Fibril drawing

Based on the description of craze thickening due to Kramer et al. [31,32], Schirrer [45] proposed a phenomenological viscoplastic formulation for the fibril drawing velocity similar to the Eyring model as... 

The fact that each particle enclosed in the primary bulk layer transformed into a craze leaves a mark on the SEM picture of the fracture surface, does not seem surprising. But the fact that only face to face particles are detected by optical interferometry is more striking Fig. 23 shows schematically the proposed explanation. As long as only a single particle is absorbed by the craze, the craze fibril drawing... 

The above calculation, instead of being made with crack-craze velocity V, can be made with a more fundamental parameter, namely the fibril drawing velocity Vj The derivations of this Section complement the detailed calculations of the fiber drawing mechanism made by Kramer and Berger in Chapter I of this book. 

If the craze length increases with velocity (or equivalently with stress), the activation volume of the fibril drawing (l/a e) or of the crack velocity (1/cr,) is smaller than that of the fibril life-time (l/o,), and versa. 

The same conclusion can be drawn from the log (V,) or log (VJ versus log (tq) plot. If the slope is equal to —1 the activation volumes are the same. If the slope is less than — 1 the activation volume of the fibril life-time is larger than that of the fibril drawing, and vice versa. 

The fracture toughness as shown in Eq. 3, scales like the life-time times the fibril drawing stress ct,.. The Ki(Ve) curve remains unchanged in solvent vapor in spite of the changes in Tq and and hence the effects of vapor on and are about the same, but in the opposite way, resulting probably from the same physical effect. 

As shown in Sect. 3.2.1, Eqs. 11 ans 12, the most important plots are the craze length or thickness versus log (V ) and the log (V. ) versus log (Xp) plots (Fig. 44). Both will give the relative environmental action on fibril breakage and fibril drawing. On the other hand, Kramer proposed a simple model for a diffusion controlled craze growth Therefore, the action of the solvent vapor on craze fibril drawing and their breakage can be worked out, as well as the numerical value of diffusion coefficient of gas in polymer. 

Fig. 44. FibrUs life-time versus drawing velocity V. Symbols as in Fig. 39 the slope in toluene vapors is no longer — 1, indicating that the fibrils drawing and breaking mechanisms do not have the same activation volumes in toluene vapors. From Ref. by permission of the publishers, Butterworth and Co. Ltd.

Fibril drawing mechanism versus fibril breakage mechanism The most interesting point in that comparison is that the mechanisms are the same in the case of a crack-craze system propagating in air, and differ notably in the case of a toluene vapor environment for low velocities. 

Kramer showed the relationship between the craze growth velocity and the diffusion coefficient in a very simple case when the craze growth is diffusion controlled and due to fibril drawing from the bulk... 

The constant craze fibril volume fraction assumption is rather restrictive, but seems realistic in the case of PMMA. Moreover, if the calculated craze surface stress distribution is constant, then, a posteriori, the assumption is correct, because in the case of a craze growing by means of fibrils drawing from the bulk (as it is the case for PMMA) a constant stress along the craze can hardly generate a variable craze fibril structure (i.e. a variable volume fraction) along the craze. 

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. 

Some parameters, such as craze length or craze thickness are constant versus temperature or stress when the thermal activation energies or the stress activation volumes are the same for the fibrils drawing and breakage. 

While theoretically the full-field continuum solution, Eq. (13), is an approximation for the stress in the last fibril, simulations that take into account the discrete nature of the craze and the detailed displacements of the craze/bulk interface due to fibril drawing near the crack tip [51, 54] show that it, and thus Eq. (19), are very good approximations. Note however that Eq. (19) is meaning-... 

For each branch point, it is possible to set up an inequality that expresses the criterion for one fork or the other. The most important branch point of the scenario is the one involving the high-energy step, of fibril-drawing and so we will write down the inequalities that pertain to stages 3 and 4 only. 

Here, Aj is the base area at time t at the time when fibril drawing may be said to start, we may take Ajj = A (0). A (t) is the area of a fibril at time t. Of course, all fibrils will not have the same initial areas Ajj(O) and A (0). 

It is clear that if the criterion (la) or (3a) holds for interfacial separation before fibril drawing (whether on account of AG being small or Oy being large) then there will not be a large dissipation of energy,, per unit advance of the macroscopic separation front, and there will be very little work for the applied force to do. So the force required to open up an interfacial crack, in brittle separation, will be small ... 

If the condition, (12b), develops before appreciable work has been done in fibril drawing and craze thickening, the observed adhesive strength will be low. 

The theory that we have developed does not demand that all fibrils and their bases be the same size, or that their mechanical properties be identical. Chain entanglement is a statistical property, and (as already noted) the number of chains per fibril is small enough that serious fluctuations in local properties are to be expected. Even if, in a particular case, the vast majority of fibrils detach cleanly and without leaving any polymer on the solid, a small fraction of the fibrils may rupture, in an experiment of "adhesive" separation. Likewise in a frictional experiment even when, at the majority of points of adhesional attachment, detachment occurs without appreciable fibril drawing, there may be fibrildrawing and rupture at a few sites and consequently, wear will occur. 

Fig. 16 (a) Representation of a block copolypeptide chain and (b) proposed packing of block copolypeptides into twisted fibrillar tapes. Polylysine chains were omitted from the fibril drawing for clarity. Reproduced from [105] with permission of The Royal Society of Chemistry... 

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