a linear standpoint with no synergistic effects from damage mechanisms - in other words this rule assumes that all damage increments add together independently and synergistic effects are ignored. It is also assumed that failure is independent of the order in which the cycles are applied.

Now for nonlinear cumulative damage, the Marco-Starkey theory uses an exponent in the Miner's equation. The exponent is a function of STRESS level. This is a derived quantity based on curves of damage fraction versus cycle ratio plotted as a function of stress levels.

So, in other words, you have to conduct fatigue tests to determine the exponent for use. Here sequence of loading does impact damage fraction curves and provides a better correlation to experimental data.

 

[TVP]

prost,

I meant that the p in the "torque equivalent" equation is not a material constant (see third post by morris9791. P is essentially a material constant in the proper Marco-Starkey equation.

 

[morris9791]

Dear folks,

I understoond P to be a material constant for the Marco-Starkey eqn but for the torque equivalent equation I am trying to determine what p is. There is no sufficient reference given with the equation.


Regards

Eddie

 

[TVP]

Eddie,

In your torque equivalent equation the p is a fitting parameter that must be determined by experimental testing. You won't find this type of information in a handbook, on a website, etc.