Viscoelastic behaviour normal stresses

The practical and computational complications encountered in obtaining solutions for the described differential or integral viscoelastic equations sometimes justifies using a heuristic approach based on an equation proposed by Criminale, Ericksen and Filbey (1958) to model polymer flows. Similar to the generalized Newtonian approach, under steady-state viscometric flow conditions components of the extra stress in the (CEF) model are given a.s explicit relationships in terms of the components of the rate of deformation tensor. However, in the (CEF) model stress components are corrected to take into account the influence of normal stresses in non-Newtonian flow behaviour. For example, in a two-dimensional planar coordinate system the components of extra stress in the (CEF) model are written as... 

Viscoelastic fluids are thus capable of exerting normal stresses. Because most materials, under appropriate circumstances, show simultaneously solid-like and fluid-like behaviours in varying proportions, the notion of an ideal elastic solid or of a purely viscous fluid represents the commonly encountered limiting condition. For instance, the viscosity of ice and the elasticity of water may both pass unnoticed The response of a material may also depend upon the type of deformation to which it is subjected. A material may behave like a highly elastic solid in one flow situation, and like a viscous fluid in another. 

As discussed before ( 5.2), a molten polymer shows also elastic behaviour, particularly on a short time-scale the fluid is visco-elastic. This can, in a simple experiment, be demonstrated in two ways. When we let a bar rotate around its axis in a viscoelastic fluid, then, after removal of the driving torque, it will rotate back over a certain angle. Moreover the fluid will, during rotation, creep upward along the bar, which indicates the existence of normal stresses next to shear stresses. 

Though a simple Maxwell model in the form of equations (1) and (2) is powerful to describe the linear viscoelastic behaviour of polymer melts, it can do nothing more than what it is made for, that is to describe mechanical deformations involving only infinitesimal deformations or small perturbations of molecules towards their equilibrium state. But, as soon as finite deformations are concerned, which are typically those encountered in processing operations on pol rmers, these equations fail. For example, the steady state shear and elongational viscosities remain constant throughout the entire rate of strain range, normal stresses are not predicted. 

However, although it has some thermodynamic consistency, the latter model failsto describe the non linear viscoelastic behaviour properties, especially in shear, wherein the shear-thinning behaviour of the viscosity and of the normal stress coefficients are not predicted. As a consequence, more complex... 

It has been a common practice to describe visco-elastic fluid behaviour in steady shear in terms of a shear stress Ty and the first normal stress difference (N ) both of which are functions of shear rate. Generally, a fluid relaxation or characteristic time, Xf, (or a spectrum) is defined to quantify the viscoelastic behaviour. There are several ways of defiiung a characteristic time by combining shear stress and the first normal stress difference, e.g. the so-called Maxwellian relaxation time is given by ... 

Singh S (2000) Phase transitions in liquid crystals. Phys Rep 324 107-269 Susanne EM, Gleissle W, Mckinley GH, Buggisch H (2002) The normal stress behaviour of suspensions with viscoelastic matrix fluids. Rheol Acta 41 61-67 Tai-Shung C (1986) The recent developments of thermotropic liquid crystalline polymers. Polym EngSci26(13) 901-919... 

All polymer materials used in reinforced plastics display some viscoelastic or time-dependent properties. The origins of creep in composites stem from the behaviour of polymers under load together with local stress redistributions between fibre and matrix as a function of time. There is little creep at normal temperatures in the reinforcing fibres. The origin of the creep mechanisms is related to the nature and levels of internal bonding forces between the chains of the polymer, which are influenced by temperature and moisture. 

As in the previous chapter, we rely upon an adaptation of the Kolosov-Muskhelishvili equations. Problems for which the normal and shear forces are prescribed on the surfaces of open, and possibly growing, cracks may be solved without any restriction on viscoelastic material behaviour. The case of a single crack is studied in detail and explicit formulae are derived for stress intensity factors and displacements across the crack surface. 

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