Fibril breakage

The master curve shows that the life-time is thermally activated. In Fig. 28, two Arrhenius plots for PMMA have been reproduced one from the mechanical P loss peak measurements and the other from the life-time measurements. The life-time plot is the same. Many authors have already associated the P loss peak with the fracture properties Here it is shown that the fibrils breakage itself is controll-... 

Fig. 36. The slope of the crack velocity versus life-time plot is perfectly — 1, showing that the activation volume of fibrils breakage and growth is the same for PMMA. From Ref. by permission of the publishers. Butterworth and Co. Ltd.

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. 

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. 

The final mechanism of stress relief is thermomechanically activated chain scission. Primary bond breakage can be homolytic, ionic or by a degrading chemical reaction. It is worthwhile to note that the relative slippage of chains, microfibrils and fibrils reduces or prevents the mechanical scission of chains in quasi-isotropic polymeric solids. In other words, chain scission is an important mode of fracture only in highly oriented thermoplastic fibers or in thermosets. 

Breakage of polymer through crazing involves two steps first the bulk material must cavitate and fibrillate, and then the fibrils must break. The first step is often... 

Figure 25 shows that, in the case of a stable crack-craze growth with breakage of fibrils in the midrib, the oldest part of a fibril (the part having carried the craze stress for the longest time) is just at the middle Hence, if the breakage is due to some additional creep phenomena, it must break in the midrib. A straightforward consequence is that the life-time tq of the fibril under a load cs may be easily defined as ... 

In the case of cyclic loading, the definition of the life-time of craze fibrils remains the same. But in that case, another quantity may be defined the number of cycles No during which the fibrils may carry a certain load level before breakage. 

Figures 31 and 32 show the cyclic fibril s life-time Xo and Nq versus stress applied on the fibrils for the same two materials. The point to note is that in the first PMMA the frequency independent parameter is the life-time of the fibril, whereas in the second case it is the number of cycles before breakage. The breaking...

As shown above, there are two important plots the craze length S or thickness Tmax versus log (VJ and the log (V ) versus log (%) plots. Both will give the relative activation volumes of the craze fibrils growth and breakage. It has been shown by early experimental work that for PMMA and other materials the craze length or thickness remains almost constant over severeal decades of velocity as well... 

Whereas in Sect. 2 the use of optical interferometry to study qualitatively the morphology of the running crack-tip craze has been shown, this section shows several quantitative craze material models adapted to the experimental results obtained from optical interferometry in the case of a running crack-tip. As mentioned in Sect. 1, the lack of information about the inner craze structure confines the choice to models not sensitive to details in the craze structure. The proposed mechanisms are the following in the case of a steady-state propagating crack-craze system, with breakage in the craze midrib, the fibril breaks at the oldest part. The drawing... 

Figure 47 shows taken from Equation 20 versus Vj. It shows that S. is quite sensitive to Vp and is therefore a good means to evaluate v, with the numerical values of Fig. 47. It can be estimated that the tensile modulus E of the bulk PMMA is not affected by the very low pressure toluene gas environment during the short duration of the experiment. The optical craze index in PMMA in air without load is known as n = 1.32, which corresponds to v = 0.6. From the optical interferometry, it is known that the craze just before breakage is twice as thick as unloaded, (v, = 0.3) and hence using Lorentz-Lorenz equation its optical index is n = 1.15. From Figs. 46 and 47 it can be concluded that the bulk modulus around the propagating crack is about 4400 MPa, which is a somewhat high value, in view of the strain rates at a propagating crack tip (10 to s" ). Using the scatter displayed in Fig. 46, it can be concluded from Fig. 47 that the fibril volume fraction is constant, v = 0.3, within a scatter band of 0.08, and is therefore not sensitive to the toluene gas.

The drawing of fibrils and their breakage have been described by means of a classical stress and temperature activated process, with activation energies and... 

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. 

---