To add on above comments,

CTOA(Critical tip opening angle) can be used as a fracture criterion for ductile material. In ductile material, SIF is found to be dependent on a/W ratio, but CTOA remains constant. The following paper gives a fair idea about this approach(Look at the Fig.3)

"A review of the CTOA/CTOD fracture criterion" :JC Newman, M James - Engineering Fracture Mechanics, 2003 

Arash,

I will take a "crack" at this, with a disclaimer at the outset: my opinions are derived only from the few texts and one class I have taken. If any of my arguments are incorrect or outdated, I would appreciate them being pointed out as such.

For a globally brittle material with small scale yielding, such as you describe, you should not have trouble applying K based criteria, or, as we have been discussing in the other thread, the SED theory. In general, I imagine these are the relevant questions you need to resolve, listed below. Of course after you answer each question, there may be sub-issues to deal with.

1.  Is your material considered generally ductile or brittle? This you have answered. If your material is ductile, you cannot apply G or K based criteria. 

2. Assuming your material is "generally brittle" and you have conditions of small-scale yielding, you still must ask: Are your cracks self-similar? In other words, is the increment of the crack similar to the pre-existing one? If not, again you may not be able to apply the above criteria and will have to, in all likelihood, resort to another approach - SED may be of use to you here.

3. Finally, generally speaking, if you have significant plasticity, you may want to use the J-integral approach, provided that your loading conditions are monotonic. The J-integral approach is essentially based on a "deformation Plasticity" model, which is essentially a nonlinear elastic model - so no history is kept track of, which may be a problem for materials and loading conditions that need this (e.g. fatigue in viscoplastic materials like solder).

4. If all else fails, you need to enter the domain that some people call "Nonlinear Fracture Mechanics" (I think the J-integral is included in this group when applied to nonlinear materials). Here you can use the CTOA and CTOD methods, but there is a lot of skepticism about their generality, including the issues Prof. Chao mentioned. The more promising approach is that of the Cohesive Zone Models (CZM), which actually has a critical "separation". This approach is almost a back door approach to solving the problem, but a very powerful one and there are several review papers (including one by Ingo Scheider that you can google for).

I hope that sums up the criteria for you. My point really is this: the kind of problem helps you select the criteria. It is a true (and somewhat unsatisfying) fact that almost every theory in fracture seems to come with its cautionary list of limitations. Fortunately, there are several approaches out there and you should find one to fit your need.

With regard to the second question you bring about, regarding the relationship between different criteria, the K-G-J-SED equivalence is well known for elastic materials, Anderson's text can help with the K-G-J equivalence. SED can be written in terms of Ks quite easily too. The problems start to arise for nonlinear materials. Hopefully someone can shed some light on this. 

I think it would make sense for us to reach some sort of summary at the end of threads of this nature - perhaps the author of the thread can summarize the points learnt so that a quick read of the summary can help future readers.

Thanks.