Chain direction slip

In a face-centred cubic metal h = a/VS and b = /V6 where a is the lattice parameter and so the theoretical shear strength is predicted to be (Tu—G/9. For chain direction slip on the (020) planes in the polyethylene crystal b = 2.54 A and h is equal to the separation of the (020) planes which is 2.47 A. The theoretical shear stress would be expected to be of the order of G/6. However, more sophisticated calculations of Equation (5.31) lead to lower estimates of which come out to be of the order of G/30 for most materials. Even so, this estimate of the stress required to shear the structure is very much higher than the values that are normally measured and the discrepancy is due to the presence of defects such as dislocations within the crystals. The high values are only realized for certain crystal whiskers and other perfect crystals. 

Fig. 5.43 Schematic representation of chain direction slip in a chain-folded polymer crystal.

Analogous results have been found for stress relaxation. In fibers, orientation increases the stress relaxation modulus compared to the unoriented polymer (69,247,248,250). Orientation also appears in some cases to decrease the rate, as well as the absolute value, at which the stress relaxes, especially at long times. However, in other cases, the stress relaxes more rapidly in the direction parallel to the chain orientation despite the increase in modulus (247.248,250). It appears that orientation can in some cases increase the ease with which one chain can slip by another. This could result from elimination of some chain entanglements or from more than normal free volume due to the quench-cooling of oriented polymers. 

The rapid disappearance of these lamellae at EDR >4.6 suggests that when the chain tilt reaches at an angle, the lamellae suddenly broke into smaller blocks due to shear slip along the chain direction and are reorganized in microfibrils oriented along the draw direction. 

Because of chain inextensibility, the shear rate of any slip system is not dependent on the normal-stress component in the chain direction (Parks and Ahzi 1990). This renders the crystalline lamellae rigid in the chain direction. To cope with this problem operationally, and to prevent global locking-up of deformation, a special modification is introduced to truncate the stress tensor in the chain direction c. Thus, we denote by S° this modification of the deviatoric Cauchy stress tensor S in the crystalline lamella to have a zero normal component in the chain direction, i.e., by requiring that 5 c,c = 0, where c,- and c,- are components of the c vector (Lee et al. 1993a). The resolved shear stress in the slip system a can then be expressed as r = where R is the symmetrical traceless Schmid tensor of stress resolution associated with the slip system a. The components of the symmetrical part of the Schmid tensor / , can be defined as = Ksfw" + fs ), where if and nj are the unit-vector components of the slip direction and the slip-plane normal of the given slip system a, respectively. 

The crystalline regions become more prominent at low temperature relative to amorphous regions and they may permit easy slip at low temperatures probably via a dislocation mechanism. However, there is no evidence of dislocations in semicrystalline polymers. In PTFE the increase in yield point with decreasing crystallinity may be due to grain size effect. As the crystallinity is reduced, the lamella size also decreases. It is most likely that the direction of easy slip is parallel to the chain direction. Since the chains are parallel to the thin dimension of the crystal, it is likely that the lamella thickness should directly affect the srield point at low temperatures—as was observed experimentally (25). 

One of the most interesting alternative approaches is the slip-link model, which incorporates the effects of entanglements [40,41] along the network chains directly into the elastic free energy [42]. Still other approaches are the tube model [43] and the van der Waals model [44]. 

For the determination of critical shear stress of one of the most important deformation mechanisms of iPP crystals, namely the crystallographic slip in the (100) planes along chain direction, i.e., (100)[001] chain slip [113,114], biaxially oriented film was used [115]. 

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