Craze interface velocity

Pc> Pb> Pf cumulative number fraction of grid squares that exhibit craze formation, craze fibril breakdown, and catastrophic fracture, respectively probability that a given entangled strand survives craze fibril formation disentanglement time of i strands in a fibril that survive fibril formation craze interface velocity volume fraction of polymer within craze... 

Suppose now that there is a wide spectrum of craze microstructures with different values of the fibril spacing D,. For the crazes with very small and very large Dq the craze interface velocity from Eq. (9) is miniscule, since for these crazes Vctq is small. Clearly there will be a value of D which maximizes Wq, and hence v, and this value is given by... 

This craze widening stress, which can be considered to be the crazing stress of the polymer, is only weakly dependent on the craze interface velocity but proportional to the geometric mean of the flow stress and the craze surface tension per unit width of the... 

Beside the craze interface velocity, the polymer molecular weight is expected to have a sutetantial effect on the crazing stress, as already mentioned above, and thus potentially on the crazing to shear transition. Figures 16d and 16e show the results of a calculation of the crazing stress for two lower molecular weights of PS, 750,000 and 300,000 respectively at the low interface velocity of 1 nm/s. Note that... 

An alternative model is shown schematically in Fig. 10. Just as for the craze tip, the strain-softened polymer being actively deformed at the bulk polymer interface is idealized as a thin layer of non-Newtonion fluid. The velocity v of plastic advance of the craze interface depends on the gradient in hydrostatic tension Van as... 

The craze front velocity v can be governed by one of two distinct mechanisms of craze matter production. As Argon and Salama have discussed in detail, under the usual levels of service stresses or stresses under which most experiments are carried out, craze matter in single phase homopolymer is produced by the convolution of the free surface of the sohd polymer at the craze tip. This occurs by a fundamental interface instability present in the flow or deformation of all inelastic media when a concave, meniscus-like surface of the medium is being advanced locally by a suction gradient. This is the preferred mechanism of craze advance in homopolymers. In block copolymers with uniform distributions of compliant phases of a very small size, and often weaker interfaces than either of the two phases in bulk, craze advance can also occur by cavitation at such interfaces to produce craze matter as has been discussed by Argon et al. Both of these mechanisms of craze advance lead to very similar dependences of the craze front velocity on apphed stress and temperature that is of the basic form... 

Furthermore, the interface velocity of this craze is much larger than those with just slightly smaller or larger Dq s, since the large exponent n on Vctq in Eq. 9 means that even small deviations of Vctq from its maximum value will result in large decreases in velocity. The microstructure (D,) of this dominant, fastest growing, craze will be the microstructure of the average craze in the sample. 

The craze interface stress required for craze with the optimum microstructure to grow at the velocity v can be shown to be... 

In Eq. (10) that gives the toughness in dilatational plasticity the factors C and A are dependent on craze microstructure and will not vary significantly. The stress and temperature dependence of the craze velocity while quite determinate in the interface convolution process of craze matter production will also be quite sensitive to micro-structural detail of phase distribution in block copolymers. The appUed stress = Y ... 

Combining Eqs. (54), (55) and (57) and using the same approach to the establishment of the equivalent plastic resistance of the deforming polymer that was introduced in connection with the mechanism of craze growth by the interface convolution process, we write the craze velocity to be... 

The craze tip growth velocity V can be limited by the liquid flow velocity within the craze. Figure 10.17 shows a craze containing a length L of liquid. The liquid pressure pi at the crack tip is atmospheric, but p2 at the liquid/air interface due to the capillary attraction. If the liquid moves inside the craze with the same velocity V as the advancing craze tip, and the pore area A of the craze cross section is constant, D Arcy s law for the flow of a liquid of viscosity tj through a porous medium... 

For comparison of model predictions with experimental measurements three sets of experimental information were used for craze velocity dc/dt vs. applied stress (Too at 293 K (1) PS/PB diblock with c = 0.18 and p = 39.5 nm (code B) (2) PS/PB diblock with c = 0.058 and p = 20—25 nm (codes L and M) and (3) PS/PB diblock with c = 0.11 (for both 293 and 253 K) (code F). The actual velocity measurements, not given here, can be found in Schwier (1984). For contrasting the craze-growth rate based on PB phase cavitation discussed in Section 11.10.3 with an interface-convolution mechanism in a reference homo-polystyrene eqs. (11.50) and (11.51) were used together with values of PS material parameters listed in Table 11.4. Figure 11.23 shows the actual craze velocity for code B. Here the model prediction for the diblock according to the developments in Section 11.10.3... 

There is, however, a theory for the growth of crazes that is consistent with all the experimental evidence. Argon, Hannoosh and Salama [52] have proposed that the craze front advances by a meniscus instability mechanism in which craze tufts are produced by the repeated break-up of the concave air/polymer interface at the crack tip, as illustrated in Figure 12.15. A theoretical treatment of this model predicted that the steady-state craze velocity would relate to the five-sixths power of the maximum principal tensile stress, and support for this result was obtained from experimental results on polystyrene and PMMA [52]. 

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