Critical crazing stress

The criteria (Eqs. 11 and 12) are similar and are derived from studies on materials that are elastic at initiation of crazing, while more ductile materials like polycarbonate show a more pronounced sensitivity to the hydrostatic tension. This has been found experimentally by Ishikawa and coworkers [1, 27] for notched specimens of polycarbonate. Crazing appears ahead of the notch root, at the intersection of well-developed shear bands. From a slip fine field analysis, the tip of the plastic zone corresponds to the location of the maximum hydrostatic stress. This has been confirmed by Lai and Van der Giessen [8] with a more realistic material constitutive law. Therefore, Ishikawa and coworkers [1,27] suggested the use of a criterion for initiation based on a critical hydrostatic stress. Such a stress state condition can be expressed by Eq. 11 with erg = 0 and I r = B°/A°. Thus, the criterion (Eq. 11) can be considered general enough to describe craze initiation in many glassy polymers. For the case of polycarbonate, a similar criterion is proposed in [28] as... 

Since oy is the major principal stress, we have an = oy > crm = (oy + a2)/2 and the side condition that the normal stress has to exceed the hydrostatic stress for craze initiation is satisfied. Equation 21 defines a critical normal stress which appears to be hydrostatic stress dependent. As long as an < oTr(am), crazing does not occur and when an reaches o/jr(crm) crazing initiates. Once initiated, the craze thickens and the condition (Eq. 21) is no longer relevant. 

Craze breakdown is experimentally characterized by a critical craze thickness Acr which is primarily dependent (Eq. 20) on the craze stress ac, the force for chain scission, and the entangled chain density along the craze surface vs. The craze stress ac is assumed to be rate and temperature depen-... 

The cohesive surface description presented here has some similarities to the thermal decohesion model of Leevers [56], which is based on a modified strip model to account for thermal effects, but a constant craze stress is assumed. Leevers focuses on dynamic fracture. The thermal decohesion model assumes that heat generated during the widening of the strip diffuses into the surrounding bulk and that decohesion happens when the melt temperature is reached over a critical length. This critical length is identified as the molecular chain contour. 

Critical (true) stress for craze initiation Area... 

As an example, Fig. 8 shows the fracture toughness for PMMA and Fig. 9 the fringe pattern transition at the critical temperature, whereas Fig. 10 shows the lateral face of the sample with the crack-tip above and below the critical temperature. It has also been shown that neither the bulk modulus nor the craze stress varies near the critical temperature (Fig. 11 and 12). It seems that the local material property varying near that particular temperature is the craze stiffness, as shown in Fig. 13. 

Fig. 12. Craze stress of PMMA near the critical temperature there is no transition at T. From Ref courtesy of Chapman and Hall, Ltd.

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. 

Some criteria have been proposed for craze initiation. The earliest criterion states that crazing occurs when the uniaxial tensile stress reaches a critical value (27). Since the crazing stress depends on the strain rate and... 

In particular, the crazing stress does influence the onset of the pullout-to-crazing transition as well as the maximum width /y of the plastic zone according to Eq. (19). From Sect. 3.4, the critical areal density for the onset of crazing, 2, is given by ... 

The crack growth condition of Eq. (9.15) can be used A craze fails when its opening displacement reaches a critical value. Flowever, this does not explain the failure mechanism. It could be by failure of the entanglement network in the craze fibrils. Crazes in some polymers fail at their midplanes, and in other polymers at the bulk-craze interface. For viscoelastic materials, in which both the craze stress and the Young s modulus vary with the strain rate, Eq. (9.19) predicts that the crack tip opening displacement is no longer proportional to the stress intensity factor. Figure 9.11 shows that... 

Figure 7.8. Failure transitions in block copolymer reinforced interfaces. The critical stress versus the areal chain density is sketched for chain pull-out (dotted lines) and chain scission (solid). The dashed lines show the crazing stress, which is independent of the areal chain density. For large N (a) there is a transition from failure by chain scission to failure by crazing at a critical areal chain density whereas for a smaller value of N (b) chains are pulled out before they break and there is a transition from failure by chain scission to failure by crazing at a critical areal chain density After Kramer et al. (1994).

Fig. 11.23 Critical tensile stress for craze initiation as a function of (cavitated) rubber particle diameter, calculated using Eq. 11.26 with three different values of Gcraze the specific energy of craze initiation (From Bucknall and Paul (2009) reproduced with permission of Elsevier)...

The question arises whether there is a lower threshold for the stress intensity factor too, below which no craze can develop at all. No crack could then be initiated and stress crack formation would no longer be possible. There are indications in the literature that such a threshold value may be around a tenth of the discussed critical stress concentration factor providing an upper limit for the range of pure stress crack formation. This issue about critical local stresses and critical deformations, which must be exceeded, so that stress crack formation occurs, leads to the third group of... 

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