Cross-tie fibril

A simple model for the formation of the cross-tie fibrils follows directly from the discussion of the formation of fibril surfaces given above. In that discussion it was assiuned that all the strands in the entanglement network which span the plane of separation must either break or disentangle. For most of the strands this statement is correct. However, occasionally several polymer strands may be strongly stretched on the void interface simultaneously so that they can not be broken as shown schematically in Fig. 7 a. Under such circumstances, it will be energetically favorable for the 

A schematic of the advancing craze-interface showing a A pile-up of entangled strands on the void ceiling, b A stretched cross-tie fibril produced by convolution, and c A cross-tie fibril after the polymer strands relax and concomitantly pull the main fibrils out of alignment 

In view of the fact that the cross-tie fibrils contain some of the entangled strands that were imagined to either break or disentangle in the development of Eqs. (15) and (20), one can ask how accurate these formulae are given the cross-tie fibril microstructure of a typical craze. From the meridonal LAED reflections, Miller estimated that the cross-tie fibrils comprised only at most about 15% of the volume of the main fibrils and therefore that the corrections required to Eqs. (15) and (20) for the cross-tie fibrils are negligible. 

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Fig. 4 Description of a craze (a) with a Dugdale zone, and the local analysis (b) as a long strip representing the anisotropic craze structure made of main fibrils oriented along direction 2, connected with lateral cross-tie fibrils along direction 1...

Fig. 6. A schematic showing the parameters which describe the cra2B fibril microstructure, including the cross-tie fibrils...

Finally, the effect of the cross-tie fibril structure on craze breakdown is unknown. We have emphasized here a very simplified picture of the fibril breakdown process in which the nucleation event of a breakdown is the failure of a single transfer length of a main load-bearing fibril. Yet we have excellent evidence that cross-tie fibrils exist and that they can transfer stress between main fibrils. These cross-tie fibrils may have to be considered in developing more exact models of craze fibril breakdown. 

The ratio C66/C22 depends only on the craze microstructure and the elastic properties of the fibrils, i.e. the spacing L between cross-tie fibrils which bridge between one main fibril and the next as well as the distance, d, between main fibrils. Estimates of C66/C22 based on the micromechanics of the craze microstructure can be found in [54]. For crazes in PS, L 60 nm and d 20 nm, leading to an estimate for C66/C22 of 0.02. 

The stress through most of the craze has a constant value acrazeJ this crazing stress is essentially a material constant for a given type of polymer. This stress is carried primarily by the main craze fibrils which run perpendicular to the craze/bulk interface. However, there are in addition to the main craze fibrils cross-tie fibrils, which connect the main craze fibrils laterally. These permit some transfer of stress in the lateral direction (see figure 7.7), with the result that there is a stress concentration at the crack tip. It is this stress concentration that causes the breakdown of the last load-bearing fibril and the growth of the crack. At the crudest level we can model the craze as an elastic continuum and write the stress as a function of the distance x from the end of the crack as... 

M. G. A. Tijssens and E. van der Giessen, A Possible Mechanism for Cross-Tie Fibril Generation in Crazing of Amorphous Pol5rmers , Polymer 43, 831-838 (2002). 

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... 

Figure 12.13 Schematic illustration of the fibril structure of a craze showing a regular arrangement of cross-tie fibrils. (Reproduced with permission from Brown, Mater. Sci. Rep., 2, 315 (1987))...

This approach incorporates the stress-concentrating effect of cross-tie fibrils, widely observed in crazes in glassy polymers (compare Figure 14.14). In the absence of any stress-concentrating effect, that is, for a —> 0, a time-independent fibril failure criterion oy implies crack advance can never occur, because the stress in a given fibril can never exceed Oc- This result has been confirmed by more detailed micromechanical modeling, and is important in that it provides a direct link between the... 

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