This suppose to be material properties.  So based on material yuo use, you can illustrate.

In addition, there is a geometrical representation in paris hand book related to structure geometry.

Dear Bakr,

my material is 7075-T6 aluminium alloy; I found c and m parameters related to the Paris Law, but abaqus asks me different parameters (c1, c2, c3, c4) and I do not know how to obtain these from c and m (if it is possible). Do you have suggestions?

Hi，danilo

I am also working on that problem, and I have found some exlaination about c1,c2,c3 and c4 from the Abaqus Analysis user's Guid ,  there are two equations , one is f=N/c1(deltaG)^c2, which f represents the damage of the modeling material and N is the number of cyclic loading, when f≥1 ，the damage occurs.  the other is da/dN=c3(deltaG)^c4 , I think c3 equals to C ，c4 equals to m. But I do not understand how to get c1 and c2 .  

Exactly, I did not find anything except the following paper in which there are examples of c parameters. It is clear what the parameters are but it is hard to find examples of values!

Moreover, I do not think hat c3 and c4 are equal to c and m, respectively. As a matter of fact, the form of the relationship is equal but the parameters involved are different: DG instead of DK and dD/dN instead of da/dN.

We can try with the following values and then modify them... I have no idea about alternatives... You can read the following papers:

http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2205584

http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1816313

hello, did you manage to c3 and c4 from C and m? If you did, can you please explain here? Thank you very much

Dear Nazirah,

using few theoretical relations it is possible to relate (c,m) to (c3,c4):

a) da/dN = c3 Gc4

b) da/dN = c Km

c) G = K2/E'

where:

for thick plates (plane strain): E' = E/(1-ni2), where ni is the Poisson's ratio and E is the Young Modulus,

for thin plates (plane stress): E' = E.

So, the following relations can be derivated:

1) c4 = m/2

2) c3 = c E' m/2

I found these relations in the papers I referenced in the previous comment.

Actually, I found a lot of confusion about that issue, so let  me know, please, if you find something clearer or a more detailed reference.

I hope this can help you.

Regards,

Danilo

Danilo indeed lists the correct relationships to be used in Abaqus. To understand the derivation, it helps to look at when the Paris law is linear (e.g., on log scale). e.g.

log(da/dN) = m log(K) +log (C)

And so, "m" is the slope of the linear relationship, and "C" is the intercept.

As mentioned, the following relation hold:

G=K2/E

or

K = (GE)1/2

Plugging this into the first equation:

log(da/dN) = m log( (GE)1/2 ) + log C

log(da/dN) = (m/2 log (G) )+ (m/2 log E) + log C

This is still a linear relationship, now the slope is m/2, and the intercept is (m/2 log E)+log C. Bringing this back into the original scale (e.g. take exp()) You'll indeed see:

da/dN= (CEm/2)(Gm/2)

or

C3=CEm/2

C4=m/2

Of course, this doesn't explain why Abaqus requests the constants in terms of G and not K. This only leads to confusion and possible errors since nobody defines Paris's law in terms of G. An unfortunate bit of programing.

Hi, Could I know how did you find the Mode 1/2/3 critical energy release rate?

Danilo D'Angela , Brian Eick you are right about c3 and c4. Do you have ideas about abaqus material constants for fatigue crack initiation c1 and c2?

Brian's explanation is fine.

I also agree that the use of da/dN = c3*DGc4 in Abaqus is not happy, since Paris’ Law is always given as da/dN = C*DKm, with DK measured in MPa*m1/2.

Without logarithms, c3 and c4 can be obtained as follows.

For plain stress DK = (DG*E)1/2, thus

da/dN = C*(DG*E)m/2 , then

da/dN = C*Em/2*DGm/2

from where

c3 = C*Em/2

and

c4 = m/2.

If plain strain is considered, DK = (DG*E )1/2/(1-nu) and then we get

c3 = C*Em/2/(1-nu)m

and

c4 = m/2.

My answer comes a little late, sorry.

hello, Danilo D'Angela did you manage to find out how to determine constants c1 and c2? thanks

Hello, if you email at:

[email protected]

after 22nd August I will send you some references.

Best regards,

Danilo

Hello,

A general approach has been proposed in the following paper to address this issue (see sections 2 and 5):

https://onlinelibrary.wiley.com/share/author/EDVDWUMEIUKZMB4NZ4XN?target=10.1111/ffe.13735

Oisin Conway