Traction separation laws in Cohesive zone models - Some Questions
As a student who has spent a lot of time studying cohesive zone models in fracture mechanics, I have several questions that have bothered me over the past year or so, and I have not been able to find suitable answers to them. I am limiting myself here to questions related to the traction-separation law, which invariably forms the basis of CZM as it is implemented today. I am raising these questions in the hope that I can receive some response here, even if it means my question is invalid (as I suspect a few may be). So here is my list:
1. Basis: It seems that the only basis cited is for the exponential one, when it is tied to the Rose-Smith-Ferrante traction separation law. Is this a justified basis? Have any attempts been made to DERIVE the form of the traction separation law as opposed to propose it on a phenomenological basis? Would this even be possible?
2. The "separation": Why do CZMs operate with separation, and is it correct to do so? Fracture mechanisms involve, in my understanding, complex phenomena such as strengthening and bridging. By lumping all these phenomena into the traction-separation law, are we making erroneous assumptions? Is there truly a "critical separation"? Can this be expected to be a material parameter? Would not separation suffer from the similar problems that make us prefer stress-strain plots to stress-displacement ones?
3. Statistical origins: Could the traction-separation law be nothing more than a probability distribution, similar to that proposed by Weibull for the distribution of flaws? Is the exponential form used by Needleman and others just a manifestation of this probabilistic distribution of critical strengths? Can/has this been proved?
4. Mixed mode: Is there a consensus on the treatment of mixed mode? Can shear and normal separations be combined to form a resultant separation?
5. Parameters: The maximum stress and critical separation? Is there any reason to believe they are/are not material constants?
I hope you find my questions appropriate. Thanks for your time. There are other questions I have regarding singularity removal, mesh sensitivity etc., but that is for another post. :-)