Craze refractive index

It follows that for a constant refractive index the craze strain is also constant. Our observations on polystyrene indicate that neither the craze refractive index nor the ratios kB/kc and kB/kh are constant along the length of the craze (Figure 6). The values of A calculated from Equation 4 are shown in Figure 7. That the craze strain is not constant does not preclude the possibility that the craze stress is still constant, as might be the case for an ideal plastic material. However, the experiments on craze stress-strain properties by Kambour (10) and Hoare and Hull (11) indicate that this is not the case. 

There is no direct information available on any possible temperature dependence of the craze refractive index. However, it might be expected that the temperature dependence is similar to that of the bulk material, which e.g. in PMMA increases by less than 1 % in the temperature range of 60 °C to —30 °C Also, measurements of the refractive index of the broken craze layer in PMMA at 25° and 60 C showed a constant value of 1.32 + 0.01 which is just the same as for the unloaded craze at room temperature. 

Experimental results show typical values of nj/no in PMMA at break in the range of 2-3 and in PC of 1.4-1.5 leading to craze refractive indices p of 1.15-1.09 and 1.19-1.12, respectively. A similar restriction on the range of values of Hj/ng is found in the experimental results for quasistatic and cyclically loaded cracks in the other sections of this review. Hence, with reference to Fig. 2.6, the variation in craze refractive index is not nearly as great as might initially have been expected. 

From observations of interference patterns and interferometric measurements of the refractive index, the profile of a craze preceeding a crack in polystyrene has been determined. The strain along the length of the craze was calculated and found to increase toward the crack tip. The opening displacements across the craze boundaries show a deviation from those predicted for the simple Dugdale yield zone. 

Figure 4. Refractive index of craze vs. distance from edge of...

If the craze layer extends with complete lateral constraint, the strain in the craze is related to the change in its density. From a relationship between density and refractive index, an equation between strain in the craze and its refractive index can be derived. Although it is usual to start with the Lorenz-Lorentz equation, this may not be the correct relationship for a material having the structure of the craze (9). For the present purposes a linear relationship is assumed. The error introduced is at most 10% and only a few percent for the stretched craze with a high void content. 

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... 

Owing to their structure, crazes have a lower density and a lower refractive index than the bulk polymer. Thus it is possible to measure their sizes and shapes using optical interference, provided that the separations involved are comparable in order of magnitude to the wavelength of light, that the refractive index of the craze is significantly different from that of the bulk material, that the boundary between the two regions is sharp and last but not least that the material is transparent. 

Fig. 6. Refractive index of the craze zone as a function of relative fringe number n...

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... 

Crazing is an important source of toughness in mbber-modified thermoplastics. A craze can be described as a layer of polymer a nanometer to a few micrometers thick, which has undergone plastic deformation approximately in the direction normal to the craze plane as a response to tension applied in this direction [Kambour, 1986]. Crazing occurs without lateral contraction. As a result, the polymer volume fraction in the craze is proportional to 1/, where is the draw ratio in the craze. The reduction in density occurs on such a small scale that the refractive index is markedly reduced, which accounts for the reflectivity of the craze [Kramer, 1983]. 

As there is approximately 50% air in a dry craze, their refractive index is intermediate between that of air (1.0) and solid polymer (1.5). Consequently, crazes can be distinguished from cracks by obliquely incident transmitted light. Figure 10.16 shows the schematic arrangement of multiple crazes on a surface affected by ESC. 

Measurements of the critical angle for reflection at a craze yield a value for the refractive index of the craze and show that it must consist of approximately 50% polymer and 50% void. Investigations by electron microscopy, electron diffraction and small-angle X-ray scattering show... 

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