Polymers strain-rate dependence

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

In order to calculate, for a considered polymer under defined experimental conditions (constant strain rate or temperature), the occurrence of the micromechanism transition, one has to plot the temperature or strain rate dependence of the various critical stresses. Hereafter, we will assume that experiments are performed as a function of temperature at constant strain rate. 

Several models that are used to represent the strain rate dependence of polymer melts are presented later in this chapter. 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

It is usual to assume that the shear yield stress has the same temperature dependence and strain rate dependence as the flow stress of the polymer in the active zone of the craze, i.e., n, = n, and in fact usually one go even further and sets How-... 

Strain Rate Dependence. The outline given above is, however, an oversimplification, because it has been implicitly assumed that the flow would not affect orientation or conformation of the polymer coil. This is not true. It is always observed that r, and thus [ /], is affected by the shear rate applied. As discussed in Section 5.1.1, various types of flow can occur and, more generally, we should say strain rate or velocity gradient, rather than shear rate. However, we will restrict the discussion here to simple shear flow. 

The above analysis shows that the nonlinear dynamic viscoelastic behavior of polymers can be resolved into three components the nonlinear elasticity resulting from the variation of modulus with the phase angle or strain during the cycle nonlinear internal friction resulting from strain and strain-rate dependence and eflFects associated with the reversible, strain-induced structural changes. 

Polymers are very sensitive to the rate of testing. As the strain rate increases, polymers in general show a decrease in ductility while the modulus and the yield or tensile strength increase. Figure 13.32 illustrates this schematically. The sensitivity of polymers to strain rate depends on the type of polymer for brittle polymers the effect is relatively small, whereas for rigid, ductile polymers and elastomers, the effects can be quite substantial if the strain rate covers several decades. 

Mechanical properties of polymers, unlike those of other engineering materials, are highly strain rate and temperature dependent. Modulus increases with increasing strain rate and decreasing temperature (Fig. 11.8). The strain-rate dependence for mechanical properties shows that polymers exhibit viscous behavior in addition to solid or elastic behavior. 

Therefore, creep and stress relaxation should be accounted for when designing with polymers. The strain rate for a given application must also be known since modulus, ductility, and strength are strain rate dependent. 

Most polymer processes are dominated by the shear strain rate. Consequently, the viscosity used to characterize the fluid is based on shear deformation measurement devices. The rheological models that are used for these types of flows are usually termed Generalized Newtonian Fluids (GNF). In a GNF model, the stress in a fluid is dependent on the second invariant of the stain rate tensor, which is approximated by the shear rate in most shear dominated flows. The temperature dependence of GNF fluids is generally included in the coefficients of the viscosity model. Various models are currently being used to represent the temperature and strain rate dependence of the viscosity. 

Other estimates of the ultimate shear strength of amorphous polymers have been made by a number of authors and generally all fall within a factor of 2 of each other (38,77,78). Stachurski (79) has expressed doubt as to the validity of the concept of an intrinsic shear strength based on the value of the shear modulus, G, for an amorphous solid. He questions which modulus is the correct value to use— the initial small strain value or the value at higher strain (the yield point or the ultimate extension). Further, the temperature and strain-rate dependence of both the yield strength and modulus (however defined) suggests that perhaps the ratio of yield strength to modulus is not a true intrinsic material property. We remark however that the temperature and strain-rate dependence of both the yield stress and the shear modulus are often similar. 

In view of the fact that the polymer strain resistance depends much on strain rate and temperature, in plimger extrusion and plimger version of hydrostatic extrusion the extrusion pressure increases with the velocity of plunger motion... 

Bao S P and S. C. Tjong (2009) Temperature and strain rate dependences of yield stress of polypropylene composites reinforced with carbon nanofibers, Polym Compos 30 1749-1760. 

Our first task in this chapter is to discuss the relevance of classical ideas of plasticity to the yielding of polymers. Although the yield behaviour is temperature and strain rate dependent it will be shown that, provided that the test conditions are chosen suitably, 3deld stresses can be measured that satisfy conventional yield... 

Figure 11.20 The strain rate dependence of the octahedral shear stress Toct at atmospheric pressure using data from torsion (o), tension (A) and compression ( ). (Reproduced with permission from Duckett et al., Br. Polym. J., 10, 11 (1978))...

Kobayashi, M., Takahashi, T., Takimoto, J., Koyama, K., Influence of glass beads on the elongational viscosity of polyethylene with anomalous strain rate dependence of the strain-hardening. Polymer 37 (1996) 3745. 

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