Craze boundary

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. 

Many attempts have been made to predict fracture toughness Kj(V ) of polymers as a function of material structure. Such calculations can start from statistical and molecular points of view, or from rheological points of view . In the context developed above, the fracture toughness may be expressed as a function of Xo in the following way if a simple constant stress model (i.e. the Dugdale model) is assumed along the craze boundary, then the fracture toughness yields ... 

As discussed extensively in the previous sretions, some craze material properties may be inferred from the craze shape. The plots showing these properties are much more meaningful than the direct experimental values plotted previously. Nevertheless, they are calculated by means of models whose validity might be open to discussion. The simplest assumption that can be made is that the craze stress is constant along the craze boundary. This has been shown to be true for PMMA air crazes. Section 4.3 wilt be devoted to stress profile along these crazes in solvent vapors. 

Craze stress The craze grows (at least partially) by drawing new material out of the bulk. This mechanism requires a certain stress at the junction between craze fibril and bulk. It is sometimes compared to the propagation of a neck in a tensile test on ductile material. In the constant stress assumption , the value of craze stress calculated is actually a mean value over the whole interface between craze and bulk, neglecting the fact that the sum of the fibrils cross section area is smaller than the craze boundary surface. 

Instead of using a constant craze stress, a stress distribution S(x) along craze boundary can be used. Although the overall results shown previously will remain the same. 

The Fourier transform method has been used to calculate the craze surface stress distribution from craze shapes obtained by means of optical interferometry — the craze shapes are the same in air and in toluene gas, only their sizes vary — the craze surface stress is almost constant along the craze boundary — the craze fibril volume fraction remains constant in air and in toluene gas over the whole velocity range, despite the fact that at low velocity in toluene gas the craze length reaches 4 times the length in air — the optical interference setup may give valuable information on the variations of craze fibril volume fraction, but not on its absolute numerical value. 

Line Zone or Dugdale Model, in many polymers, crazes form at stress concentrations such as crack tips (12). A craze is a planar structure, which can be realistically modeled by a line zone, as shown in Figure 14. Here, microyielding at the craze boundaries is modeled by a line of elastic tractions as in the Dugdale model. There is mechanical equilibrinm if the zone length is... 

Fig. 21. Block-and-tackle arrangement for disentanglement at the craze boundary as proposed by McLeish and co-workers. Reprinted from Ref 142 and 144, with permission from Elsevier.

It is likely that both occur depending on the conditions and morphology of the material. The first step in considering the likelihood of fibril failure is to look at the stress levels within the fibril. Because of the reduced cross-sectional area in the craze region, the true stress on the fibrils (uct) can be considerably higher than the stress at the craze boundary (draw ratio of the fibril (A.) ... 

The fibrillated crazes grow through the continuous stretching of new material at the craze boundaries surface drawing or pull-out mechanism). The situation at a craze/bulk interface is illustrated in Fig. 1.7. Stretching of the fibrils occurs up to an elongation that depends on the parameters f and d of the entanglement network. The transition zone (active zone g) forms the craze interphase with a characteristic thickness g. 

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