Rheological behaviour elastic materials

The most straightforward rheological behaviour is exhibited on the one hand by Newtonian viscous fluids and on the other by Hookean elastic solids. However, most materials, particularly those of a colloidal nature, exhibit mechanical behaviour which is intermediate between these two extremes, with both viscous and elastic characteristics in evidence. Such materials are termed viscoelastic. 

In formal rheology, relations between these three tensors are formulated and analyzed. Only for the two extremes of viscoelastic behaviour are such relations simple. For purely elastic materials there is a relation between the stress tensor and the strain tensor it contains the elasticity modulus and the Poisson ratio, accounting for the extent to which extension in one direction is accompamied by concomitant compression in the other two. For purely viscous fluids there is a relation between the stress tensor and the strain rate tensor. As extension in one direction is concomitant with (viscous) compression in the other two, in this case only one viscosity is required. For incompressible Newton fluids eventually an expression with only one viscosity results, see (1.6.1.131. 

As long as stresses and rates of shear are proportional we Ccui speak of linear viscous behaviour. We shall not consider situations and systems where linearity is not satisfied. For the elastic equivalent, see [3.6.6], linearity is also supposed to apply. Fluids obeying linear viscous behaviour are called Newton fluids. Only one material parameter, the viscosity 77, is needed to define their rheological behaviour. 

The viscous behaviour of material could be rather complex. As aforementioned, it may be described with time-dependant functions. Time-dependant deformations can be both reversible and/or irreversible but in either case dissipation of energy is involved. This point will be clarified in section 3. According to material rheology, a reversible mechanism means that the deformations would be recovered once the material is unloaded. For example, the elastic deformation is fully reversible and instantaneous. On the other hand, an irreversible mechanism means that the deformations will not be recovered once the material is unloaded. However, emphasis will be put on a reversible mechanism such as the creep/ relaxation phenomenon. 

Just as the structural properties of soft materials have some elements of a liquid and some elements of a solid, the flow or rheological properties do too. A good example of this is silly putty , which is a rubbery polymer called silicone. This will flow out of a container like a liquid. However, if it is formed into a ball and dropped on the floor, it bounces back, i.e. it behaves like an elastic material. The crucial factor is the time for which the force is applied. Pouring is a slow flow due to gravitational forces, but the brief impact of the ball with the floor means the force acts for an instant. One of the most important characteristics of soft materials is the dependence of mechanical behaviour on the rate of deformation. Because at low rates... 

The rheological behaviour of molten polymers is of prime importance as it relates to their microstructure and governs their processing characteristics [1]. Rotational rheometers, specifically cone-plate, parallel plate, and sliding plate rheometers are routinely used to characterize the linear viscoelastic properties of polymer melts. Small amplitude oscillatory shear experiments are employed to measure the storage (G ) and loss moduli (G"), which are related to the elastic and viscous character of the material, respectively, and the complex viscosity (77 ) as functions of angular frequency (a). 

Colloidal suspensions and polymer solutions have interesting mechanical properties. In general these materials have both viscosity and elasticity and hence are called viscoelastic. Colloidal suspensions show curious nonlinear hysteresis effects called thixotropy, rheopexy, and dUatancy. These unusual flow behaviours are the central problems of rheology. 

Rheology is not just about viscosity, but also about another important property, namely the elasticity. Complex fluids also exhibit elastic behaviour. Similar to the viscosity defined above being similar to the definition of a Newtonian viscosity, the elasticity of a complex material can be defined similar to its idealised counterpart, the Hookean solid. The modulus of elasticity is defined as... 

The science of rheology encompasses the behaviour of both solid and liquid materials. This extends from a perfectly elastic solid, defined by Robert Hooke in 1678, to a perfectly viscous liquid, defined by Newton in 1687, and to the myriad of viscoelastic materials in between. The rheology of natural thickeners is primarily concerned with viscosity and viscoelasticity. 

Viscoelasticity of materials could be expressed in many ways. In this chapter, it will be described as the ability of the material to deform elastically, viscously and/or a combination of those. The interaction between the elastic and viscous behaviours could be explained with the help of the rheology of materials, as discussed in section 3.4. 

There is a widespread but mistaken belief that solids do not flow, but only show elastic behaviour. However, all solids when stressed, while certainly deforming elastically on a time-scale of less than a second, consequently creep (i.e. continue to deform very slowly) over a very long time scale of days, months and even years. If we replace the word creep with flow , we have moved smoothly from material science into rheology, and we can happily talk about the viscosity of solids, because, as we have seen so far, viscosity determines flow-rate. 

Figure 3 shows the load (P) - load line displacement (5) records obtained from fracture tests at room temperature and at quasi-static conditions (low loading rates) of propylene homopolymer, PPO, and thee controlled-rheology PPs. The mechanical response for all the materials presented clearly elastic-plastic behaviour and this justifies the use of the EPFM multiple specimen method to evaluate the fracture behaviour. In addition, all the curves deviated from linearity and at a certain deflection level, sudden instability occurred and the specimen broke in two halves. The difference in stiffness is due to the different initial crack lengths. 

---