Strain-hardening behavior

Bogaerds et al. (47) developed a linear flow stability analysis toolbox in conjunction with the single-mode extended pom-pom (XPP) constitutive equation (56-58). Their analysis did not show the periodic nature of the flow-front motion observed experimentally with instabilities. On the other hand, their simulations do show that the onset of the linear instability can be postponed by increasing the number of the pom-pom-bearing arms of the XPP model, which would render in the melt increased, strain-hardening behavior. 

Strands that terminate with a branch point at both of its ends can neither reptate nor completely retract. Relaxation of such strands presumably occurs by more complex, hierarchical processes discussed by McLeish (1988b). Here we simply note that the presence of branch points at both ends of a strand leads to much more strain hardening in extensional flows (Bishko et al. 1997 McLeish and Larson 1998). Low-density polyethylenes (LDPEs), which are highly branched, are well known for their extreme strain hardening behavior in extensional flows (Meissner 1972 Laun 1984) (see Fig. 3-39). The steady-state shear viscosity, as a function of shear rate, seems to be little affected by long-chain branching, however. 

Strain-hardening behavior can also be observed in Figure 1 for the Ca telechelic beginning near 50% elongation, and to a lesser extent for the Ni ionomer near 100% elongation. This feature is absent in the other three materials. As these telechelics are copolymers of the two types of vinyl addition, stress-induced crystallization cannot be the source of the strain-hardening, nor is it due to the finite extensibility of the primary chains, of molecular weight 8000, which should occur above 300% extension. 

Due to the strain-hardening behavior of HPFRCC, the cracks thus formed are often under 100 pm in width, which warrants its superior permeability characteristics. 

Morphology of three polypropylene (PP)/polyethylene (PE) blends with different viscosity ratios. The viscosity ratio is 3.9 for PP/PE-1 (a), 1 for PP/PE-2 (b), and 0.5 for PP/PE-3 (c). The surface of the blend was etched with xylene to improve morphology observation. (Reproduced from Hong, J. S., K. H. Ahn, and S. J. Lee. 2005a. Strain hardening behavior of polymer blends with fibril morphology. Rheologica Acta 45 202-208, with permission.)... 

Hong, J. S., K. H. Ahn, and S. J. Lee. 2005a. Strain hardening behavior of pelymer blends with fibril morphology. Rheologica Acta 45 202-208. 

For a second comparison we chose the strain-hardening behavior of nearly glassy PET between 298 K and the glass-transition temperature of 346 K, which was studied by Zaroulis and Boyce (1997) in compression flow. Figure 8.18 shows the compression stress-strain curves of PET at a strain rate of 10 s at seven temperatures between 298 and 349 K, slightly above Tg. The DSC experiments showed that as-received material contained nearly a 9% crystalline fraction. It also needs to be noted that PET undergoes considerable strain-induced... 

Finally, in Fig. 12.6(c) the external applied stresses are larger still and the plastic zone has now increased over the entire cross section where > D — a). Here the entire part response is importantly altered by the plasticity of the material and the nature of its strain-hardening behavior. 

Table 2 lists n values for several materials [1]. Typically, the n values for most metals vary between 0.1 and 0.5. The n values of aluminum alloy sheets decrease sharply with an increase in the tensile strain and are lower than those of steel sheets. The n value of commercial HSLA steels decreases with increasing strength and its low n value makes it less formable than mild steel [38]. There are different strain hardening behaviors for mild steels and high-strength steels. The strain distribution ability of steels increases with the increase in overall n value. The peak n value at a low strain level increases the strain distribution ability of the steel. Aging of rimmed steels causes the n value to decrease with time. Additionally, excessive temper rolling beyond that required to eliminate YPE (Cv) will also reduce the n value. 

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