Crazing kinetics

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. 

At the fundamental level, current understanding of crazing and fracture in semicrystalline polymers remains less advanced than in glassy polymers. Even in these latter, phenomena such as disentanglement are generally subject to unverified assumptions concerning their kinetics, or even their exis-... 

Kramer EJ, Bubeck RA (1978) Growth kinetics of solvent crazes in glassy polymers. J Polym Sci Polym Phys 16(7) 1195-1217... 

Wyzgoski MG, Novak GE (1987) Stress cracking of nylon polymers in aqueous salt solutions. Part 3 Craze-growth kinetics. J Mater Sci 22(7) 2615-2623... 

To illustrate the influence of the craze thickening kinetics on fracture, two sets of craze parameters are used and listed in Table 3. The two sets are borrowed from [22] (cases 8 and 1) and named here A and B. In Fig. 8, we report the plastic strain rate distribution observed near the crack tip. This variable is suitable to track the development of plasticity and is normalized with To = Ki/soy/Fi as a reference strain rate at the tip of the notch (the radius is rt = 0.1 mm and T = 293 K). We compare the cases for which no crazing is considered (Fig. 8a) to those where crazing is accounted for (Fig. 8b), with the set A of craze parameters in Table 3. When crazing is not present and at the particular loading rate considered, plasticity develops in the form of shear bands which originate from the tip of the notch, where the stress concentrates. 

Table 3 The sets of craze parameters used in this study the only difference originates from Ac and hence the sets exhibit different craze thickening kinetics (from [22])...

The cohesive surface considered in the foregoing is based on observations made under quasistatic conditions. In particular, the incubation time for craze initiation is neglected and a critical stress state for craze nucle-ation is used (Eq. 11). For dynamic loading, a time-dependent craze initiation criterion is to be included in the kinetics, since the characteristic timescale associated with the loading can be comparable to that involved in the craze nucleation process. If the time for craze initiation is accounted for, another timescale is involved in the competition between crazing and shear yielding that determines whether or not crazing takes place. Therefore, a switch... 

The diffraction pattern registers the volume effect regarding the distribution of crazing. In principle if the distribution of crazing is random, the measurements of the diffracted laser intensity should yield the kinetic information on the accumulation of crazing. 

The kinetics and mechanisms of tensile deformation in ASA and ABS polymers were studied using high accuracy creep tests. Crazing was detected by volume strain measurements. 

In both polymers, creep of compression-molded specimens is caused mainly by crazing, with shear processes accounting for less than 20% of the total time-dependent deformation. Crazing is associated with an increasing creep rate and a substantial drop in modulus. The effects of stress upon creep rates are described by the Eyring equation, which also offers an explanation for the effects of rubber content upon creep kinetics. Hot-drawing reduces creep rates parallel to the draw direction and increases the relative importance of shear mechanisms. 

The first quantitative study of deformation mechanisms in ABS polymers was made by Bucknall and Drinkwater, who used accurate exten-someters to make simultaneous measurements of longitudinal and lateral strains during tensile creep tests (4). Volume strains calculated from these data were used to determine the extent of craze formation, and lateral strains were used to follow shear processes. Thus the tensile deformation was analyzed in terms of the two mechanisms, and the kinetics of each mechanism were studied separately. Bucknall and Drinkwater showed that both crazing and shear processes contribute significantly to the creep of Cycolac T—an ABS emulsion polymer—at room temperature and at relatively low stresses and strain rates. 

The effect of stress upon the kinetics of crazing can be represented by two rate quantities obtainable from the creep data. The linear portion at the end of the volume strain-time curve defines a maximum rate of... 

Despite this lack of reproducible experimental evidence on kinetics, one may postulate several microscopic steps involved in craze nucleation. Imagine a polymer surface under simple tension as shown in Fig. 2 a. The first is logically plastic... 

It is observed that the normal craze fibril structure can be observed just behind the craze tip where the craze is as thin as 5—lOnm . This observation was difficult to reconcile with early models of craze tip advance which postulated that this occurred by repeated nucleation and expansion of isolated voids in advance of the tip. One problem was to explain how the void phase became interconnected while the craze was still so thin. Another was that the predicted kinetics of craze growth appeared to be incorrectly predicted indeed since this mechanism almost involves the same steps as the original craze nucleation, it is hard to understand how craze growth could be so much faster than craze nucleation as observed experimentally. 

J/m. In turn these values of F produce substantial predicted differences in craze growth kinetics. Substituting these values into Eq. (7) the craze tip velocity at constant S, = 100 MPa is predicted to decrease by a factor of 10 from PTBS to PC (values for h of 10 nm and for n, the power law exponent, of 17 are assumed for both) or equivalently the value of Sj to give the same craze tip growth rate increases by a factor of 2.8. Since the measured stress S at the craze tip in PTBS is 27 MPa, the craze tip stress in PC is predicted to be 74 MPa, well above its... 

The author is well aware of the fact that many aspects which have been treated in the extensive literature on extrinsic crazing have not been considered in this article and that more information is needed for a comprehensive account of the observed craze phenomenon. For instance the recent work on the intrinsic crazing of PC and on related phenomena which has been re wed here has primarily been based on structural considerations. It is believed that future work on the kinetics of craze formation and on the underlying molecular dynamics of the system may contribute considerably to a more detailed account of this phenomenon. Nevertheless, it is hoped that this work has opened up some new paths which may lead to a better understanding of the phenomenon of cavitational plasticity in polymers. 

In this Section the kinetics of craze growth at crack tips in air will be considered in some detail. We shall not be concerned with the initiation phase and any micro mechanism (e.g. leading to craze initiation. 

For a steady state to exist, a kinetic balance is necessary between initiation and inactivation, i.e. dg/dt = 0. This gives immediately the required steady state craze front density as... 

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