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# Goodman fatigue diagram - which static stress to use?2

## Goodman fatigue diagram - which static stress to use?

(OP)
I have a cylindrical cantilevered titanium rod whose cross section varies along its length. The rod vibrates axially at high frequency and so may fatigue. The free end of the rod has a static axial tensile force and also a static transverse force. These static forces may affect the fatigue life. If I want to use a Goodman diagram (mean stress on the horizontal axis, alternating stress on the vertical axis) to determine the possibility of failure:

Should I use the von Mises static stress as the stress for the horizontal axis? (The von Mises stress would give a composite value for the effect of both tensile and shear stresses.) If not the von Mises stress, then which stress?

Thanks.
Replies continue below

### RE: Goodman fatigue diagram - which static stress to use?

Do not use the von Mises stress to do fatigue calculations unless you have a fully reversed stress duty cycle. As described, you don't. Von Mises applied to fatigue can give wildly inaccurate, and horribly unconservative results when used for fatigue. It only really works in the zero mean stress case because the peak von Mises is nearly equal (sometimes exactly equal) to the max principal and directional stresses.

This is a more complicated problem than it might at first appear to be. You'll need to look at principal stresses due to the combined loads (axial static and dynamic and static transverse) at both extremes of the vibration. Use a Goodman diagram to combine the mean and alternating stresses due to those extremes and judge whether the duty cycle is acceptable.

Doug

### RE: Goodman fatigue diagram - which static stress to use?

(OP)
However, SolidWorks help states "The program always uses the von Mises stress to calculate the mean stress. Since von Mises is a positive quantity, the program assigns the sign of the first mean principal stress to it for the purpose of calculating the associated mean stress." (http://help.solidworks.com/2012/English/SolidWorks... you explain further why von Mises might give inaccurate results?

### RE: Goodman fatigue diagram - which static stress to use?

Depending on the R-Ratio of your stress duty cycle, von Mises may be good enough (full reversed, it's OK) but if you have a non-zero mean stress or when you have non-proportional stress duty cycle using von Mises has been shown to produce unconservative results. It's non-directional and provides no information about the plane accumulating damage during the stress changes. You can have a duty cycle where the von Mises stress does not change but the shear and normal stresses have a wide range.

I've seen several schemes for interpreting von Mises and using the sign from principal stresses but I've never seen any theoretical justification for doing that. I suppose there are ways to pick magnitude and sign that will usually give conservative predictions but I'll bet there's no way to define a universally conservative scheme that won't sometimes lead to excessive over-design.

I wouldn't rely on an FEA software company as a reference for interpreting results, especially not for something as complicated as fatigue analysis. Check out some of the better references on fatigue:
Fundamentals of Fatigue by Bannantine, et.al.
Fatigue of Structures and Materials by J. Schijve
Metal Fatigue by Fuchs & Stevens
Multiaxial Fatigue by Socie & Marquis - this one specifically warns against using von Mises - see page 418

Doug

### RE: Goodman fatigue diagram - which static stress to use?

Hi,

The von Mises Fatigue Criterion, that can be applied ONLY to proportional loading. This criterion can not correctly predict the fatigue life of components subject to non-proportional loading. In some softwares, this criterion is called as "signed von Mises Fatigue Criterion" because the von Mises stress receive the same sign of the 1st principal stress, as mentioned by "dculp1". This is the case of software "MSC.Fatigue" and "nCode".
This criterion can be used to solve problems of proportional loading that have mean stress different from zero. The book "Multiaxial Fatigue" of "Darrell Socie et al." says this on pg 132. The book "Metal Fatigue Analysis Handbook" of "Yung-Li Lee" also shows this on pg 171. So, when mean stress are present, the engineer just need to use SWT, FKM, Goodman or other mean stress correction method to consider the effect of the mean stress. The von Mises Fatigue Criterion is also applicable to uniaxial fatigue problems.

There are dozens of Multiaxial Fatigue Criteria that can be used to solve problems of non-proportional loading. The image attached shows the name of some of these criteria. I recommend to use Findley Criterion to solve this type of problem. This criterion is based on the famous theory of "Critical Plane". But you can use other criteria like McDiarmid, for example. The "Dang Van Criterion" has become well-known in the past years; this is because it has been introduced in some known commercial FE-Fatigue softwares as "nCode Design Life" and "fe-safe". But take care: the Dang Van Criterion are not able to calculate the LIFE (in cycles) that your component will last. This criterion is a "zero or one" criterion, i.e., it only indicate if a component will have an infinite life or if there will occur a fracture.

I hope I have helped in some way.

Regards.

Bruno

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