A Microscopic Model of Craze Fibril Breakdown

From the microscopic picture for the craze growth it seems clear that one important microscopic variable must be the mean number n of entangled strands within each fibril which survive the geometrically necessary strand loss associated with the interface formation. If the number of such strands is zero, the fibril will fail, since the polymer fluid which flows from the active zone into the fibril has no strain hardening capability and will not be able to support the relatively high tensile stresses necessary to propagate the interface. To obtain n one first estimates n, the total number of strands in the undeformed phantom fibril from which a craze fibril is drawn and which is given by  

For a diluted network v = [v] and d = [d]/x where [ ] denotes the value for the undiluted high molecular weight species (Note that the relation for v was previously given incorrectly by Kramer to be v = [v] x)- All the quantities in Eq. (33) are known with the exception of which must be measured using LAED. 

The mean number of effectively entangled strands is then given by  

A simple estimate of the probability P fO) that all strands in a given fibril will break yields  

From the preceding discussion it is apparent that we.must consider the probability that a given fibril will fail (which we now realize can occur when a certain number i 

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