Craze growth velocity

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 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. 

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... 

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... 

For completeness DiCorleto and Cohen also examined the effect of aging on craze growth in low volume fraction PB diblocks of spherical morphology which craze according to the meniscus instability mechanism As expected from the work of Kefalas and Argon on homopolystyrene, aging had also no measurable effect on craze velocities in this case as well. 

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... 

The stress dependences of the craze velocity for the three diluent concentrations using the craze growth relation of eq. (13.34) with the new values of Pg = 0.688 and Ag = 1-10, together with the factors nip(p above, are plotted in Fig. 13.27 with dotted lines that give a very good fit to the experimental results. 

Though a somewhat idealized picture of craze growth, the basic premise of the Taylor meniscus instability model has been verified by Donald and Kramer (135), who measured a critical wavelength in polystyrene crazes that was in close agreement with the interfibrillar distance. Further, following the procedure of Fields and Ashby (134) a steady-state craze tip velocity may be estimated by assuming a non-Newtonian fiiud of the form... 

We expect that the critical capture distance 5 will not be very stress dependent. This is because the main body of the craze transmits full traction while the expected deficiency in the craze traction near the craze tip will scale with the applied stress so will the allowable decrease in stress at the critical distance 8 that stops the growth of the oncoming craze. Hence the stress dependence in results from both the craze velocity and the craze initiation time. 

Once crazes have developed, however, their growth is governed by the repeated cavitation of the rubbery domains, and the developments of Section 2.3 apply. The velocity of the craze is given by... 

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... 

The life-time of the craze fibrils and the craze stress required for fibril growth are drastically affected by the environment below the critical velocity. 

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