A craze-growth model

In the fracture of ductile solids, generally cracks grow by a mechanism whereby stresses and plastic strains concentrated in a process zone at the tip of a crack first produce some cavitation in the path of the erack at second-phase particles with 

14 Total craze length 2c in PS vs. time under an applied simple shear stress = 15.74 MPa at 293 K, growing normal to the tensile stress component, ctw — 15.74 MPa at 45° to the shear axis (from Argon and Salama (1977) courtesy of Taylor and Francis). 

Noting the possibility that a variant of the meniscus instability of Taylor (1950) could be the mechanism of craze advance, Argon and Salama (1977) proposed a continually repeating interface-convolution model shown in Fig. 11.16 as the 

In the craze-growth model an advancing craze-tip process zone of extent A, as depicted in Fig. 11.17, develops a craze-tip opening displacement in a 

---

In the following section we develop a craze-growth model in PS/PB diblocks with spherical domains, where in terms of the phenomenology there exists a direct parallel with the crazing in homo-polymers. The model presented here is an abbreviated form of the model described in greater detail by Schwier et al. (1985a). 

One of the great successes of the craze growth model is that it predicts a transition from scission-dominated crazing to shear deformation as the strand density of the network is increased. While the shear yield stress is essentially unaffected by dian ... 

Fig. 17. A plot of the ratio r of the initial crazing stress to the crazing stress for van-der-Waals crazing as a function of temperature for PS having a molecular weight of 260,000 ( ) and 1,150,000(0). The jo/fd carve corresponds to the prediction based on the craze growth model (using Eq. (20)) and a value of V = 6,7 nm s" ...

Argon and Salama 1976). As Fig. 11.10 shows, in the temperature range of 100 130 °C of experiments over which the value of the product Doy remains constant, ay varies considerably as in all glassy polymers, where the value of D shows a compensating change consistent with the craze-growth model discussed in Section 11.8. 

In the craze-growth model the craze-tip opening displacement S of eq. (11.44) is taken as a reinterpretation of the crack-opening displacement of the Argon and Salama (1976) perturbation model, but properly downscaled by the attenuation factor a described above, giving... 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

Having set out a detailed model of craze growth, we now compare its predictions with recent experiments in two principal areas 1) the effects of entanglement density and 2) the effects of temperature. 

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. 

Fig. 12. Craze growth rate as a function of applied stress for SB5/S4 blend containing 18 vol.% PB (O) quenched sample, (O) slow-cooled sample, ( ) sample isothermally aged 7 days at 87 °C and ( ) sample isothermally aged 5 days at 87 °C solid line and dashed line show predictions of the cavitation model and the meniscus convolution model, respectively...

The development of linear elastic fracture mechanics is given with a special emphasis on its application to the testing of polymers. The modelling of crazes and plastic zones is discussed and then developed to describe time-dependent crack md craze growth, including crack stability phenomena. 

A cursory examination of the experimental results for the craze-growth rate and their stress dependence presented in Fig. 11.15 compared with model predictions obtainable from eqs. (11.50), (11.51), and (11.52) using the specifie material parameters of Table 11.2 shows that the model significantly overpredicts the craze-growth rates and their stress dependences both for PS and for PMMA. This suggests that some basic parameters of the model are very different from those present in the experimental behavior. To understand the causes of this differenee the general form of the model expression for the craze-growth rate vc = dc/dt is stated simply as... 

---