Craze fibril diameters

Craze fibril diameters determined by TEM and SAXS are of the order of 10 nm. Craze fibril volume fractions Vf range from 0.5 to 0.1, depending on the entanglement network of the polymer and the local craze stress. 

In another study by Brown et al. craze fibril diameters were determined by SAXS measurements during fatigue cycling of samples of a commercial PS (M = 3 X 10 ) in 3-point bending at the low rate of 1 cycle in 12 s. Displacements were varied from zero to maximum in a saw-tooth manner and the maximum strain was sufficiently high so that crazes developed on the first cycle. SAXS measurements of... 

Fig. 13. Craze fibril diameter vs cycles of fatigue loading in PS. Data from Ref.

Many craze parameters are molecular weight dependent. As M rises, craze length, craze width and craze density all continue to increase. In PS, the craze fibril diameter decreases slightly with increase of M but it increases with cycles of loading. 

B Zero stress limit of activation energy for plastic deformation C SAXS constant product of flow stress and craze fibril diameter C Pre-exponential factor for craze strain rate, (=Qb )... 

Fig. 11.10 Flow stress ay and the product Day of average craze fibril diameter and flow stress, as a function of temperature (from Paredes and Fischer (1979) courtesy of Springer-V erlag).

SAXS determination that the product of the craze-flow stress and the craze-fibril diameter is constant. The reason for this discrepancy is not clear. 

In Fig. 24.1 we show a part of a craze. The parameter/) is the (mean) craze fibril diameter while Do is the craze fibril spacing. Both D and Do increase somewhat with increasing He. Berger [42] traced the craze fibril breakdowns to the formation of small pear-shaped voids at the craze/bulk interface. The results in [42] confirm the microscopic model of Kramer and Berger [38] which we see in Fig. 24.1. 

Vlymer/air Vlymer/1 iquid craze fibril diameter. The above predicts that the stress depression is simply a function of the surface tension and fibril geometry of any polymer. Thus, Equation 1 should be applicable to all microfibrillated polymers. 

Transmission electron microscopy (TEM) and birefringence studies of strained and/ or fractured epoxies have revealed more direct experimental evidence that molecular flow can occur in these glasses. Films of DGEBA-DETA ( 11 wt.- % DETA) epoxies, 1 pm thick, were strained directly in the electron microscope and the deformation processes were observed in bright-field TEM 73 110). Coarse craze fibrils yielded in-homogeneously by a process that involved the movement of indeformable 6-9 tan diameter, highly crosslinked molecular domains past one another. The material between such domains yielded and became thinner as plastic flow occurred. 

Cavitation is often a precursor to craze formation [20], an example of which is shown in Fig. 5 for bulk HDPE deformed at room temperature. It may be inferred from the micrograph that interlamellar cavitation occurs ahead of the craze tip, followed by simultaneous breakdown of the interlamellar material and separation and stretching of fibrils emanating from the dominant lamellae visible in the undeformed regions. The result is an interconnected network of cavities and craze fibrils with diameters of the order of 10 nm. This is at odds with the notion that craze fibrils in semicrystalline polymers deformed above Tg are coarser than in glassy polymers [20, 28], as well as with models for craze formation in which lamellar fragmentation constitutes an intermediate step [20, 29] but, as will be seen, it is difficult to generalise and a variety of mechanisms and structures is possible. 

Primitive and mature fibril diameter Craze thickening rate Fibril lifetime... 

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... 

SAXS has proved to be a very powerful tool for a quantitative analysis of the craze microstructure. This is not surprising since characteristic craze parameters such as the fibril diameters and the interfibrillar spacings frequently fall into the range of 1-5 X 10 nm covered by SAXS. The general theory of SAXS has extensively been treated in the literature (see e.g. Some basic elements of the SAXS theory,... 

In the above Equations x the total area created by the intersection of a plane perpendicular to the cylinder axis and passing through the origin. denotes the interfacial length of the two dimensional cells in this plane. Crazes may be modeled by a system of parallel cylinders. For a realistic description of the craze microstructure, a distribution in fibril diameter, D, must be taken into account. This yields... 

The equatorial SAXS curve of extrinsic crazes in PC is shown in Figure 17 for a sample which has been stretched at T = 129 °C to = 1.8, i.e. to 7. < The scattering curve exhibits the well pronounced interfibrillar interference maximum discussed in the previous section. From the position, s, of this maximum the average fibril diameter, D, may be evaluated. If the volume fraction of craze I fibrils is assumed to be vj = 0.5 (see Section 3.2), Equation (49) yields D = 37 nm, which compares well with results obtained under approximately the same drawing conditions by Paredes and Fischer and Brown and Kramer... 

Since v is known, either of the Equations (44) and (49) may be used to evaluate the fibril diameter.Thefact that both Equations yield exactlythesamevalueofD = 94 nm strongly supports the scattering model outlined in the previous section. For crazes II, the fibril diameter turns out to be much larger than for crazes 1. Some evidence will be presented subsequently that the difference in fibril diameter primarily reflects the distinct stress-srain state of the matrix at craze I and II initiation. 

Fig. 19. Volume fraction, Vf , of fibrils within crazes 11 and average fibril diameter, D, as a function of...

Fig. 21. Inverse of the average fibril diameter, D, and product of D with the true stress, ct", at craze II initiation as a function of the logarithm of the true strain rate, s...

Vf" remains virtually constant as a function of the pre-orientation. However, as shown in Figure 24, D increases linearly with the total extension ration, k, at craze initiation. It is interesting to note that the fibril diameter of D = 36 nm which is obtained by extrapolating the straight line to = 1 is in excellent agreement with the value of D = 37 nm measured for extrinsic crazes. This result seems to indicate that the different fibril diameter of extrinsic and intrinsic crazes primarily reflects the distinct extension ratios X and k of the matrix at craze initiation. However, further investigations are necessary to substantiate the above result. 

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