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Question on Fatigue crack growth C and m Paris Law

Are m and C in the paris law equation dependant on the material property or geometry?

For example if using the same material with different thickness, do the C and m values change? For clarity assume centre notched plates, with different plate thicknesses but same material (steel or aluminium).


I appreciate your time.




Ruobing Bai's picture

Hi Rem,

The coefficients m and C in Paris' Law should be material constants, based on the idea that in small scale yielding condition the stress intensity factor K is the only parameter that connects the local stress field to the far away boundary conditions. Others please correct me if you know more.

The reason I am asking is that in a paper I saw the authors using different C and m values for the same material but with change in thickness of plate.

That's what has confused me.

Hi Rem, 

C and m coefficients of Paris law just provide you a correlation between fatigue crack growth rate and applied stress intensity factor range. Since crack is acts as a stress concentrator, there is a small plasticity zone surrounding tip of the crack. SIF can be used with assumption that this plastic zone is small. Difference in thickness leads to change of the plasticity zone size and it effects the fatigue crack propagation rate. That is most likely why you could have seen different C and m values. It have to be remembered that Paris Law isn't always adequate and modified Walker or Forman laws (such as total driving force from UniGrow model or NASGRO equation for FASTRAN) are advantageuos. 

Mike Ciavarella's picture

Hi Rem

  maybe this is an old question, so my answer is too late, but yes C, m are normally considered to be material constants, but strictly they are not, and size and thickness of plate are certainly possible parameter which influence them.

One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growthCiavarellaM Paggi, A Carpinteri - Journal of the Mechanics and Physics …, 2008 - ElsevierBarenblatt and Botvina with elegant dimensional analysis arguments have elucidated that 
Paris' power-law is a weak form of scaling, so that the Paris' parameters C and m should not 
be taken as material constants. On the contrary, they are expected to depend on all the 


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