Craze thickness

Parameters in the craze initiation criterion of Sternstein et al. [24] Parameters in the craze initiation criterion of Oxborough and Bowden [26] Critical craze thickness Craze length... 

These observations appear to be in contradiction with a creep mechanism for craze fibrillation, and the currently accepted description refers to the drawing-in mechanism due to Kramer [31,32], Kramer argued that fibrillation takes place within a thin layer (about 50 nm) at the craze/bulk interface, in which the polymer deforms into highly stretched fibrils similar to the mechanism of drawing of polymer fibers, as illustrated in Fig. 2. Craze thick-... 

Depending on the material, a critical molecular weight for the observation of a stable craze has been found, for PMMA [29,30] and for PC [42], Below this critical value, crazes are not seen by interferometry and the material is very brittle. The molecular weight has to be sufficiently large (about Mw = 3 x 105 g/mol for PMMA and Mw = 12 x 103 g/mol for PC) for the development of a stable craze. The critical craze thickness and craze length (Acr and Ac) are also temperature dependent [29,30,43,44] and this effect is amplified with increasing molecular weight [29,30]. 

Craze breakdown is experimentally characterized by a critical craze thickness Acr which is primarily dependent (Eq. 20) on the craze stress ac, the force for chain scission, and the entangled chain density along the craze surface vs. The craze stress ac is assumed to be rate and temperature depen-... 

Such a phenomenological definition of the critical craze thickness Acr hides much of the underlying physics. Further insight is expected to reveal how this parameter changes with loading rate as well as its temperature dependence, which could then be incorporated in the present framework. 

When the craze thickness attains the critical value A , craze fibrils break down and a microcrack nucleates with a related vanishing normal stress. 

The temperature distribution during crack propagation is shown in Fig. 15. As the crack advances, the heat continues to diffuse along the normal to the craze surfaces but the size of the hot zone remains comparable to that of the craze thickness. The maximum temperature increase is located at the crack/craze interface, where the craze thickening and related heat flux into the bulk are maxima. At this location, the temperature reaches the glass transition temperature Tg but plasticity is not enhanced in the bulk, which remains primarily elastic during crack propagation. 

Experiments by D511 and KOnczOl [29,30] revealed that the critical craze thickness Acr is temperature dependent in some cases. To get some feeling for its influence, we consider the case where Acr varies linearly from its value... 

Fig. 17 Temperature distributions a at the onset of craze fibril breakdown and b during crack propagation for = 3000MPa in/s, when a temperature-dependent critical craze thickness is considered...

The cohesive surface formulation for crazing implemented within a thermomechanical framework provides insight into the heat generation during crack propagation, and indicates that the temperature-dependent critical craze thickness can result in an increase in toughness, but the marked rise reported in [60,62] probably has another origin. Here, we believe that dynamic effects need to be considered. 

As the craze microstructure is intrinsically discrete rather than continuous, the connection between the variables in the cohesive surface model and molecular characteristics, such as molecular weight, entanglement density or, in more general terms, molecular mobility, is expected to emerge from discrete analyses like the spring network model in [52,53] or from molecular dynamics as in [49,50]. Such a connection is currently under development between the critical craze thickness and the characteristics of the fibril structure, and similar developments are expected for the description of the craze kinetics on the basis of molecular dynamics calculations. 

Figure 8. Craze thickness, d, and equivalent bulk layer thickness, d6...

Verheulpen-Heymanshas measured the fibril volume fraction profile along isolated crazes in polycarbonate using an optical technique whereas Trent, Palley and Baer have measured it in isolated polystyrene crazes in thin films by comparing craze displacements measured from the displacement of bars of an evaporated metal grid intersecting the craze thicknesses. They use TEM of the unstressed film to make the measurements. Both groups find that Vf is independent of craze thickness. 

Fig. 26. The calculated probability that at least one entangled chain remains unbroken in each entanglement transfer length along craze fibrils of total length (total craze thickness) T as a function of x the weight fraction high M PS in the blend...

We note further, however, that if the craze thickening were to cease after a given time when a certain craze thickness 2kp were achieved at the center of the craze, the aspect ratio p would monotonically increase with a, and g would monotonically approach CT. This would result in an ever decreasing craze tip driving force... 

Figure 26 shows the life-time at 3 temperatures (—10, 20 and 60 °C) for Polymethylmethacrylate (PMMA). As many physical properties of bulk polymers, the life-time may be shifted along the time axis to get one single master curve shown in Fig. 27. It should be noted that none of the other craze properties (Ki(Vj), craze length, craze thickness) can be shifted like the life-time to obtain a master curve. This fact tends to prove that the life-time is a more relevant material property than craze length or craze thickness alone.

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