Kink formation

The possible fatigue failure mechanisms of SWCNT in the composite were also reported (Ren et al., 2004). Possible failure modes mainly include three stages, that is, splitting of SWCNT bundles, kink formation, and subsequent failure in SWCNTs, and the fracture of SWCNT bundles. As shown in Fig. 9.12, for zigzag SWCNT, failure of defect-free tube and tubes with Stone-Wales defect of either A or B mode all resulted in brittle-like, flat fracture surface. A kinetic model for time-dependent fracture of CNTs is also reported (Satapathy et al., 2005). These simulation results are almost consistent with the observed fracture surfaces, which can be reproduced reasonably well, suggesting the possible mechanism should exist in CNT-polymer composites. 

The Argon theory, therefore, consistently interprets the yield behavior of both thermosets and thermoplastics. This indicates that crosslinks in thermosets do not introduce appreciable deviation to the kink formation process described. This point is also supported by Ygmani and Young s finding of the molecular parameters, z and a, being insensitive to crosslinking density for DGEBA cured with different amount of TETA. 

Actually, crosslinks control the molecular packing and indeed significantly affect the elastic modulus of the material. As the intermolecular energy of kink formation is also determined by elastic modulus, the yield stress will definitely vary with modulus and thus the cross -linking density. In other words, crosslinks may not seriously affect the activation segment configuration in the molecular chain but will indirectly control the yield stress. 

Fig. 6.2.12. (a) Schematic diagram of the indentation on the sectioning crack, s—s. (b), (c) and (d) illustrate the three types of flow-line intersections and (e) is a schematic diagram of kink formation at A and the suppression of slip on kinked flow lines. (After Hagan, 1980)... 

Eurthermore, we may determine the energy of the kinked configuration in light of our solution in conjunction with the first integral of the motion found above. The definition of the kink formation energy is... 

Wn is an energy of interaction between steps, and Wa is the energy of kink formation. 

Data recalculated by present authors assuming a pre-exponential factor for kink-formation of 10 s compared to those measured in Refs. [95Peal] and [95Swal]. 

In [97], an alternative model not implying kink formation was proposed based on the results of conformational energy calculations and geometrical analysis. The conformational space was sampled for short atactic portions of PAN chain containing m isolated diads and mm isolated triads in a syndiotac-tic configurational environment, with the aim to find extended conformations of minimum energy suitable for PAN in the crystalline state. 

The relative contributions of the kink formation energy (2Fk) and the kink diffiision energy (Qd) are unknown. However, should be of the form a (ib h, where a is a constant of the order 0.1 for an abrupt kink (a kink with a width of atomic dimensions), and an order of magnitude smaller for a relaxed kink (a kink with a width much greater than atomic dimensions) [23], so that ... 

In another molecular approach Argon (28) has proposed a theory of yielding for glassy polymers based on the concept that deformation at molecular level consists in the formation of a pair of molecular kinks. The resistance to double kink formation is considered to arise from the elastic interactions between chain molecule and its neighbors, ie, from intermolecular forces. This is in contrast to the Robertson theory, where intramolecular forces are of primary consideration. We need to recall that the intramolecular forces are by several orders of magnitude stronger than the intermolecular ones—except for entanglements which operate as if they were primary chemical bonds. 

Note that both the energy release rate Q for crack penetration into the substrate given by (4.85) and the energy release rate k for single or double interface kink formation depend on the increment of crack advance Aa in the same way. Consequently, the ratio of k fo Q, which specifies the relative energy release for kink crack formation of some length Aa to substrate penetration to the same depth, is independent of Aa. This ratio, which is given by... 

The stress measure and closed within parentheses is defined so that (6.29) reduces to (6.28) in the limit as the film becomes very thick. It is likely that glide is accomplished by the thermally activated motion of kinks along the threading segment (Tuppen and Gibbings (1990) Hull et al. (1991)). A free surface or bimaterial interface may offer a better site for kink formation than interior points along the dislocation line, and this is an influence on relaxation that cannot be addressed directly by approaches based on continuum mechanics. 

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