Normal Stresses during Shear Flow

In contrast to simple fluids under shear that generate stresses parallel to the direction of shear, polymeric fluids also generate normal stresses perpendicular to the flow direction [Eqs. (29), (30), where Ni and N2 are called the first and the second normal stress difference, respectively, and are dependent on the shear rate]. 

---

Unfortunately, a few papers are known where normal stresses during shear flow of filled polymers were measured directly. Here an additional problem is connected with the solution of the problem what is considered a one-valued measure of elasticity of a material and under what conditions to compare the measured values of normal stresses. Moreover, the data at hand often represent rather a contradictory picture. 

More than 40 years qfter Weissenberg s pioneering proposal [Figures 4.1.1 and 8.1.1] for die measurement of shear and normal stresses during shear flow of elastic Uquids, the determination of the rheological material functions of polymers in simple shear flow is still a nightmareforthe experimenter. J. Meissner et al. (1989)... 

During dynamic measurements frequency dependences of the components of a complex modulus G or dynamic viscosity T (r = G"/es) are determined. Due to the existence of a well-known analogy between the functions r(y) or G"(co) as well as between G and normal stresses at shear flow a, seemingly, we may expect that dynamic measurements in principle will give the same information as measurements of the flow curve [1],... 

During shear flow, polymer chains are deformed and orientate in the direction of flow. (The results of this orientation in standard injection mouldings was discussed in Section 2.1.) The tension of the polymer in the flow direction is called the first normal stress. In contrast to this, flow in other directions is relatively small. First normal stress can be defined by the difierence between the normal stress component in the flow direction and the normal component in the direction of the shear plane. Combinations of some or all of these forces are applied to the molten polymer material dining the moulding process depending upon where on the moulding they are. Analysis using methods such as these, allows material interactions to be better understood. 

The existence of a positive first normal stress difference during shear flow can be used to explain die swell. If the fluid being sheared between parallel plates in Figure 14.5 were to emerge into the atmosphere, Tjj would obviously equal... 

Fig. 13. Shear stress t12 and first normal stress difference N1 during start-up of shear flow at constant rate, y0 = 0.5 s 1, for PDMS near the gel point [71]. The broken line with a slope of one is predicted by the gel equation for finite strain. The critical strain for network rupture is reached at the point at which the shear stress attains its maximum value...

Real world materials are not simple liquids or solids but are complex systems that can exhibit both liquid-like and solid-like behavior. This mixed response is known as viscoelasticity. Often the apparent dominance of elasticity or viscosity in a sample will be affected by the temperature or the time period of testing. Flow tests can derive viscosity values for complex fluids, but they shed light upon an elastic response only if a measure is made of normal stresses generated during shear. Creep tests can derive the contribution of elasticity in a sample response, and such tests are used in conjunction with dynamic testing to quantity viscoelastic behavior. 

Critically consolidated. If a powder is sheared sufficiently, it will obtain a constant density or critical porosity e for this consolidation normal stress Gc- This is defined as the critical state of the powder, discussed below. If a powder in such a state is sheared, initially the material will deform elastically with shear forces increasing linearly with displacement or strain. Beyond a certain shear stress, the material will fail or flow, after which the shear stress will remain approximately constant as the bulk powder deforms plastically Depending on the type of material, a small peak may be displayed originating from differences between static and dynamic density. Little change in density is observed during shear, as the powder has already reached the desired density for the given applied normal consolidation stress a . 

Elastic liquid-. As a result of elasticity, normal stress also occurs during flow in addition to shearing stress normal stress or WeiBenberg effect... 

---