Provide the load vs. Cmod curve

Dr. Nandana:

You have a few options open to you. 

First, as Dr. Bind mentioned, if we can see the load vs. CMOD (crack mouth opening displacement) curve, there may be an indication, such as a pop-in or other crack instability, where you could delineate the onset of crack initiation or outright fracture.  You would then know the critical load and if it's crack initiation, you would know the initial crack length, or if it's crack instability, you could tell the crack length at that point by a transition in the fracture mode as dictated by the fractography of the crack surfaces. Armed with the critical load and crack length at fracture, you could then compute the effective (usually termed critical) crack length ac and critical Kc value at fracture.

If you want the entire R-curve, that's a little more complicated.  You would need to find a relationship between the CMOD and the crack-tip opening displacement (CTOD); with the latter value you can relate this to K or J using the standard mode I CTOD vs. J and J-K equivalence.  All this is described in T. L. Anderson's text book "Fracture Mechanics: Fundamentals and Applications" (4th ed., CRC Press, 2017).

The relationship between CMOD and CTOD, which naturally is specimen-dependent, can be deduced by considering equal triangles about a point of rotation ahead of the crack tip.  It's somewhat approximate but was the standard experimental method in the early days of CTOD measurements, and is explained in that early literature, by such authors as J. F. Knott and his colleagues.  However, the method is also described in Anderson's text book, which may be worth getting from the library!

ROR 

Please find the Load vs CMOD curve.

I did not measure the physical crack size wile conducting the test, now i want to measure the effective crack length as the crack propagated from compliance based equations. Is it possible to do that, please answer.

Dear Nandana,

You can use load normalization technique to estimate the crack length. 

Dear Nandana:

Provided that you're under nominally elastic conditions, you can estimate the crack length from the crack mouth opening displacement using compliance-based equations.  However, as the compliance will be a function of the specimen geometry, you will need to find those equations for your geometry.  I would look in the appendix of T. L. Anderson's book "Fracture Mechanics: Fundamentals and Applications" (3rd or 4th edition, CRC Press), where he lists a bunch of such compliance equations for test various specimen types.  If the relationship for your geometry is not there, you'll need to search the literature, or in the worst case derive the equation either experimentally or numerically yourself.

ROR

I Totally Agree with Robert, if you are using a standard specimen shape, you can find the COD - compliance relations in Reference books..... However, you can use FEM and get the relation for your specimen if you are using special specimen shape.

Thank you all for the suggestions and answers.