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cracking analyses in a bended sandwich beam

I'm studying cracking analyses in a three point loaded specimen of a composed beam.I'm using ANSYS and i want to create codes for estimation of J integral and energy release rate in the vicinity of crack tip.After that i'll calculate the stresses and strains fields,and then i can compare the equivalent fields i retrived using CTOD  and K(I,II,III) factors (according to ANSYS algorithm).

My problem is that I'd like to find a relationship between the above mentioned quantities(J,G)  with K(I,II,III)factors.

Another subject i'm thinking of ,is that i'm studying the pressed area of the beam (negative normal stresses -the cracking faces are parallel with the beam axis-),so i retrived KI nearly 0.It sounds logical but i am not sure that the method of K factors estimation using CTOD IS CORRECT.Actually i have negative desplacements between the crack faces and in some cases penetration to each other.

I would appreciate any ideas for the above.

 

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