SN and da/dN-dK curve fit

[Fatstress]

Dear All,

I would like to curve fit fatigue S-N and crack growth da/dN-dK data. Can anybody suggest me a regression analysis and curve fitting software suitable for this? Thanks.

Fatstress

 

[CoryPad]

You mean because there are two regions that require different equations? Usually the data are separated and each region is analyzed with standard methods.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[Andries]

Hi Fatstress,

The "S-N" approach will give you the stress cycles to crack initiation while the da/dN - Dk relation, when integrated, gives crack growth as a function of stress cycles. The two approaches cannot be combined using a single regression analysis.

Regards

Andries

 

[rb1957]

S/N tends to be log-linear (log cycles (x-axis) and linear stress (y-axis).

da/dN tends to be log-log.

for da/dN i prefer a set of bounded linear equations (3 seems to be enough).

 

[prost]

Fatstress--did you mean to say you are using two different curve fits? One each for the S/N and the da/dN vs. DK?

You could use the MIL-HDBK-5 type curve fitting form,
Seq=Smax*(1-R)^A
Log Nf=B-C*log(Seq-D) (this log is base 10, not base e)

Find A,B,C and D. You can use your eye, or something more formal like a Newton numerical scheme.

There's been quite a bit of ink spilled on the da/dN vs. DK. Started with Paris law, which fits only the nice linear (on log-log) Region 2 (in the middle, between the long crack threshold at small DK and the runaway crack growth near the fracture toughness Kc). This is a simple form,
da/dN=C*(DK)^B, find B and C.

Gets progressively more complicated from there: Forman, Walker, NASGRO, "Harter-T" (one found only in AFGROW, I think). You could even do your own, a double hyperbolic sine or something similar. The possibilities are practically endless.

 

[Fatstress]

Hello Prost,

Actually as you suggested, for the S-N data analysis I have already used the fatigue life model according to the MIL-HDBK-5 procedure and derive the curve fitting equation using Microcal Origin software. The equation can be typed and you can get the parameters A, B, ... as you suggested. Using the MIL-HDBK-5 (up to 5J) procedure you can also test whether some of your data points are outliers so that you can decide to remove them before you perform your regression. As you know in MMPDS-01, this procedure is not available anymore (does anybody know why they remove it?). But unfortunately although I have used Microcal Origin, I still could not get the same statistical values (Std. error; Std. deviation; and R2)of the S-N equation as given in MIL-HDBK-5 although I have used the exact S-N data points from a NASA report. I was just simply assuming if I can get the exact values then the software can be considered OK to be used. Just as a reminder the S-N equation and its statistical data for Al-2024-T3 Kt=1.5 as given in MIL are as follows:

Equivalent Stress Equation:
Log Nf = 7.5-2.13 log (Seq-23.7)
Seq = Smax (1-R)0.66
Std. Error of Estimate, Log (Life) = 0.30
Standard Deviation, Log (Life) = 0.95
R2 = 90%

Then back to my question, I would appreciate if anybody of you can suggest me a regression/curve fitting software other than Microcal. I have heard about Matlab, Mathcad, but to tell you the truth I have never used them. With Excel, as far as I know you cannot type your own equation, or can I...?

Cory,
using the MIL fatigue life model, you can have one equation for each S-N curve. You can also use the Colliepriest equation to curve fit the da/dN-dK data.

Andries,
I did not mean to combine the 2 type of data points. I would only like to know if there is a suitable scientific regression/curve fitting software for this.

rb1957,
I agree with you. For a simple quick calculation, I used linear equations (2 or 3 equations) to represent the da/dN-dK data.


Thanks guys for the comments and suggestions.

 

[rb1957]

i do my curve-fit with excel ... solving linear equations ...
(log Nf) = B+C*(log Seq)

Seq = Smax*(1-R)^A - D

i guess you have some data you're trying to fit ?

i thought at one time to try to interpolate S/N for different Kt ... using the MIL-HDBK parameters, but they're all over the map so it didn't seem like a good idea.

 

[CharlesRobert]

Hi all,
As I know,
S-N curve are used to calculate fatigue life, da/dn vs dk curve are used to calculate crack propagation, it is for damage tolerance.

So, there are different model for them.