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# Stress-life vs strain life approaches in efatigue.com ?

dear collegue

have you ever tried to compare the stress-life approach with the strain-life?

I was experimenting with some students using the website https://www.efatigue.com/with normal notches and normal materials included in the web site database.

It seems that a greater life results with the strain life of a factor 3 - 10, which is frankly much more than I expect.

Is that much possible, or even usually observed? I am doing this simply as a project work, so I haven't looked at the problem very hard, nor I can check what the web site does, but Darrell Socie has a strong reputation so it should be good.

Socie's https://www.efatigue.com/ makes a modification of the SN curve slope ("b-notch") in the stress life approach, well documented in the literature, to account for plastic deformation at shorter lives. This is to take into account of the notch effect, but only towards the very long lives, and not towards static failure. Otherwise you get the illogical conclusion that the stress concentration factor is fully effective in static loading when all of the experiments show that there is stress distribution due to plastic deformation.

In the strain approach plasticity is dealt with directly so no plasticity corrections are needed to the slope. But there remains a correction for surface finish effect.

However, experts like Gregory Glinka tell me that in general, fatigue life predictions based on the strain-life (local notch tip strain) method should be shorter than those obtained by using the S-N (nominal stress) approach. [ The opposite happens sometimes and it is particularly true if one uses the standard S-N curves from IIW or other standardized S-N data bases, shifted down by 2 (more often by 3) standard deviations down from the mean S-N curve corresponding to 50% probability of failure. But this is not the case of the https://www.efatigue.com/ database, which for the nominal smooth and polished specimendoes report the same SN curve for stress-life and strain-life approach.]

Here is an example of the weird results with https://www.efatigue.com/

Material: Steel 1045, Annealed, BHN=225

Steel 1045, Annealed, BHN=225

Material Typesteel

Material Specification AISI 1045

Material Alloy1045

Material ProcessAnnealed

Brinell Hardness Number 225

Elastic Modulus E=207000 MPa

Ultimate Strength Su=752 MPa

Curve Intercept Sf′=867 MPa

Curve Slope b=-0.079

Material Reference SAE J1099 - June 1998 (from eN data)

tension-compression load: sigma_a (R=-1) 300MPa

with stress life approach

N smooth N (ksf=0.5) N (ksf=0.5, Kt=2)

683000 3700 371

with strain life approach

N_smooth N (ksf=0.5) N(ksf=0.5, Kt=2)

671000 120900 6225

So as you can see for smooth specimen, everything is OK: but with surface finish effect, the strain-life results in much longer lives, a factor 30! And when we consider also a notch effect a factor 20 (some improvement!). Notice that I haven't specified the notch radius, so I am not sure what efatigue has assumed!

And this is not corresponding to any fatigue literature, nor even the https://www.efatigue.com/ manual

- Mike Ciavarella's blog
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## Comments

## What types of cyclic

What types of cyclic plasticity models they use? I have checked the website but it is not clear (unless they use the Ramberg-Osgood equation only).

## good point, Kiriakos

Kiriakos

the technical background they use is explained here. The main calculation is using Neuber's rule, with the cyclic curve of the material (which indeed uses RO equation only). The surface finish coefficient is "included in the analysis by altering the slope of the elastic portion of the strain-life curve". The surface finish corrected slope is given by

It is important to note that this correction should be done after the cyclic strength properties are determined.

Now, this means that at static failure, this correction doesn't work, which is fine because one assumes there are no surface finish effects at static failure. But is this done also in stress-life approach? It seems so, if one reads the technical background for stress-life approach here. So it is a mistery what they do, maybe it is a bug in the software? I notice that even ALTAIR supports this software. Prof. Socie would not comment further.

By the way, I notice you are an expert of ratchetting. Long time ago I tried to understand Rolling Contact Fatigue by ratchetting, following the indication of KL Johnson from Cambridge. However, ratchetting in RCF occurs over millions of cycles and it is extremely delicate to model. See my two papers here and here I would be interested to know your opinion.

## p.s. more explanation of the stress-life approach

Notice that in the stress-life approach, the notch and surface finish (as well as the load-type factor) are all treated similarly by modifying the SN curve slope b. This has the effect of changing the slope of the material's SN curve and leaving the intercept unchanged. If we include the modifying factors this new slope, bnotch, can be computed as

and the new notched SN curve will be given by

In the strain-life, as I summarized below, only surface finish remains to modify b-notch, because the other three are not included. However, even the surface finish one doesn't seem to work properly. It is perhaps that the entire SN curve is shifted? I would need to make more numerical tedious experiments to find out.

## Ratcheting

Certainly Mike, I will have a look at your work. Seems very interesting.

We've done some similar work on rail steel ratcheting simulation, which can be found here (employed the Multi-AF model with an alteration to take into account yield stress variation in depth):

Characterisation of head-hardened rail steel in terms of cyclic plasticity response and microstructure for improved material modelling(2016) [https://doi.org/10.1016/j.wear.2016.03.024]A unified material model to predict ratcheting response in head-hardened rail steel due to non-uniform hardness distributions(2017) [https://doi.org/10.1016/j.triboint.2017.02.018]## ratchetting vs other approaches

Ajay Kapoor did a lot of work along these lines with with Johnson, following Allan Bower who did his phd with Johnson. The papers I have written are mostly comparing with other approaches to the problem, which may not include detailed investigations of ratchetting. I also shown that the Dang Van criterion, widely used in France also by railways people, is not remotely useful for the case of RCF where there is very high hydrostatic compression.

A comparison of

multiaxialfatiguecriteriaas applied to rolling contact fatigue## p.s. another apparent bug

Another bug in the software seems to be that if I forget to specify the notch radius, the software doesn't stop me, and I am not sure what is the Kf factor computed, given Kt. Since they use classical equations similar to Peterson', one needs the ultimate strength of the material, but also the notch radius, to obtain Kf, the true effect in fatigue.

## another example

Smooth specimen, no surface finish, no notch factorStress lifeNf= 683000Strain lifeNf = 670851 cycles

This is fine.But when I add surface finish effect alone, there is a dramatic effect in stress-life, life drops by a factor 185, while strain life by a factor 5.6 only.Stress lifeKsf=.5,Kt = 1Analysis ResultsNf= 3700SpecifiedStrain lifeKsf=.5,Kt = 1Analysis Results

Nf = 120962 cycles

Specified