Craze fibrils spacing

In Fig. 24.1 we show a part of a craze. The parameter/) is the (mean) craze fibril diameter while Do is the craze fibril spacing. Both D and Do increase somewhat with increasing He. Berger [42] traced the craze fibril breakdowns to the formation of small pear-shaped voids at the craze/bulk interface. The results in [42] confirm the microscopic model of Kramer and Berger [38] which we see in Fig. 24.1. 

Porod analysis of the SAXS and SAEX measurements provided a quantitative estimate of the mean craze fibril spacing. Brown [40] subsequently made the key observation that the presence of the cross-tie fibrils has a profound effect on the failure mechanism of a craze because they enable stress transfer between broken and unbroken fibrils. Brown [40], and then Kramer [41], followed this idea through to produce a quantitative theory of craze failure of the molecular chains at the mid-rib of the craze. Brown s theory is a very ingenious mixture of the macroscopic and the microscopic. Starting at the macroscopic level the craze can be modelled as a continuous anisotropic elastic sheet. The stress on the craze plane in front of the crack is then... 

WLF constant WLF constant [K] characteristic ratio tensile compliance [Pa ] craze fibril spacing [m]... 

Studies of craze microstructure and the surrounding displacements of crazes have established that the only parts around a craze that undergo plastic deformation are concentrated into a process zone at the tip of the craze, and into a fringing layer all around the entire craze body. In the process zone craze matter is generated by one of the two processes discussed above, and fibrils are necked down to the final extension ratio. In the fringing layer, additions are made to craze fibrils by drawing polymer out of half space. Outside the idetifiable parts of a craze, the solid polymer remains entirely elastic while inside the craze body the fully drawn fibers carry the required craze tractions purely elastically in their orientation hardened state at the... 

The miCTOstructure, in particular the mean fibril spacing D, of the growing craze is a consequence of the geometry of the surface drawing process and the surface energy of the fibrils being created. It is useful to model the polymer in the active zone as a strain-softened non-Newtonian fluid with the following flow law,... 

Suppose now that there is a wide spectrum of craze microstructures with different values of the fibril spacing D,. For the crazes with very small and very large Dq the craze interface velocity from Eq. (9) is miniscule, since for these crazes Vctq is small. Clearly there will be a value of D which maximizes Wq, and hence v, and this value is given by... 

Fig. 12. Mean fibril spacing D versus temperature for crazes grown in a 1,800,000 molecular weight PS deformed at a rate of 4.1 x 10 s (From Ref. courtesy J. Polymer Sci.-Polymer Phys. (Wiley))...

T < Tg (T Tg) Intense thermally induced disentanglement (lower disentanglement stress than yield stress) results in coarsening of craze structure with increasing fibril thickness and fibril spacing. 

The highest stress in the craze is assumed to be in the fibril closest to the crack tip, and can be approximated by putting r = dll, where d is the fibril spacing, to calculate... 

A crack is an open fissure, whereas a craze is spanned top to bottom by fibrils that act to resist entrance of opportunistic molecules such as water vapor. Even here, some smaller molecular interactions can occur within the void space, and eventually the specimen is weakened. 

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