Craze widening stress

This craze widening stress, which can be considered to be the crazing stress of the polymer, is only weakly dependent on the craze interface velocity but proportional to the geometric mean of the flow stress and the craze surface tension per unit width of the... 

The surface tension F of the void ceiling that appears in the capOlarity equation (Eq. (12)) is the key quantity to be specified in understanding the effects of network strand density v on the craze widening stress. For the moment suppose this network is comprised entirely of crosslinked drains. Then to create a surface requires the scission of a certain number of strands per unit area, a geometricaUy necessary strand loss, which is given by (1/2) vd. The energy required to create this surface is then... 

Fig. 11 Craze in commercial polystyrene showing the characteristic steps nucleation through void formation in a pre-craze zone, growth of the fibrillar structure of the widening craze by drawing-in of new matrix material in the process zone, and final breakdown of the fibrillar matter transforming a craze into a crack (the crack front is more advanced in the center of the specimen, shielded by a curtain of unbroken fibrils marked by the arrow). The fibril thickness depends—of course—on the molecular variables, the strain rate-stress-temperature regime of the crazing sample and on its treatment (preparation, annealing) and geometry (solid, thin film) for PS typical values of between 2.5 and 30 nm are found [1,60,61]...

The cohesive surface description presented here has some similarities to the thermal decohesion model of Leevers [56], which is based on a modified strip model to account for thermal effects, but a constant craze stress is assumed. Leevers focuses on dynamic fracture. The thermal decohesion model assumes that heat generated during the widening of the strip diffuses into the surrounding bulk and that decohesion happens when the melt temperature is reached over a critical length. This critical length is identified as the molecular chain contour. 

The craze just behind the tip, however, is only a few nanometers wide, whereas crazes typically can attain widths of a few micrometers or so before fracture. Clearly, while the craze tip advance mechanism is responsible for initially generating very short lengths of fibrils, most of the fibril structure is generated by the mechanism of craze width growth. Even the stress conditions at the craze tip can be dramatically altered by the widening of the craze well behind the tip if the craze continues to widen without the craze tip advancing, the stress at the craze tip will rise until the craze tip... 

---