Ideal rubber simple shear

So-called sandwich rheometers have sometimes been used in the study of rubber elasticity and melt viscoelasticity [141]. In a sandwich rheometer, twin sample plaques are placed in gaps formed by a central steel plate and two outer plates that are part of the same frame. These instruments are difficult to load and clean, and there is no direct control of the gap. Sliding plate melt rheometers were developed to make measurements of nonlinear viscoelastic behavior under conditions under which cone-plate flow is unstable, ie. in large, rapid deformations [ 142 ]. The sample is placed between two rectangular plates, one of which translates relative to the other, generating, in principle, an ideal rectilinear simple shear deformation. Creep tests can be carried out either by use of a feedback loop that generates a plate displacement that gives rise to a constant stress, or by use of a pneumatic drive, as in Laun s sandwich rheometer [143]. 

A rectangular block of ideal rubber is deformed in simple shear 1 the action of a shear stress r, as shown below. 

So far, we have been concerned with uniaxial deformations of rubbers only. Utilizing Eq. (7.75) we can analyze in a straightforward manner any kind of deformation and, in particular, the important case of a simple shear. To begin with, we check once again for the results obtained for the known case of uniaxial strain or compression of an ideal rubber. Here, the transformation equations are... 

Non-linearity shows up in the second finding. We observe that simple shear is accompanied by the development of a non-vanishing normal stress difference < xx — The effect is non-linear since it is proportional to the square of 7. The result tells us that in order to establish a simple shear deformation in a rubber, application of shear stress alone is insufficient. One has to apply in addition either pressure onto the shear plane gzz < 0) or a tensile force onto the plane normal to the x-axis a x > 0), or an appropriate combination of both. The difference Gxx zz is called the primary normal stress difference likewise Oyy — Ozz is commonly designated as the secondary normal stress difference. As we can see, the latter vanishes for an ideal rubber. 

For simple shear, we have thus obtained again linearity for as for ideal rubbers, but non-vanishing values now for both, the primary and the secondary normal stress difference. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

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