The physical meaning or the numerical effect of the parameter, r, in the exponential cohesive zone model

Dear All:

Here I have a question about the physical meaning or the numerical effect of the parameter, r, in the exponential cohesive zone model. In the original papers by Xu and Needleman, the parameter, r, was defined as "r=Δ*/δn, where the Δ* is the value of the normal displacement jump after the complete tangential separation occurs under the condition of nomal traction being zero, and δn is the normal interface characteristic length parameter".

And my question is that  what kind of effect will this parameter bring to the numerical calculation process? How to choose a appropriate value for this parameter? 0.5 or 0?

Thank you!

 Yan