Fibre viscoelasticity

The authors state that their approach that leads to Eq. (13.171) does not take into account that during the first loading of the fibre viscoelastic and plastic deformation contribute to the shear deformation. Therefore they have applied a slightly different method for the calculation of the tensile strength as a function of the initial modulus. However, there is still room for a slight discrepancy between the theoretical and experimental results as the derivation of Eq. (13.171) is based on the application of a single orientation angle as a measure of the whole distribution in the fibre. 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

The viscoelastic nature of the matrix in many fibre reinforced plastics causes their properties to be time and temperature dependent. Under a constant stress they exhibit creep which will be more pronounced as the temperature increases. However, since fibres exhibit negligible creep, the time dependence of the properties of fibre reinforced plastics is very much less than that for the unreinforced matrix. 

The data confirmed that gels can be obtained for all the extruded fibres. However, a slight decrease in G with the frequency can be observed indicating that they did not behave as true viscoelastic solids. Indeed they contain some insoluble fibres embedded in the network and it is a composite gel rather an ideal gel. 

Random collagen fibres provide an insoluble gel-like primary network and polyanionic hyaluronic acid a secondary network, which confers the viscoelastic property and stabilizes the collagen network (Balzas and Delinger, 1984). 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

The relation between the end points of the tensile curve, ab and eh (= b), can be calculated with Eqs. 9,23 and 24. This relation is now by definition taken as the fracture envelope. Note that these equations only hold for elastic deformation. In order to account for some viscoelastic and plastic deformation, a value gv is used, which is somewhat smaller than the value for elastic deformation g. The dashed curves in Figs. 8 and 9 are the calculated fracture envelopes (neglecting the chain extension) for the cellulose II and the POK fibres, respectively. These figures show a good agreement between the observed and calculated fracture points. 

Because of the viscoelastic nature of the polymer fibre the modulus is a function of the rate of measurement, which is indicated by E(t). We might as well... 

Fig. 58 The rheological model of a polymer fibre consists of a series arrangement of an elastic tensile spring representing the chain modulus, ec, and a shear spring, g(t), with viscoelastic and plastic properties representing the intermolecular bonding...

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

In order to simplify the discussion and keep the derivation of the formulae tractable, a fibre with a single orientation angle is considered. In a creep experiment the tensile deformation of the fibre is composed of an immediate elastic and a time-dependent elastic extension of the chain by the normal stress ocos20(f), represented by the first term in the equation, and of an immediate elastic, viscoelastic and plastic shear deformation of the domain by the shear stress, r =osin0(f)cos0(f), represented by the second term in Eq. 106. 

The total contribution of the shear strain to the fibre strain is the sum of the purely or immediate elastic contribution involving the change in angle, A0e=0o- , occurring immediately upon loading of the fibre at f=0, and the time-dependent or viscoelastic and plastic contribution A0(f)=0(f)-0o [7-10]. According to the continuous chain model for the extension of polymer fibres, the time-dependent shear strain during creep can be written as... 

The maximum shear strain criterion is now applied for the calculation of the creep curve up to fracture for increasing creep stress. The total creep strain of the fibre, q(f), is the sum of the elastic strain, cf, and the viscoelastic plus plastic strain, cj(f),... 

Northolt MG, Kampschreur JH, Van derZwaagS (1989) Viscoelasticity of aramid fibres. In Lemstra PJ.Kleintjes LA (eds) Integration of fundamental polymer science and technology. Elsevier, London, p 157... 

The final main category of non-Newtonian behaviour is viscoelasticity. As the name implies, viscoelastic fluids exhibit a combination of ordinary liquid-like (viscous) and solid-like (elastic) behaviour. The most important viscoelastic fluids are molten polymers but other materials containing macromolecules or long flexible particles, such as fibre suspensions, are viscoelastic. An everyday example of purely viscous and viscoelastic behaviour can be seen with different types of soup. When a thin , watery soup is stirred in a bowl and the stirring then stopped, the soup continues to flow round the bowl and gradually comes to rest. This is an example of purely viscous behaviour. In contrast, with certain thick soups, on cessation of stirring the soup rapidly slows down and then recoils slightly. 

The mechanical properties of fibres and yams are quite complex and have been the subject of much experimental work. A stressed fibre is a very complicated viscoelastic system in which a number of irreversible processes, connected with plasticity, can take place. 

In a subsequent investigation, with Roos and Kampschreur (1989), Northolt extended the modified series model to include viscoelasticity. For that an additional assumption was made, viz. that the relaxation process is confined solely to shear deformation of adjacent chains. The modified series model maybe applied to well-oriented fibres having a small plastic deformation (or set). In particular it explains the part of the tensile curve beyond the yield stress in which the orientation process of the fibrils takes place. The main factor governing this process is the modulus for shear, gd, between adjacent chains. At high deformation frequencies yd attains its maximum value, ydo at lower frequencies or longer times the viscoelasticity lowers the value of gd, and it becomes a function of time or frequency. Northolt s relations, that directly follow from his theoretical model for well-oriented fibres, are in perfect agreement with the experimental data if acceptable values for the elastic parameters are substituted. 

For low-oriented fibres the theory leads to a much more complicated expression, which can only be simplified under special conditions. Moreover, in low-oriented fibres not only elastic and viscoelastic, but also plastic deformations play a part. So no analytical relations can be derived for low-oriented fibres and we have to resort to empirical equations. 

Understanding of the mechanism of creep failure of polymeric fibres is required for the prediction of lifetimes in technical applications (Northolt et al., 2005). For describing the viscoelastic properties of a polymer fibre use is made of a rheological model as depicted in Fig. 13.103. It consists of a series arrangement of an "elastic" spring representing the chain modulus ech and a "shear" spring, yd with viscoelastic and plastic properties... 

For a more complete description of the time and the temperature dependence of the fibre strength a theoretical description of the viscoelastic and plastic tensile behaviour of polymer fibres has been developed. Baltussen (1996) has shown that the yielding phenomenon, the viscoelastic and plastic extension of a polymer fibre can be described by the Eyring reduced time model. This model uses an activated site model for the plastic and viscoelastic shear deformation of adjacent chains in the domain, in which the straining of the intermolecular bonding is now modelled as an activated shear transition between two states, separated by an energy barrier. It provides a relation between the lifetime, the creep load and the temperature of the fibre, which for PpPTA fibres has been confirmed for a range of temperatures (Northolt et al., 2005). 

Chapter five introduces highly organized, quasi one-dimensional crystals, namely micellar rod and vesicular tubular fibres. They are compared to equally fascinating liquid threads found in viscoelastic gels and to phospholipid tubules. These membraneous assemblies build a bridge to the secondary structures of... 

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