Orientation hardening

The second term on the right-hand side of Eq. (8.5) describes the increase in true yield stress with true strain rate. If the initial yield stress is measured in a tensile test, the low strain means there is no contribution from orientation hardening (see the next section), and there is insignificant heating. Consequently, the strain rate effect can be isolated. The initial yield stress was foimd, for HOPE at 20 °C, to vary with the true strain rate according to 

If a plastic is subjected to a constant high creep stress for a long time, the creep rupture failure that occurs may be by yielding, or by crazing and crack growth. Creep rupture is important for the design of gas or water pipes (Chapter 14), where the cylindrical shape is stable during creep. It is less important for products that are bent or twisted, where excessive deflection is likely before any rupture process starts. 

To quantify orientation hardening in a tensile test, the strain rate and temperature should be kept constant, since changes in these variables may 

Variation of true tensile yield stress with true strain, fitted by Eq. (8.20), for various polymers. K is the slope of the lines in MPa (From G Sell C and Jonas, J.J. Mater. Sc/., 16, 1966, 1981, Chapman and Hall). 

Molecular and/or crystal orientation increases the yield stress in the direction of drawing (Fig. 8.16). However, the yield stress at right angles to the draw direction hardly changes or may even decrease. The resulting 

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It seems reasonable to assume that crazing is a process which can occur quite naturally in any orientation hardening material, which exhibits plastic instability at moderate strains and in which the yield stress is much higher than the stress required for the nucleation of voids (cavitations). 

Studies of craze microstructure and the surrounding displacements of crazes have established that the only parts around a craze that undergo plastic deformation are concentrated into a process zone at the tip of the craze, and into a fringing layer all around the entire craze body. In the process zone craze matter is generated by one of the two processes discussed above, and fibrils are necked down to the final extension ratio. In the fringing layer, additions are made to craze fibrils by drawing polymer out of half space. Outside the idetifiable parts of a craze, the solid polymer remains entirely elastic while inside the craze body the fully drawn fibers carry the required craze tractions purely elastically in their orientation hardened state at the... 

For T < Tg, the viscoplastic model used here accounts for intrinsic softening upon yielding followed by progressive orientational hardening. Rate dependent flow is taken to be governed by Argon s formulation [5] of the equivalent plastic strain rate... 

I) Gaussian orientation hardening function Boltzmann s constant yield strength in shear rate constant... 

Wu, P.D. and Van der Giessen, E. (1993) On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers. Journal of the Mechanics and Physics of Solids, 41, 427-456. 

The effect of orientation hardening of matrix polymers on the toughness of polymer blends was examined by Ishikawa et.al. (Ishikawa et al., 1996). Both PMMA and PVC with different characteristics of orientation hardening were used as matrix polymers and a silicon/acrylic composite rubber graft copolymer was used as the... 

P. D. Wu and E. van der Giessen, On Improved Network Models for Rubber Elasticity and Their Applications to Orientation Hardening in Glassy Polymers , J. Mech. Phys. Solids 41, 427-456 (1993). 

In the case of cross-linked polymers (eg epoxy pol5miers), the SSE induces the increase in microhardness, tensile modulus, 5ueld stress, and strength (68). Moreover, depending on EDR value these parameters are changing because of the competition between the processes of orientational hardening and mechanical destruction. SSE influences the structure and properties of polymers based on interpenetrating polymer networks similarly (68). 

We found that the true axial stress-strain curves in the three studies showed similar trends when comparing notched specimens to smooth specimen controls (Figure 31.6). All of the notched specimens showed an elevation of the yield stress and a reduction of the ultimate stress. Also, the stress-strain curves of the notched specimens appear truncated when compared to the smooth specimens in that they lack the steep final portion of the curve that is typically associated with orientation hardening. In all of the studies and notched conditions tested, the crosslinked materials showed decreased ductility when compared to the conventional material. 

FIGURE 31.6 True stress-strain curve from study II showing the orientation hardening region in smooth specimens and showing the truncation of this region and the elevated yield stress in notched specimens. 

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