Crazing fibril extension ratios

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... 

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... 

Weibull scale parameter monomeric friction coefficient craze fibril extension ratio (=l/vj) average extension ratio in stretch zone... 

The first molecular variable to be considered is chain entanglement density. It is known that this factor, as well as a related parameter, viz. the average chain contour length between entanglements, can have an appreciable effect on deformation modes observed in thin films and on various aspects of crazing such as the craze stress and the craze fibril extension ratio. Examples of these effects will be presented and dis-... 

As the chain contour length between physical entanglements is reduced, so too is the maximum craze fibril extension ratio, Provided the entanglement network remains intact upon straining, X is given by... 

Fig. 7. Craze stress and craze fibril extension ratio vs. chain entanglement contour length in thin films of PTBS, PS, PSAN and PPO. Data from Ref.

In Eq. (2), U is the energy for bond rupture, the macroscopic craze flow stress, X the craze fibril extension ratio accounting for the first order stress concentration, Q an activation volume of monomer dimensions, Vd a pre-exponential frequency factor of the order of atomic frequencies, and q a further stress concentration factor relatel to the fraction of the taut bundle of molecules in the fibril given by ... 

Fig. 11.11 Experimentally determined craze fibril extension ratios X for various homopolymers and copolymers plotted against maximum possible extension ratios of a single entangled chain (from Kramer (1983) courtesy of Springer Verlag).

A n = 1.853, the effective craze-fibril extension ratio (Schwier et al. 1985a) ffpBcav = 60 MPa at 293 K, scaled from Bates et al. (1983)... 

They prepared thin films c. 0.5 fim thick by spin casting diblock and triblock copolymers of PS and PVP from benzene onto a rock salt substrate [393]. The dry films were exposed to benzene vapor for 24 h and the glassy films were floated off the rock salt onto a water bath surface where they were picked up onto a grid coated with a thin film of PS. The film adhered to the grid after a brief exposure to the solvent. An SEM beam was used to bum a thin slit in the material and cracks 50-100 /xm long by 10 //m wide were introduced in the center of each grid square. Grids were deformed as described above and examined by OM to locate areas of interest for TEM study and measurement of craze fibril extension ratios [382]. 

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... 

This result is consistent with Kramer s results showing that the fibril extension ratio (which is just the inverse of the fibril volume fraction) is equal to the bulk polymer network full extension ratio. As a matter of fact, it is unlikely that the toluene vapor changes the physical and chemical structure of the bulk it just makes the fibril drawing easier . On the other hand, it is generally admitted that the fibril diameter times the craze surface stress is constant. Therefore, the craze surface stress being lower in toluene vapor, the fibrils are probably thicker. 

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. 

Much attention has been focused on the microstructure of crazes in PC 102,105 -112) in order to understand basic craze mechanisms such as craze initiation, growth and break down. Crazes I in PC, which are frequently produced in the presence of crazing agents, consist of approximately 50% voids and 50% fibrils, with fibril diameters generally in the range of 20-50 nm. Since the plastic deformation of virtually undeformed matrix material into the fibrillar craze structure occurs at approximately constant volume, the extension ratio of craze I fibrils, Xf , is given by... 

In the discussion of the shear yielding and crazing behavior of PC (in Sect. 3.2 and 4.1), the existence of characteristic extension ratios has become apparent (1) The extension ratio, 7. , after shear yielding referred to as natural draw ratio, (2) the extension ratio, V, of craze I fibrils and (3) the extension ratio, at craze II initiation. 

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