Craze initiation model

In the craze-initiation model, the above mechanistic considerations are combined in an approximate manner (Argon 2011). Thus, at craze initiation at the local plastic enclaves of the surface grooves, the local mean normal stress must reach such a level as to satisfy... 

Comparison of the predictions of the craze-initiation model with experiments... 

The comparison between the craze-initiation model and the global experimental craze-initiation condition is performed by stating the model expression in a similar linear form to the global form of Fig. 11.3 of the experimental results, followed by a quantitative comparison of corresponding parameters of the experimental and model forms. 

In summary, the craze-initiation model presented above can be stated for the local environment as... 

A description of crazing with a cohesive surface appears appropriate for the crazes observed in glassy polymers, since the trends reported experimentally are quite well captured. The cohesive surface model distinguishes the three steps of crazing (initiation, thickening, and breakdown) and is flexible enough to incorporate more sophisticated formulations of one of these stages when available. 

In order to test the model of intrinsic craze initiation it would be desirable to produce entanglement networks of different structures and study X as a function X. This may be achieved by pre-orientation of PC above T. In fact, there is much evidence that the entanglement network in polymer melts is modified increasingly with the magnitude of deformation i32,i5o.i59,i6i> -j-jjg modification must be assumed to arise... 

Fig. 17. A plot of the ratio r of the initial crazing stress to the crazing stress for van-der-Waals crazing as a function of temperature for PS having a molecular weight of 260,000 ( ) and 1,150,000(0). The jo/fd carve corresponds to the prediction based on the craze growth model (using Eq. (20)) and a value of V = 6,7 nm s" ...

Fig. 35 a. Median tensile strains for craze initiation s, (A) and craze fibril breakdown ( ) in the ultraclean samples versus molecular weight. Also shown are the values of (O) for the unfiltered samples (From Ref. courtesy Macromolecules (ACS)), b Craze fibril stability — 8 in nearly monodisperse PMMA as a function of molecular weight c Craze fibril stability in nearly monodiaperse PaMS as a function of molecular weight . The solid lines in b and c are predictions from the model of fibril breakdown (Eq. (41)) using values for of 88 s (PMMA) and 364 s (PaMS)... 

Fig 11.3 Measurements of craze initiation under combinations of normalized mean normal stress and normalized deviatoric shear stress rj aXT — 293 K (O) and T — 253 ( ) with lines giving model predictions from eqs. (11.19) and (11.22) H gives the intrinsic crazing response at 293 K (from Argon (2011) courtesy of Elsevier). 

In eq. (11.15) the concentrated local mean normal stress ai and deviatoric shear stress Si are in the plastic enclaves that result in craze initiation (the time taken for the formation of 10 crazes per cm in 10 s in the tension torsion experiments is taken as the mean period r of craze initiation), which needs to be stated in terms of global stresses a and s through the use of the average stress eoneentrations and of surface grooves. How this is done is discussed below in Section 11.6 comparing the model predictions with the results of the tension torsion experiments. 

For the term-by-term comparison of the model and experimental forms of craze initiation, the following factors are recalled q — 3.53 as stated above and q = 2.04 is taken as the average for cases 1-3 given in Table 11.1. These establish the following connections between global and local parameters, in the model ... 

GghI (1970). Gent (124) proposed a model in which the hydrostatic tensile stress at an inclusion or local heterogeneity increases the free volume and therefore effectively reduces the Tg of the material. At a sufficiently high stress concentration, the reduction in Tg is sufficient to reduce the local Tg to the test temperature. The reduced yield stress of the material in this mbber-like phase and the hydrostatic tensile stress then leads to cavitation and craze initiation. Implicit in this free-volume approach is that an imposed hydrostatic pressure will tend to prevent the formation of crazes in accordance with experimental observation. The criterion is summarized in the equation for the critical applied stress for initiation,... 

However, experimentally it has been observed that craze growth occurs faster than craze initiation and so it is difficult to explain growth with such a model as it is essentially the same mechanism as initiation. Also, some of the featnres of the craze predicted from such a mechanism, such as a closed cell structure formed... 

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