Craze flow stress

We expect that when craze sources are plentiful, resulting in a high active craze front length Q, the craze velocity that needs to be maintained to match the imposed strain rate can be proportionally lower resulting in a lower craze flow stress and an increased craze fracture time tf. The contrary will hold when craze sources are few, requiring high velocities and high craze flow stresses to be maintained. There is very little information available currently on the important dependence of the craze fracture time tf on the applied stress implied by Eq. (9). 

CTq Craze flow stress of unmodified glassy polymer... 

Craze flow stress of PS with sorbed diluent at the solubility limit Cavitation strength of heterophase domain in block copolymer 6 Ratio of des( nding to the ascending slopes of the traction displacement law locally accompanying craze matter production, as defined in Ref. 

In Eq. (2), U is the energy for bond rupture, the macroscopic craze flow stress, X the craze fibril extension ratio accounting for the first order stress concentration, Q an activation volume of monomer dimensions, Vd a pre-exponential frequency factor of the order of atomic frequencies, and q a further stress concentration factor relatel to the fraction of the taut bundle of molecules in the fibril given by ... 

Finally, our interest will be limited here exclusively to the phenomenon of crazing in heterogeneous polymers. Thus, apart from the considerations of improving toughness by manipulation of the processes that govern the craze flow stress and, thus, rendering the extrinsic flaws inoperable that result in craze fracture, we will not consider the mechanics of fracture of crazable polymers. A brief survey of this subject related to the crazing process can be found elsewhere... 

The strain to- fracture is expectai to be related to the craze flow stress, with craze fibril breakdown occurring more rapidly at higher stresses. Since the flow stresses are related to the volume fraction of PB through the craze growth velocities, the strains to fracture are also expected to relate to the rubber content. 

Fig. 27. Dependence of craze flow stress on weight fraction of low molecular weight PB rubber. The upper branch is for homogeneous blends, the lower for heterogeneous blends ->-2...

In Eq. (10) the only unknown parameter is the exponential coefficient which can be determined as an adjustable parameter by matching Eq. (10) to the upper branch of the craze flow stress curve in Fig. 27. This gives p = 43.6. 

When the dUuent has precipitated out into PB-2.76K pools for diluent concentrations v > Vg then much more concentrated plasticization is possible in the craze borders in the manner illustrated in Fig. 31. Now the free PB, coating the surfaces of the craze subject to deformation induced negative pressures can be sorbed into a fringing craze surface layer to a depth of od, where d is the craze tuft diameter. However, the tuft diameter is itself dependent on the local plastic resistance by a product expression that is a principal finding of the meniscus interface convolution model, and is usually given in terms of the craze flow stress in the form... 

As Fig. 13.3 demonstrates, the tensile toughness of a particle-modified crazabie glassy polymer can be stated simply as the product of the craze-flow stress (Tcc and its strain to fracture Sf as... 

The tensile toughness Wp exhibited by homo-PS and the three PS blends containing particles of KRO-1 resin, HIPS, and concentric spherical shells (CSSs) is presented in Fig. 13.5. It shows the very substantial improvement in toughness achievable by lowering the eraze-flow stress <7oo by incorporation of compliant particles, but demonstrates also that the peak toughness achievable eventually plateaus when the craze-flow stress becomes too low as in the case of blends with the CSS particles. 

Craze initiation from compliant particles and the craze-flow stress... 

A model for the craze-flow stress of particle-toughened polystyrene... 

Figure 13.11 shows the tensile test results of (a) the disassembled and reconstituted original HIPS with the wide particle-size distribution having a craze-flow stress of = 19.0 MPa as a standard for comparison (b) the special blend containing only the large particles with a flow stress (Tco = 18.17 MPa (c) the special blend containing only the small particles with a flow stress of around CTco = 20.46 MPa, but a substantial upper yield stress of 24.0 MPa. Clearly, the two special blends with narrow particle-size distributions have substantially different behaviors and bracket the behavior of the reassembled original HIPS. 

Table 13.4 lists the properties of PS at 293 K that enter into the model predictions for the craze-flow stress (To,. Table 13.5 gives the pre-exponential factors A of the kinetic expression for the craze-border velocity appearing in eq. (13.30) and defined by eq. (13.31), and also the experimentally measured properties of the two special HIPS-type blends their average particle size D, experimentally determined craze-flow stresses aooe, from Fig. 13.11, and, finally, the model predictions of craze-flow stresses iTcom, which were obtained using the tabulated properties for PS. We note that all model predictions for the craze-flow stress are roughly 17%... 

We note further from Fig. 13.12 that fully 40% of the small-particle size distribution falls below the critical particle-size estimate of Dc = 0.93 pm, reducing the effective fraction of the particle volume fraction from 0.22 to 0.13. This results in a substantial upper yield stress of 24 MPa, as Fig. 13.11(c) shows. However, once an effective craze network has developed the actual craze-flow stress of this blend drops to 20.5 MPa, in keeping with expectations. 

Moreover, considering that the craze-tuft diameter d is related to the craze-flow stress (Too (Paredes and Fischer 1979 Brown et al. 1989) with the product duoD = C remaining constant at C = 2.5 x 10 MPa m, the diluent concentration in the flow zone becomes... 

With these parameters, the dependence of the craze-flow stress of the four PS/PB blends with different PB isomer contents at volume fractions/in the range 0. 05 and at strain rates of s = 2.6 x 10 " s are determined for T = 295 K and presented in Fig. 13.26. The flow-stress measurements of Spiegelberg et al. (1994) for the diluent with a fraction 0.71 of PB 1,4 isomer shown as the circular data points agree very well with the model. 

Fig. 13.26 The dependence of calculated craze-flow stresses on the volume fraction of total diluent content in PS/PB blends, comparing the calculated results with experimental results of Gebizlioglu et al. (1990), for 293 K and 253 K, at strain rate e = 2.6 x 10 s . The flow stresses increase markedly with decreasing fraction of PB 1,4 linear isomer diluent (Argon (1999) courtesy of Wiley).

Comparing model predictions with experiments, we note, first, that the Spiegelberg et al. (1994) experiments are quite different from the earlier experiments of Argon and Salama (1977). Therefore, new constants and for eq. (13.34) were determined by a best fit to the new homo-PS results in Fig. 13.27, namely ySg = 0.688 and le = 1.0. With these new constants, a similar procedure to that with the craze-flow stresses discussed above was followed by considering the set of ordered results for the craze velocity s stress dependence for/ = 0.03. This established that the plasticization product m ip for this blend was relatively constant over the entire stress range at = 0.825. Since in the product (p depends directly on/, appropriate values for diluent fractions of 0.01 and 0.05 are determined by re-scaling the results of/ = 0.03. 

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. 

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