# Small values problem on Fatigue life cycles

Dear All,

I'm performing a fatigue life analysis of some standard specimens. The problem is I always get very small values (less than 1e-5) for the number of load cycles for each step of crack propagation! I used Paris and NASGRO formulas, but quite the same results. The SIF calculations are wroking correctly, since I'm using a commercial code to do that and I did double checked them to see if they are accurate enough. So, only Paris or NASGRO's parameters may bring some errors. But, I got them from the literature, for example: c = 1e-13 and m = 3.2 for Al 7075-T6. It's a simple caculation, don't know what exactly causes the problem!

Any advice would be greatly appreciated,

### what are the dimensions of C?

be careful of the units in Paris' law

### Dimension of the C parameter

Dear Mike,

You were right, there was a little problem with the dimension of the C parameter, it was (mm/cycle)/([MPa mm^0.5]^m). I used 'Pa' unit for SIFs extracted from the model, while I had to use 'MPa' for that also. Thanks for your help!

### the dimensions of Paris law are fundamentally strange!

Paris law is what Barenblat calls incomplete similarity, nothing really fundamental.  They work in limited sense, may depend on specimen size, on R ratio, on microstructure, even on size of the crack!

Paul Paris was really fortunate to make a big career out of this finding --- after his paper was rejected 3 times by journals, he was in high demand of aeronautical companies who would fly him around.  Billions of dollars have been spent on "damage tolerance", and yet I am not sure it is really working.  Insurance companies do not like to hear about "cracks" anyway any longer, and so today "damage tolerance" is no longer very fashionable.  Are you still using it?

Ciavarella, Michele, Marco Paggi, and Alberto Carpinteri. "One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth." Journal of the Mechanics and Physics of Solids 56, no. 12 (2008): 3416-3432.

Pugno, N., Ciavarella, M., Cornetti, P., & Carpinteri, A. (2006). A generalized Paris’ law for fatigue crack growth. Journal of the Mechanics and Physics of Solids54(7), 1333-1349.

### What do you suggest?

Thank for your explanations. I just downloaded the first paper mentioned by you and had a brief look, It seems to have interesting materials on this topic.

On the uselessness of the 'damage-tolerance' fatigue design approach, what are your suggestions to do or study instead of that?