Craze extension ratios

To test the idea that % should scale approximately as measurements of X were made in both crosslinked polymersFig. 8a, and entangled polymers Fig. 8 b. These results convincingly demonstrate that the molecular network, whether due to chemical crosslinks or to physical entanglements, is the primary determinant of the extension ratio of the craze. 

There are several other consequences of the model of craze growth which can be tested, however. The model suggests that the craze extension ratio should reflect the loss of entanglement density caused by the strand loss. There seems to be no doubt 

One can estimate the strand survival fraction q theoretically. The relevant parameters are the strand end-to-end distance d and the phmtom fibril diameter D, the diameter of starting polymer glass that is drawn into the final fibril, determined from smaU-angle electron (or X-ray) scattering. One can show that q is only a function of the ratio, Dg/d. The best method of calculation treats the strand as a Gaussian coil, with rms end-to-end distance d, and computes the probability that if one places one end at random in a cylindrical phantom fibril, the other end will be also inside For typical D s for polystyrene crazes (of the order of 14-20 nm at room temperature) the predicted values of q lie between 0.5 and 0.6, in satisfactory agreement with the experimental estimates (which include effects of the tie-fibrils not included in the theoretical method ° ). 

More direct evidence of the chain scission is difficult to obtain. Mills and Donald have showed that crazes in PS and other polymers can be weakly stainal and the stain detected by transmission electron microscopy on healed crazes by any reagents (e.g., OSO4, Br2, I2, Hg(CH3COO)2) which will react with double bonds. 

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For craze growth at temperatures well below the glass transition temperature it is observed experimentally that the natural craze extension ratio X is nearly a constant value characteristic of the particular polymer under investigation It was ob-... 

An increase of the craze stability of tensile-induced crazes with rising M has been noted in various glassy polymers. In a study made on thin PS films by Berger and Kramer the craze extension ratio was determined at various temperatures for polymers of varying M. For measurements made at room temperature, X varied little with molecular weight but, as the temperature was raised, and chain disentanglement processes became more probable, the situation changed. For example, at 50 °C,... 

The evaluation of the craze profile shown in Fig. 1.1 is based on the assumption of a constant craze extension ratio A along the craze zone, defined by... 

Nevertheless, differences in refractive index can be a measure for variations in craze extension ratio A,., as can be estimated from Eq. (12). For crack tip crazes in PMMA as well as in PVC a slight but continuous drop in extension ratio from a maximum value next to the crack tip to a minimum at the craze tip has been found. In the same material crazes of different length exhibit nearly the same minimum extension rate A. at the tip, as can be taken from Fig. 2.8. Thus, for PMMA a threshold extension ratio for crazing of approximately 1.5 can be derived... 

TEM micrographs of crazes in thin films have been used to determine the extension ratio, k, of the polymer chains along the craze [19]. At the crack tip a higher extension ratio is observed, which remains in the midrib. Otherwise, the measured k is identical along the craze and depends on the polymer being... 

The extension ratios obtained at room temperature on a large number of homopolymers and copolymers have been analysed [19]. Polymers with high A.max, i.c. large Me or low entanglement density, ve, lead to crazes. In contrast, polymers with low A.max, and thus low Me and large ve, show SDZs. 

Fig. 5. Craze fibril extension ratio vs. distance from crack tip in a craze grown in a polyftert-butylstyrene) film (From Ref. courtesy of John Wiley Sons.)...

As implied by the discussion above craze fibril extension ratio or its inverse the fibril volume fraction of the craze is an important parameter of the microstructure. Fibril volume fractions can be measured by several different methods. The refractive index n of the craze can be measured by measuring the critical angle for total reflection of light by the craze surface. Using the Lorentz-Lorenz equation Vf then can be computed from The method is difficult because small variations... 

To this point the craze fibril volume fraction Vf and fibril extension ratio X have discussed as if they were true constants of the craze. While this view is approximately correct, one would expect the draw ratio of the polymer fibrils to depend somewhat on the stress at which they are drawn, since the polymer in the fibrils should have a finite strain hardening rate. Experimental evidence for just such stress effects on X, is discussed below. 

Fig, 13. Fibril extension ratio profile l.(x) and surface stress profile S(x) along an air craze in PS. From Ref courtesy Taylor and Francis, Ltd... 

Fig. 16. Experimental extension ratio of crazes in various hranopolymers and copolymers plotted against the theoretical maximum extension ratios of a single entangled chain and the entanglement network, and A.,., respectively...

Craze fibril extension ratio plotted against weight fraction PPO for two types of PS/PPO blends. 0, high M PS blend. A, low M PS blend. The theoretical curves for are also shown as solid lines... 

Prior molecular orientation (either above or just below T ) should change the starting extension ratios of the entanglement network and therefore X of any crazes produced. Consider a polymer melt extended in uniaxial extension to X = J p, X2 =Xi — The new. ax in a direction parallel to the molecular orientation... 

Craze growth occurs in a lateral direction by advance of a thin finger-like craze tip by the meniscus instability mechanism. Crazes increase in thickness by a surface drawing mechanism in which more polymer is drawn into the craze fibrils at essentially constant extension ratio X from the craze-bulk polymer interface. 

Correlation function Elongational strain Strain rate Craze strain Elastic strain Shear strain Interfacial length Extension ratio... 

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